The complete musician: an integrated approach to theory, analysis and listening Workbook 2 [4th edition] 9780199347094, 0199347093, 9780199347117, 0199347115

Table of contents :
PrefacePart 1: The Foundations of Tonal MusicChapter 1A: Musical SpaceChapter 1B: Musical Time: Pulse, Rhythm, and MeterChapter 2: Harnessing Space and Time: Introduction to Melody and Two-Voice CounterpointChapter 3: Musical Density: Triads, Seventh Chords, and TexturePart 2: Merging Melody and HarmonyChapter 4: When Harmony, Melody, and Rhythm ConvergeChapter 5: Tonic and Dominant as Tonal Pillars and Introduction to Voice LeadingChapter 6: The Impact of Melody, Rhythm, and Meter on Harmony
Introduction to V7
and Harmonizing Florid MelodiesChapter 7: Contrapuntal Expansions of Tonic and Dominant: Six-Three ChordsChapter 8: More Contrpuntal Expansions: Inversions of V7, Introduction to Leading-Tone Seventh Chords, and Reduction and ElavorationPart 3: A New Harmonic Function, The Phrase Model, and Additional Melodic and Harmonic EmbellishmentsChapter 9: The Pre-Dominant Function and the Phrase ModelChapter 10: Accented and Chromatic Embellishing TonesChapter 11: Six-Four Chords, Revisiting the Subdominant, and Summary of Contrapuntal ExpansionsChapter 12: The Pre-Dominant Refines the Phrase ModelPart 4: New Chords and New FormsChapter 13: The Submediant: A New Diatonic Harmony, and Further Extensions of the Phrase ModelChapter 14: The Mediant, the Back-Relating Dominant, and a Synthesis of Diatonic Harmonic RelationshipsChapter 15: The PeriodChapter 16: Other Small Musical Structures: Sentences, Double Periods, and Modified PeriodsChapter 17: Harmonic SequencesPart 5: Functional ChromaticismChapter 18: Applied ChordsChapter 19: Tonicization and ModulationChapter 20: Binary Form and VariationsPart 6: Expressive ChromaticismChapter 21: Modal MixtureChapter 22: Expansion of Modal Mixture Harmonies: Chromatic Modulation and the German LiedChapter 23: The Neapolitan Chord (bII)Chapter 24: The Augmented Sixth ChordPart 7: Large Forms: Ternary, Rondo, SonataChapter 25: Ternary FormChapter 26: RondoChapter 27: Sonata FormPart 8: Introduction to Nineteenth-Century Harmony: The Shirt from Asymmetry to SymmetryChapter 28: New Harmonic TendenciesChapter 29: Melodic and Harmonic Symmetry Combine: Chromatic SequencesPart 9: Twentieth and Twenty-First-Century MusicChapter 30: Vestiges of Common Practice and the Rise of a New Sound WorldChapter 31: Noncentric Music: Atonal Concepts and Analytical MethodologyChapter 32: New Rhythmic and Metric Possibilities, Ordered PC Relations, and Twelve-Tone TechniquesAppendicesAppndix 1: Invertible Counterpoint, Compound Melody, and Implied HarmoniesAppendix 2: The MotiveAppendix 3: Additional Harmonic-Sequence TopicsAppendix 4: Abbreviations and AcronymsAppendix 5: Selected Answers to Textbook ExercisesGlossaryIndex

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T H E C OM PL E T E M U S IC I A N

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The

COMPL ET E MUSICI A N

A N I N T E G R AT E D A PPROAC H TO T H E ORY, A N A LY S I S , A N D L I S T E N I NG

Fourth Edition

Steven G. Laitz Eastman School of Music and The Juilliard School

New York Oxford OX FOR D UNIV ERSIT Y PR ESS

Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Th ailand Turkey Ukraine Vietnam Copyright © 2016, 2012, 2008, 2004 by Oxford University Press. For titles covered by Section 112 of the US Higher Education Opportunity Act, please visit www.oup.com/us/he for the latest information about pricing and alternate formats. Published in the United States of America by Oxford University Press. 198 Madison Avenue, New York, NY 10016 http://www.oup.com Oxford is a registered trademark of Oxford University Press. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Laitz, Steven G. (Steven Geoff rey) The complete musician : an integrated approach to theory, analysis and listening / Steven G. Laitz. — Fourth edition. pages cm Includes index. ISBN 978-0-19-934709-4 (pbk. : alk. paper) 1. Music theory—Textbooks. 2. Tonality. 3. Musical analysis. I. Title. MT6.L136C66 2015 781.2—dc23 2015023385 Printing number: 9 8 7 6 5 4 3 2 1 Printed in the United States of America on acid-free paper

For Anne-Marie and Madeleine

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BRIEF CONTENTS P R E FAC E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ....... x x v i i

PART 1

CHAPTER 1A

THE FOUNDATIONS OF TONAL MUSIC ............................... 1

Musical Space ..................... 3

Musical Time: Pulse, Rhythm, and Meter ..................... 44

CHAPTER 1B

Musical Density: Triads, Seventh Chords, and Texture ...................................................... 106

CHAPTER 3

Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint ......................... 78

CHAPTER 2

PART 2

MERGING MELODY AND HARMONY ...................................141

When Harmony, Melody, and Rhythm Converge ....... 143

CHAPTER 4

Tonic and Dominant as Tonal Pillars and Introduction to Voice Leading ........................................... 166

CHAPTER 5

The Impact of Melody, Rhythm, and Meter on Harmony; Introduction to V 7; and Harmonizing Florid Melodies.......... 186 CHAPTER 6

Contrapuntal Expansions of Tonic and Dominant: Six-Three Chords................................................................... 211

CHAPTER 7

More Contrapuntal Expansions: Inversions of V 7, Introduction to Leading-Tone Seventh Chords, and Reduction and Elaboration ...................................................... 231 CHAPTER 8

vii

viii

THE COMPLETE MUSICIAN

A NEW HARMONIC FUNCTION, THE PHRASE MODEL, AND ADDITIONAL MELODIC AND HARMONIC EMBELLISHMENTS .......................................................................................................261

PART 3

The Pre-Dominant Function and the Phrase Model...... 263 CHAPTER 9

The Pre-Dominant Refines the Phrase Model ...................... 324 CHAPTER 12

Accented and Chromatic Embellishing Tones ........ 280 CHAPTER 10

Six-Four Chords, Revisiting the Subdominant, and Summary of Contrapuntal Expansions ........................................................ 303 CHAPTER 11

PART 4

NEW CHORDS AND NEW FORMS ............................................345

The Submediant: A New Diatonic Harmony, and Further Extensions of the Phrase Model ......................................... 347 CHAPTER 13

The Mediant, the Back-Relating Dominant, and a Synthesis of Diatonic Harmonic Relationships........................ 366 CHAPTER 14

PART 5

CHAPTER 15

The Period .......................... 378

Other Small Musical Structures: Sentences, Double Periods, and Modified Periods......... 393 CHAPTER 16

CHAPTER 17

Harmonic

Sequences............................................................ 409

FUNCTIONAL CHROMATICISM ................................................433

CHAPTER 18

Applied Chords ............... 435

CHAPTER 19

Tonicization and

Modulation....................................................... 461

CHAPTER 20

Binary Form and

Variations .......................................................... 482

ix

Brief Contents

PART 6

CHAPTER 21

EXPRESSIVE CHROMATICISM ....................................................507

Modal Mixture ............... 509

Expansion of Modal Mixture Harmonies: Chromatic Modulation and the German Lied .............................. 531 CHAPTER 22

PART 7

The Neapolitan  Chord ( II)........................................................ 554 CHAPTER 23

CHAPTER 24

The Augmented

Sixth Chord ...................................................... 568

LARGE FORMS: TERNARY, RONDO, SONATA ...............593

CHAPTER 25

Ternary Form .................. 595

CHAPTER 26

Rondo ..................................... 616

CHAPTER 27

Sonata Form..................... 630

INTRODUCTION TO NINETEENTH- CENTURY HARMONY: THE SHIFT FROM ASYMMETRY TO SYMMETRY ............................................................................................................................661

PART 8

CHAPTER 28

New Harmonic

Tendencies.......................................................... 663

Melodic and Harmonic Symmetry Combine: Chromatic Sequences............................................................ 694 CHAPTER 29

TWENTIETH- AND TWENTY- FIRST- CENTURY MUSIC ........................................................................................................................................727

PART 9

Vestiges of Common Practice and the Rise of a New Sound World..................................................................... 729 CHAPTER 30

Noncentric Music: Atonal Concepts and Analytical Methodology .................................................... 790 CHAPTER 31

New Rhythmic and Metric Possibilities, Ordered PC Relations, and Twelve-Tone Techniques ......................................................... 828 CHAPTER 32

x

THE COMPLETE MUSICIAN

O N L I N E A PPE N DIC E S

Invertible Counterpoint, Compound Melody, and Implied Harmonies......................................................... A-1 APPENDIX 1

APPENDIX 2

The Motive ........................ A-16

APPENDIX 4

Abbreviations and

Acronyms .......................................................... A-61 Selected Answers to Textbook Exercises .................................... A-65 APPENDIX 5

Additional HarmonicSequence Topics .......................................... A-54 APPENDIX 3

G L O S S A R Y ....................................... ... G -1 C R E D I T S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C -1 I N DE X OF T ER MS A N D C O N C E P T S ....................................... ... I1-1 I N DE X OF M USIC A L E X A M PL E S A N D E X E R C I S E S .............................. .. I 2-1

CONTENTS P R E FAC E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. ....... x x v i i

PART 1

CHAPTER 1A

THE FOUNDATIONS OF TONAL MUSIC ............................... 1

Musical Space ..................... 3

Chapter Overview ....................................................3 Tonality in Context: Bach’s Violin Partita no. 3, Prelude .........................................4 Specifics of the Pitch Realm .................................7 Charting Musical Sound: Staff and Clef ...........7 Pitches and Pitch Classes .............................9 The Division of Musical Space: Intervals ........10 Accidentals...........................................................11 Scales ....................................................................12 Enharmonicism...................................................13 Scale Degree Numbers and Names ..................14 Specific Scale Types: Major and Minor ...........15 Building Scales in the Major Mode .................15 A Major .....................................................15 F Major......................................................16 Key Signatures and the Circle of Fifths ...........17 Mastering Key Signatures ..........................17 Building Scales in the Minor Mode .................19

Naming Generic Intervals .................................27 Intervals in Context ...........................................28 Melodic and Harmonic .............................28 Simple and Compound..............................28 Tips for Identifying Generic Intervals................................................29 Naming Specific Intervals..........................30 Transforming Intervals ......................................32 Minor Major and Major Minor ...............32 Augmented and Diminished Intervals................................................32 Interval Inversion ...............................................34 Generating All Intervals ....................................36 Method 1 ...................................................37 Method 2 ...................................................37 Enharmonic Intervals.........................................39 Consonant and Dissonant Intervals ................40

Terms and Concepts ..............................................41 Chapter Review .......................................................42

Key Signatures in Minor ...................................22 Relative Major and Minor Keys .......................22 Intervals ...............................................................27

xi

xii

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Musical Time: Pulse, Rhythm, and Meter ..................... 44

Two-Voice Counterpoint as Musical Foundation ..........................................................87

Chapter Overview ..................................................44 Rhythm and Durational Symbols ....................45

First-Species Counterpoint ...............................88

CHAPTER 1B

Notes and Rests ..................................................45 Dots and Ties ......................................................46

Meter ...........................................................................49 Beat Division.......................................................51 Simple and Compound Meters ........................51 The Meter Signature ..........................................55 Meter Signatures for Compound Meters ....................................................56 Asymmetrical Meters .........................................59 Clarifying Meter .................................................59

More Rhythmic Procedures ................................61 Accent in Music.......................................................64 Temporal Accents ...............................................64 Nontemporal Accents ........................................65

Metrical Disturbance ............................................72

Contrapuntal Motions ...............................90 Perfect Intervals: Handle with Care.................91 Beginning and Ending First-Species Counterpoint.........................................94 Rules and Guidelines for First-Species (1:1) Counterpoint ...............................94 Second-Species Counterpoint...........................97 Weak-Beat Consonance .............................97 Weak-Beat Dissonance ..............................98 More on Perfect Consonances ....................99 Beginning and Ending Second-Species Counterpoint.......................................100 Rules and Guidelines for Second-Species Counterpoint ..............101

Terms and Concepts ............................................103 Chapter Review .....................................................104

Syncopation .........................................................72 Hemiola ...............................................................73

Terms and Concepts ..............................................76 Chapter Review .......................................................77

Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint .............. 78

CHAPTER 2

Chapter Overview ..................................................78 Melody: Characteristics and Writing ..............79 Controlling Consonance and Dissonance: Introduction to Two-Voice Counterpoint......................................................84 Counterpoint in History .....................................86 Fux, Mozart, and Attwood ................................86 Fux’s Method .......................................................87

Musical Density: Triads, Seventh Chords, and Texture ...................................................... 106

CHAPTER 3

Chapter Overview ................................................106 Adding Voices: Triads and Seventh Chords.................................................................107 Triads ..................................................................107 Voicing Triads: Spacing and Doubling .............................................108 Triad Inversion ........................................109 Figured Bass ......................................................111 Analyzing and Composing Using Figured Bass .............................111 Additional Figured Bass Conventions: Abbreviations and Chromaticism ......112

xiii

Contents

Triads and the Scale: Harmonic Analysis ......117

Musical Texture .....................................................130

Roman Numerals .....................................118

Analytical Method ............................................133

Introduction to Harmonic Analysis.........118

Distribution of Chord Tones and

Harmony and the Keyboard ....................120

Implied Harmonies .............................133

Seventh Chords .....................................................123

Fluency .....................................................133

Definitions and Types......................................123

Harmonic Reduction ...............................135

Musical Characteristics of Seventh Chords ...........................................................124 Inverted Seventh Chords..........................124

Terms and Concepts ............................................137 Chapter Review .....................................................138 Summary of Part 1 ...............................................140

Analytical Tips ..................................................125 Seventh Chords and Harmonic Analysis.......126

PART 2

MERGING MELODY AND HARMONY ...................................141

When Harmony, Melody, and Rhythm Converge............................. 143

Tonic and Dominant as Tonal Pillars and Introduction to Voice Leading ........................................... 166

CHAPTER 4

CHAPTER 5

Chapter Overview ................................................143 Tonal Hierarchy in Music .................................144 Embellishing Tones..............................................146

Chapter Overview ................................................166 Characteristics and Effect of V and I ............167

Neighboring Tones, Chordal Leaps, and Arpeggiations ................................................146 Analysis: Distinguishing Between Chord

Stability of the Tonic .......................................168 Instability of the Dominant ............................168 Tonic and Dominant Combined....................169

Tones and Embellishing Tones ..................147

Closure on the Dominant ...............................170

The Importance of Context in Analysis .......148 Analytical Interlude.............................................151

The Cadence ...........................................................171

Another Example of Long-Range Pitch Structure .............................................152 Reflections on “Clementine” and “God Save the King” ...................................153

Melodic Fluency ...................................................154

Mozart’s Rondo.................................................171

Introduction to Voice Leading ........................174 Texture and Register ........................................174 Notating Four-Voice Textures ..................174 Vocal Registers ..........................................176 Three Techniques to Create Voice

Cognition and Perception ...............................154

Independence Within a Four-Voice

Analytical Application: Relying on

Texture ...........................................................176

Instincts and Human Perception ...............155

The Arch and Nested Lines ...............................157 Melody as Harmony ............................................159 Terms and Concepts ............................................163 Chapter Review .....................................................164

Technique 1: Smoothness .........................177 Technique 2: Registral Independence.......................................177 Technique 3: Contrapuntal Independence.......................................178

xiv

THE COMPLETE MUSICIAN

Creating the Best Sound: Incomplete

Final Interpretation .................................195

and Complete Chords, Doubling,

Interpretative Analysis .............................195

and Spacing ...................................................179

The Deepest Level.....................................195

Omitted Chord Tones ..............................179

Summary............................................................196

Doubled Chord Tones ..............................179

The Dominant Seventh and Chordal Dissonance ........................................................197

Spacing and Voicing ................................180

Summary of Voice-Leading Rules and Guidelines ..........................................................182

Derivation and New Melodic Possibilities....................................................198

Move the Voices as Little as Possible When

New Harmonization Possibilities...................200

Changing Chords .........................................182

Part Writing the Dominant Seventh

Maintain the Independence and Musical

Chord .............................................................201 7

Territory for Each Voice ..............................182

V and I Chords....................................................201

Construct Chords Logically ............................182

Incomplete V 7 ...................................................201

Tips for Avoiding Problems ............................182

Incomplete I ......................................................201

Terms and Concepts ............................................183 Chapter Review .....................................................184

Both V 7 and I Are Complete ..........................201 Unequal Fifths ..................................................202 Analytical Interlude..........................................202

Harmonizing Folk-Type Melodies .................204

The Impact of Melody, Rhythm, and Meter on Harmony; Introduction to V 7; and Harmonizing Florid Melodies .............................................................. 186 CHAPTER 6

Chapter Overview ................................................186 The Interaction of Harmony, Melody, Meter, and Rhythm: Embellishment and Reduction ..................187 Embellishment ..................................................188 Distinguishing Between Structural and Embellishing Harmonies: Second-Level

Step 1: Identify Cadences ................................204 Step 2: Identify Harmonic Rhythm...............205 An Example from Classical Music .............................................................206

Summary .................................................................207 Terms and Concepts ............................................209 Chapter Review .....................................................209

Contrapuntal Expansions of Tonic and Dominant: Six-Three Chords ............ 211

CHAPTER 7

Tones....................................................190

Chapter Overview ................................................211 Chordal Leaps in the Bass: I6 and V6 ............212 Neighbor Tones in the Bass (V6) .....................216

Reduction ..........................................................192

Another Neighboring Motion ........................217

Levels of Embellishment .................................193

Second-Level Analysis.........................................218 Passing Tones in the Bass: vii°6........................221

Analysis ...............................................190 Elaborating Structural and Embellishing

Application of Second-Level Analysis ......193

xv

Contents

Tonic Expansion the Long Way: Descending a Sixth from 1 to 3 through V or IV6 .......223

Neighboring Seventh in V65 .............................234

IV6 as Part of Arpeggiation .............................223

V42 ........................................................................236

Dominant Expansion with Passing 6

V43 ........................................................................235 Voice-Leading Inversions of V 7 ......................237

Tones: IV ...........................................................224

Combining Inversions of V 7 ...........................237

Combining First-Inversion Chords ...............225 Summary .................................................................226

Leading-Tone Seventh Chords: vii°7 and viiø7.....................................................240

Demonstration that Harmony Is a

Relationships Between vii°7 and V 7...............241

By-Product of Melody .................................226

Voice Leading for vii°7 .....................................241

Terms and Concepts ............................................229 Chapter Review .....................................................229

Analytical Interlude..........................................243

More Contrapuntal Expansions: Inversions of V 7, Introduction to Leading-Tone Seventh Chords, and Reduction and Elaboration ........................................... 231 CHAPTER 8

Chapter Overview ................................................231 V 7 and Its Inversions...........................................232 V65 ........................................................................233 Passing Seventh in V65.......................................233

viiø7 .....................................................................244

Compositional Impact of Contrapuntal Chords ....................................246 Summary of Contrapuntal Expansions ........248 Reduction and Elaboration: Compositional and Performance Implications ......................................................250 Reduction ..........................................................250 Elaboration ........................................................253

Terms and Concepts ............................................257 Chapter Review .....................................................258 Summary of Part 2 ...............................................259

A NEW HARMONIC FUNCTION, THE PHRASE MODEL, AND ADDITIONAL MELODIC AND HARMONIC EMBELLISHMENTS .......................................................................................................261

PART 3

The Pre-Dominant Function and the Phrase Model...... 263 CHAPTER 9

Chapter Overview ................................................263 The Pre-Dominant Function............................264 The Subdominant (IV in Major, iv in Minor) ..........................264 The Phrygian Half Cadence ....................265 The Supertonic (ii in Major, ii° in Minor)....267 ii( 6) and ii°6 ............................................267

Pre-Dominants and the Stepwise Ascending Bass .............................................268 Part Writing Pre-Dominants ..........................268 Extending the Pre-Dominant .........................272 Chordal Skip ............................................272 IV–ii Complex .........................................272

Introduction to the Phrase Model .................273 The Phrase Model’s Flexibility ........................273

xvi

THE COMPLETE MUSICIAN

Analytical Interlude: Stylistic Diversity Within the Constraints of the Phrase Model ................................................276

Terms and Concepts ............................................279 Chapter Review .....................................................279

Accented and Chromatic Embellishing Tones ........ 280 CHAPTER 10

Chapter Overview ................................................280 Unaccented Tones of Figuration .....................281 Accented Tones of Figuration ..........................282 Specifics of Unaccented and Accented Tones of Figuration ........................................282 Accented Embellishing Tones ..........................283 The Accented Passing Tone (APT) .................283 The Chromatic Passing Tone (CPT) ..............284 Metric Placement and Contour......................285

Six-Four Chords, Revisiting the Subdominant, and Summary of Contrapuntal Expansions ........................................................ 303 CHAPTER 11

Chapter Overview ................................................303 Unaccented Six-Four Chords ...........................304 Pedal ...................................................................304 As Passing Tones .......................................304 Passing................................................................306 Arpeggiating ......................................................307

Accented Six-Four Chords in Cadences .......308 Cadential Six-Four Chord as a By-Product of the Suspension ....................308 Cadential Six Four Chord as a By-Product of the Accented Passing Tone .................................................309 Preparing Cadential Six-Four Chords ...........310 Additional Uses of Cadential

Sample Analysis ................................................285

Six-Four Chords ...........................................310

The Accented Neighbor Tone (AN) ................286

As Part of Half Cadences .........................310

Metric Placement and Contour......................286

Preceding V 7 ............................................311

The Chromatic Neighbor Tone (CN) ............287

Within a Phrase .......................................311

Analytical Interlude..........................................287

Evaded Cadences: Elision and

The Appoggiatura (APP) ...................................288 The Suspension (S) ..............................................289

Triple Meter .............................................314

Characteristics of Suspensions........................289

Writing Six-Four Chords.........................315

Components of Suspensions ...........................290

Revisiting the Subdominant ...........................316

Suspensions in Four Voices .............................290

Contrapuntal Expansion with IV ...........316

Labeling Suspensions .......................................291

IV in Two Very Different Contexts..........317

Writing Suspensions.........................................292

Plagal Cadence ........................................317

Additional Suspension Techniques ................293

Summary of Harmonic Paradigms ................318 Harmonizing Florid Melodies .........................318 Terms and Concepts ............................................322 Chapter Review .....................................................323

The Anticipation (ANT) ....................................295 The Pedal (PED) ...................................................296 Summary of the Most Common Embellishing Tones ........................................297 Terms and Concepts ............................................301 Chapter Review .....................................................301

Extension .............................................312

xvii

Contents

The Pre-Dominant Refines the Phrase Model ...................... 324 CHAPTER 12

Chapter Overview ................................................324 Nondominant Seventh Chords: IV7 (IV65) and ii7 (ii65) ..............................................325 Supertonic Seventh Chords (ii7) .....................326 Subdominant Seventh Chords (IV 7) .............327 Analyzing Nondominant Seventh Chords: Ear Versus Eye ...............................................327

Embedding the Phrase Model .........................329 Phrase Extension ..............................................331

Contrapuntal Cadences .....................................332

2: Passing Chord Between IV and IV6 (or Between IV6 and IV) .............................334 3: Passing Chord Moving from IV6 (IV65) to ii65 .....................................................334 4: Restate Tonic Material Up a Step ..............335

Subphrases ..............................................................337 Pauses Without Subphrases ............................337 Subphrases Without Pauses ............................337 Composite Phrases ...........................................339

Terms and Concepts ............................................343 Chapter Review .....................................................344 Summary of Part 3 ...............................................344

Analysis and Interpretation .............................332

Expanding the Pre-Dominant .........................333 1: Passing Chord Between ii and ii6 (or Between ii6 and ii) .................................334

NEW CHORDS AND NEW FORMS ............................................345

PART 4

The Submediant: A New Diatonic Harmony, and Further Extensions of the Phrase Model ......................................... 347 CHAPTER 13

Chapter Overview ................................................347 The Submediant (vi in Major, VI in Minor) .....................................................348 The Submediant as Bridge in the Descending-Thirds Progression .................348 The Submediant in the DescendingCircle-of-Fifths Progression ........................349 Contextual Analysis .................................349 The Submediant as Tonic Substitute in Ascending-Seconds Progressions ...............351 Deceptive Motion as Part of a Larger Progression ...............................353 The Submediant as the Pre-Dominant ..........353

Voice Leading for the Submediant .................353 The Descending-Thirds Progression, I–vi–IV...........................................................354 The Descending-Fifths Progression, I–vi–ii (or I–vi–ii6) .......................................354 The Ascending-Seconds Progression, V–vi .........................................354

Contextual Analysis .............................................355 vi Overshadows V .............................................355 vi Overshadows I ..............................................356 Apparent Submediants ....................................356

The Step Descent in the Bass ...........................358 Two Types of Step-Descent Basses ................359 Writing Step-Descent Basses ..........................360

Terms and Concepts ............................................364 Chapter Review .....................................................365

xviii

THE COMPLETE MUSICIAN

The Mediant, the Back-Relating Dominant, and a Synthesis of Diatonic Harmonic Relationships........................ 366 CHAPTER 14

Chapter Overview ................................................366 The Mediant (iii in Major, III in Minor) .....367 The Mediant in Arpeggiations ........................367 A Special Case: Preparing the III Chord in Minor ........................................................369

Melody ...............................................................385 Harmony ...........................................................385 Period Label ......................................................385

Sample Analyses of Periods and Some Analytical Guidelines ....................................387 Summary for Analyzing Periods .....................388

Composing Periods .............................................389 Terms and Concepts ............................................391 Chapter Review .....................................................391

Voice Leading for the Mediant .......................370

More Contextual Analysis: The BackRelating Dominant ........................................372 Analytical and Aural Quandary ......................372 The BRD at Deeper Levels..............................373

Synthesis: Root-Motion Principles and Their Compositional Impact ......................374 Compositional Application .............................375

Summary .................................................................376 Terms and Concepts ............................................377 Chapter Review .....................................................377

CHAPTER 15

Other Small Musical Structures: Sentences, Double Periods, and Modified Periods......... 393 CHAPTER 16

Chapter Overview ................................................393 The Sentence: An Alternative Musical Structure .............................................................394 The Double Period...............................................400 Modified Periods ..................................................402 Terms and Concepts ............................................407 Chapter Review .....................................................407

The Period .......................... 378

Chapter Overview ................................................378 Form as Process .....................................................379 Aspects of Melody and Harmony in Periods ...........................................................380

CHAPTER 17

Harmonic

Sequences............................................................ 409

Comparisons .....................................................380

Chapter Overview ................................................409 Components and Types of Sequences ...........412

Contrasts............................................................380

The Descending-Second (D2) Sequence .......413

Melodic ....................................................380

The Descending-Second Sequence

Harmonic.................................................380

in Inversion .........................................414

Two Other Options..................................383

The Descending-Third (D3) Sequence ..........414

Sectional ...................................................383

The Descending-Third Sequence

Progressive ................................................384

in Inversion .........................................415

Representing Form: The Formal Diagram..............................................................384

The Ascending-Second (A2) Sequence ..........416

Phrases and Periods ..........................................384

Sequences with Diatonic Seventh Chords ....421

Another Ascending-Second Sequence ...........417

xix

Contents

Sequences with Inversions of Seventh Chords ...........................................................422

Writing Sequences................................................423

PART 5

CHAPTER 18

Terms and Concepts ............................................429 Chapter Review .....................................................430 Summary of Part 4 ...............................................431

FUNCTIONAL CHROMATICISM ................................................433

Applied Chords ............... 435

Chapter Overview ................................................435 Applied Dominant Chords ...............................437 More-Extensive Tonicizations of Nontonic Harmonies .....................................438

CHAPTER 19

Tonicization and

Modulation....................................................... 461 Chapter Overview ................................................461 Extended Tonicization ........................................461 Modulation .............................................................467

Applied Chords in Inversion...........................438

Closely Related Keys ........................................468

Tonicized Half Cadences .................................439

Analyzing Modulations ...................................469

Recognizing Applied Chords ..........................440

Writing Modulations .......................................470

Voice Leading for Applied Chords .................440

Modulation in the Larger Musical

Cross Relation ..........................................441

Context ..........................................................471

Applied Leading-Tone Chords ........................443 Incorporating Applied Chords Within Phrases ................................................................444

The Sequence as a Tool in Modulation .........473

Terms and Concepts ............................................480 Chapter Review .....................................................480

Analytical Shorthand .......................................444 An Example Composition ...............................445 Phrase One ...............................................445 Phrase Two ...............................................446

CHAPTER 20

Binary Form and

Variations .......................................................... 482

The D2 (⫺5/⫹4) Sequence ............................450

Chapter Overview ................................................482 Binary Form ...........................................................483

The D3 (⫺4/⫹2) Sequence ............................451

Simple Sectional Binary ..................................483

The A2 (⫺3/⫹4) Applied-Chord

Simple Continuous Binary .............................484

Sequences with Applied Chords .....................450

Sequence ........................................................453

Rounded Sectional Binary...............................485

Writing Applied-Chord Sequences ................455

Rounded Continuous Binary..........................487

Summary of Diatonic and Applied-Chord Sequences............................455 Terms and Concepts ............................................459 Chapter Review .....................................................459

Balanced Binary Form .....................................488 Summary of Binary Form Types ....................489

Variation Form ......................................................493 Continuous Variations .....................................494

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Sectional Variations ..........................................499 Compositional Risks and Solutions...............500

Terms and Concepts ............................................501

PART 6

CHAPTER 21

Chapter Review .....................................................501 Answers to Exercise Interlude 20.1 ................503 Summary of Part 5 ...............................................504

EXPRESSIVE CHROMATICISM ....................................................507

Modal Mixture ............... 509

Chapter Overview ................................................509 Altered Pre-Dominant Harmonies: ii° and iv .............................................................512 Application: Musical Effects of Melodic Mixture ..........................................512

Altered Submediant Harmony: VI ................513 Altered Tonic Harmony: i..................................514 Altered Mediant Harmony: III .......................516 Voice Leading for Mixture Harmonies .........517 Chromatic Stepwise Bass Descents ................520 In Minor ............................................................520 In Major .............................................................520

Plagal Motions ......................................................522 Brahms, Symphony no. 3 in F major, op. 90, Andante ............................................522

Modal Mixture, Applied Chords, and Other Chromatic Mediants ......................................524 Grieg, “Morning” from Peer Gynt Suite, op. 46, no. 1..................................................524

Summary of Third Relations ............................526 Terms and Concepts ............................................529 Chapter Review .....................................................529

Expansion of Modal Mixture Harmonies: Chromatic Modulation and the German Lied.......................................... 531 CHAPTER 22

Chapter Overview ................................................531

Chromatic Pivot-Chord Modulations ..........532 Analytical Interlude: Schubert’s Waltz in F Major ..........................................534 Writing Chromatic Modulations ...................536

Unprepared and Common-Tone Chromatic Modulations......................................................537 Schubert, Sonata in B major, op. posth, D. 960, Molto moderato ..............................539

Analytical Challenges .........................................542 Modal Mixture and the German Lied ...........543 Schubert “Lachen und Weinen,” D. 777, and “Die liebe Farbe” and “Die böse Farbe” from Die schöne Müllerin............................543 Analytical Interlude: Schumann’s “Waldesgesprach” from Liederkreis, op. 39 ........................................547 Analytical Payoff: The Dramatic Role of VI ..........................................552

Terms and Concepts ............................................552 Chapter Review .....................................................552

The Neapolitan  Chord ( II) ........................................................ 554 CHAPTER 23

Chapter Overview ................................................554 Characteristics, Effects, and Behavior of the Neapolitan Chord ..............................554 Writing the Neapolitan Chord ........................556 Expanding II .........................................................559

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The Neapolitan Chord in Sequences .............562 The Neapolitan Chord as a Pivot Chord......562 Terms and Concepts ............................................567 Chapter Review .....................................................567

Elided Resolution of the Augmented Sixth Chord...................................................573

()VI and the Ger65 Chord ...................................575 Augmented Sixth Chords as Part of PD Expansions ................................................575 Chromaticized Bass Descents .........................577

CHAPTER 24

The Augmented

Sixth Chord ...................................................... 568 Chapter Overview ................................................568 Characteristics, Effects, and Behavior of the Augmented Sixth Chord ..................569 Derivation of the Augmented Sixth Chord .............................................................570

Types of Augmented Sixth Chords.................571 Writing Augmented Sixth Chords ..................572

Voice Exchange .................................................577 The German Diminished Third Chord .........578

The Augmented Sixth Chord and Modulation: Reinforcement .......................581 The Augmented Sixth Chord as Pivot in Modulations ................................................583 Terms and Concepts ............................................589 Chapter Review .....................................................589 Summary of Part 6 ...............................................591

Augmented Sixth Chords in Major................573

PART 7

CHAPTER 25

LARGE FORMS: TERNARY, RONDO, SONATA ...............593

Ternary Form .................. 595

Chapter Overview ................................................595 Characteristics .......................................................595 Transitions and Retransitions ..........................597 Illustration .........................................................597

Da Capo Form: Compound Ternary Form.....................................................................600 Da Capo Aria .........................................................602 Minuet-Trio Form ................................................602 Ternary Form in the Nineteenth Century ...605 Terms and Concepts ............................................614 Chapter Review .....................................................614 CHAPTER 26

Rondo ..................................... 616

Chapter Overview ................................................616

Context.....................................................................616 The Classical Rondo ............................................617 Five-Part Rondo................................................619 Coda, Transitions, and Retransitions ............619 Compound Rondo Form .................................620 Seven-Part Rondo .............................................623 Distinguishing Seven-Part Rondo Form from Ternary Form ...................623 Missing Double Bars and Repeats .................623

Terms and Concepts ............................................629 Chapter Review .....................................................629

CHAPTER 27

Sonata Form..................... 630

Chapter Overview ................................................630

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Historical Context and Tonal Background .......................................................631 The Binary Model for Sonata Form ...............632 Beethoven, Piano Sonata No. 19 in

Sonata-Rondo Form ............................................645 Analytical Synthesis: Sonatas of Haydn and Mozart .........................................648 Haydn, Piano Sonata no. 48 in C major,

G Minor, op. 49, no. 1, Andante ...............633

Hob XVI.35, Allegro con brio .....................648

Transition.................................................636

Exposition ................................................648

Closing Section.........................................636

Development ............................................650

Development and Retransition ................637

Recapitulation..........................................651

Recapitulation and Coda ........................637

Mozart, Piano Sonata in B major,

Additional Characteristics and Elements of Sonata Form .............................638

K. 333, Allegro ..............................................652

Monothematic Sonata Form ...........................638

Development ............................................653

The Slow Introduction.....................................638

Terms and Concepts ............................................658 Chapter Review .....................................................658 Summary of Part 7 ...............................................660

Harmonic Anomalies .......................................640

Other Tonal Strategies ........................................642

Exposition ................................................652

Three-Key Exposition ......................................642 Extended Third-Related STAs ........................642

INTRODUCTION TO NINETEENTH- CENTURY HARMONY: THE SHIFT FROM ASYMMETRY TO SYMMETRY ............................................................................................................................661

PART 8

CHAPTER 28

New Harmonic

Tendencies.......................................................... 663 Chapter Overview ................................................663 Tonal Ambiguity: The Plagal Relation and Reciprocal Process ..........................................664 Tonal Ambiguity: Semitonal Voice Leading ...................................................667 Semitonal Voice Leading and Remote Keys ................................................................667

Tonal Clarity Postponed: Off-Tonic Beginning...........................................................670 Double Tonality ....................................................670 Symmetry: The Diminished Seventh Chord and Enharmonic Modulation .......674 Analysis ..............................................................676

Analytical Interlude..........................................677

A Paradox: “Balanced” Music Based on Asymmetry ..................................................680 Symmetry and Tonal Ambiguity .....................682 The Augmented Triad .........................................683 Altered Dominant Seventh Chords................687 The Common-Tone Diminished Seventh Chord..................................................689 Common-Tone Augmented Sixth Chords .....................................................690 Terms and Concepts ............................................692 Chapter Review .....................................................692

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Melodic and Harmonic Symmetry Combine: Chromatic Sequences............................................................ 694 CHAPTER 29

Chapter Overview ................................................694 Distinctions Between Diatonic and Chromatic Sequences ....................................695 Details of Chromatic Sequences .....................696 Chromatic Sequence Types ...............................697 The D2 (⫺P4/⫹m3) Sequence ......................697 The Chromatic Forms of the D2 (⫺5/⫹4) Sequence ........................................................698 The Chromatic Forms of the A2 (⫺3/⫹4) Sequence ........................................................701

Other Chromatic Step-Descent Basses .........703

Diminished Seventh Chords ...........................705 Augmented Sixth Chords ................................705

Writing Chromatic Sequences .........................707 Chromatic Contrary Motion ...........................708 The Omnibus ....................................................710

A Final Equal Division of the Octave ...........711 Sequential Progressions .....................................713 Nonsequential Progressions and Equal Divisions of the Octave.................................716 The Intervallic Cell ..............................................718 Analytical Interlude: Chopin, Prelude, op. 28, no. 2..................................................720

Terms and Concepts ............................................724 Chapter Review .....................................................724

Six-Three Chords ..............................................704

TWENTIETH- AND TWENTY- FIRST- CENTURY MUSIC ........................................................................................................................................727

PART 9

Vestiges of Common Practice and the Rise of a New Sound World ...................................... 729 CHAPTER 30

Chapter Overview ................................................729 Centricity ................................................................737 Form and Process .................................................741 Always the Same, but Never in the Same Way: Melodies, Motives, Harmony, and Line ........................................744 Triadic Extensions ................................................752 Split-Third Ninths ............................................755 Another Way to Stack Intervals ......................756

Pitch Classes (PCs) and Collections..............762 Seven-Note Collections: Diatonic Modes .....763 Five-Note Collections: Pentatonic .................768 More Symmetry: Six-Note Collections .........771

Pitch-Class Collections with Six Members #1: Whole-Tone Collection .....771 Combining Collections: The Intersection of Quartal and Whole-Tone Worlds ..........776

Pitch-Class Collections with Six Members #2: Hexatonic Collection .........776 Major and Minor Triads Within the Hexatonic Scale ............................................777

Eight-Note Collections: Octatonic ................778 Subsets................................................................781 Seventh Chord Subsets ....................................782

Form ..........................................................................784 Terms and Concepts ............................................787 Chapter Review .....................................................787

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Noncentric Music: Atonal Concepts and Analytical Methodology .................................................... 790 CHAPTER 31

Chapter Overview ................................................790 A New Sound World ............................................791 A First Analysis......................................................792 Limitations ........................................................795

Pitch and Pitch-Class Space .............................795 Equivalence ............................................................796 Equivalence in Tonal and Nontonal Music .............................................................797 Demonstration of Equivalence in

Step 3: Best Normal Order (BNO)................817 Wrinkles ...................................................817 Step 4: Prime Form (PF) and Set Class .........818 Enter the Clock: Normal Order Straight to Prime Form.....................................818

Symmetrical Sets...................................................819 Invariance ..........................................................820 Interval Class Vector ........................................821 Checking Your Work ........................................823 A Curiosity in the PC World ..........................824

Terms and Concepts ............................................825 Chapter Review .....................................................826

Nontonal Music ...........................................797

Integer Notation ...................................................799 In Pitch Space ...................................................799 In Pitch-Class Space .........................................799

PC Sets and Modular Arithmetic ...................799 The Clock ..........................................................799

More on Equivalence Classes ...........................802

New Rhythmic and Metric Possibilities, Ordered PC Relations, and Twelve-Tone Techniques ......................................................... 828 CHAPTER 32

Transposition ....................................................802

Chapter Overview ................................................828 Meter and Rhythm ..............................................829

Inversion ............................................................802

Assymetrical Meters .........................................830

Computing and Comparing: P and PC Space ................................................804

Added Rhythmic Values ..................................832

Ordered Intervals..............................................804

Changing Meters ..............................................833

Ordered Pitch Intervals ...........................804

Nonretrogradable Rhythm ..............................833 Accelerating or Decelerating Tempo:

Ordered Pitch-Class Intervals .................804

Metric Modulation ......................................836

Unordered Intervals .........................................805

Twelve-Tone Music ..............................................838

Unordered Pitch Intervals .......................805

Row as Melody and Harmony........................839

Unordered Pitch-Class Intervals..............805

Analyzing Twelve-Tone Music: Schoenberg’s

Mod-12 Inverses and Interval Classes ...........806

“Walzer,” op. 23, no. 5 ................................840

P Sets and PC Sets with Three or More Members .................................................806

A Cursory Glance at the Rest of the Piece ....846

Index numbers ..................................................809

Transforming the Row: Twelve-Tone Operators (TTOs) ...........................................846

A Systematic Approach ......................................814

Definitions and Properties of TTOs .............847

Step 1: Segmentation → Pitch Collection → Pitch-Class Collection ........816 Step 2: Normal Order ......................................816

Labeling Row Forms ........................................847

Application of Twelve-Tone Rows ..................848

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Berg, Lyric Suite ...................................................852

Emergence of P9 and I2 ....................................864

Contour .............................................................852

The Violin Concerto’s Surface.........................866

Ordered PC Intervals .......................................853

Generalizing Inversional

Unordered P Intervals ......................................854

Combinatoriality..........................................866

Multiple Row Forms ...........................................855 The Twelve-Tone Matrix ....................................856

Variance Versus Invariance................................867

Shortcuts ............................................................859

Simultaneous Row Forms: Combinatoriality ............................................860 Schoenberg’s Signature Procedure: Inversional Combinatoriality .....................862

Invariance and Symmetry................................868 Generalizing Inversional Combinatoriality and Inversional Invariance ..........................870

Summary .................................................................872 Terms and Concepts ............................................873 Chapter Review .....................................................873

O N L I N E A PPE N DIC E S

Invertible Counterpoint, Compound Melody, and Implied Harmonies......................................................... A-1 APPENDIX 1

APPENDIX 2

The Motive ........................ A-16

APPENDIX 4

Abbreviations and

Acronyms .......................................................... A-61 Selected Answers to Textbook Exercises .................................... A-65 APPENDIX 5

Additional HarmonicSequence Topics .......................................... A-54 APPENDIX 3

G L O S S A R Y ...................................... .... G -1 C R E D I T S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C -1 I N DE X OF T ER MS A N D C O N C E P T S .......................................... I1-1 I N DE X OF M USIC A L E X A M PL E S A N D E X E R C I S E S ............................. ... I 2-1

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Preface Music students often suffer through their theory and aural skills courses, viewing them as not particularly relevant—perhaps even painful—sidelines of their musical studies. This is a shame, because an unsatisfying experience with theory early on in students’ studies frequently has a negative effect on their attitude throughout their college years and beyond into their professional lives. Some students express the concern that much of the theory and aural skills curriculum has little bearing on their music making. Students often view part writing and figured bass as arcane and antiquated activities, and ear training and dictation—activities that should be intimately linked to music making—as scarcely more meaningful. Intervals out of context and chords strung together in disembodied harmonic progressions strip music of its very life. Analysis—arguably the most important component of any music theory curriculum—is sometimes reduced to nothing more than learning roman numerals and form labeling. There’s little question that reading and comprehending theory texts can be especially daunting, given their encyclopedic nature and the number of details that represent exceptions rather than the norms of tonal music. This fourth edition of The Complete Musician is specifically designed to meet students’ needs by making the material more accessible and more immediate to their experience as musicians, resulting in an engaging, musical, and integrated theory text for music majors.

U N DE R LY I N G A PPROAC H The Complete Musician is founded on two simple premises that I believe in strongly: 1. Students can learn to hear, comprehend, and model the structure and syntax of the music that they love. 2. Students will rise to the challenge when all of their senses are stimulated and they are immersed in instrumental and vocal music from the tonal and posttonal repertoire. The same simple processes underlie all tonal music. However, they are fleshed out in wondrously diverse ways. Contemporary music—works written after c. 1910 to the present—share very few consistent underlying principles, but rather must be approached on a piece-by-piece basis. The musical language is new, extraordinarily varied, and even the rather lengthy introduction to the theory, processes, and analytical methods in the final three chapters of the book only barely begin to scratch the surface of this vast body of music. xxvii

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Rather than rote learning of concepts and memorizing terms, The Complete Musician emphasizes how theory informs the work of performers. Composers respond not only to their instincts, experiences, and training in every work that they write, but also they follow certain ideals and models when appropriate, and modify them to fit their own personal vision. Theory is not a “theoretical” activity; it is a living one that responds to how music is composed and performed. Understanding how theory intersects with composition and performance is key to seeing its relevance to students’ wider musical lives. The Complete Musician makes this connection. The Complete Musician’s premise is that all music is a fusion of melody, counterpoint, rhythm, and harmony. The text presents a multistage writing and aural process through which students consider a passage’s outer-voice counterpoint and metrical setting in order to discern its harmonic flow. With a foundation of the tonal norms, students should be able to connect their basic musical instincts with what they hear and see. For example, students will learn to notate the missing cello line of a string quartet when the given score contains only the upper instruments, but the recorded performance includes all four instruments. By integrating an understanding of tonal and post-tonal procedures, analytical strategies, and the ability to read music with singing, playing, and listening, students should emerge from the course as independent and well-rounded musicians. The book’s user-friendly and multitiered analytical approach stresses the distinction between description (i.e., labeling a given sonority according to its scale degree relation to the tonic using roman numerals and figured bass) and interpretive analysis (i.e., exploring the metric-rhythmic placement, spacing, voicing, duration, texture and possible motivic context of a sonority in order to determine its function). Interpretive analysis draws heavily on the students’ musical instincts and experiences. Students should be given significant responsibility to discover that successfully negotiating an exercise depends more on a series of well-supported musical decisions than on “yes” or “no” answers. The students’ roles as active participants—whose opinions matter—are central to the spirit of this text.

AU DI E N C E The Complete Musician should appeal to music majors with varied levels of competency. The text assumes that there are as many levels of student experience and background as there are students using the text. To that end, every topic is presented in a graduated fashion and tailored to meet specific student needs. For those with a limited background in music theory, the book’s first part, “The Foundations of Tonal Music,” gives a basic introduction to important concepts and terminology with numerous straightforward exercises to help reinforce learning. Students with a broader exposure to music theory may wish to skip ahead to Chapter 2 in which melody and species counterpoint are explored. Instructors will find that the fourth edition can be implemented with a variety of curricula. As an integrated text, it can be used for both written theory and aural skills classes. Given the detailed chapters on musical form (periods, binary, ternary, rondo, and sonata), an instructor can choose to incorporate them as the class progresses through harmonic topics or defer them until later in the curriculum. For instructors with students who desire to learn what happens beyond the usual end of the common-practice harmonic spectrum, Chapters 28 and 29 introduce nineteenth- and early twentieth-century tonal practices.

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Chapters 30 through 32 explore a variety of twentieth- and twenty-first-century posttonal practices. In addition, entire chapters on motivic structures, compound melody, and invertible counterpoint appear in the online Appendices. These may or may not be taught, depending on the student population and curricular requirements of the institution.

M U S IC A L E X A M PL E S The driving force behind the book is the music literature, because, obviously, this is what theory illuminates. The included repertoire ranges from Wipo’s eleventh-century setting of “Victimae paschali laudes” to John Coltrane’s “Giant Steps,” from solo vocal and instrumental music to the orchestral repertoire, from Haydn’s “London” Symphonies to Scriabin’s later piano preludes. The inclusion of music from an entire millennium (focusing on the common-practice repertoire) dramatically underscores the fact that specific contrapuntal and harmonic procedures are a common thread that runs through the stylistic differences of this music. Further, though examples in a purely homophonic texture tidily illustrate common-practice harmonic idioms, they do not develop the students’ ability to negotiate the array of textures and styles fundamental to the repertoire they listen to and perform. For this fourth edition, most of the examples and exercises in the text and workbooks are available in high-quality streaming audio format on the book’s website, www.oup.com/us/laitz. The music is performed by soloists and ensembles from the Eastman School of Music and the Rochester Philharmonic Orchestra. Further, a new Score Anthology has been prepared to correspond with the repertory discussed in the text. Here, 84 complete scores are available for student analysis and understanding. Each score is preceded by a brief headnote, relating it to the textual discussion. Also included are brief study questions that illuminate the process of how to analyze a score. In addition, the anthology includes numerous pieces (both tonal and post-tonal) not specifically discussed in the text but that are rich and varied exemplars of the compositional procedures developed in the text.

I N T E G R AT IO N The Complete Musician integrates the tasks that comprise both a tonal and post-tonal theory curriculum, explicitly connecting written theory (part writing, composition, and analysis), musicianship skills (singing, playing, improvisation, and dictation), and music making outside of theory class. The text includes an array of musical examples drawn from the literature, as well as detailed treatment of both small and large forms and keyboard application.

I N T RODUC T IO N A N D PAC I N G OF T OPIC S The Complete Musician includes a thorough introduction to fundamentals (which includes discussions of melody writing and analysis, hierarchy, and species counterpoint). In addition to diatonic and chromatic procedures, other dimensions of the tonal tradition receive full treatment, including small formal structures (the motive, phrase, period, and

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sentence) as well as larger forms (binary, ternary, rondo, sonata, and sonata-rondo), and stylistic distinctions between eighteenth- and nineteenth-century tonal practice. New to this edition is an exploration of post-tonal music for those who wish to extend their discussion of theory into the twentieth and twenty-first centuries. The Complete Musician is neither an overview of the high points of music theory nor a survey of every topic associated with tonal and post-tonal music. Rather, it strives to develop a deep understanding of concepts by devoting one or more chapters to crucial topics related to the tonal tradition, such as sequences, compound melody, the motive, invertible counterpoint, and non-diatonic collections. The materials are presented at a pace that maximizes learning. Concepts are introduced in their most common musical contexts and then are immediately reinforced with a broad array of exercises that include singing, writing, analyzing, listening, and playing. Exercises progress from more passive written, aural, and tactile activities (such as identifying, correcting, and comparing) to those requiring active understanding (such as unfigured basses, melody harmonization, model composition). These are carefully arranged so that the skills the students develop lead from mere identification to substantive composition. Topics such as voice-leading norms and harmonic usage are presented in order of importance so that students never feel overwhelmed by endless rules. Nor are they misled that all harmonies occur with equal frequency and are of equal importance. The emphasis on varied styles and genres illuminates the ways in which a small number of consistent contrapuntal and harmonic procedures are found throughout the tonal tradition. A focus on the power, flexibility, and beauty of the interval itself provides the foundation for 20th-century music. To counter any misconception that tonal pieces are cut from the same musical cloth with a limited range of compositional possibilities, emphasis is placed on motivic relationships that make a given work unique. Post-tonal procedures are introduced in a discovery-oriented fashion, always following from the presentation of a piece and the unique issues it presents. Concepts and analytical techniques are then presented in order to illuminate the piece. Thus, theory explains the artwork rather than the artwork merely shoring up the theory. Students learn that only through active study of the score can they discover these musical processes.

T E R M I N OL O G Y A N D S C OPE The Complete Musician aims to take a neutral, and hopefully ecumenical, path. For example, no particular system is recommended for singing melodies. Students should employ whatever system is used in class, whether it is scale degree numbers, moveableor fixed-doh solfège, and so forth. Whenever possible, I use commonly accepted terminology in the text. On occasion, however, when I felt that currently popular terminology was insufficient or vague, I’ve departed from and added to what is usually taught. For example, considerable attention is devoted to harmonic sequences, given the ubiquitous presence and crucial role that they play in tonal music. In order for students to master hearing (and writing) sequences, I have devised a nomenclature system that captures both the general rise and fall of sequences, and the chord-to-chord root intervals that create these motions.

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Another reason to depart occasionally from conventional terminology results from my desire to reveal tonal music’s hierarchical processes and to model how we hear various harmonic motions. To that end, the analytical method employed in The Complete Musician involves considering a chord’s relative importance within a given musical context. For example, a dominant harmony that leads conclusively to tonic as part of a strong authentic cadence is a different type of dominant from one that occurs within a phrase and merely helps to connect tonic and submediant, or one that occurs at the half cadence, but which does not actually move to the following tonic. It might be more logical to view such a dominant as referring back to the initial tonic and therefore not moving the progression ahead. By distinguishing between these functions, students should learn that analysis is a creative enterprise that embraces their instincts and which has implications for their own music making. Conversely, the terminology used for the post-tonal section of The Complete Musician closely follows the established nomenclature and analytical procedures established over the past 30 years. The reader will encounter important topics not often explored in a music theory textbook, including two-voice counterpoint, invertible counterpoint, compound melody, and late nineteenth-century intervallic motivic cells, all crucial compositional procedures in eighteenth- and nineteenth-century music. Knowledge of the application of these concepts will not only affect students’ ability to hear harmony in time but will also have a profound impact on their playing and singing.

N E W T O T H E F OU R T H E DI T ION

The Main Text Integrated coverage of fundamentals. Instead of splitting the coverage of fundamentals into two parts, I have now placed all discussion of fundamentals at the beginning of the text. Each chapter is structured so that basic concepts are covered first, for those who need just an overview of the topic. This is followed by more in-depth analysis of each topic, for those who wish to take their study to the next level. This can also serve as a brief review for students who have already studied some or all of this material. Some can move directly to the material that most needs their attention. New coverage of post-tonal/twentieth- and twenty-first-century theory and analysis. In Chapters 30 through 32, I have expanded this text beyond the tonal world to offer an introduction to many musical examples of the core repertoire, compositional procedures, and a variety of analytical techniques. New trends reflect the influence of the past; some ideas are rejected, some expanded, while others inspire new approaches. New chapter overviews, outlines, and subheads. I’ve added new overviews to the opening of each chapter along with complete chapter outlines to highlight the key topics that will be discussed. I have also placed additional subheads in the text to make it easier for students to quickly locate the information that they need. Heads are presented in a second color, making it easier to scan for discussion of key topics. New end-of-chapter study questions and lists of key terms. Each chapter closes with basic study questions that will help students review and master the new concepts

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introduced in each chapter. By completing these quick review questions, students will know whether they are ready to proceed in their study or whether they need to continue to review the current material. Additionally, the key terms at the end of each chapter help students identify the concepts that they should know. The book concludes with a complete glossary for those who find it more convenient to locate information in that manner.

Recordings of most examples in streaming audio format. At the request of users of previous editions, we now offer recordings of nearly all of the examples and exercises in the text and both workbooks. There are new recordings of examples that are carried over in the fourth edition that were not recorded in the third, as well as recordings that accompany excerpts and complete pieces new to the fourth edition. Students can access these recordings online free of charge on the book’s website at www.oup.com/us/laitz.

The Workbooks Expanded and reorganized workbooks. We continue to offer two separate workbooks that complement the main text: • Workbook 1: Writing and Analysis is dedicated to written and analytical activities, including figured bass, melody harmonization, model composition, and analysis. • Workbook 2: Skills and Musicianship contains musicianship skills. Exercises within each chapter are organized by activity type: one-line and two-part singing, dictation, keyboard, and instrumental application. Both workbooks have been reorganized to reflect the new text organization. Additionally, over 200 new exercises have been written to cover twentieth-century music (Chapters 30 through 32 in the main text). Additional space has been added to many exercises to allow for students to easily complete their work in each volume. A library of streaming online recordings is available for most of the exercises in the workbooks. Students will be able to access these recordings online free of charge on the book’s website.

All New: Score Anthology I’ve prepared a new Score Anthology for students and instructors to use with both the text and workbooks. This includes complete scores for many key works discussed in the text. Further, over 60 supplementary works are included that are crucial staples in undergraduate theory courses, including several works by Chopin, Bach, Beethoven, Haydn, and so on. Each score is presented with a short headnote that summarizes the key compositional and theory elements illustrated in the work and many scores include sample questions that address crucial elements in the piece. Additionally, the anthology includes a variety of new works written in the past 10 years by major contemporary composers. These show how contemporary composers have drawn on and expanded the concepts discussed in the text.

Companion Website: www.oup.com/us/laitz This open-access website contains supplemental analytical and writing exercises that focus on the basics of each concept. In addition, the website includes chapter outlines for quick

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Preface

study and review. Streaming audio for most of the examples in the text and workbooks is also included.

AC K N OW L E D G M E N T S I wish to thank my students and colleagues who provided support and guidance in the creation of this new edition. They include my Eastman faculty colleagues, Jonathan Dunsby and Robert Wason, each of whose suggestions were instrumental in crafting the posttonal chapters. Jonathan’s generosity in the many discussions of theory and pedagogy in general were of inestimable help. Neil Minturn, my colleague at Eastman for many years and now associate professor at the University of Missouri–Columbia, provided insights in approaching twentieth-century pedagogy. Several individuals played sustained and multiple roles in this vast project. Ian Sewell, a graduate student in music theory, analysis, and criticism at Cambridge University, worked steadily on both the textbook and the writing and analysis workbook. His knowledge of the repertoire, analytical sensitivity, and critical acumen can be seen in his work on the anthology, of which he is coauthor. Ian provided the introductions and study questions for each anthology example. His critical eye (and prose) were of inestimable value, especially in the crafting of the twentieth-century chapters. Phil Lambert, professor of music at Baruch College and the Graduate Center of CUNY, refined the new post-tonal chapters and created the exercises that accompany these chapters. Owen Belcher in Eastman’s PhD program created the answers for the writing and analysis exercises in Workbook 1. Derek Remeš, a DMA organist and PhD student in music theory at Eastman, performed the organ examples and created each chapter’s comprehension questions and the glossary. Pamela Palmer Jones, professor of music at the University of Utah, proofed the skills workbook and in her critical listening of hundreds of exercises found those in which a particular instrument was out of tune, if only for a beat or two. Many of these exercises have been rerecorded. And lastly, my heartfelt thanks to composer, theorist, and extraordinary Sibelius engraving expert Christopher Winders, who spent countless hours artfully engraving hundreds of examples and complete works and clarifying complex diagrams in the later chapters of the textbook. I thank the following reviewers, who evaluated several different versions of this new manuscript, and provided sage theoretical and pedagogical advice:

Reginald Bain University of South Carolina

Charles Ditto Texas State University

Steven Harper Georgia State University

Vincent Benitez Pennsylvania State University

Stefan Eckert University of Northern Colorado

Brian Head University of Southern California

John Brackett University of North Carolina–Chapel Hill

Gretchen Foley University of Nebraska–Lincoln

Áine Heneghan University of Washington

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THE COMPLETE MUSICIAN

Jason Hooper University of Massachusetts Amherst Roman Ivanovitch Indiana University Richard Konzen Grove City College Charles Leinberger University of Texas–El Paso Jeffrey Loeffert Oklahoma State University David Marcus Georgia State University Matthew McDonald Northeastern University Mark McFarland Georgia State University Jonathan McNair University of Tennessee at Chattanooga Justin Merritt St. Olaf College

Jeffrey Miller California State University–East Bay

Ciro Scotto University of South Florida

Neil Minturn University of Missouri–Columbia

Jim Scully California State University– Bakersfield

Rachel Mitchell University of Illinois at Urbana-Champaign Alex Nohai-Seaman Suffolk County Community College Jeff Perry Louisiana State University Boyd Pomeroy University of Arizona

Michael Slayton Vanderbilt University Aleksander Sternfeld-Dunn Wichita State University Eliyahu Tamar Duquesne University Reynold Tharp University of Illinois at Urbana-Champaign

Brian Post Humboldt State University

Don Traut University of Arizona

Alex Reed University of Florida

Leigh VanHandel Michigan State University

Toby Rush University of Northern Colorado

I also extend my thanks to the staff at Oxford University Press for their continued faith in this project. Jan Beatty, past Executive Editor, spearheaded this project in the mid-1990s. It was her faith and dedication through three editions of The Complete Musician that made the book what it is. For the current fourth edition, Richard Carlin has been there on a nearly daily basis (sometimes twice daily…), providing insightful, creative, and savvy guidance. He has unwaveringly supported the development of each new feature of the text and very often got his hands dirty by editing prose and dealing with a vast array of details. Emily Schmid, Editorial Assistant, Music and Art, kept the trains running, overseeing the logistics of what ultimately turned out to be a nearly full-time job. David Bradley, Senior Production Editor, was meticulous and consistent.

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Preface

Nothing got by him as he carefully shepherded this complex project through the many stages of production. I am especially indebted to Debbie Nichols, musician, copy editor, and friend, who painstakingly worked through every word and pitch of the 2,200 pages of text and workbooks, with an amazing eye for clarity, consistency, and correctness: I thank you. I also wish to express my deep gratitude to the Eastman School of Music, which has supported this project in countless ways since 1997. The late Douglas Lowry, Dean of the Eastman School, and Jamal Rossi, Eastman’s Dean, have been sources of inspiration. I express my deep gratitude to the Eastman faculty and students, who played and sang the 25 recorded hours of musical examples so artfully. These performers include:

Antonova, Natalya—Piano Arahata, Yoshiko—Piano Arciola, Marissa—Bass Beaudry, Chris—Bass Trombone Berkebile, Jennifer— Mezzo Soprano Bezuidenhout, Kristian—Piano, Harpsichord, Forte-Piano Binkley, Jennifer—Horn Block, Christina— Clarinet Boover, Alta—Alto Brickman, David—Violin Brooks, Liz—Mezzo Soprano Cheetham, Andy—Trumpet Chen, Po Yao (Richard)— Bassoon Choi, Hyunji— Cello Cowdrick Catherine— Soprano Dawson, Andrea—Violin Franco, Allison— Oboe Fuller, Valerie—Horn Fulton, John—Baritone

Germer, Molly—Violin Gliere, Jennifer— Soprano Grandey, Ali— Soprano Hennings, Dieter— Guitar Hermanson, Brian— Clarinet Hibbard, Ashley— Soprano Hileman, Lynn—Bassoon Hurwitz, Hanna—Violin Hwang, Margery— Cello Jin, Min—Tenor Jorgensen, Michael—Violin Karney, Laura— Oboe Kellogg, Mark—Bass Trombone Kelly, Mike—Tenor Ketter, Daniel— Cello Kim, Albert—Piano Kim, Sophia—Flute Kohfeld, Cheryl—Viola Laitz, Madeleine—Violin Laitz, Steve—Piano Lange, Amy—Bassoon

Leung, Chun Chim—Violin Liu, Liu—Piano Matson, Melissa—Viola Manolov, Emanouil—Violin Marks, Matt—Horn Martin, Rob—Violin Mayumi Matzen—Piano Nulty, Dennis—Tuba Orlando, Courtney—Violin OuYang, Angel—Violin Penneys, Rebecca—Piano Pritchard, Jillian—Timpani Prosser, Doug—Trumpet Qian, Jun— Clarinet Remeš, Derek— Organ Salatino, Mark—Trombone Salsbury, Josh—Trombone Schneider, Nicolas— Cello Schumacher, Tom—Piano Shaw, Brian— Trumpet

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THE COMPLETE MUSICIAN

Sheldrick, Braunwin—Viola Shewan, Paul—Trumpet Slominsky, Johnandrew—Piano Sugitani, Mune—Baritone Sunwoo, Patricia—Violin

Swensen, Matthew—Tenor Swensen, Robert—Tenor Traficante, Sara—Flute Walsh, Diane— Piano Wensel, Ben— Cello

Widmer, John—Trombone Wilcox, Kathy— Oboe Winchell, Katie—Flute Wood, Lindsey—Horn Zabenova, Ainur—Violin

Mike Farrington, recording engineer and supervisory editor for all four editions, has, for nearly 15 years, consistently done a magnificent job; he is a true artist. Thanks also go to Helen Smith, Director of Eastman’s Recording Services, for her help and support. I continue to thank Carl Schachter and the late Edward Aldwell for their artistic models of scholarship, musicality, and pedagogy, which play no small role in the philosophic undergirding of this book. Finally, to my life partner of 40 years, Anne-Marie Reynolds, and my extraordinary daughter, Madeleine, I thank you both for your love, humor, and patience.

PA R T 1

THE FOUNDATION OF TONA L MUSIC

C

hapters 1A, 1B, 2, and 3 provide a review of concepts and terminology related to pitch and time. From notation, scale, and interval in Chapter 1A to rhythm and meter in Chapter 1B, the basic fundamentals are set in place. Chapter 2 combines the world of pitch and time through an exploration of two-voice counterpoint. Chapter 3 presents vertical structures of three and four tones (triads and seventh chords) and reveals how these sonorities unfold in time and in various contexts called “musical texture.” Taken as a whole, these four chapters will provide you with the background to explore subsequent chapters, which present a vast amount of material that will illuminate the structures and processes of the music you play and sing.

1

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CH A PTER 1A

Musical Space OV E RV I E W

This chapter begins with a brief discussion of the opening of Bach’s Violin Partita in E major, which will provide a springboard for our later studies in musical terminology, structure, and analysis. The second half of the chapter introduces elements of the pitch world. CHAPTER OUTLINE Tonality in Context: Bach’s Violin Partita no. 3, Prelude .................................... 4 Specifics of the Pitch Realm ......................................................................................... 7 Charting Musical Sound: Staff and Clef ................................................................ 7 Pitches and Pitch Classes.................................................................................. 9 The Division of Musical Space: Intervals ............................................................. 10 Accidentals................................................................................................................ 11 Scales ......................................................................................................................... 12 Enharmonicism........................................................................................................ 13 Scale Degree Numbers and Names ....................................................................... 14 Specific Scale Types: Major and Minor ................................................................ 15 Building Scales in the Major Mode ...................................................................... 15 A Major............................................................................................................15 F Major ............................................................................................................16 Key Signatures and the Circle of Fifths ................................................................ 17 Mastering Key Signatures ...............................................................................17 Building Scales in the Minor Mode ...................................................................... 19 Key Signatures in Minor ........................................................................................ 22 Relative Major and Minor Keys ............................................................................ 22 Intervals .................................................................................................................... 27 (continued)

3

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THE COMPLETE MUSICIAN

Naming Generic Intervals ...................................................................................... 27 Intervals in Context ................................................................................................ 28 Melodic and Harmonic .................................................................................. 28 Simple and Compound .................................................................................. 28 Tips for Identifying Generic Intervals ........................................................... 29 Naming Specific Intervals .............................................................................. 30 Transforming Intervals ........................................................................................... 32 Minor Major and Major Minor ....................................................................32 Augmented and Diminished Intervals ...........................................................32 Interval Inversion .................................................................................................... 34 Generating All Intervals ......................................................................................... 36 Method 1......................................................................................................... 37 Method 2......................................................................................................... 37 Enharmonic Intervals.............................................................................................. 39 Consonant and Dissonant Intervals .............................................................. 40

Terms and Concepts for Pitch, Scale, and Key ..................................................... 41 Terms and Concepts for Intervals ............................................................................ 42 Chapter Review ............................................................................................................. 42

W E S T E R N M U S I C W R I T T E N during the Baroque, Classical, and Romantic periods

(ca. 1650–ca. 1900) is called tonal music, or music of the common-practice period. Compositions written during these three centuries have a point of gravitation, an explicit or implicit center around which all its pitches orbit. This phenomenon is called tonality, and the gravitational center—a single pitch (labeled using letters of the alphabet from A through G, plus various possible modifiers, including “flat” and “sharp”)—is called the tonic. Music with some sort of gravitational center has existed since antiquity and continues to flourish to the present day in film scores, popular and commercial music, folk music, and jazz. Furthermore, music with a tonal center or other such point of reference can be found throughout the world. In our studies here, however, we focus on the repertory that emerged in Europe during the common-practice period.

T O N A L I T Y I N C O N T E X T: B AC H ’ S V IOL I N PA R T I TA N O. 3, PR E LU DE We will use the opening passage of the Prelude from Bach’s Violin Partita in E Major (Example 1A.1) as a springboard to launch our studies. The purpose of this brief discussion is to connect some of the basic musical knowledge you have already acquired in your instrumental and vocal lessons with specific instances of those terms and concepts. Listen to the excerpt and consider the following questions: What is the most aurally important or prominent pitch in the phrase? How did you come to this decision?

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Chapter 1A Musical Space

EXAMPLE 1A.1 Bach, Violin Partita no. 3 in E major, BWV 1006, Prelude STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

bar lines measure

4

7

10

The basic criteria for determining the importance of a pitch include how often the pitch appears, the degree to which other pitches are drawn to it, and its prominence as part of musical gestures. You may have selected B as the most important pitch, because it occurred most frequently. Or perhaps you chose E, since it stood out aurally. In fact, E often occurred conspicuously just after the bar lines, which indicate the beginning and end of measures (mm.); see Example 1A.1. Pitches occurring after the bar lines have a special function in tonal music because they are accented. Accented musical events stand out because our attention is drawn to them. We will examine a variety of ways in which composers create accents in their music. One reason our attention is drawn to an event is that it heralds something new or different, such as a change in pattern. However, many changes in a short time span can be confusing to the listener, so composers balance the new (contrast and motion) with the familiar (similarity and stability). Bach uses a variety of melodic gestures and contours: Some fall while others rise; some comprise a series of skips, while others have no skips at all, and some gestures seem to go nowhere. When one of these melodic gestures ends and another begins, the change draws our attention. For example, the Prelude begins with a falling gesture. The next gesture, in mm. 3–6, is rhythmically and melodically repetitive. In m. 7, a two-measure rising gesture begins. The pitches that initiate these changes are audibly distinguished from the surrounding pitches and thus are accented. Pitch prominence and melodic patterning may be only part of what you heard as you listened to Bach’s composition. You may have also noticed that some of the pitches occupied more time than others. Longer pitches generally create a musical accent. Also, pitches that occur on beats are generally more accented than those that occur between beats, just as pitches that occur on a strong beat (beat 1 in a measure of è) are more accented than

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THE COMPLETE MUSICIAN

those that occur on weaker beats (beats 2 and 3). If we compare the pitches that occur between the beats to the pitches that occur on the beat, we notice that E is again emphasized. When an accented duration (i.e., a longer pitch) and metric placement (i.e., a pitch that occurs on a beat) align, they create a particularly strong accent. Such powerful accents help the listener group musical events into intelligible units. If you relate the rising, falling, or static contours to their temporal placement, you will notice that most measures begin after a large leap in the musical line. Leaps, like longer durations and dynamic accents, attract our attention more when they occur on a downbeat. When two or more different types of accented musical events are coordinated, they create a powerful standard by which to measure pitch prominence. A glance at the score reveals that E is in fact the most important pitch, since it is a focal point of several types of musical accent. Further, E, unlike any of the other pitches in the passage, is able to invoke a feeling of arrival and stability, a sense of “home” or “rest.” Finally, you might have sensed a deeper, slower-moving type of accent characterized by the completion of longer melodic gestures. Such accents occur over two or more measures (as at the beginning of mm. 3, 5, 7, 9, 10, and 12), and they can project one of the strongest types of musical emphasis. We can musically represent the preceding remarks concerning pitch prominence, accent, and melodic contour in the notated summary in Example 1A.2A and B. Example 1A.2A shows the pitches that occur on each beat of each of the 12 measures. Phrasing slurs group the two-measure patterns. Example 1A.2B reveals the two types of melodic activity: sweeping gestures that fall (mm. 1–2) and rise (mm. 7–8), and more stationary gestures, which themselves are repeated to create longer, four-measure groupings (mm. 3–6 and mm. 9–12). Clearly, there is a hierarchy of pitch and meter in Bach’s piece, and, indeed, hierarchy is a defining feature of tonal music. Since E has the most gravitational pull, it is the most

EXAMPLE 1A.2 Bach Prelude, Accented Pitches A. 3/5

1

7

11

9

B.

13

stable falling

stable rising

4 mm.

2 mm. 1

4 mm.

2 mm. 2

3

4

5

6

7

8

9

10

11

12

13

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Chapter 1A Musical Space

important pitch in the passage: we call it the tonic pitch. The only other prominent— albeit less important—pitches to emerge in the foregoing analysis are G and B. Because the remaining pitches occur only within the melodic gestures and because they function merely as the glue that connects E with its satellites G and B, they are less important in the hierarchy.

S PE C I F IC S OF T H E PI T C H R E A L M We have seen that important principles of tonal music include pitch prominence, musical accent, melodic contour, and hierarchy. We will now explore the basic elements of the pitch world.

Charting Musical Sound: Staff and Clef Tonal music is often written down in order to preserve it and to ensure that its pitches (the musical sound generated by a vibrating body) and their placement in time—rhythm— receive relatively consistent performance. Such musical scores begin with several defining elements, including the staff and clef, which make it possible to fix pitches and define the relationships between them. The modern staff (plural: staves) contains five horizontal lines and four spaces, each of which, in conjunction with a clef, represents a specific pitch, thus permitting the performer to see exactly how much higher or lower a given pitch is in relation to some other pitch. The earliest clefs indicated the location of what has become middle C. Example 1A.3 shows what the C clef looks like in modern notation.

EXAMPLE 1A.3 C Clefs soprano clef middle C

alto clef middle C

soprano range

alto range

tenor clef middle C

tenor range

C clefs may occur on any of the five lines of the staff. Notice that the names of the sample C clefs in Example 1A.3 correspond to the names of the voice ranges, which indicate why C clefs are useful: The range of the vocal melodies written in these clefs rarely exceeds the range of the staves. Today, only two C clefs are commonly in use: the alto (in which viola music is written) and the tenor (in which some trombone, bassoon, and cello music is written). Two other clefs came into prominence centuries after the C clefs were well established; and they represent a good compromise for notating all vocal music because they can accommodate both the bass and soprano voices at their extremes, and the alto and tenor within. The treble (or G clef ) indicates the location of G above middle C, and the bass (or F clef ) indicates the location of F below middle C. The G clef encircles the G staff line, and the two dots of the F clef define the F line. These two clefs have become the most

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THE COMPLETE MUSICIAN

widely used in the twentieth and twenty-first centuries; it is imperative that you can read them both fluently. Bass and treble clefs often appear one above the other, in the grand staff (Example 1A.4).

EXAMPLE 1A.4

G clef G

Grand Staff Grand staff

F clef middle C

middle C F

G middle C

Ledger lines extend a staff in order to accommodate pitches that exceed its range. Since so many instruments and voices are now commonly written in either the bass or treble clef, ledger lines are commonplace. When composers write extended passages of music that would require a performer to navigate numerous pitches above or below the treble or bass staves, they often notate them comfortably within the staff and simply add the octave sign (“ottava,” 8va or 8vb), which specifies that the pitches that follow are to be performed one octave higher or one octave lower than written (“8va” above a pitch indicates performing the pitch one octave higher; “8vb” [or “8va” below] or “8va bassa” indicates performance one octave lower). Example 1A.5A contains ottavas in both the bass and treble clefs because Liszt takes advantage of the piano’s huge range, yet the use of the ottavas makes it much easier to read than the alternate version, notated without the octave signs (Example 1A.5B). In vocal music, octave indications are shown most often in the treble clef and are intended for the tenors; the “8” appended to the bottom of the treble clef indicates performance of pitches one octave lower.

EXAMPLE 1A.5 Liszt, “Sursum corda” from Années de Pèlerinage, Year 3 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

92

8va

grandioso

8vb

8va

9

Chapter 1A Musical Space

EXAMPLE 1A.5 (continued) B.

92

Pitches and Pitch Classes A pitch is a tone that is generated by a vibrating body, whether it be a plucked violin string or the air moving a clarinet reed. The speed of the regularly recurring vibrations— called the frequency—determines the pitch. The faster the vibrations, the higher the pitch and the slower the vibrations, the lower the pitch. If a pitch’s frequency is twice that of another pitch (or in the ratio of 2:1), then the two pitches are separated by an octave. Since pitches that are separated by an octave sound very similar, we give these pitches the same letter name (chosen from A through G) with an octave designation. Example 1A.6 shows one common way to describe pitches: Each pitch is assigned an octave number, with new octave numbers beginning on each subsequent C. The lowest C on the piano is “C1,” the next is “C2,” and so on, with each higher octave increased by one numeral.

EXAMPLE 1A.6 Pitch and Octave Designations 8va

B 6 C7 C4

2

C1

B1 C

B2 C3

B 3 C4

B4 C5

B 5 C6

B 7 C8

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We refer to a pitch’s placement as its register. For example, C3 to C5 is a “middle” register, while C6 to C8 is a “high” register. These are relative, however. For example, given the following sonority, the highest and lowest pitches are “high” and “low” register (Example 1A.7).

EXAMPLE 1A.7

“”w

"high"

&

{

?

"middle"

w

"low"

w

Pitch class refers to all pitches with the same letter name. Thus, the notes in Example 1A.8 are in the pitch class “E,” but they are the pitches E4, E5, and E6. In this text, we will generally refer to a pitch by its pitch-class designation, unless it is necessary to distinguish pitches by octave number.

EXAMPLE 1A.8 Pitch Versus Pitch Class

The Division of Musical Space: Intervals The distance between any two pitches is called an interval. Musicians have been exploring different-sized intervals for more than two millennia. They universally considered the octave to be a crucial interval, for it marks an important sonic boundary. With the octave in place, musicians divided this distance in various ways, most of which were attempts to distribute pitches rather evenly over the octave’s span. Eventually, the music created by Western (European) musicians used pitches that divided the octave into seven steps, each of which was given its own name, corresponding to the first seven letters of the alphabet (A through G). These steps are two different sizes, one exactly twice as large as the other. The smaller step is called a half step (half steps on the keyboard occur between any two adjacent keys, such as E and F or B and C). The larger step is called a whole step, defined as two half steps (whole steps on the keyboard occur between any two keys separated by one intervening key, such as between C and D or A and B). See Example 1A.9, which marks various half (H) and whole (W) steps on the keyboard.

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Chapter 1A Musical Space

EXAMPLE 1A.9 Half and Whole Steps

H

H

W

W

W

W

-

H

Accidentals There are seven different pitch names within an octave (A–G), but the piano keyboard reveals twelve different keys: seven white and five black. In order to name each of the 12 keys, we refine the names of the seven basic (or natural ) keys by adding various modifiers called chromatic alterations or accidentals. Two common accidentals are the flat (), which lowers a pitch one half step, and the sharp (), which raises it one half step. Another common accidental is the natural (), which cancels a previous accidental. For example, an F following an F removes the sharp, resulting in a pitch that is one half step lower. Two more accidentals complete the alteration family. A double sharp () raises a pitch by two half steps (or an already-sharped pitch by one half step). Similarly, a double flat () lowers a pitch by two half steps (or an already-flatted pitch by one half step). A chromatic alteration applies only in the octave register in which it occurs and will remain in effect until the end of the measure. That is: accidentals operate on pitches, not on pitch classes. Composers

EXAMPLE 1A.10 Accidentals C

F

C

F

B

B

 sharp

raises a pitch a half step

 flat

lowers a pitch a half step

 natural

cancels a previous accidental or indicates an unaltered pitch

 double sharp

raises an unaltered pitch two half steps or a sharped pitch one half step

 double flat

lowers an unaltered pitch two half steps or a flatted pitch one half step.

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THE COMPLETE MUSICIAN

often add courtesy accidentals in parentheses to clarify ambiguities. If a composer wishes to continue the alteration, he or she must repeat it in subsequent measures. Example 1A.10 summarizes all the accidentals and demonstrates how various notated examples correlate with the keyboard. Note that each of the five possible accidentals has been applied to F.

Scales The piano keyboard shows us that the octave has been divided into 12 pitches, each equidistant from the next by the interval of a half step. We refer to the entire collection of 12 possible pitch classes as the chromatic system; arranged in order, these pitch classes form the chromatic scale, as shown in Example 1A.11. This ordering looks like a staircase or ladder, thus giving us the Latin term for scale, scala. However, the large, 12-pitchclass chromatic system is really more a collection of possible pitches; composers tend to use a seven-pitch-class scale that mixes half and whole steps. Consider the pitch classes E–F–G–A–B–C–D (notated as unfilled pitches in Example 1A.11). Notice that there are five whole steps (W) and two half steps (H) (occurring between G/A and D/E).

EXAMPLE 1A.11 The Chromatic and Diatonic Scales W

chromatic half step

W

H

W

W

W

H

diatonic half step

This scale, based on the ordered succession of the seven different letter names, is the foundation of Western music. A composition based on such a scale is said to be in a specific key. For example, a composition is in the key of E if it is based on a scale generated from the pitch class E. Since each letter of the musical alphabet is represented once and only once, we refer to this type of scale as diatonic (or “through the tones”). A diatonic scale may begin on any of the 12 different pitch classes and may ascend or descend. Pitches that are members of the seven-pitch-class scale are diatonic (shown in Example 1A.11 as unfilled pitches), and pitches that lie outside the scale are chromatic (from the Latin, chroma, or “color”). Listen to the opening of Mozart’s well-known Piano Sonata in C major (Example 1A.12). Taking an inventory of the pitch-class content of the passage, we see in m. 1 Cs, Es, and Gs. In m. 2, Ds, Fs, and Bs enter the picture; in m. 3, A is the single new pitch class. If we list this collection alphabetically, we get A, B, C, D, E, F, G. In fact, a review of the content of the rest of the example reveals that no new pitch classes occur. Even though these seven pitches freely circulate throughout the example, Mozart has organized his music in such a way that certain pitches seem more stable than others. The excerpt begins on C, and there are points of repose where C is conspicuously present: at the end of mm. 2 and 4 and in m. 8. It also seems that other pitches are strongly attracted to C, such as the B in m. 2. Finally, still other pitches seem to partner with C, and they too

Chapter 1A Musical Space

13

EXAMPLE 1A.12 Mozart, Piano Sonata in C major, K. 545, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Allegro

(dol.)

5

have their own power to attract pitches, such as the Gs and Es in m. 1; A in m. 3 is strongly attracted to the following G, while the F in m. 4 is pulled toward E (see arrows in Example 1A.12). As we discovered earlier, when pitches are hierarchically arranged in a diatonic scale and one pitch is stronger and more stable than all the others, this effect is referred to as tonality. Since C is the most important pitch in Example 1A.12, we emphasize it by beginning the scale with C and saying that C is the tonic of the excerpt. Half steps have two different names: diatonic half steps, which include two different letter names (e.g., G and A, as in the E scale in Example 1A.11) and chromatic half steps, which share the same letter name (e.g., A and A; see Example 1A.11).

Enharmonicism

Example 1A.10 illustrates that, on the keyboard, pitches such as C  and B, and B and C are the same key and therefore sound the same. Pitches and pitch classes that have the same location on the keyboard but have different names or “spellings” are enharmonically equivalent. Since enharmonically related pitches sound the same, we consider them to be in the same pitch class. Example 1A.11 lists B as a member of the E diatonic scale, yet it is enharmonically equivalent to C (and the same pitch class). The specific name given to a pitch is determined by how it functions within a musical context. There are two general principles for determining when to use one enharmonically equivalent pitch rather than another. 1. Use the note name that represents membership within the prevailing key; this explains why we use B rather than C  in Example 1A.11. 2. In a chromatic environment, employ the notation convention in which sharps (or naturals) are used in ascending lines and flats (or naturals) are used in descending lines. Example 1A.13 contains an ascending and descending chromatic

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scale. The pitch F is used when the line ascends to G, while G  is used when the line descends. Enharmonic pitches in Example 1A.13 are connected with arrows (e.g., F and G ). Enharmonicism is more abstract than real. For fixed-pitch instruments, such as the piano, enharmonically related pitches are identical; but for moveable-pitch instruments, players will slightly alter, or temper, the pitches according to the context (e.g., string players would most likely play a G somewhat higher than an A in order to intensify the expected ascending motion to A). Common-practice composers draw most of their pitch material from the diatonic scale, but they also incorporate elements from the chromatic system. When most of the pitch material comes from the seven pitch classes of a scale, we refer to the music as diatonic. As more nondiatonic pitches are used in a composition, it becomes increasingly chromatic. Later, we will learn how composers incorporate chromatic elements into their music.

EXAMPLE 1A.13 Enharmonically Equivalent Pitches

F

G

A

B

C

D

E

D

C

B

A

G

Scale Degree Numbers and Names As shown in Example 1A.14, each of the seven members—or scale degrees—of the scale can be numbered in ascending order, beginning with the tonic. Such scale degree numbers are distinguished by the caret, or cap, that is placed above each number in order to avoid confusion with other numbers with different meanings. Scale degrees may also be identified by names that reflect their relationship to the tonic pitch class. In order of importance, the next scale members are the dominant and the mediant. If the tonic is the first step, the dominant is the fifth step of the scale and the mediant the third step. The mediant’s name is logically derived from the fact that it lies midway between the tonic and the dominant. The supertonic, as the name implies, lies immediately above the tonic. The subdominant, the fourth scale degree, is so called because it lies the same distance below the tonic as the dominant lies above the tonic. Similarly, the submediant, the sixth scale degree, lies midway between the tonic and subdominant below. Finally, the leading tone, scale degree 7, lies one step below the tonic, to which it usually leads.

15

Chapter 1A Musical Space

EXAMPLE 1A.14 The E Scale with Scale Degree Numbers and Names 1

tonic

2

3

supertonic

mediant

4

5

subdominant

dominant

6

7

submediant

1

leading tone

tonic

Specific Scale Types: Major and Minor An easy way to memorize scale patterns is to arrange the pitch classes in ascending order. It is crucial that this ordering use every pitch letter name once and only once. A major scale consists of a collection of seven different pitch classes with the intervallic order W–W– H–W–W–W–H. Major and its companion, minor (which has a slightly different intervallic ordering), refer to the mode of the piece. The major mode is sometimes considered brighter than the minor mode and more stable. Example 1A.15A illustrates a passage in D minor from Schubert’s “Gute Nacht,” followed by the passage cast in the major mode (Example 1A.15B). Although the term mode has been used since antiquity to refer to many different scalar constructions, nowadays we also use mode to refer to the two types of scales that occur regularly in tonal music: major and minor. The name of a key provides two kinds of information: It identifies both the tonic pitch and the mode.

Building Scales in the Major Mode A Major We can generate a major scale on each of the remaining 11 pitch classes by using the same pattern of half and whole steps found in the E-major scale shown in Example 1A.14.

EXAMPLE 1A.15 Schubert, “Gute Nacht” from Winterreise STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

Fremd lch

bin kann

ich zu

ein mei

ge ner

zo Rei

gen, fremd sen nicht

zich wäh

ich wie len mit

der der

aus. Zeit,

16

THE COMPLETE MUSICIAN

EXAMPLE 1A.15 (continued) B.

Will

dich

im Traum nich

stö

ren,

wär’

Schad’

um dei

ne

Ruh,

Moving any pitch pattern so that it begins on a different pitch is called transposition. Let’s build a major scale on A. 1. Since a scale consists of stepwise motion, we must use every letter name in turn, and end our scale by repeating the tonic pitch one octave higher in order to create closure: A–B–C–D–E–F–G–A. 2. We refine our scale and create the sound of the major mode by using the appropriate pattern of half and whole steps (W–W–H–W–W–W–H). A to B, the first interval, is a whole step, so we move on to the next, which must also be a whole step. However, B to C is only a half step, so we must increase its size by adding a sharp to C, raising the pitch a half step (C ). The next interval should be a half step, and, indeed, C  moves a half step to D. Continuing this process, we determine that the pitches of the major scale on A are A–B–C –D–E–F–G–A (Example 1A.16). Since the scale of A major contains three sharped pitches, we say that “the scale of A major contains three sharps.”

EXAMPLE 1A.16 The A-Major Scale A

B

W

C

W

D

H

E

W

F

W

G

W

A

H

F Major Using the same process to create the F-major scale, we begin with the ordering F–G–A– B–C–D–E–F. Applying our formula of whole and half steps to the first two intervals, we find that F to G and G to A are both whole steps, as they should be. Moving ahead, the distance from A to B is another whole step, rather than the requisite half step. Therefore,

17

Chapter 1A Musical Space

we must lower B one half step by adding a flat, changing B to B. Next, we need another whole step, which B to C provides. By continuing this process, we see that the major scale on F requires just one flat: F–G–A–B–C–D–E–F (Example 1A.17).

EXAMPLE 1A.17 The F-Major Scale

W

W

H

W

W

W

H

Key Signatures and the Circle of Fifths The key signature is a symbol that appears near the beginning of each musical staff, to the right of the clef. It presents a pattern of either sharps or flats, conveying the pitch classes of a key. Indeed, the key signature often implies the key of the composition (keys are made explicit by how the pitches are actually used). Imagine the notational nightmare of writing a piece in C major without a key signature: Every pitch in the piece would need a sharp sign. Example 1A.18 shows the four-sharp key signature for E major. Note that there is only one F, one C, one G, and one D shown in the key signature; when you indicate a sharp or flat in a key signature, the accidental applies to the entire pitch class (if you write a sharp for one F, then all Fs become Fs).

EXAMPLE 1A.18 The Key Signature for E Major

Mastering Key Signatures

G major has one altered pitch (F), so its key signature has one sharp; D major has two altered pitches (F, C), so its key signature has two sharps. The complete list of major keys with sharps is: G (1 sharp), D (2), A (3), E (4), B (5), F (6), C (7). Note that the tonic note for each key on the list is five steps (or a “fifth”) higher than in the previous key. The sharps in a key signature—when read from left to right—are also a fifth apart: F, C, G, D, A, E, B. An easy way to remember the relationship between the key signature and the tonic is to note that the pitch one half step above the final sharp in the key signature is the tonic. For example, if the last sharp is F, the tonic is G; if the last sharp is B, the tonic is C. The flat keys follow the same pattern of fifths but in the opposite direction from C: F, B, E, A, D, G, C. Flats are added in a specific order of descending fifths:

18

THE COMPLETE MUSICIAN

B, E, A, D, G, C, F. For flat keys, the tonic can be determined by reading the penultimate flat in the key signature. If the key signature contains B and E, the second-to-last flat, B, is the tonic. Likewise, if the key signature contains B, E, A, and D , then the tonic is A. Note that when we ascend by fifths, we end with C major; when we descend by fifths, we end with C major. The opposing process of flat and sharp key relations may be represented graphically as in Example 1A.19, using a circle that illustrates both the key signatures and their relationships to one another. This diagram is called the circle of fifths, since each key on the circle lies a fifth above the preceding key (if you move clockwise around the circle) or a fifth below the preceding key (if you move counterclockwise around the circle). Notice that there are 15 keys listed, although there are only 12 chromatic pitches. This is because of three enharmonic keys that occur at the bottom of the circle: B/C, F/G, and C/D. Keys that are adjacent to one another on the circle—that is, their key signatures differ by one sharp or flat—are called closely related keys (e.g., A major is closely related to both D major and E major).

EXAMPLE 1A.19 The Circle of Fifths

C G

F B

D

E

A

E

A C /D

B/C F /G

19

Chapter 1A Musical Space

EX ERCISE INTER LUDE 1A.1 Writing Scale Fragments Study each scale fragment that follows and determine in which major scales the fragments could be members; write out the complete scales and include scale degrees. For example, given the fragment A and B and the instruction to list the major scales to which the pitches belong, the answer would be F major and B major. List as many major scales as would fit each fragment; there may only be a single solution or there may be multiple solutions. A. D–E E. G–C

SOLVED/APP 5

C. C–D  G. F–A 

B. A–B F. E –G

D. B –D

1A.2 Scale Practice: Error Detection Below are incorrectly written major scales; correct the errors by adding or removing the appropriate accidentals and/or pitch. Extra credit: Transpose scales that appear in the bass clef down a whole step and scales that appear in the treble clef up a fifth.

A.

B.

C.

D.

E.

Building Scales in the Minor Mode The minor mode is the other mode commonly used in tonal music, and, like its major counterpart, it comprises a particular sequence of half steps and whole steps. The minor mode is distinguished primarily by its mediant (3), which lies one half step lower than the third scale degree of the major mode. For example, in the key of D major, the third scale degree is F, while in the key of D minor, the third scale degree is F. Another important difference between the major and the minor modes is that 6 and 7 in the minor mode are variable; depending on the melodic line’s direction, their scale degrees may be raised or lowered, which is why the minor mode is often considered to be more flexible than the major mode. The minor mode is characterized by a darker sound, in contrast to the bright sound of the major scale. Listen again to Example 1A.15.

20

THE COMPLETE MUSICIAN

Example 1A.20 presents D-major and D-minor scales. Notice that the minor scale has a different pattern of half and whole steps than the major. Pitch differences are shown as filled-in notes. We refer to this form of the minor scale—with a half step between 2 and 3 and between 5 and 6—as the natural minor scale. Notice that both 6 and 7 are a half step lower than in major.

EXAMPLE 1A.20 Major and Natural Minor Scales 1

D Major:

2

W

1

d minor: (natural)

3

W 2

W

4

5

H 3

H

6

W 4

W

H

6

W

8

W

5

W

7

7

H

8

W

W

Composers often intensify melodic motion in the minor mode, resulting in the slight rearrangement of half steps and whole steps in the final three pitches. These variations take two forms and result in what are traditionally called the harmonic minor scale and the melodic minor scale. Example 1A.21 presents the three forms of the minor scale: natural, harmonic, and melodic. The differences are based on the natural tendency for melodic lines to move toward a goal. That is, raising pitches enhances the pull of an ascending line, and lowering pitches enhances the direction of a descending line. One can view these two variations of the minor scale as a means of creating both this goal-directed motion and a smooth melodic line, because forward motion in tonal music is generally enhanced by half-step motion. For example, the natural minor scale, with its

EXAMPLE 1A.21 Natural, Harmonic, and Melodic Minor Scales 1

2

3

4

5

6

7

8

7

6

natural: W+H

harmonic:

melodic:

W+H

5

4

3

2

1

21

Chapter 1A Musical Space

smooth stepwise motion from 5 to 8 does not possess much goal-oriented motion in its ascent because it does not contain a leading tone. The harmonic minor scale remedies this situation by raising 7 to create a leading tone. Notice in Example 1A.15A that Schubert adds the leading tone (C) in the piano accompaniment (m. 4) in order to create a sense of musical closure that complements the end of the first line of text. However, as shown in Example 1A.21, the addition of the leading tone sacrifices the smooth melodic motion between 6 and 7 by producing a gap of one and a half steps. The melodic minor scale contains both smooth stepwise motion and the leading tone, since 6 as well as 7 are raised, which leads nicely upward to 1, the primary tonal pillar and point of stability. The descending version of the melodic minor scale is different from its ascending version: 6 and 7 are lowered to enhance the descent toward 5, the secondary tonal pillar. We call the lowered 7 the subtonic rather than the leading tone; the subtonic does not rise to the tonic as the leading tone does; rather, it is the crucial first step in a falling line that leads toward the dominant. The three forms of the minor scale should be viewed more as slight variations of a single “minor collection” than as three different scales, because of their constant circulation within a musical context. Thus, the minor scale is really a nine-pitch-class repository from which the composer draws material. Indeed, as shown in Example 1A.22A, Mozart’s descending chromatic line touches on both forms of 7 and 6 on its way to an arrival on 5; the musical “point” is less what form of minor is used than what musical procedure creates the most dramatic tension. To avoid potential ambiguity, up and down arrows will represent raised and lowered scale degrees, respectively. Example 1A.22B arranges the entire minor collection in ascending order. Example 1A.22C illustrates how the minor collection is really a by-product of the melodic requirements of individual lines. For example, the opening descending bass line is intensified by the lowered forms of 6 and 7 while the following ascent is supported by using their raised

EXAMPLE 1A.22 Melodic Tendencies in the Minor Mode STR EA MING AUDIO

A. Mozart, Piano Sonata in D major, K. 284, Polonaise en Rondeau

f :

B.

8

↑7

↓7

Scale 1

2

3

4

5

↓6

↑6

↓7

↑7

↑6

W W W.OUP.COM/US/LAITZ

↓6

5

22

THE COMPLETE MUSICIAN

EXAMPLE 1A.22 (continued) C. Bach, “Verleih’ uns Frieden gnädiglich” 8

5

f :

8

↓6

↓7

↓6

↑7

8

5

5

5

8

↑6

↑7

↑7

8

8

forms. Notice that the unwieldy interval of three half steps, that occurs between lowered 6 and raised 7 of the harmonic form of minor, is actually moot, since this interval rarely occurs within a single melodic line. In the Bach chorale, ↑7 (E) arises either from a stepwise ascent through ↑6 (D) or from the half-step descent from 1 to 7 and return to 1 (F–E–F); E is not in any way connected to ↓6 (D). Similarly, ↓6 arises from an upward movement from 5 to which it returns. Thus, ↓6 gravitates toward 5 and ↑7 gravitates toward 1.

Key Signatures in Minor Minor keys are represented by key signatures derived from the natural minor scale. The order of minor key signatures proceeds in exactly the same pattern as the major key signatures. See Example 1A.23, which summarizes the number and names of the sharps or flats for all major and minor keys; C, with no flats or sharps, is in the middle, with added sharps and flats fanning out above and below C. That is, one sharp is added to the key signature for each scale that lies a fifth higher than the previous scale (i.e., from 1 up to 5). One flat is added to the key signature that lies a fifth lower than the previous scale (i.e., from 1 down to 4).

Relative Major and Minor Keys We refer to major and minor keys with the same key signatures as relative. The relative major key of a minor key lies three half steps (i.e., skipping one letter name) above the tonic of the minor key; we also can think of relative minor keys as lying three half steps below the tonic of the major key. Example 1A.24A, from one of Beethoven’s piano sonatas, illustrates the relative-major relationship between D minor and F major. Usually, however, such literal restatements of material in a different harmonic area are not as common as the use of contrasting material, as illustrated in another example from Beethoven’s piano sonatas (Example 1A.24B). Here, the relative relationship works the other way: from a major key (D major) to a minor key (B minor). Beethoven’s dramatic statement of the D-major opening theme in octaves is followed by a tumultuous theme in B minor. (See the Anthology nos. 28 and 29 for two other Beethoven piano sonatas.) Such dramatic harmonic shifts, however, are uncommon. The diagram in Example 1A.25 illustrates the pairing of relative major and minor keys around the circle of fifths.

23

Chapter 1A Musical Space

EXAMPLE 1A.23 Sharps and Flats in Major and Minor Keys

MAJOR KEY

→ C F B E A D G →C F B E A D G C

MINOR KEY

NUMBER OF ACCIDENTALS

a d g c f b e a d g c f b e a

7 sharps 6 sharps 5 sharps 4 sharps 3 sharps 2 sharps 1 sharp 0 l flat 2 flats 3 flats 4 flats 5 flats 6 flats 7 flats

ACCIDENTALS IN KEY

F C  G  D  A  E  B  F C  G  D  A  E  F C  G  D  A  F C  G  D  F C  G  F C  F B B E B E A B E A D B E A D G B E A D G C B  E  A  D  G C  F

Major keys are represented by uppercase letters and minor keys by lowercase letters on the circle of fifths. Parallel major and parallel minor scales and keys are those that share the same tonic but do not share the same key signatures. For example, the parallel minor of D major is D minor, and the parallel major of B minor is B major. The key signatures of parallel keys differ by three accidentals (e.g., the D major and d minor of Schubert’s “Gute Nacht” in Example 1A.15 contain two sharps and one flat respectively [i.e., two sharps plus one flat equals three accidentals]). Example 1A.26 illustrates back-to-back statements of material in the parallel keys of G major and G minor.

EXAMPLE 1A.24 Relative-Key Relations STR EA MING AUDIO

A. Beethoven, Piano Sonata in D major, op. 28, Andante

W W W.OUP.COM/US/LAITZ

cresc.

d:

sempre staccato

F:

24

THE COMPLETE MUSICIAN

EXAMPLE 1A.24 (continued) B.

Beethoven, Piano Sonata in D major, op. 10, no. 3

cresc.

D:

b:

EXAMPLE 1A.25 Relative Major and Minor Key Signatures

F B

E

d

C a

e

G b D

g

c

A

f A c

f a /g

b /a D /C

e /d G /F

C /B

E

25

Chapter 1A Musical Space

EXAMPLE 1A.26 Mozart, Piano Sonata in C major, K. 545, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

26

29

EX ERCISE INTER LUDE W R ITING WORKBOOK 1 Assignments 1A.1–1A.5

1A.3 Writing Scales (I) Notate the following scales on manuscript paper. Use accidentals instead of key signatures, and mark each half and whole step. Begin by writing the first scale (B major) in bass clef and the next in treble clef. Continue alternating clefs for each scale. A. Major: 1. D (sample solution):

W

W

H

W

W

2. B  3. E  4. G 5. B 6. E 7. D  B. Melodic minor: 1. F 2. A 3. B C. Harmonic minor: 1. G 2. B  3. C  D. Natural minor (ascending and descending): 1. D 2. E  3. E

W

H

26

THE COMPLETE MUSICIAN

1A.4 Writing Scales (II) Write the following scales on manuscript paper, using accidentals instead of key signatures. A.

The major scale in which: 1. G  is 3 (sample solution): 3

2. C is 4 3. G  is 6 4. C  is 6 5. B  is 2 6. B  is 4 7. B  is 7 B. The major scale in which: 1. A is supertonic 2. D is mediant 3. F is submediant 4. B is dominant 5. E is supertonic 6. E is subdominant 7. E is leading tone C. The harmonic minor scale in which: 1. A is 3 2. C  is 7 3. E is 5 4. E is 6 D. The relative major scale of: 1. G minor 2. C  minor 3. B  minor 4. G  minor E. The relative minor scale (melodic form) of: 1. F major 2. A major 3. E  major F. The parallel major scale of: 1. E minor 2. A minor 3. A  minor

1A.5 Scale Fragments Study each scale fragment that follows and determine in which minor scales the fragments could be members; write out the complete scales and include scale degrees. For example, given the fragment A and B, the answer would be B melodic and harmonic minor, G minor, and D harmonic minor. Make sure that you specify the form of minor. A. D–E B. A –C C. A –B D. F–G  E. B–F F. F–A G. C –F 1A.6 Scale Practice: Error Detection Below are misspelled minor scales; correct the errors by adding the appropriate accidentals and/or pitches. Accidentals apply only to pitches they precede; they do not carry over. A. Harmonic Minor

B. Melodic Minor

Chapter 1A Musical Space

27

C. Natural Minor

D. Harmonic Minor

E. Melodic Minor

Intervals In our discussion of scales, we explored various relationships between pairs of pitches. We call a pair of pitches a dyad, and the distance between the pitches in a dyad is an interval––the basic building block of tonal music. The one-measure excerpt in Example 1A.27A contains dozens of intervals, some formed between pitches in the same voice, others formed between pitches sounding simultaneously between different voices. Example 1A.27B shows the six intervals in the first beat.

EXAMPLE 1A.27 Handel, Concerto Grosso in C minor, op. 6, no. 8, HWV 326, Allegro A.

B.

Naming Generic Intervals The distance between one pitch and any other pitch is represented by a number derived from the number of pitch letter names that separate the two notes. The distance is measured by the number of lines or spaces on the staff that are spanned. (When we speak of intervals, we use the ordinal number, such as third, fifth, and seventh. When we label intervals, we use cardinal numbers, such as 3, 5, and 7.) The numerical label that identifies the distance between letter names is called the generic name. We have focused on those intervals that are formed by successive scale degrees in major and minor scales. The distance between adjacent scale degrees, or steps, is called a second because it involves two successive letter names (for example, A up to B or E down to D).

28

THE COMPLETE MUSICIAN

Example 1A.28A presents the interval from G4 up to E5. Given that there are six different letter names involved, G–A–B–C–D–E, we refer to the interval as a sixth. Notice that we compute the generic size by including both the first and last notes. Further, contour and accidentals do not change an interval’s generic size. For example, whether you ascend from G4 to E5 or descend from E5 to G4, the interval remains a sixth; and no matter what combination of G (G, G, G) up to E (E, E, E), all are sixths (Example 1A.28B).

EXAMPLE 1A.28 Generic Sixths A. 6 5 4 3 2

B.

6th

6th

6th

6th

Intervals in Context Melodic and Harmonic When one pitch follows another in time, the interval is called a melodic interval, or linear interval. We specify the direction, or contour, of the interval by reading from left to right. For example, the first interval in Example 1A.28B is an “ascending sixth” and the last interval is a “descending sixth.” If the two pitches sound simultaneously, as in the sixth formed by G and E, the interval is called a harmonic interval. You cannot specify contour for harmonic intervals because they sound together. The smallest interval is the unison, or prime; it is the interval from a pitch to the same pitch—for example, the distance from middle C to middle C. The octave is the interval from a pitch to the pitch with the same letter name that lies seven steps away.

Simple and Compound Intervals no larger than the octave are called simple intervals (Example 1A.29). Intervals larger than the octave are called compound intervals. Since the labeling of compound intervals can become cumbersome (for example, the distance from C2 to C4 would be an unwieldy “fifteenth”), we use the names of these larger intervals only up to the distance of a twelfth. We use the simple form names for intervals larger than the twelfth, but append the adjective “compound” before the generic size. Thus, the interval from C4 to E5 is a

29

Chapter 1A Musical Space

EXAMPLE 1A.29 Simple Intervals

unison

2nd

3rd

4th

5th

6th

7th

octave

tenth, while the interval from C2 to C4 is a compound octave. (You can also use “octave plus” instead of “compound”; the distance from D4 to B5 is either a “compound sixth” or an “octave plus a sixth”); see Example 1A.30.

EXAMPLE 1A.30 Compound Intervals 8va

8ba

tenth

double octave

eleventh compound fourths

Tips for Identifying Generic Intervals Here are some techniques for quickly determining intervals up to a twelfth for pitches in the treble or bass clef. If the pitches are both on lines or both on spaces, they will form an odd-numbered interval (i.e., 1, 3, 5, 7, 9). For example, a third is formed when pitches are on adjacent lines or spaces, and a fifth is formed when one line or one space separates the two pitches. This technique works when accidentals precede the notes (Example 1A.31).

EXAMPLE 1A.31 Odd-Numbered Intervals with Accidentals (Note: Both pitches on lines or both pitches on spaces form odd intervals: 3, 5, 7, 9.)

3rd

5th

7th

9th

3rd

5th

7th

9th

By contrast, if one of the pitches falls on a line and the other falls on a space, the result will be an even-numbered interval (i.e., 2, 4, 6, 8, 10). For example, pitches on an adjacent line and space form a second, and an interval occurring on a line and a space that is

30

THE COMPLETE MUSICIAN

EXAMPLE 1A.32 Even-Numbered Intervals with Accidentals (Note: One pitch on a line and one pitch on a space form even intervals: 2, 4, 6, 8, 10.)

2nd

4th

6th

8th

2nd

4th

6th

8th

separated by one line is a fourth. Two lines separating an interval will result in a sixth, and three lines separating an interval produce an octave (Example 1A.32).

Naming Specific Intervals A generic label is usually not specific enough to be of much use. For example, the label second does not differentiate between what we already know from our scale studies to be an interval that comes in three different sizes, spanning one half step (between 3 and 4 in major), two half steps (between 1 and 2), and even three half steps (between 6 and 7 in harmonic minor). Further, and more importantly, a generic label in no way reflects the audible differences in sound between these various forms of a second. Comparing the sound of a harmonic second with only one semitone against seconds with two or three semitones is striking, since the smaller second sounds more unstable and harsher than the larger seconds. We must identify intervals not only by their generic name, but also by their quality; together, the generic name and quality produces their specific size. Using the major and minor scales, we can identify intervals precisely. We group intervals into two basic categories: perfect (P) and major (M)/minor (m). In Example

EXAMPLE 1A.33 A. Specific Intervals Above 1 in the Major Scale

P1

M2

M3

P4

P5

M6

M7

P8

m6

m7

P8

B. Specific Intervals Above 1 in the Minor Scale

P1

M2

m3

P4

P5

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Chapter 1A Musical Space

1A.33, each interval of the C major and C natural minor scale above 1 is identified by a generic name in conjunction with a modifier (here, uppercase P or uppercase M or lowercase m): • P designates a perfect interval (which includes the unison (P1), the fourth (P4), the fifth (P5), and the octave (P8). Perfect intervals retain their specific size in both major and minor modes. • Uppercase M designates major intervals, and lowercase m designates minor intervals; major and minor are applied to seconds, thirds, sixths, and sevenths. Major intervals occur above the tonic in the major scale, and minor intervals occur above the tonic in the minor scale (except for the second from 1 to 2, which is major in both modes). Note that not all intervals are generated from 1 in major and natural minor scales. We will investigate other diatonic intervals (intervals found in either major or minor mode) later. To find the specific size of a diatonic interval, follow this two-stage process: 1. Determine the generic size of the interval. 2. Determine whether the interval’s upper pitch is a member of the major or the minor scale of the lower pitch. Example 1A.34 presents several examples. • In Example 1A.34A, the generic interval size is a fourth (D–E–F–G). The upper pitch, G, lies in the scale of D (major and minor), so the interval is a perfect fourth. • In Example 1A.34B, C is a third above A (A–B–C) and C is a member of the A-major scale, so the interval is a major third. • In Example 1A.34C, G lies a third above E, and G is a member of the E-minor scale, so the interval is a minor third. • In Example 1A.34D, G lies a sixth above B, and since G is a member of the B-major scale, the interval is a major sixth.

EXAMPLE 1A.34

A.

B.

P4

C.

M3

D.

m3

M6

32

THE COMPLETE MUSICIAN

EX ERCISE INTER LUDE W R ITING 1A.7

WORKBOOK 1 Assignment 1A.6

Sample solution:

P5

Generating Diatonic Intervals

• Notate the required interval above each given pitch. • Transpose each interval a major third lower than written.

A.

B.

M6

C.

m3

D.

M7

E.

m6

F.

M3

G.

P4

H.

m7

I.

M3

m6

Transforming Intervals Minor Major and Major Minor Because minor intervals are a half step smaller than major intervals, you can transform any minor interval into a major interval by increasing its size by a half step, by either raising the upper note or lowering the bottom note. Example 1A.35 increases the size of a m3 to a M3 by raising the upper note a half step (A1) or lowering the bottom note a half step (A2). Likewise, a major interval can be transformed into a minor interval by decreasing the size of the major interval by a half step. In this case, the upper note can be lowered by a half step or the lower note can be raised by a half step. Example 1A.35B1 decreases the size of a M6 to a m6 by lowering the upper note, and B2 decreases the M6 to a m6 by raising the lower note a half step.

EXAMPLE 1A.35 Increasing and Decreasing the Size of Minor and Major Intervals A1.

half step higher

m3

M3

A2. half step lower

m3

M3

B1.

half step lower

M6

m6

B2. half step higher

M6

m6

Augmented and Diminished Intervals It is possible to increase the size of major and perfect intervals by a half step (Example 1A.36A and B), resulting in augmented intervals. It is also possible to decrease the size of minor and perfect intervals (Example 1A.36C and D), resulting in diminished intervals (Example 1A.36A–D). We find several augmented and diminished intervals in major and minor scales (Example 1A.36E). Major and minor intervals can never become perfect, and perfect intervals can never become major or minor.

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Chapter 1A Musical Space

EXAMPLE 1A.36 Augmenting and Diminishing Intervals A. Augmenting a M3

B. Augmenting a P5

half step higher

M3

half step higher

half step lower

A3

M3

P5

A3

C. Diminishing a m3

half step lower

half step higher

d3

A5

P5

A5

D. Diminishing a P5

half step lower

m3

half step lower

m3

P5

d3

d5

E.

half step higher

P5

d5

A4/d5 1

2

3

4

5

6

7

1

A4/d5

d5/A4

A2/d7

The complete list of labels and abbreviations that reflect an interval’s quality are as follows: • P for perfect • M for major • m for minor • A (or ⫹) for augmented • d (or °) for diminished Let’s work through four intervals for practice (Example 1A.37).

EXAMPLE 1A.37 A.

B.

C.

D.

• In Example 1A.37A, the fourth (E up to A) is not perfect, since A, not A, lies in the E scale. Since the interval is a half step larger than a perfect fourth, it is an augmented fourth (A4 or ⫹4).

34

THE COMPLETE MUSICIAN

• In Example 1A.37B, the fifth (C up to G) is also not perfect, since G, not G, lies in the C scale. The interval is a half step larger than a perfect fifth; therefore, the interval is an augmented fifth (A5 or ⫹5). • In Example 1A.37C, A is not a member of either the F -major or F-minor scale; it is a half step smaller than a minor third, so the interval is a diminished third (d3 or °3). • In Example 1A.37D, B is a half step higher than B, which lies in the D-major scale. Since D to B is a major sixth, D to B would be an augmented sixth (A6 or ⫹6). Example 1A.38A shows how perfect intervals may be increased or decreased in size and Example 1A.38B summarizes how major and minor intervals may be increased or decreased in size.

EXAMPLE 1A.38 A.

Transforming Perfect Intervals (1, 4, 5, 8)

smaller diminished

d5

B.

larger Perfect

Augmented

P5

A5

Transforming Major and Minor Intervals (2, 3, 6, 7) smaller diminished

minor

Major

d3

m3

M3

larger Augmented

A3

Interval Inversion When we move the lower pitch of a simple interval up one octave so that it is placed above the higher pitch, we have inverted the interval. Inversion also occurs when we place the higher pitch of a simple interval below the lower pitch. Example 1A.39A shows what happens when we invert generic intervals; Example 1A.39B does the same for an interval’s quality. Arrows represent the inversion process; the inversion process can move in either direction (e.g., a second becomes a seventh, or vice versa). Notice that the inversion of generic intervals always sums to 9 (e.g., a third becomes a sixth: 3 ⫹ 6 ⫽ 9). Also notice in Example 1A.39B that perfect intervals retain their quality when inverted. However, quality is swapped for augmented/diminished and major/minor intervals. Finally, the number of half steps between inversionally related intervals always sums to 12 [for example, the single half step of the minor second becomes 11 half steps when inverted as a major seventh (1 ⫹ 11 ⫽ 12)]. Example 1A.40 shows the resulting pattern.

35

Chapter 1A Musical Space

EXAMPLE 1A.39 Inverting Intervals A. Generic Interval Inversion unison ←→ octave (1 ⫹ 8 ⫽ 9) second ←→ seventh (2 ⫹ 7 ⫽ 9) third ←→ sixth (3 ⫹ 6 ⫽ 9) fourth ←→ fifth (4 ⫹ 5 ⫽ 9)

B. Quality perfect ←→ perfect augmented ←→ diminished major ←→ minor

EXAMPLE 1A.40

interval: P1 → P8 m2 → M7 M2 → m7 m3 → M6 M3 → m6 1→ 11 2→ 10 3→ 9 4→ 8 half step: 0→ 12

P4 → P5 5→ 7

A4 → d5 6→ 6

P5 → P4 7→ 5

m6 → M3 M6 → m3 m7 → M2 M7 → m2 P8 → P1 8→ 4 9→ 3 10→ 2 11→ 1 12 → 0

There is only one inversional pair of intervals whose number of half steps remains the same following inversion: both the diminished fifth and the augmented fourth contain six half steps. The augmented fourth is a tritone, since it contains three whole steps; we also refer to the diminished fifth as a tritone, even though it actually spans five letter names (e.g., B–C–D–E–F). Notice also how inversionally related pairs of intervals in effect “repeat” themselves in reverse order from the center point A4/d5; for example, the P4/P5 pair becomes a P5/P4 pair. Play each inversionally related pair of intervals, noticing how their sound quality and level of stability remain relatively the same. For example, the inversional pair of a minor second and a major seventh are both very unstable sounding, while a major third and a minor sixth are much more stable, and the octave and unison are absolutely stable.

EX ERCISE INTER LUDE W R ITING 1A.8 Intervallic Transformations A. Identify the following intervals when you increase their size by one half step without changing their generic name (e.g., a major second would become an augmented second, not a minor third). 1. M3 2. M2

36

THE COMPLETE MUSICIAN

3. 4. 5. 6. B.

P4 M6 d3 m7

Identify the following intervals when you decrease their size by one half step without changing their generic name. 1. m2 2. P5 3. A2

4. M6 5. A4 6. A3

C. Identify the following intervals when you increase their size by two half steps without changing their generic name. 1. m2 2. d3 3. d5 D. Identify the following intervals when you decrease their size by two half steps without changing their generic name. 1. M6 2. A5 3. A2 4. M3

1A.9 Label the following intervals as they would occur in the given keys. You will need to consider the key signature of each key. An uppercase key name indicates major mode; a lowercase key name indicates minor mode. The first exercise is solved for you: in f minor, there is a G, and G up to B is a minor third. Consider the key signature for each example.

f :

m3

B:

B :

d:

D:

A:

A :

d:

D:

A :

C :

D:

A:

A:

F :

F:

F:

E :

f:

g :

Generating All Intervals So far we have generated intervals only above a given pitch, a process based on (1) the generic size of the interval and (2) the quality (the specific size of the interval, based on whether the upper pitch lies in the major or minor scale of the lower pitch). When we create an interval below a given pitch, we still begin by calculating the generic size. However,

37

Chapter 1A Musical Space

to determine the quality (i.e., whether any accidentals are needed) use one of the two following methods.

Method 1 This method draws on our knowledge of inversion and is especially helpful in constructing large intervals. 1. Take the requested interval and invert it so that you are looking for a note above the given pitch. 2. Find the appropriate note above the given pitch, using scale membership (i.e., determine if the upper note is a member of the major or minor scale of the lower pitch). 3. Transpose this inverted pitch down one octave. For example, to find the pitch that lies a major seventh below C, first determine the inversion of a M7, which is a m2. Then, generate a m2 above C, which is D. Finally, notate D one octave lower to create a major seventh below C. You may wish to check your work using our method of scale membership: C is indeed a seventh above D, since C is a member of the D-major scale. See Example 1A.41.

EXAMPLE 1A.41 Generating Intervals Through Inversion Step 1: M7

M7 below C

m2

m2

Step 2: notate 1 octave below

M7

Method 2 This method requires adjusting the lower pitch. 1. Count down by generic interval from the given pitch—do not worry about accidentals yet. 2. Determine the resulting specific interval using the scale membership. 3. If the interval you have constructed is the requested interval, you are finished! If not, add an accidental to the lower pitch to change the specific interval. If the interval is too small, add a flat to the lower pitch (which increases the size of the interval). If the interval is too large, add a sharp to the lower pitch (which decreases the size of the interval). For example, given the pitch F, construct the interval of a perfect fifth below it. First, determine the generic fifth, which is B. Second, ask yourself whether or not F is a perfect fifth above B. If it is, you’re done. However, F is a diminished fifth above B. Thus, we must

38

THE COMPLETE MUSICIAN

lower B to B to increase the diminished fifth to a perfect fifth. Again, check your work: F is indeed a perfect fifth above B. See Example 1A.42.

EXAMPLE 1A.42 Generating Intervals Through Chromatic Adjustment Step 1: generic 5th

Step 2: not a P5, but ˚5, so add a flat to increase size to P5

P5 below F

d5

P5

EX ERCISE INTER LUDE W R ITING 1A.10 Name all possible intervals requested in the given key. For example, “In A major, name all possible perfect fifths.” Answer: A–E, B–F, C–G, D–A, E–B, and F–C. A. In F major, name all possible major seconds. B. In B  major, name all possible minor seconds. C. In the C harmonic minor scale, name all possible major thirds. D. In F major, name all possible minor sixths.

SOLVED/APP 5 SOLVED/APP 5

1A.11 Notate the requested intervals below the given pitch, and label each interval’s inversion.

SOLVED/APP 5

m3

m3

d5

P5

M3

m3

m2

M6

M2

d4

A5

A NA LYSIS 1A.12

Identify the interval formed by each circled pair of pitches. 4

2

18

 Alt.       

        1



se

-

 

 

pp

 

-



     p



-

3

  

8

                     

    

    Qui

6

5

-

        

-

-

     

des ad

dex - tram Pa - tris,

qui

                     7   pp 9           

39

Chapter 1A Musical Space

23

 

12

 se

-

     -

-

        

 -

-

-

15

11

             p 10           1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

-

        13  14       

____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________

   

des ad

21

          

dex - tram 18

16

Pa - tris,

ad

20

               22   pp                  17

13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23.

 

 23



19

____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________ ____________

Enharmonic Intervals Just as there are enharmonic pitches, so too are there enharmonic intervals. For example, the minor third from C up to E sounds identical to the augmented second from C up to D (see Example 1A.43A; dotted slurs indicate enharmonic pitches). The notation of intervals depends entirely on the musical context. For example, one would expect to find many instances of the minor third C–E in any number of major and minor keys that contain flats because the interval is diatonic in these keys. However, the more unusual augmented second C–D would occur only in the scale of E minor and only if its harmonic form were used (Example 1A.43B).

EXAMPLE 1A.43 A.

m3

B.

A2

m3

A2 c minor

e minor

40

THE COMPLETE MUSICIAN

Consonant and Dissonant Intervals When you compare the sound of an octave with that of a seventh, the octave seems stable and firmly planted, with no need to move on to some other, more stable interval. On the other hand, the seventh seems active, unstable, and even tense, as if it were searching for something to resolve its inherent discontent. At least as early as the ancient Greeks, Western musicians have felt that different-sized intervals provoked certain feelings, ranging from a pleasing stability to a restless yearning. These musicians also discovered that the same interval in two different musical contexts could be perceived as either stable or unstable. For example, Example 1A.44 presents the perfect fourth C–F in four different contexts. Listen to each, and order the examples from most stable to least stable. If you heard D and the first chord in E as most stable and C as least stable (with B and the second chord in E somewhere in between), you were sensitive to the fact that intervallic stability and instability is highly determined by musical context.

EXAMPLE 1A.44 Intervallic Stability and Context

A.

B.

relatively stable

C.

unstable

P4

D.

F:

E.

relatively stable

stable stable

stable

Although we usually consider intervallic stability and instability to be on a continuum, we can place all intervals into one of two categories. The stable intervals—including the diatonic forms of the unison, the third, the fifth (perfect only), the sixth, and the octave—are called consonant intervals; unstable intervals are called dissonant intervals. Dissonant intervals include the second, the seventh, and all diminished and augmented intervals. The perfect fourth is usually viewed as a dissonant interval, although as we saw in Example 1A.44 it can be stable, depending on the context in which it appears. The five consonant intervals are further divided into two types. Perfect consonances are the most stable and include the perfect unison, the perfect octave, and the perfect fifth. Imperfect consonances include major and minor thirds and sixths, which are moderately

Chapter 1A Musical Space

41

stable yet more fluid than the perfect consonances. Imperfect consonances are central to moving the music forward. Example 1A.45 summarizes the types of intervals. Composers create motion in their music by circulating through the various types of intervals; for example, from perfect consonances and imperfect consonances to dissonances, and back. WORKBOOK 1 Assignments 1A.7–1A.8

EXAMPLE 1A.45 Consonant Intervals

Dissonant Intervals

perfect: P1, P5, P8

all forms of 2nds, 4ths, and 7ths

imperfect: M3, m3, M6, m6

all augmented and diminished intervals

T E R M S A N D C O N C E P T S F OR PI T C H , S C A L E , A N D K E Y • accidentals • bar line • chromatic, chromatic system, chromatic scale, chromatic alteration • circle of fifths • clef • common-practice period • diatonic • enharmonic equivalence • interval: half step and whole step; diatonic and chromatic half steps • key • key signature • major scale • minor scales: • natural, harmonic, and melodic • mode, major and minor • parallel major and parallel minor • pitch, pitch class • register • relative major and relative minor • scale • scale degree names and numbers • staff • step • tonal, tonal center, tonality • tonic • transposition

42

THE COMPLETE MUSICIAN

T E R M S A N D C O N C E P T S F OR I N T E RVA L S • chromatic and diatonic half steps • compound and simple intervals • consonances: perfect versus imperfect • diatonic intervals • dissonance, dissonant intervals • enharmonic intervals • generic interval versus specific interval; intervallic quality • harmonic interval versus melodic interval • interval types: augmented, diminished, major, minor, and perfect intervals • intervallic consonance versus dissonance • inversion of intervals • tritone

CH A PTER R EV IEW 1. Complete the table for the five accidentals, or chromatic alterations. natural

NAME NUMBER OF HALF STEPS AND DIRECTION SYMBOL

cancels previous accidental











2. Define enharmonic equivalence. Using accidentals, give an example of two pitches that are enharmonically equivalent.

3. Write the name of each scale degree number in the table below. Scale degree 7, which is not diatonic to the major scale, has been added to illustrate the symmetry of the naming system around tonic. SCALE DEGREE

5 3 2 1

NAME

43

Chapter 1A Musical Space

SCALE DEGREE

NAME

7 7

subtonic

6 4

4. Using the letters W (whole) and H (half ), write the pattern corresponding to the major scale.

5. Using the letters W (whole) and H (half ), write the pattern corresponding to the natural minor scale.

6. List the three types of minor scales.

7. Relative keys share the same [tonic/key signature], whereas parallel keys share the same [tonic/key signature].

8. Simple intervals are [less/more] than an octave, whereas compound intervals are [less/ more] than an octave.

9. Name two intervals, one augmented and one diminished, that equal a tritone.

10. List the generic intervals (unison through octave) that will always belong to each category of label: 1. Diminished/Perfect/Augmented: 2. Diminished/Minor/Major/Augmented:

C H A P T E R 1B

Musical Time: Pulse, Rhythm, and Meter

OV E RV I E W

This chapter explores the ways that music is organized in time. We will give an overview of notation, including how to show notes and rests and how to indicate the duration of each note. We will cover simple and compound meter and how to use meter signatures. Finally, we will discuss accent and how it is used to underscore or to disturb the underlying meter. CHAPTER OUTLINE Rhythm and Durational Symbols ............................................................................ 45 Notes and Rests ....................................................................................................... 45 Dots and Ties ........................................................................................................... 46 Meter ................................................................................................................................ 49 Beat Division............................................................................................................ 51 Simple and Compound Meters ............................................................................. 51 The Meter Signature ............................................................................................... 55 Meter Signatures for Compound Meters ....................................................... 56 Asymmetrical Meters .............................................................................................. 59 Clarifying Meter ...................................................................................................... 59 More Rhythmic Procedures ....................................................................................... 61 Accent in Music ............................................................................................................. 64 Temporal Accents .................................................................................................... 64 Nontemporal Accents ............................................................................................. 65 (continued)

44

45

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

Metrical Disturbance ................................................................................................... 72 Syncopation .............................................................................................................. 72 Hemiola .................................................................................................................... 73 Terms and Concepts for Rhythm and Meter ......................................................... 76 Chapter Review ............................................................................................................. 77

T H E T I M E , O R T E M P O R A L ( H O R I ZO N TA L ) , aspects of music and the pitch (vertical) aspects of music are intimately intertwined and complement each other. This chapter concentrates on the essential concepts and terminology related to temporality. First, some basic terminology: Undifferentiated (e.g., same quality, loudness, and length) and equally spaced clicks or taps are called pulses. When you nod your head or tap your foot at a steady rate when listening to music, these pulses are called beats, because they now occur within a context that differentiates them; for example, some beats feel stronger than others. The tempo is the speed of the beat; that is, how fast or how slowly you nod or tap. Meter refers to the grouping of both strong and weak beats into recurring patterns. Rhythm refers to the ever-changing combinations of longer and shorter durations and silence that populate the surface of a piece of music. Rhythm is often patterned, and rhythmic groupings may divide the beat, align with the beat, or extend over several beats. The following discussion proceeds from temporal events that take place on the rhythmic surface of a piece to the metric grid that regulates the rhythmic surface.

R H Y T H M A N D DU R AT IO N A L S Y M B OL S

Notes and Rests We use two basic notational devices to provide rhythmic information to performers (Example 1B.1): the notehead, which may be unfilled or filled (blackened), and the stem, which is added to the notehead. One or more flags may be added to stems of filled noteheads. Each added element—stem, filled-in notehead, and flag—shortens a pitch’s duration. The unfilled notehead may occur by itself, but in the common-practice period, the

EXAMPLE 1B.1 Rhythmic Notation Shorter relative durations unfilled notehead

÷2

unfilled notehead with stem

filled notehead with stem

filled notehead with stem plus flag

filled notehead with stem plus multiple flags

x2

46

THE COMPLETE MUSICIAN

EXAMPLE 1B.2 Notes and Rests Notes

Rests whole

half

quarter

eighth

sixteenth

thirty-second

filled notehead is always accompanied by a stem. In order to balance notehead and stem on the staff, we use the following notational convention: If the notehead appears on or above the third line of any staff, the stem points down. Conversely, if the notehead appears on or below the third line of any staff the stem points up. By itself, rhythmic notation does not indicate how long a note lasts, but it always precisely identifies the proportional relationships among notes. For example, each successive note in Example 1B.1 has a duration precisely half that of the preceding note. Each additional flag decreases a pitch’s duration by half. But it is only when rhythms occur in a context regulated by meter and tempo (described later)—that performers know the actual rhythmic durations. In contrast to notes, rests indicate a silence in music, and shown in Example 1B.2, they correspond exactly to the durational symbols for notes. For example, the quarter rest (  ) indicates a silence that occupies the duration of a quarter note. The “hook” characterizes the eighth rest. Like the flag that characterizes the eighth note, each successive hook shortens the rest’s duration by half. Example 1B.2 summarizes the relationships between notes and rests. Notice that each durational symbol is twice as long as the symbol directly below it.

Dots and Ties The use of additional features, dots and ties, fine-tune the rhythmic system to permit more subtle rhythms. The dot occurs after a pitch or rest, and it lengthens the value of the pitch or rest by half. For instance, if a half note is equivalent to two quarter notes, a dotted half is equivalent to three; a dotted quarter rest is equivalent to a quarter rest plus an eighth rest.

47

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

EXAMPLE 1B.3 Dotted Notes and Their Divisions A.

division by 2’s

division by 3’s

B.

+

=

=

=

+

+

+

+

+

In general, undotted notes and rests are divided evenly into twos—a quarter note is divided into two eighth notes. Dotted notes and rests are usually divided evenly into threes; a dotted half note is divided into three quarter notes (Example 1B.3A). Each successive dot adds one-half the duration of the preceding dot, as shown in Example 1B.3B. Like dots, ties lengthen the duration of a pitch. The tie’s curved line combines the duration of two or more adjacent identical pitches. Ties are commonly used in two musical contexts: to sustain a pitch whose duration would exceed the normal length of the measure and to clarify rhythmic groupings in a measure. Listen to Example 1B.4, which illustrates the use of dots and ties. As you heard in Example 1B.4, the tie sustains the first note by extending its duration without rearticulating it. Ties are distinguished from phrasing slurs, which are also shown by curved lines but connect two or more different pitches. Phrasing slurs indicate that the grouped pitches should be played as a single musical idea. This is usually accomplished by playing the notes smoothly connected and uninterrupted, or legato. A phrasing slur is labeled near the end of Example 1B.4.

EXAMPLE 1B.4 Beethoven, String Quartet no. 9, op. 59, no. 3, Andante con moto ties

sempre

sempre

sempre

sempre

ties

phrasing slur

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

48

THE COMPLETE MUSICIAN

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 1B.1–1B.2

1B.1 Matching Match each rhythm in column X with one or more examples in column Y that have the same total duration. The first example is completed for you. X

Y c,d

1.

=

2.

=

B.

3.

=

C.

4.

=

D.

5.

=

E.

6.

=

F.

7.

=

G.

8.

=

H.

9.

=

I.

10.

=

J.

A.

W R ITING 1B.2 Rhythmic Values Subdivide each of the rhythmic series (A–D) into various rhythmic groupings, each of which sums to the original value. Follow the instructions provided for parts A–D. You have at your disposal the following devices: shorter note values, ties, dots, and rests. Sample solution: Given is a dotted quarter note, followed by various divisions: =

A.

B.

=

=

=

=

=

etc.

Given a half note and dotted quarter note: write six different rhythmic solutions for the given half note and the dotted quarter note, each of which contains ever-shorter note values. Given a half note: write four different solutions for the half note, each of which includes the use of at least one dotted-note value.

49

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

C. Given a quarter note: write six different solutions, each of which includes the use of ties. D. Given a dotted quarter note: write four different solutions, each of which displays the use of rests.

METER Meter provides the framework that organizes groups of beats and rhythms into larger patterns of accented beats and unaccented beats. The patterns—commonly found in groups of two, three, or four beats—are collected into measures, which are demarcated by bar lines. But what creates meter? A series of identical pulses does not group into larger units but remains an undistinguished stream that simply punctuates the passage of time. For example, the following dots represent a series of pulses; tap them out with your right hand:

.

.

.

.

.

.

.

.

.

.

.

.

.

.

You can hear and feel that each pulse is the same as every other; there is no differentiation between them. It is impossible to establish a meter because the pulses do not form groups. But if we add another level of pulse, one that moves proportionally faster or slower, then meter arises based on the interaction of the two hierarchical levels. Meter means “to measure,” and the regularly recurring strong beat, separated by a consistent number of weaker beats creates a metrical accent. Perform the following series of pulses, the right hand tapping the faster pulses and the left hand tapping the slower pulses:

. . . . . . . . . . . . .

•

•

•

•

•

S w w S w w S w w S w w S Now the faster pulses are grouped into regularly recurring units of three beats. Notice the distinction between accented, or strong (S), beats and unaccented, or weak (w), beats, as illustrated. Accented beats occur when both hands tap at the same time; unaccented beats occur when only the right hand taps. This hierarchy is crucial in creating meter. A clear meter emerges only through the addition of a second level of pulse. Perform Example 1B.5 and identify the prevailing meter. It includes a pattern of repeating quarter notes around which rhythms of quarter notes, eighth notes, and sixteenth notes occur.

EXAMPLE 1B.5

pulse =

:

50

THE COMPLETE MUSICIAN

This example does not have a strong sense of meter, even though there are two levels of activity. This is because only one level of a pulse regularly recurs, instead of the minimum of two. Once we add another level of pulse in the form of a half note, the hierarchical relationship is clarified. With the third line added in Example 1B.6, the rhythmic irregularity does not undermine the prevailing meter. Notice that bar lines—which identify the beginning of a metric group as well as the span—have been added, since there is now a clear metric patterning. Now we can sense either a duple (strong–weak) or quadruple (strong–weak– semistrong–weak) meter. You can usually distinguish between a two-beat or four-beat

EXAMPLE 1B.6 Building a Clear Meter rhythm: pulse =

:

pulse =

:

measure by rhythmic patterning. In Example 1B.6, the dotted eighth–sixteenth pattern recurs every four beats in the first part of the example, creating four-beat, rather than twobeat, patterns: • In duple meter, a simple alternation of strong and weak occurs. • In quadruple meter, an intermediate type of metrical accent occurs on the third beat—one that is weaker than the downbeat but stronger than the second or fourth beat, as shown in Example 1B.7. Example 1B.8 shows how using a dotted half note can create a different level of pulse. Here the quarter notes are grouped into threes to create a triple meter (strong–weak–weak).

EXAMPLE 1B.7 Mozart, Piano Sonata in C minor, K. 457, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

23

S

w

ss

w

S

w

ss

w

S

w

ss

w

S

w

ss

w

51

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

EXAMPLE 1B.8 Building Triple Meter rhythm: pulse =

:

pulse =

:

Beat Division Most music contains note values that are shorter than the basic beat. Beat division refers to the equal division of the beat into either twos or threes: • Undotted note values divide naturally into twos (Example 1B.9A) • Dotted note values divide equally into threes (see Example 1B.9B) We refer to further division of the beat as a subdivision of the beat. At the level of the subdivision, beats divide naturally only into twos (Example 1B.9C).

EXAMPLE 1B.9 Beat Division A.

=

B.

=

=

=

=

=

C.

=

=

=

=

=

Simple and Compound Meters Meters in which the beat is divided into twos are simple meters, while compound meters are meters in which the beat is divided into threes. Recall that there are three basic metrical accent patterns: duple (strong–weak), triple (strong–weak–weak), and quadruple (strong–weak–semistrong–weak). Example 1B.10 shows the six possible types of meters (with the most common beat values shown). Example 1B.11A–C illustrates each of the six most common simple and compound meters.

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THE COMPLETE MUSICIAN

EXAMPLE 1B.10 Six Types of Meters Simple

Duple

Compound

or

Triple

or

or

Quadruple

EXAMPLE 1B.11A I.

Simple and Compound Duple STR EA MING AUDIO

Simple Duple (“Oh, Susanna”)

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beat:

division:

subdivision:

I

II.

come

from

A

la

ba

ma

with

my ban

jo

on

my

Compound Duple (Bach, Flute Sonata no. 2 in E  major, BWV 1031, Siciliano)

beat:

division:

subdivision:

knee,

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Chapter 1B Musical Time: Pulse, Rhythm, and Meter

EXAMPLE 1B.11B

Simple and Compound Triple STR EA MING AUDIO

I. Simple Triple (“Flow Gently”)

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beat:

division:

Flow

II.

gen

tly

sweet

Af

ton,

a

mong

thy

green

braes;

Compound Triple (“Down in the Valley”)

beat:

division:

Down in

the

val

EXAMPLE 1B.11C I.

ley,

the

val

ley

so

low,

Hang your head

Simple and Compound Quadruple STR EA MING AUDIO

Simple Quadruple (“Adeste”)

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beat:

division:

Ad O

es come ,

te all

fi ye

de faith

les, ful,

lae joy

ti fu l

tri and

um tri

phan umph

tes; ant;

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THE COMPLETE MUSICIAN

EXAMPLE 1B.11C II.

(continued)

Compound Quadruple (Schubert, “An den Mond”)

beat:

division:

Geuß, lie

ber Mond,

geuß dei

ne Sil

ber flim

mer

Any note value may serve as the beat. In example 1B.12, we see examples where the half, quarter, and eighth notes are the beat units. Note that simple meters can have beats of any duration that are not dotted; compound meters have beats that are dotted. For example, both excerpts in Example 1B.12A are in simple duple. However, the beat in “A Mighty

EXAMPLE 1B.12 Various Rhythmic Values Assigned the Beat A1.

A Our

A2.

STR EA MING AUDIO

“A Mighty Fortress Is Our God” ( ⫽ beat)

might - y help - er

fort He,

-

ress a

-

is mid

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our the

God, flood

Beethoven, Symphony no. 7 in A major, Allegretto ( ⫽ beat) ten.

ten.

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

55

EXAMPLE 1B.12 (continued) B1.

Bach, French Suite in B minor, Menuet ( ⫽ beat)

B2.

Bach, French Suite in B minor, Gigue ( ⫽ beat)

Fortress” is the half note, while that in the slow movement from Beethoven’s seventh symphony is the quarter note. Similarly, Example 1B.12B shows two examples in simple triple: The quarter note is the beat unit in B1 and the eighth note is the beat unit in B2.

The Meter Signature Composers indicate the number of beats in a measure (accented and unaccented), the beat unit (the rhythmic value that is assigned to the beat), and the beat division (i.e., whether the beat value is divided into twos or threes) in the meter signature. The meter signature, or time signature, appears once, at the beginning of the piece, immediately after the key signature. A composer may change the meter within a piece or section, in which case the new meter signature will appear at the point of change. The meter signature takes the form of two numbers, one on top of the other (Example 1B.13). A meter signature of #4 indicates three beats in each measure and that the quarter note is assigned the beat. Since Example 1B.12B1 is felt strongly in three, a “3” would appear as the upper number. The basic beat is the quarter note (the piece begins with three quarter notes in the left hand (and attendant division by eighth notes); thus a “4” would appear as the lower number. Similarly, since Example 1B.12B2 is also felt in three, albeit a fast three, and the eighth note is the basic pulse, the meter signature would be #8. Common simple meter signatures include #8, $8; @4, #4, and $4; @2, #2, and $2; where the eighth note, the quarter note, and the half note, respectively, are the beat unit and measures contain two, three, and four beats. Two simple meter signatures do not use numbers:  and . The symbol  stands for $4 and is sometimes known as common time. The  stands for @2 and is known as cut time or alla breve. Both these symbols were used before meter signatures with numbers were established.

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THE COMPLETE MUSICIAN

EXAMPLE 1B.13 Meter Signatures for Simple Meters

Top number

Bottom number

2 ⫽ two beats per measure 3 ⫽ three beats per measure 4 ⫽ four beats per measure 2 ⫽ one half notes make up the beat unit 4 ⫽ one quarter notes make up the beat unit 8 ⫽ one eighth notes make up the beat unit 16 ⫽ one sixteenth notes make up the beat unit and so on

Meter Signatures for Compound Meters One determines the meter signature for compound meters in a slightly different way than one would determine simple meter signatures. Because we do not have numbers that can represent dotted notes, we choose to represent beat divisions (rather than beats) in the meter signature. Consider Example 1B.14, where Beethoven employs the dotted quarter as the beat unit (two per measure to create the duple meter). Its three eighth-note divisions create a lilting effect that contributes to the pastorale, outdoors feeling. Beethoven’s meter signature of ^8 seems quite unable to represent the actual two-beat measures (and compound division). The disparity arises because it is not possible to represent the dotted-value beat units that characterize compound meters (e.g., dotted quarter and dotted half ). The solution, then, is to show the total number of beat divisions per measure, in the time signature, leaving the performer the job of determining the actual number of beats within a measure. This is accomplished by dividing the upper number by three

EXAMPLE 1B.14 Beethoven, Piano Sonata in D major, op. 28, “Pastorale,” Rondo, Allegro ma non troppo STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

57

(since compound meters divide the beat into threes). To determine the beat unit, divide the lower number by 2: the 8 (of ^8) would be 4. However, one must remember that this quarter note is dotted (Example 1B.15).

EXAMPLE 1B.15 Meter Signatures for Compound Meter

Top number

6 ⫽ two dotted beats per measure 9 ⫽ three dotted beats per measure 12 ⫽ four dotted beats per measure

Bottom number

2 ⫽ three half notes make up the beat unit ( ) 4 ⫽ three quarter notes make up the beat unit (  ) 8 ⫽ three eighth notes make up the beat unit (  ) 16 ⫽ three sixteenth notes make up the beat unit (  ) and so on

The chart in Example 1B.16 shows the most common simple and compound meters for duple, triple, and quadruple accent patterns. Notice that all meters with an upper number of 4 or smaller are simple (e.g., 2, 3, 4) and that all compound meters contain an upper number of 6 or larger (e.g., 6, 9, 12).

EXAMPLE 1B.16 Commonly Used Meter Signatures Duple meters: simple: @4 and @2

compound: ^8 and ^4

Triple meters: simple: #4 and #2

compound: 98 and 96

Quadruple meters: simple: $4 and $2

compound: ~8 and ~4

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THE COMPLETE MUSICIAN

EX ERCISE INTER LUDE

WORKBOOK 1 Assignments 1B.3–1B.4

1B.3 Beat Groupings in Simple and Compound Meters A. Provide the note value for divisions of the following beats, and specify whether the meter is simple or compound. Solution: beat

B.

=

division

=

1.

beat

=

division

=

2.

beat

=

division

=

3.

beat

=

division

=

4.

beat

=

division

=

compound simple or compound

simple or compound? simple or compound? simple or compound? simple or compound?

The meter type and beat are given. Provide a meter signature, and notate one full measure of the given rhythm and the division of the given beat. Sample solution:

simple duple:

=

1 beat

1.

compound duple:

=

1 beat

2.

simple triple:

=

1 beat

3.

simple quadruple:

=

1 beat

4.

simple quadruple:

=

1 beat

5.

compound triple:

=

1 beat

24

1B.4 Determining Meter Supply an appropriate meter signature for each of the following examples. Consider both the number of beats in each measure and their division and subdivision. Hint: Consider the beaming patterns. A.

F.

B.

G.

C.

H.

D.

I.

E.

J.

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

59

Asymmetrical Meters In the vast majority of common-practice tonal music, the number of beats per measure is dependent on multiples of either 2 or 3 (e.g., @4, ~8, $2, ^4, and 98). On occasion, however, composers write in asymmetrical meters, which are defined in one of the following two ways: 1. as measures whose number of beats is not divisible by either 2 or 3 (such as %8 and &4) 2. as measures whose number of beats combines both 2’s and 3’s (such as 04 created from 2 ⫹ 3 ⫹ 3 ⫹ 2). In moderate-to-fast tempi, such meters are usually performed so that the combination of 2’s and 3’s create larger beats of different durations. For example, in a fast tempo, %8 would be felt (and conducted) in 2; that is, a combination of one 2 and one 3, either 2 ⫹ 3 or 3 ⫹ 2. Composers who use such signatures often indicate in their meter signatures the way they wish the large beats to be grouped; for example, the common meter signature of 98 combines the divisions of the dotted quarter note into three equal groups of 3. However, a composer might wish to divide the beats asymmetrically, such as 2 ⫹ 3 ⫹ 2 ⫹ 2. Folk music of Eastern Europe and the Balkans makes constant use of such asymmetrical meters. The opening of the Greek folk song in Example 1B.17 is cast in the asymmetrical meter of &8 Often the meter signature of asymmetrical meters clarifies the recurring patterns within each measure. The repetition pattern in the tune shown in Example 1B.17 feels like a combination of #8 and $8 (although one could also hear the pattern as 3 ⫹ 2 ⫹ 2).

EXAMPLE 1B.17 Greek Folk Song STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Clarifying Meter It would be frustrating to identify meter if rhythmic durations were not organized into logical groups that clearly indicate both the number of beats in each measure and their divisions. Rhythmic symbols must visually organize the beat unit for the performer. For example, the three-beat units of the #4 meter in Example 1B.18A are not visually clear because there is no grouping of rhythms. In Example 1B.18B, however, the grouping becomes clear with the addition of beams, which are horizontal lines that connect two or more flagged notes (i.e., eighth notes or any combination of shorter rhythmic values). The number of beams corresponds to the number of flags; therefore, one beam will connect two eighth notes, two beams will connect two sixteenth notes, and so forth. Example 1B.19A presents an example of compound 98 meter without grouping beams. Again, the underlying three beats are difficult to discern, but the addition of beams and longer note values in Example 1B.19B instantly reveals the three beats within each

60

THE COMPLETE MUSICIAN

EXAMPLE 1B.18 Beams to Clarify Simple Meter

A. beats:

3

1

2

3

1

2

3

1

2

B.

EXAMPLE 1B.19 Beams to Clarify Compound Meter

A. beats:

1

2

3

1

2

3

B. measure. Beams generally do not connect across beats; each beat starts with a new beam in order to clarify the meter. In vocal music, however, beams were often used differently. Rather than highlighting the meter, beams connected two or more pitches that were to be sung on a single syllable. Therefore, pitches and their rhythms were, for the most part, separated from one another. This older convention—which has recently been replaced by the regular beaming tradition found in instrumental music—makes it difficult to perceive rhythmic patterns and their placement within and between beats. Notice in Example 1B.20, from Berlioz’s L’Enfance du Christ, how difficult it is to group beats in a single $4 measure of recitative (Example 1B.20A). The renotated version in Example 1B.20B makes it much easier to negotiate the rhythms.

EXAMPLE 1B.20 Berlioz, L’Enfance du Christ, recitative of the Father, scene 2 A. Recit. Le P. bien , c’est mon mé tier; was, das bin auch ich, done, that is my trade

B.

Vous ê wir bei as well,

tes de we’ll

mon sind work

com Ge to

pè nos ge

re. ser. ther.

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

61

Always attempt to clarify the location and grouping of each beat within a measure, avoiding long durations or dots that can obscure natural groupings by connecting rhythms across beats. Example 1B.21A shows a sampling of incorrectly notated rhythms; Example 1B.21B clarifies the notation.

EXAMPLE 1B.21 Rhythmic and Metric Correspondence A. Incorrect

B. Correct

beat unit:

rhythm: beat unit:

rhythm: beat unit:

rhythm:

MOR E R H Y T H M IC PRO C E DU R E S Typically the division of the beat unit in simple meters is by 2 and in compound meters is by 3. However, composers often import the 3’s from compound into simple and the 2’s from simple into compound. Such borrowed divisions permit considerably more rhythmic flexibility. Borrowed from compound meter, three-note divisions are called triplets. Triplets may occur not only at the primary division of the beat (see Example 1B.22A), but also at the subdivision (for example, as triplet sixteenth notes in $4). Triplets also occur over two or more beats. Example 1B.22B illustrates several types of triplets in $4. Measure 1 contains an eighth-note triplet, which occurs within one beat unit and therefore is at the level of the beat division. Measure 2, with its sixteenth-note triplet, illustrates triplets at the subdivision (i.e., within an eighth-note division). Triplets are illustrated in mm. 3–4: The triplet occurs first at the half-measure level and then at the measure level. Similarly, though not as common, the two-note divisions found in simple meter are imported into compound meters. Such duplets, like triplets, can occur within divisions

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THE COMPLETE MUSICIAN

EXAMPLE 1B.22 Borrowed Divisions STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

Brahms, “Von ewiger Liebe,” op. 43, no. 1 lei:

Lei - dest

du

Schmach 3

3

3

B.

3

3

3

Several Types of Triplets 3

3

3

3

and subdivisions of the beat as well as encompassing more than one beat unit (Example 1B.23). Less common divisions, called irregular divisions, include fives (called quintuplets) and sevens (septuplets). Most borrowed and irregular divisions are shown with a bracket

EXAMPLE 1B.23 Schumann, “Schlummerlied,” from Albumblätter, op. 124 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

2

2

that groups the note values and the appropriate number into which the beat is divided. Example 1B.24 illustrates several types of divisions against its unwavering and very clear dotted-eighth-note pattern in the accompaniment of this ^8piece. In m. 138, an eight-pitch

63

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

EXAMPLE 1B.24 Chopin, Nocturne in B major, op. 9, no. 3 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

136

8

3

5

5

141 3

3

3

7

145 4

right-hand figure (octuplet) is juxtaposed with the three-pitch bass figure, followed two measures later with a quintuplet against the bass. In m. 141, septuplets occur, followed by more-standard sixteenth-note triplets. Finally, in m. 145, quadruplets appear against the three pitches in the bass. Composers, especially in the nineteenth century, delighted in presenting duple and triple divisions of the beat simultaneously, their juxtaposition lending a remarkable fluidity—if not metrical confusion—to a piece. Chopin, Schumann, and Brahms are three of the many composers who utilized this procedure. In Example 1B.25A, Chopin has cast his etude in the simple duple meter of @4, with the natural division of the beat into two parts (notice the eighth notes in the left hand). However, superimposed on this twopart structure are triplets (marked, in the right hand). This play of rhythms is called two against three. Finally, composers often go so far as to intentionally write patterns that cut across a meter; therefore, each hand is written in a distinct meter. Chopin’s Waltz in A clearly presents a left hand in a simple triple meter, with two eighth notes for every quarter

64

THE COMPLETE MUSICIAN

note, as one would expect in a well-behaved waltz (Example 1B.25B). However, the right hand is cast in the compound duple meter of ^8, whose two beats and division into 3’s make very strange bedfellows with the left hand.

EXAMPLE 1B.25 Simultaneous Uses of Duple and Triple Meters (Two Against Three) A.

Chopin, Etude in A major, op. posth.

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Allegretto

3

3

WORKBOOK 1 Assignments 1B.5–1B.7

B.

Chopin, Waltz in A major, op. 42

beat unit:

1

beat unit:

1

2

2

1

3

1

2

2

1

3

1

2

2

1

3

1

2

2

3

AC C E N T I N M U S IC Our brief exploration of Bach’s Prelude (Example 1A.1) illustrated several ways to create musical accent, including metric placement and changes of patterning. We now explore this important topic in more detail. We broadly define musical accent as a musical event that is marked for consciousness so that the listener’s attention is drawn to it. The manners in which composers mark events are diverse, but generally they all arise from a single intent: thwarting the listener’s expectations. This can be accomplished simply by changing an established pattern. Indeed, pattern changes create an accent, surprising us and commanding our attention. Accents can be produced not only in the domains of time (rhythm and meter) and pitch (melody and harmony) but also in the areas of dynamics, register, and texture.

Temporal Accents Meter arises when pulses are grouped into recurring patterns of accented and unaccented beats. Such accented beats are called metrical accents, since they occur at important points in a metrical unit (e.g., a beat or a measure). An anacrusis is an unaccented musical event that leads into an accented musical event. The anacrusis is often called an upbeat

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Chapter 1B Musical Time: Pulse, Rhythm, and Meter

because a conductor’s baton will be on its way up, in anticipation of the upcoming metrical accent. The following downbeat—the first and strongest metrically accented beat of a measure—occurs when the conductor’s baton is in the lowest position of the conducting pattern. Metrical accents provide the foundation for and standard by which we consider other types of accent, both temporal and nontemporal. Rhythmic accents occur throughout the surface of a piece of music and take many forms, the most important of which arises from rhythmic duration—a long note tends to sound accented. Such durational (or agogic) accents usually coincide with metrical accents in order to support the prevailing meter. Given that longer notes are accented, they are often followed, rather than preceded, by notes with shorter durations. That is, when a beat (or other metric unit) is divided, a long–short division is more likely to occur than a short–long division. Example 1B.26 illustrates: The first example (A) follows the typical “long–short” durational pattern, while the second (B) reverses the pattern, placing shorter durations before longer durations. Clap each example to see how the first is easier to perform and is more natural sounding. Like metrical accents, durational accents occur at different levels. They occur not only on downbeats, but also on other accented beats (e.g., the third beat of m. 2 of Example 1B.26A) and even within beats (the dotted eighth–sixteenth rhythm is more common than its reverse).

EXAMPLE 1B.26 Durational Accents A. 1

Long–Short Durations 2

3

L

B.

4

S

1

2

3

4

1

L

S

L

S

L

2

3

4

1

S/L S

L

2

3

2

3

4

Short–Long Durations

1

2

3

S

S

L

4

1

2

3

4

1

S

L

S

L

S

2

3

L/S L

4

1

4

L

Nontemporal Accents Every nontemporal element of music has the potential to create accents. We will examine six common types of nontemporal accents, all of which arise from a single source—pattern change: harmonic change and registral, articulative, textural, contour, and pitch accents. Harmonic change creates a powerful accent. Listen to the opening of Chopin’s Waltz in A minor, in which a different chord appears in each measure (Example 1B.27). Notice that the metric accent on beat 1 is accompanied by a different bass note in each measure (A–D–G–C); the chords on beats 2 and 3 fill out harmonies that are implied by the bass pitches. Metric accents are shown by the accent sign (⬎) above the treble staff.

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THE COMPLETE MUSICIAN

EXAMPLE 1B.27 Chopin, Waltz in A minor, BI 150 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

a minor:

a

d

G

C

Composers usually balance the accent created by harmonic change with a consistent pattern in the rate of harmonic changes. (The rate at which harmonies change is called harmonic rhythm, an important topic that we explore throughout this text.) Once the speed of harmonic change is established, a composer will usually continue this pattern. Further, the changes usually align with the metric accents, as we saw in Chopin’s waltz. Since a pattern change creates an accent, let’s see what happens when we modify Chopin’s waltz slightly (Example 1B.28 contains two recompositions). Example 1B.28A

EXAMPLE 1B.28 Chopin, Waltz in A minor (modified) STR EA MING AUDIO

A.

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etc.

1

a minor:

2

3

1

a

2

3

1

d

2

3

G

4?

5?

6?

(G)

B.

1

a minor:

a

2

3

1

d

2

3

1

G

2

3 1?

C

begins like the original, with harmonic changes once per measure. However, here the bass G and its harmony in m. 3 continue through m. 4, disrupting the established pattern of one harmonic change per measure and thereby marking the effect for consciousness and

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

67

creating an accent. Example 1B.28B does the opposite: Rather than extending the G harmony over two measures, it shortens it with the premature appearance of the C harmony. The question marks that accompany the beat patterns indicate the metric confusion that arises with breaking the harmonic rhythm pattern. You may have noticed the strong left-hand accent that occurred on beat 1 of each measure and nicely aligned with the metric accent, yet wondered how such an accent is created when beats 2 and 3, which consistently contain three times as many pitches, remain quite unaccented. Such registral accents happen because the first-beat low notes occur in a lower register than the rest of the left-hand notes, thus setting them in bold relief. Registral accents are very powerful, and when they do not align with the meter or when there is a pattern change, they are even more noticeable. Example 1B.29 establishes the registral accents in mm. 1–2 and then deviates, with accents occurring instead on weak beats. The low pitch followed by a single chord creates two-beat groupings that cut across the triple meter.

EXAMPLE 1B.29 Chopin, Waltz in A minor (modified) STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

a minor:

a

d

G

C

Registral accents can occur in any register. In fact, registral accents in a high register often seem to be more accented than accents in a low register, because their frequency (vibration rate) is faster, and they sound brighter than pitches with slower frequencies. Registral accents are often intensified by articulative (or phenomenal) accents, which include changes in dynamics (both gradual and immediate, such as sforzandi), and various types of articulations, such as staccato/legato, pizzicato, slurring, tenuto, and ornamentation (such as trills, turns, and mordents). Beethoven was fond of such accents, as illustated in his “Tempest” sonata (Example 1B.30), where the sforzandi (marked sf and signifying a strong accent) occur mid-measure and are attacked by the left hand, which dramatically crosses over the right hand. Notice that registral accents actually begin in m. 21, where the left hand’s low, sustained D3 begins the passage. An ascending line is created by the left hand’s registral accents: D rises to E (m. 25) and then to F (m. 29). Notice that the articulative accents (that is, the sforzandi in the highest register starting at m. 30) are the same pitch classes but are moving at a rate twice as fast as the left hand (encompassing two measures instead of four). Most often the mood, general tessitura, accompanimental figures, and number and general character of voices (often referred to as density) remain consistent throughout long passages of a piece or even throughout an entire piece. We refer to the combination of

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THE COMPLETE MUSICIAN

EXAMPLE 1B.30 Beethoven, Piano Sonata in D minor, op. 31, no. 2, “Tempest,” Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

18

3

3

22

26

30

34

38

3

3

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Chapter 1B Musical Time: Pulse, Rhythm, and Meter

these elements as musical texture. A textural accent, then, involves a change in the overall patterning of a piece and can be quite striking. In fact, entire style periods, such as the Baroque, are predicated on creating music that maintains a single mood, or affect, which in large measure is created by a consistent and unchanging texture. For example, Bach’s C minor Prelude (Example 1B1.31) is a study in fast sixteenth notes that are relegated to the same register and melodic patterning (Example 1B.31A). Thus, when the texture changes drastically to a more improvisatory, single-line, registrally roving cadenza near the end of the piece, the accent created certainly draws the listener’s attention (Example 1B.31B). (See the Anthology no. 14 for the full score.) From the Classical period forward, composers filled their works with textural accents, often between sections, as in Schubert’s song “Der Lindenbaum,” where the plaintive major

EXAMPLE 1B.31 Bach, C minor Prelude, from Well-Tempered Clavier, Book 1 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A. 1

4

B. 22

25

textural accent

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THE COMPLETE MUSICIAN

mode, soft dynamic level, and soothing accompaniment give way to the stormy section in the parallel minor (Example 1B.32). (See the Anthology no. 50 for the complete score.)

EXAMPLE 1B.32 Schubert, “Der Lindenbaum,” from Winterreise STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

41

Komm her,

zu mir, Ge

sel

le,

hier find'st

du dei

ne Ruh!

3 3

3

3

45

Die 3

3

3

3

3

3

textural accent

Finally, textural changes and the accents they create can be very subtle, as in the opening of Mozart’s piano sonata in F major (Example 1B.33). The gentle rocking accompaniment supports a rising melody, but in m. 5 the melody falls, without any aid from the accompaniment. This textural change is intensified by the left hand’s abandoning its accompanimental role and imitating the right hand in the falling gesture in m. 7. In m. 9 both hands are reunited. Finally, in m. 12 yet another new texture appears, as all of the voices participate in the same rhythmic gestures. These textural changes are not capricious but, rather, are carefully planned, occurring every four measures. The Mozart excerpt illustrates two additional nontemporal accents. The first type involves melody, specifically its shape, which is created by changes in melodic direction. These shapes are part of a melody’s contour, and changes in melodic contour create contour accents. They can be quite obvious (as in the overall rising line of mm. 1–3 that is followed by the descending contour in mm. 5–8, represented by arrows) or very subtle

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Chapter 1B Musical Time: Pulse, Rhythm, and Meter

EXAMPLE 1B.33 Mozart, Piano Sonata in F major, K. 332, Allegro Allegro

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re 3 textu

7

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texture 2

texture 1

texture 4

(cresc.)

14

(as in the falling scalar line in m. 10, which changes direction on the downbeat of m. 11). Like most accents, contour accents usually align with metric accents. Finally, when you listened to Example 1B.33 for the first time, your attention may have been drawn to the E4 in m. 2, even though it occurred as part of the prevailing eighthnote pattern, on a weak beat, and hidden inside the texture. The accent on this single pitch is called a pitch accent. Such accents arise when one or more pitches are perceived as unstable. Such tendency tones are accented because they are foreign to the immediately surrounding pitch environment; the term dissonant refers to musical events that are in one or more ways unstable. Pitch accents can occur in unaccented or accented metrical contexts. Compare the effect of the unaccented E4 in Mozart’s F-major sonata with the unprepared, strongly accented D5 that opens his A-minor sonata (Example 1B.34).

EXAMPLE 1B.34 Mozart, Piano Sonata in A minor, K. 310, Allegro maestoso Allegro maestoso

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THE COMPLETE MUSICIAN

M E T R IC A L DI S T U R B A N C E

Syncopation Longer durations—which are inherently accented—usually are coordinated with accented beats or accented parts of beats, and shorter durations usually follow, occurring on weak beats or weak parts of beats. Composers often reverse this pattern, and while the established meter continues, they challenge it with a new, conflicting accent. This phenomenon—in which a musical accent occurs on a metrically unaccented beat or part of a beat—is called syncopation. Example 1B.35 presents two examples in which a regularly recurring pulse stream or series of accents occurs off the beat.

EXAMPLE 1B.35 Syncopation STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

Mozart, Symphony in G minor, K. 183, Allegro con brio

Oboi.

Violino I.

Violino II.

Viola.

Violoncello e Basso.

B.

Mozart, Piano Concerto in D minor, K. 466, Allegro

3

3

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Chapter 1B Musical Time: Pulse, Rhythm, and Meter

Syncopation is a mainstay in popular and commercial music, one example of which appears in Example 1B.36, which contains accents not only at the beat unit, but also within the beat unit. Note that the left hand is regular and that it aligns with the natural accentual pattern of $4. The lower of the two notes, marked by a registral accent, occurs on the metrically strong first and third beats. This stable left hand provides the metrical grid above which the right hand and vocal line playfully deviate, highlighting the fanciful lyrics. Syncopation appears already in the first vocal utterance: “Say” occurs on a weak part of the division of the first beat, and its quarter-note value cuts through the accented part of the second beat. The same situation is heard in the second half of the measure, up one octave. Articulative accents intensify the right hand of the piano part. The horizontal slashes, called tenuto marks, indicate that the note beneath should be sustained for its full value and also imply an accent; notice that these accents all occur on weak parts of beats. Similarly, the staccato marks, which shorten notes and thus weaken accents, occur on the accented parts of beats. Finally, notice how the semistrong accented third beat is weakened in mm. 2 and 4, since they occur as tied notes.

EXAMPLE 1B.36 Arlen, “It’s Only a Paper Moon” STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

-

a tempo

Say

-

it’s on ly

a

pa per

moon,

Sail

ing o ver

a card board sea,

a tempo

Hemiola Another important type of metrical disturbance, closely related to syncopation, is the hemiola. In a hemiola, the established meter temporarily is displaced by a competing meter. It occurs most often when a duple meter is imposed on a triple meter. To create this effect, accents are placed on every other beat rather than on every third beat, either by literal accent markings, by duple durations, or by one or more of the nontemporal accentual techniques, such as harmonic accent, dynamic accent, or registral accent. In Example 1B.37A, hemiola is created by articulative accents: The regular placement on every other quarter note creates a duple accent pattern, effectively weakening if not overtaking the triple pattern. Only in the penultimate measure is the triple pattern reinstated. In Example 1B.37B, hemiola arises through the durational accents.

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THE COMPLETE MUSICIAN

EXAMPLE 1B.37 Hemiola A.

Hemiola by Surface Elements 1

B.

2

3

1

2

1

2

1

2

1

2

3

1…

1

2

1

2

1

2

3

1…

Hemiola by Duple Durations 1

2

3

1

2

Let’s look briefly at the opening of the Menuetto from Mozart’s Eine kleine Nachtmusik, which contains an example of a hemiola (Example 1B.38). The first five measures of Mozart’s eight-measure phrase unfold as expected. The downbeat of each measure is well accented, and the following two beats are quite weak. The three-beat groups behave just as the meter signature indicates they will. But in the last three measures, something happens: The surface

EXAMPLE 1B.38 Mozart, Eine kleine Nachtmusik, K. 525, Menuetto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1

2

3

1

2

3

1

2

3

1

2

3

1

2

3

1

2

1

2

1

2

1

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

WORKBOOK 1 Assignment 1B.8

75

gesture changes with the trill figure that occurs first on beat 2 and then on beat 1, giving an odd feel to the triple meter. Now we sense groupings in 2’s. Instead of 1 2 3 | 1 2 3 | 1 . . ., we feel 1 2 1 | 2 1 2 | 1. At a deeper level, hemiola usually transforms a notated meter by a factor of two. Below the passage marked 4@ , a slower moving 2# meter is shown. Hemiola tends to occur in the approach to a final cadence, especially in the Baroque period. As an event marked for consciousness, it heralds the approach to closure, which brings welcome relief from the consistent texture and avoidance of musical articulations.

EX ERCISE INTER LUDE A NA LYSIS A ND W R ITING STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

SOLVED/APP 5

1B.5 Analysis of Musical Accent The examples shown, all taken from Chopin’s Waltzes, contain various types of accents. Find and label at least one example of each type of accent. Your choices are: durational, harmonic, registral, articulative, textural, contour, and pitch. Are these accents coordinated with the metrical accents?

A. Waltz in B minor, op. posth. 69, no. 2 Moderato =152

SOLVED/APP 5

B. Waltz in D major, op. 64, no. 1

SOLVED/APP 5

C. Waltz in E minor, B1 56

cre

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THE COMPLETE MUSICIAN

SOLVED/APP 5

D. Waltz in A major, op. 64, no. 3 Moderato

T E R M S A N D C O N C E P T S F OR R H Y T H M A N D M E T E R • accent • durational, agogic, metrical, rhythmic • nontemporal: • articulative, contour, dynamic, harmonic, pitch, registral, textural • accented versus unaccented • anacrusis • bar line • beam • beat • borrowed divisions (duplets, triplets, irregular) • common time, cut time (alla breve) • downbeat, upbeat • harmonic rhythm • hemiola • measure • meter: • simple versus compound • simple duple, simple triple, simple quadruple; compound duple, compound triple, compound quadruple • asymmetrical • meter signature • musical patterning • phrasing slur • pulse • rhythm • strong and weak • syncopation • tempo • tie

Chapter 1B Musical Time: Pulse, Rhythm, and Meter

77

CH A PTER R EV IEW 1. True or False: Ties connect two of the same pitches; phrasing slurs connect two different pitches.

2. The words simple and compound refer to the subdivision of the [beat/measure].

3. The words duple, triple, and quadruple refer to the subdivision of the [beat/measure].

4. List three examples of asymmetrical meter.

5. Triplets and duplets are examples of ______________.

6. Quintuplets (5) and septuplets (7) are examples of ______________.

7. An anacrusis is analogous to a conductor’s [upbeat/downbeat].

8. Define harmonic rhythm.

9. True or False: A syncopation is a musical accent that occurs on a metrically unaccented beat or part of a beat.

10. A hemiola occurs most often when ____________ meter is imposed on ___________ meter.

CH A PTER 2

Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint OV E RV I E W

This chapter combines pitch and rhythm to create melody. Then, we will explore how to combine two melodic lines. This is called counterpoint. We will examine the central role that counterpoint plays in musical compositions written between 1450 and 1900. Finally, we will explore the concepts and procedures that will allow you write to your own counterpoint. CHAPTER OUTLINE Melody: Characteristics and Writing....................................................................... 79 Controlling Consonance and Dissonance: Introduction to Two-Voice Counterpoint ........................................................ 84 Counterpoint in History ............................................................................................ 86 Fux, Mozart, and Attwood ..................................................................................... 86 Fux’s Method ............................................................................................................ 87 Two-Voice Counterpoint as Musical Foundation ................................................ 87 First-Species Counterpoint .................................................................................... 88 Contrapuntal Motions ................................................................................... 90 Perfect Intervals: Handle with Care...................................................................... 91 Beginning and Ending First-Species Counterpoint ...................................... 94 Rules and Guidelines for First-Species (1:1) Counterpoint .......................... 94 (continued)

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Chapter 2 Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint

79

Second-Species Counterpoint................................................................................ 97 Weak-Beat Consonance .................................................................................. 97 Weak-Beat Dissonance ................................................................................... 98 More on Perfect Consonances ........................................................................ 99 Beginning and Ending Second-Species Counterpoint ................................ 100 Rules and Guidelines for Second-Species Counterpoint ..............................101

Terms and Concepts.................................................................................................... 103 Chapter Review ............................................................................................................ 104

M E L ODY: C H A R AC T E R I S T IC S A N D W R I T I N G Intervals do not exist in isolation, but rather function as part of larger musical constructs, such as melody. Example 2.1 contains numerous short melodic excerpts from a wide variety of music that spans the last one thousand years. The examples are drawn from vocal music (including both solo song and opera) and instrumental music (ranging from solo piano to full orchestra). Listen to the excerpts with the following questions in mind: 1. Are they in a key? If so how do you know? 2. Do the melodies have a shape or contour? You might want to trace the general flow of each melody, “connecting the dots” with a pencil. 3. What sorts of melodic intervals occur between pitches? Do the composers prefer some intervals more than others? 4. Are there accented events in the melodies, that is, events that draw your attention, such as leaps, chromaticism, and longer durations? If so, are these events isolated, or does the composer prepare them in some way? Each example—whether written for voice or for instrument—is singable. The pitches follow one another in what seems to be a logical and goal-oriented flow. The intervals are mostly steps, and leaps are usually small. Large leaps are followed by a change of direction

EXAMPLE 2.1

Melody Over One Thousand Years

A. Wipo, “Victimae paschali laudes” (ca. 1020)

B.

Byzantine Chant (ca. 1200)

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THE COMPLETE MUSICIAN

EXAMPLE 2.1 C.

(continued)

Guillaume Costeley “Allon, gay, gay” (ca. 1575)

Al

D.

lon, gay, gay, gay Ber

ge

res,

Al

lon, gay,

al

lon, gay, soy

ez

le

ge

res,

Suy vez moi.

Denis Gaultier, “Piece for Lute” (ca. 1650)

8

Bach, “Bereite dich, Zion,” from Christmas Oratorio (1735)

E.

Ob. d’a. Vl. I

3 8 3 8

A.

Be Fg. Org. e Cont.

rei

te

dich,

Zi

on,

mit

zärt

li

chen

Trie

ben

den

Schön sten,

den

3 8 (Vc.)

Lieb sten

F.

bald

bei

dir

zu

sehn

Haydn, String Quartet in C major, op. 76, no. 3, “Emperor,” Poco adagio; cantabile (1796) dolce

Chapter 2 Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint

EXAMPLE 2.1

81

(continued)

Beethoven, Piano Sonata in C major, op. 53, “Waldstein,” Allegro con brio (1803)

G.

4 4 H.

Schubert, Symphony no. 9 in C major, D. 944, “Great” (ca. 1827)

Andante

Scriabin, Etude in C minor, op. 2, no. 1 (1887)

I.

3 4 J.

Arlen, “Over the Rainbow” (1938)

44 K.

34

Billy Joel, “Piano Man” (1973)

and often tend to be filled in, in effect retracing and completing a musical space that was left open. Such balance, and the creation and dissipation of energy, are important components of melody. These melodies are almost entirely diatonic, and they begin with a strong sense of key—always a member of the tonic triad and usually on 1. Most of the melodies end on 1; those that end on 2 or 5 will usually continue and eventually lead to 1. Their contours usually produce arches, often taking the form of an ascent followed by a descent; but sometimes, as in Beethoven’s Waldstein Sonata, an ascent follows a descent. Finally, even though all of the melodies share these basic characteristics, each one possesses a distinct character. Melodic uniqueness is achieved via relationships between segments of the melody, most of which are formed from short rhythmic and melodic patterns called motives, a topic that we take up in Appendix 2. Our first studies in melody writing will explore a few specific attributes shared by many melodies written in the tonal style. For now, we will focus exclusively on the pitch domain, without the stylistic elements of repeated rhythmic and melodic patterns that characterize individual melodies. Initially, our melodies will be very short, about 10 to 16 pitches. They will also be entirely diatonic (except for raising 7 to create a leading tone in minor and raising 6 when ascending to raised 7) and unmetered, with no rhythmic profile. Refer to Example 2.2 for examples of each of the following points.

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EXAMPLE 2.2

Melodic Characteristics 4.

2.

E :

3.

3.

3.

1.

3.

3.

3.

Guidelines for Writing Melodies 1. Begin your melody on a member of the tonic triad (1–3–5) and end it with the two-pitch pattern 2–1 or 7–1. The approach to the final pitch by step is called a melodic cadence. (The cadence is a crucial form-defining event in music.) 2. Limit the range of your melody (the total span of pitches) to the interval of a tenth, and set most of your melodic activity within a comfortable interval (tessitura) of about a sixth. 3. Move primarily by step, which is called conjunct motion. 4. You can also move with occasional skips (of thirds, fourths and fifths) to add interest; this is called disjunct motion. However, disjunct motion should: • be generally confined to small intervals, such as thirds, although you can use one or two larger leaps if they are no larger than a perfect fifth. • traverse consonant melodic intervals (i.e., no dissonant leaps, such as a diminished fourth). • resolve tensions. Some scale members have strong melodic pulls toward another member, usually the one lying a half step away. Such tendency tones create an important tension, but you should always resolve their tension. The most important tendency tone is the leading tone, which should ascend by step to 1, unless 7 is part of a descending melodic line 8–7–6–5. • lead to a change of direction that fills in at least some of the musical space that was created by the leap, called the “law of recovery.” This is not essential for skips of a third, but it is mandatory with larger leaps, such as a fifth. • rarely use multiple skips one after the other. You can use two skips in a row if they are both thirds and if you change direction after the second skip. • avoid repeated notes and repetitive patterns, or sequences (for example, 1–2–3, 2–3–4, 3–4–5)— at least for now. Repeated notes create undesirable rhythmic groupings and rhythmic stagnation. 5. Aim for a logical shape. A melody commonly creates an arch that slowly rises to a single high point, or melodic climax, and then returns to the starting point.

Example 2.3 illustrates the basic tenets of a good melody, this time incorporating pitch, rhythm, and meter. The melody opens with a stepwise descent from 3 past 1, to the leading tone, followed by change of direction, which

Chapter 2 Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint

EXAMPLE 2.3

83

Mozart, Piano Sonata in A minor, K. 310, Presto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

9

satisfies the need for the leading tone to resolve to a tonic and to balance the falling motion with rising motion. Note that this ascent leads back to 3, but not as an arrival; instead the line falls to 2, a half step below 3, in exactly the same way that the line turned on 7 and rose to 1 in mm. 2–3. The melody then pushes higher, first to D and then to F, the climax of the melody. Note that after the leap to D, the line changes direction and falls to C, thus balancing the leap with a contour change. Further, the climax on F is followed by a stepwise descent to the melodic cadence on B (2), which leaves the listener hanging, waiting for a resolution to 1. Mozart repeats the melody from mm. 1–4 in mm. 9–12, but then immediately and dramatically leaps to F without the intermediary skip through B, from which he descends again by step, this time closing strongly on the long-anticipated A (1).

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignment 2.1

SOLVED/APP 5

2.1 Melody Comparison Play the following two melodies. Although A and B both contain the same number of pitches and each unfolds a melodic contour that rises toward the middle and then falls at the end, they could hardly be more different from one another. Which one do you like? Try to sing each one. Which is more singable and memorable? Why? In a page or two, compare and contrast the two melodies by working through the list of melodic attributes given on page 82. A.

C: B.

C:

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THE COMPLETE MUSICIAN

SOLVED/APP 5

2.2 Melodic Criticism The following melodic contours (tunes without rhythm or meter) contain weaknesses or problems. Melodies A–D are in G major; melodies E–G are in D minor. Be able to explain the problems with each example.

A.

C.

E.

B.

D.

F.

G.

C O N T ROL L I N G C O N S O N A N C E A N D DI S S O N A N C E : I N T RODUC T IO N T O T WO - VOIC E C OU N T E R P OI N T The study of harmony concerns how chords connect to one another and move through time. But chords and their connections are dependent on how individual members, or voices (or parts), move from one chord tone to the next and how they combine with one another. Listen to the excerpts in Example 2.4, all of which sound very different from one another, but each of which shares many common features, including: 1. At least four simultaneously sounding voices. These voices are labeled “Soprano,” “Alto,” “Tenor,” and “Bass” in Example 2.4A and in their abbreviated forms in Example 2.4B–D (“SATB”). 2. Individual voices that are melodic, moving from one pitch to another, usually by steps or small leaps. 3. Voices that combine vertically with one another, forming mostly consonances with the other voices (octaves, fifths, thirds, and sixths). 4. The highest- and lowest-sounding pitches as aurally the most prominent. That our ears are drawn to these outer voices is very important. Outer voices provide the structural skeleton in tonal music, and harmony is most easily viewed as the filling in of the musical space between these two melodic voices—the soprano and the bass—with usually two additional voices (alto and tenor).

Chapter 2 Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint

EXAMPLE 2.4 A.

Polyphony and Harmony

Bach, St. Matthew Passion, “O World, I Now Must Leave Thee”

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Soprano O

World,

I

now

must

leave

thee,

O

World,

I

now

must

leave

thee,

O

World,

I

now

must

leave

thee,

O

World,

I

now

must leave

thee,

Alto

Tenor 8

Bass

B.

Schumann, “Armes Waisenkind,” from Album for the Young, op. 68, no. 6 S A T B

C.

Chopin, Prelude in C minor, op. 28, no. 6

D.

Largo S

Beethoven, Symphony no. 1 in C major, op. 21, Adagio molto S A T B

B

E.

85

Mendelssohn, Midsummer Night’s Dream, Overture

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THE COMPLETE MUSICIAN

5. Voices that often move in opposite directions to one another, especially the outer voices; when one voice ascends, the other descends, and vice versa. Such “contrary motion” is shown in each excerpt in Example 2.4 by the angled lines that connect the soprano and bass pitches, which move in opposite directions most of the time. When voices move in the same direction, it is usually by imperfect harmonic consonances (i.e., thirds and sixths).

C OU N T E R P OI N T I N H I S T OR Y Clearly, the specific pitches, their combination into sonorities, their individual movement, and their interaction with other voices are not haphazard. Rather, they are part of a wellregulated and thoughtful procedure. The relationship between and movement of two or more voices is called counterpoint (“melody against melody”) or polyphony (“multiple sounds”). Counterpoint has been the focus of Western music study since the tenth century and it continues to serve musicians to this day. Contrapuntal relationships depend on two elements: (1) the behavior of consonant and dissonant intervals, and (2) the harmonies implied by their interaction. Here we examine the first element: how consonance and dissonance create musical motion. Our study of harmony, the second element, begins in Chapter 3.

Fux, Mozart, and Attwood By the early eighteenth century, musicians had developed user-friendly ways to teach counterpoint. Johann Fux is credited today with a particularly succinct pedagogy. In fact, his book Gradus ad Parnassum was closely studied by composers of the late eighteenth century, including Haydn, Mozart, and Beethoven, as well as composers throughout the nineteenth century, including Brahms. Indeed, the book and its concepts continue to this day to be a fundamental part of music theory instruction. Many composers, including Mozart, taught composition using a healthy dose of the ideas presented in Gradus. The compositional exercises of some of Mozart’s students have been preserved, including several hundred pages from the pen of a wealthy Englishman named Thomas Attwood. Mozart considered Attwood somewhat talented, remarking that he “is a young man for whom I have a sincere affection and esteem. . . . He partakes more of my style than any scholar I ever had.” However, Mozart

EXAMPLE 2.5

Mozart’s Reaction to Attwood’s Counterpoint

5

10

you are an ass. 5

6

5

3

5

6

3

6

8

6

3

6

8

6 3

6

3

3

1

you are an ass.

Chapter 2 Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint

87

wasn’t always complimentary, as we can see in Example 2.5, in which he has crossed out Attwood’s entire exercise and, in English, expressed his frustration in no uncertain terms.

Fux’s Method Fux begins with a study of melody (as we have just done). In subsequent chapters he uses these melodies, called cantus firmi [“fixed songs”; singular: cantus firmus (CF)], as the structural pillars against which he teaches how to add first one voice, then two, and, still later three, creating a total of four parts. In order to make these studies as pedagogical as possible, Fux presents a series of five steps—or species—each of which isolates the way that an added voice would move against the CF. These five species begin, logically enough, with the addition of a single pitch above or below each pitch of the CF, resulting in note-against-note counterpoint, or firstspecies counterpoint (also called 1:1 counterpoint). The newly composed voice is called the contrapuntal voice (or counterpoint). This voice can be written above or below the CF (Example 2.6A). In second-species counterpoint (also called 2:1 counterpoint), two pitches are written against a single pitch of the CF (Example 2.6B). Subsequent species add more pitches to the contrapuntal voice as well as new rhythmic procedures. Fifthspecies counterpoint combines all of the techniques of the previous four species.

EXAMPLE 2.6 A. First Species

First and Second Species B. Second Species

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counterpoint

cantus firmus (given)

Using this highly controlled environment, the musician can focus on the primary goal of writing counterpoint: to create a melody that simultaneously combines with the CF. Such harnessing of music’s horizontal plane (i.e., the linear, temporal domain) and vertical plane (i.e., the spatial, harmonic domain) is actually the goal of your entire theory studies. Our counterpoint studies will focus only on first and second species in two voices and provide a foundation for our future studies, which draw heavily on principles of melody and intervals. The study of species counterpoint will help develop your ear and show you the difference between rules, which must be obeyed, and guidelines, which are more aesthetic options.

T WO -VOIC E C OU N T E R P OI N T A S M U S IC A L F OU N DAT IO N To demonstrate briefly how thinking in terms of two-voice counterpoint is central to Western music, the excerpts in Example 2.7 are taken from nearly six hundred years of music; they range from the early Renaissance to the Baroque and Classical periods and

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THE COMPLETE MUSICIAN

span the entire nineteenth century. Each excerpt depends on the relationship between two voices moving in either 1:1 counterpoint, 2:1 counterpoint, or a mixture of the two. If there are more than two voices, the outer voices will be most prominent, like those in Example 2.4. As you listen to these excerpts, notice that each voice is a melody unto itself and that when combined, the voices maintain their independence.

First-Species Counterpoint We already know that one melodic tone most often moves to another in the smoothest manner: by step or by third. By extension, when we combine two voices, we must consider

Six Centuries of Counterpoint

EXAMPLE 2.7 A.

qui

se cu ti

es

qui

B. 8

se

tis

cu

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me,

ti

es tis me,

Josquin des Pres, Missa Pange Lingua, Kyrie (ca. 1517)

Ky

ri

e

Ky

C.

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Dufay, Missa Sancti Jacobi, Communion (ca. 1428)

e

ri

lei

e

e

lei

Bach, Invention in C minor (ca. 1723) 7

D. 54

Haydn, Sonata in C major, Hob XVI.35 (Finale) Allegro (ca. 1780)

Chapter 2 Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint

EXAMPLE 2.7 E.

89

(continued)

Beethoven, Violin Sonata in A major, op. 23, Allegro molto (1800) cresc.

Allegro molto

cresc.

F.

Brahms, “Unüberwindlich,” op. 72, no. 5 (1884)

11

bin

ich

doch

wie

neu

ge

bo

ren,

läßt mein

Schen

ke

fern

not only the intervallic movement within an individual voice, but also the intervals formed between the two voices. Example 2.8 presents an example of first-species counterpoint. The horizontal (melodic) intervals formed within each line are marked above the upper voice and below the lower voice. The vertical (harmonic) intervals formed between the two lines are labeled between the lines. All compound intervals are reduced to their simple forms (e.g., a tenth is labeled as a third). The direction and resulting shape, or contour, of each voice is traced by straight lines that appear between the pitches. We’ll begin our analysis of Example 2.8 by examining individual lines, and then we’ll address the ways the lines combine. 1. Each line moves primarily by step (major and minor seconds); leaps are restricted to small consonant intervals (mostly thirds and a single fourth). 2. Each line’s contour is varied such that the direction changes after every pitch or two. 3. The combination of lines produces only consonant harmonic intervals, most of which are imperfect (thirds and sixths). The example begins and ends with perfect consonances, and there is only one perfect consonance within the example

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EXAMPLE 2.8 2

5

First-Species Counterpoint: Motion Within and Between Voices 3

3

2

2

3

3

2

3

2

2

2

6

4

8

2

2

3

2

2

6

3

8

2

(an octave). Notice that there are no perfect fourths; they are very unstable in twovoice counterpoint and are considered to be a dissonance. 4. The two melodies rarely move in the same direction; rather, each melody maintains its own independence. Consonant harmonic intervals (P8, P5, M and m thirds and sixths, and P1) are the only intervals permitted in first-species counterpoint. The perfect fourth may not be used. Melodic lines must be smooth and independent of one another, yet they must work together, using only consonant intervals. The source of successful counterpoint is the contrapuntal motion that results from the combined play of voices.

Contrapuntal Motions Contrapuntal motion refers to the contours produced between two or more voices. Noteagainst-note counterpoint involves three types of contrapuntal motion. TYPE 1. Voices that move in opposite directions from one another create contrary

motion. For example, contrary motion is used in all but two cases in Example 2.8. Another example of contrary motion appears in Example 2.9A. TYPE 2. Voices that move in the same general direction produce similar motion. Example 2.9B shows similar motion. TYPE 3. Voices that move in the same direction and maintain the same generic interval create parallel motion. For example, parallel thirds (as tenths) characterize the motion between the second, third, and fourth intervals in Example 2.8. That these intervals are both major and minor does not affect the designation parallel; only the generic intervallic size needs to be repeated. Example 2.9C shows a string of parallel sixths.

Contrary motion creates the most independence between voices. You should therefore incorporate it as much as possible. Parallel motion can be very beautiful. But given that the voices are heard as shadowing one another, parallel motion substantially reduces voice independence and general motion. In order to maintain as much independence and momentum as possible in parallel

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Contrapuntal Motions

EXAMPLE 2.9 A.

B.

10

6

10

8

6

10

8

6

3

8

8

6

3

5

6

similar motion contrary motion

C.

D.

6

6

6

6

6

6

6

3

6

P

C

6

6

C

6

8

10

C

P

6

10

6

6

3

8

parallel motion mixed motions

motion, you may use only imperfect intervals (thirds and sixths). Further, parallel motion in thirds or sixths should be limited to a maximum of three consecutive uses (6–6–6, or 3–3–3) in order to avoid monotony. Music should include a mixture of these various motions to create a balanced and pleasing structure (Example 2.9D).

Perfect Intervals: Handle with Care While parallel sixths and thirds are allowed, moving directly from one perfect interval between the CF and the counterpoint voice to another perfect interval of the same size is forbidden. Example 2.10 contains several instances of such parallel perfect intervals, each of which is marked with parallel lines. Notice how such parallels ruin line independence

EXAMPLE 2.10 Forbidden Parallel Perfect Intervals STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5

5

5

8

8

8

5

5

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and, in the case of parallel octaves, create the unfortunate effect of one voice dropping out of the texture. Finally, similar motion provides more drama to your counterpoint because both voices ascend or descend but by different-sized intervals. Similar motion (like parallel motion) is most effective when you use imperfect consonances. You must be careful when approaching perfect consonances. As already stated, you may not move in parallel motion from a perfect consonance to another of the same size, but you also may not approach a perfect consonance by similar motion. Such direct intervals (also called hidden intervals or similar intervals) draw attention to perfect fifths and octaves, emphasizing their hollow sound (see Example 2.11A). Further, direct intervals often give the impression of parallels (hence the synonymous term hidden) because the ear tends to fill in the intervening intervals. Example 2.11B shows how the hidden fifths of Example 2.11A can be heard as hidden parallel fifths. To avoid direct intervals, approach perfect intervals by using contrary motion. There is one situation in which you may move to an octave or a fifth in similar motion: when the upper voice moves by step to the perfect interval. In Examples 2.11C and 2.11D the direct motion to the octave and the fifth are permissible, given the step motion in the upper voice. Example 2.11E contains several examples of a special setting of legal direct fifths, where the upper voice moves by step and the lower voice leaps. Given their rustic, hollow sound, such horn fifths are popular referential devices throughout the common practice. Notice how Scarlatti, Schumann, and Paganini cast their horn fifths in a playful manner, while Beethoven’s somber setting evokes the title he gave the sonata (“The Farewell”). Finally, aim for smooth lines, and avoid simultaneous leaps (fourths or larger) in both voices (Example 2.12A). When you do leap, change direction, just as you did in your melody writing (Example 2.12B).

EXAMPLE 2.11 Hidden (Direct) Intervals STR EA MING AUDIO

A.

B. 5th

5th

5th

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is heard as:

5

5

5

“bad” hidden fifths (upper voice leaps)

C.

D.

5

8

10

8

“good” hidden octaves (upper voice steps)

3

5

6

“good” hidden fifths (upper voice steps)

5

5

5

5

5

5

Chapter 2 Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint

EXAMPLE 2.11 (continued) E1.

Scarlatti, Sonata in D major, K. 96 Allegrissimo

Beethoven, Piano Sonata in E major, op. 81A, Das Lebewohl (Les Adieux)

E2.

Adagio Le -

be

-

wohl

espressivo

E3.

Schumann, “Waldesgespräch,” from Liederkreis, op. 39

E4.

Paganini, Caprice for Violin, op. 1, no. 12 Allegretto

Sulla tastiera imitando il Flauto

dolce

EXAMPLE 2.12 Treatment of Leaps A.

5

6

B.

avoid

OK

6

3

3

8

6

6

8

3

6

6

3

3

6

8

93

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THE COMPLETE MUSICIAN

Beginning and Ending First-Species Counterpoint Before we begin writing first-species counterpoint, you must know how to begin and end each exercise. The contrapuntal voice must begin on 1. However, if the contrapuntal voice occurs above the CF, you may begin on 5 (Example 2.13A). Your counterpoint must end, or cadence, on an octave or unison (1 in both voices; see Example 2.13B). The penultimate (next-to-last) measure must contain 2 and 7 which move in contrary motion to the octave on 1. In minor, raise 7 to create a leading tone; if 6 precedes 7, raise it, too (Example 2.13C). However, use only the lowered form of 7 (and 6) within the exercise. See Example 2.13 for examples of cadences. The CF is marked in each case.

EXAMPLE 2.13 Beginning and Ending First-Species Counterpoint A.

B. beginning 1

ending or: 5

CF

1 (only)

CF

CF

7

1

CF 2

1

2

1

7

1

CF

C.

CF

Rules and Guidelines for First-Species (1:1) Counterpoint

RULE 1 RULE 2 RULE 3 RULE 4

What follows is a summary of the rules and guidelines for first-species counterpoint. Rules are absolute and guidelines are suggestions. Rules create a structural foundation for your piece; guidelines, when followed, create a more aesthetically pleasing musical surface. Harmonic (vertical) intervals must be consonant (the perfect fourth is a dissonance in two-voice counterpoint). Parallel perfect intervals (unisons, fifths, and octaves) are forbidden. Approach perfect consonances using contrary motion; the single context in which similar motion is permitted occurs when the upper voice moves by step to the octave or fifth. Begin and end your counterpoint on 1 (unless the counterpoint appears above the CF, when it may begin on 5).

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RULE 5 In minor, use the lowered form of 6 and 7; raise 7 to create a leading tone only in the

penultimate measure, and raise 6 when it precedes the leading tone.

Guideline 1 Use step motion as much as possible in the contrapuntal voice, with occasional skips (jumps of a third) or leaps (jumps of a fourth or more) to add interest. Change direction and move by step after a leap. Guideline 2 Since the goal of counterpoint is voice independence, use contrary motion as much as possible. Parallel motion is restricted to imperfect consonances; limit to three consecutive uses. Guideline 3 Use imperfect consonances as verticalities when possible. Restrict the use of octaves and fifths to only one or two within the exercise. Guideline 4 Avoid two perfect consonances in a row since they create a hollow sound (e.g., a fifth to an octave, or vice versa). Guideline 5 Label every vertical interval.

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 2.2–2.3

2.3 Identification of Contrapuntal Motions The following literature excerpts demonstrate primarily first-species counterpoint. Label each vertical interval created by the outer voices, and then identify the prevailing type of motion in each example as contrary, parallel, or similar. A.

Victoria, Kyrie (1592)

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Chri

Chri

B.

ste

ste

e

e

lei son, Chri

Quantz, Duet no. 4, from Six Duets for Two Flutes Presto

lei

son, Chri

ste

e

ste

e

lei

son

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THE COMPLETE MUSICIAN

SOLVED/APP 5

C.

Schumann, “Wichtige Begebenheit,” from Kinderscenen, op. 15

D.

Beethoven, Violin Sonata in G major, op. 96, Scherzo. Consider the lowest voice of the accompaniment and the violin part (i.e., ignore the right hand of the piano).

8

2.4 Error Detection The given first-species counterpoint contains three types of errors: 1. Melodic (e.g., dissonant or multiple leaps) 2. Vertical intervals (e.g., dissonant intervals) 3. Motion from one interval to another (e.g., parallel perfect intervals or direct intervals)

SOLVED/APP 5

counterpoint

CF Key:

First, label each vertical interval. Then mark each error using the following method: D for dissonant vertical interval and P8 and P5 for parallel perfect octave and fifth, respectively. Use Dir for direct motion to perfect intervals. For melodic errors in the counterpoint voice, use your own system, such as “too many leaps,” “too big a leap,” or “must change direction after leap.”

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Second-Species Counterpoint In second-species counterpoint, the contrapuntal voice uses rhythmic values that are twice as fast as those of the CF, so for every note of the CF, there are two in the contrapuntal voice. The contrapuntal motion of one voice moving while the other voice remains stationary is called oblique motion. See Example 2.14, which, in addition to similar and contrary motion, contains oblique motion. Oblique motion, along with parallel, similar, and contrary motion, completes the list of ways that voices may move against one another.

EXAMPLE 2.14 Oblique Motion oblique

5

parallel oblique contrary oblique contrary oblique similar

3

3

5

3

6

3

3

Given that there are now strong beats (where both the CF and the added counterpoint move to new pitches) and weak beats (where only the counterpoint moves to a new pitch against the sustained CF), a metric hierarchy arises. In 2:1 counterpoint, we observe the rules and guidelines from 1:1 counterpoint concerning melody writing and the interaction of the two voices. However, we must also attend to the potential problems that may arise given that we now write two pitches in the contrapuntal voice against a single CF pitch. As with first-species counterpoint, the downbeat must be consonant, and successive downbeats must not contain parallel fifths or octaves. The weak beat, however, may be consonant or dissonant.

Weak-Beat Consonance You may move to a weak-beat consonance by step, skip, or leap. However, there is only one way to create a consonant step motion: by moving from a fifth to a sixth or a sixth to a fifth, since only this intervallic combination contains two adjacent consonances. The generic term for such step motion is 5–6 technique (Example 2.15, mm. 1–2 and m. 5). The consonant second pitch may continue its motion in the same direction, in which case we call it a consonant passing tone (CPT), or it may return to the pitch heard on the downbeat, in which case we call it a consonant neighbor tone (CNT). Example 2.15 presents examples of each. Consonant skips (CS) are motions by a third. Consonant leaps (CL) are motions by intervals larger than a third. To skip or leap, the weak-beat note must be consonant with both the preceding melody note and the CF. Examples of consonant skips and leaps are found in mm. 3–4 and 6–8 of Example 2.15. Sometimes these skips and leaps occur several times, creating the effect of splitting a single line into two separate voices, a technique which we call compound melody. An example of compound melody occurs in mm. 6–7 of Example 2.15; the two registrally separated “voices” are shown by the dotted slurs. Consonant skips and leaps are also

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possible from the weak beat to the strong beat, but, again, they must be consonant with the preceding melody note and the CF; see Example 2.15, from mm. 1–2 and mm. 4–5. Notice that the majority of leaps take place within, rather than between, measures. This is because leaps draw attention to themselves; when they occur on an accented beat, they are particularly noticeable, thus detracting from the flow of the line.

EXAMPLE 2.15 Second-Species Counterpoint Using Intervallic Consonance on All Strong and Weak Beats CNT CPT

5

6

6

5

CL

CL

6

CS

CL

CL

CS

5

CF

Weak-Beat Dissonance Dissonance is the most important new feature of second-species counterpoint. Indeed, dissonance is the source of much expression in tonal music and a powerful way to create a dynamic flow. But dissonance, like any great force, must be carefully controlled. Second-species counterpoint uses a single type of dissonance: the unaccented passing tone. Passing tones (PT) occur on a weak beat in 2:1 counterpoint, and they fill the space within the interval of a third, creating a smooth, stepwise motion. (We saw an example of the consonant passing tone using the 5–6 technique in Example 2.15.) The motion into and out of the dissonant passing tone must occur in a single direction, either ascending or descending. Since the PT may only occur on the weak beat, it will lie between two strong-beat consonances that are a third apart. Note in Example 2.16 that there are also consonant passing tones.

EXAMPLE 2.16 Consonant and Dissonant Passing Tones

* 3

CF

2

* 6

5

3

4

* 6

3

6

5

6

8

3

4

6

8

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Chapter 2 Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint

The dissonant passing tones in Example 2.16 are marked with asterisks. Consonant passing tones are not marked, but you can spot them by their telltale intervallic labels “6 5” or “5 6.” The first dissonant PT occurs in m. 1. The pitch D fills the third between E and C and creates a strong major-second dissonance that is discharged by the following sixth (m. 2). The next measure contains a consonant passing tone; B fills the third between C and A. Study the rest of the example, noting how both consonant and dissonant passing tones are used. The goal in second-species counterpoint is to include as many passing tones as possible.

More on Perfect Consonances In second-species counterpoint, you must be especially vigilant to avoid writing parallel and direct perfect consonances. For example, you might be tempted to think that the intervening weak-beat interval reduces the effects of the strong-beat parallels, but this is not the case, as demonstrated in Example 2.17.

EXAMPLE 2.17 Treatment of Perfect Intervals in Second-Species Counterpoint A.

B.

8

7

8

3

8

3

8

“bad” strong-beat parallel octaves

C.

5

6

5

3

5

6

5

6

“bad” strong-beat parallel fifths

D.

6

5

6

5

“good” strong-beat parallel sixths

Example 2.17A contains four strong-beat octaves, none of which is obscured by the weak-beat pitch. In the first measure, the dissonant PT B is unable to conceal the octave motion between C and A on the downbeats of mm. 1 and 2. Note that a dissonance can never mediate poor voice leading. Nor is the consonant skip in m. 2 able to obscure the octaves A to E between mm. 2 and 3. Even the dramatic consonant leap of a falling sixth from E to G and change of direction cannot diminish the audible octaves on the downbeats; the metric accent from one measure to the next is simply too strong to hide the perfect intervals. Example 2.17B shows a similar situation with the perfect fifth. Example 2.17C illustrates that the important 5–6 technique is not powerful enough to

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hide downbeat fifths. However, a 6–5 motion is permissible, since the ear hears parallel sixths on the downbeats rather than fifths (Example 2.17D). Finally, be aware of creating parallel perfect and direct intervals when adding a weakbeat note. In Example 2.18A, parallel fifths and octaves arise because of the added weak-beat note. Similarly, in mm. 2–3 of Example 2.18B, what was a successful strongbeat counterpoint (a third moving to a perfect fifth in contrary motion) is now flawed by the addition of the weak-beat G, which creates a direct fifth with the following downbeat.

EXAMPLE 2.18 Avoid Parallel and Direct Intervals on Weak Beats A.

B.

8

5

5

8

8

direct 5th

8

3

3

6

5

Beginning and Ending Second-Species Counterpoint Like first species, you must begin on 1 if the contrapuntal voice is below the CF. When the contrapuntal voice is above the CF, you may begin on 1, 3, or 5. In addition, you may begin with either a half note or a half rest. The half rest is particularly effective since it immediately highlights the independence of voices and it creates a strong sense of forward motion (see Example 2.19A). The last measure must be a whole note on 1. However, the penultimate measure may be two half notes or a whole note (see Example 2.19B). As with first-species counterpoint, the move to the final octave must be stepwise and in contrary motion. When the minor mode is used, raise 6 and 7 only in the final cadence (see Example 2.19C). The rest of the time use the diatonic forms.

EXAMPLE 2.19 Beginning and Ending Second-Species Counterpoint A.

B. beginning

8

7

or:

etc. 3

ending

8

etc. 3

8

3

5

6

or:

8

3

6

6

8

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101

EXAMPLE 2.19 (continued) C.

6

3

3

2

6

8

3

2

3

+4

6

8

Rules and Guidelines for Second-Species Counterpoint RULE 1 Strong beats must be consonant. RULE 2 Avoid parallel perfect intervals between:

a. successive strong beats (downbeats). b. weak beat and strong beat (upbeat and downbeat). RULE 3 Avoid direct motion to perfect intervals from weak to strong beats. RULE 4 The only permitted dissonance is the weak-beat passing tone (i.e., the dissonance must fill

the space of a melodic third by step between two downbeats). RULE 5 The added voice must begin on 1 when it appears below the CF, but it may begin on 1,

3, or 5 when it appears above the CF. You may begin with a half rest, and the penultimate measure may contain either one or two pitches. The final measure must contain a whole note. RULE 6 In minor, use the lowered form of 6 and 7; raise 7 to create a leading tone only in the penultimate measure, and raise 6 if it precedes the leading tone.

Guideline 1 Incorporate as many dissonant passing tones as possible. Guideline 2 Use consonant leaps to balance dissonant passing tones. Guideline 3 Place leaps within, rather than between, measures. Guideline 4 Label every interval, and mark each dissonant passing tone with an asterisk.

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 2.4–2.5

2.5 Analysis of Second-Species Counterpoint Based on the model analysis of A1 and A2, you can see that the first example is error free, while the second is error ridden. Study these two models carefully; then analyze the

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following example using the labeling system shown in the models. Make sure you label all musical events, correct or incorrect. You will encounter three basic types of errors: STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1. Melodic (e.g., dissonant or multiple leaps). 2. Vertical (e.g., improper use of dissonance). 3. Motion from one interval to another, either successive strong beats or weak beat to strong beat (e.g., improper use of dissonance, parallel perfect intervals, or direct intervals). Begin by labeling each vertical interval and marking each dissonance.

A. Model Analysis

consonant passing tone

consonant leap

1.

3rd

3rd

8

7

5

8

dissonant PT

2.

6

7

6

5

9

7

consonant skip

5

3

3

4

6

dissonant PT

dissonant PT

3

3

4

6

8

dissonant PT must leap to dissonance end on

dissonant leap to dissonant downbeat dissonance downbeat

3rd, but dissonance on downbeat

10

consonant leap 3rd

3rd

1

5

5

4

2

8

8

4

+4

3

7

3 6

6

skip from dissonance

SOLVED/APP 5

B.

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2.6 Analysis of Outer-Voice Counterpoint Determine whether the following examples demonstrate primarily first- or secondspecies counterpoint. Then label each interval. Example D contains three voices— examine only the outer voices. Finally, some examples shift the 2:1 relationship between voices.

Chapter 2 Harnessing Space and Time: Introduction to Melody and Two-Voice Counterpoint

A. Handel, Water Music, Minuet Tempo di Minuetto Violini

Bassi

B. Willaert, “And if out of jealousy you are making me such company” 10

e

8

8

e

se

per ge lo

si

a

se per ge lo si

a

C. Mozart, Minuet in D major, K. 94

SOLVED/APP 5

D.

Brahms, “Unüberwindlich,” op. 72, no. 5 (Ignore the two pitches in parentheses.)

und doch

bin

ich neu

ge bo

T ER MS A N D CONCEP TS • cantus firmus • contour • contrapuntal voice

ren, läßt sie

sich ins Au

ge schauen, läßt

103

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• counterpoint • first species • second species • direct interval • disjunct motion • dissonant leap • 5-6 technique • law of recovery • melodic climax • neighbor tone • motion • conjunct • contrary • oblique • parallel • similar • parallel perfect interval • passing tone • consonant • dissonant • polyphony

CH A PTER R EV IEW 1. Which two voices are contrapuntally the most important?

2. List the available consonant harmonic intervals in first-species counterpoint.

3. List the three types of contrapuntal motion. Which type creates the most independence between voices?

4. True or False: Direct fifths and octaves are only allowed when the soprano voice moves by step.

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5. The contrapuntal voice (the one you are writing—not the cantus firmus) must begin on scale degree(s) ________ when writing below the cantus firmus. However, it may begin on scale degree(s) ________ when writing above the CF.

6. True or False: The penultimate (next-to-last) measure must contain 2 and 7, in either voice, both moving by contrary motion to 1.

7. True or False: In minor, lower 7 at the cadence.

8. Name the fourth type of motion used in second-species counterpoint.

9. True or False: The 5–6 technique is the only way to make a consonant passing tone (CPT) or consonant neighbor tone (CNT).

10. Second-species counterpoint uses only which kind of dissonance?

CH A PTER 3

Musical Density: Triads, Seventh Chords, and Texture

OV E RV I E W

This chapter shows how we can add voices to the two-voice counterpoint discussed in Chapter 2 to form three- and four-note chords. The result is the creation of harmony. Harmony will provide the essential musical material for our remaining studies. We will discuss how composers used figured bass to provide a harmonic sketch to guide performers. We will begin our discussion of harmonic analysis. We will define and explore seventh chords. Finally, we will describe how to analyze musical texture. CHAPTER OUTLINE Adding Voices: Triads and Seventh Chords ......................................................... 107 Triads ....................................................................................................................... 107 Voicing Triads: Spacing and Doubling ........................................................108 Triad Inversion ..............................................................................................109 Figured Bass ........................................................................................................... 111 Analyzing and Composing Using Figured Bass ...........................................111 Additional Figured Bass Conventions: Abbreviations and Chromaticism ............................................................112 Triads and the Scale: Harmonic Analysis ........................................................... 117 Roman Numerals ..........................................................................................118 Introduction to Harmonic Analysis ..............................................................118 Harmony and the Keyboard ........................................................................ 120 (continued)

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Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

107

Seventh Chords............................................................................................................ 123 Definitions and Types........................................................................................... 123 Musical Characteristics of Seventh Chords ....................................................... 124 Inverted Seventh Chords .............................................................................. 124 Analytical Tips ....................................................................................................... 125 Seventh Chords and Harmonic Analysis............................................................ 126 Musical Texture ........................................................................................................... 130 Analytical Method ................................................................................................. 133 Distribution of Chord Tones and Implied Harmonies ...............................133 Fluency ...........................................................................................................133 Harmonic Reduction .....................................................................................135 Terms and Concepts ................................................................................................... 137 Chapter Review ........................................................................................................... 138 Summary of Part 1...................................................................................................... 140

A DDI N G VOIC E S : T R I A D S A N D S E V E N T H C HOR D S So far, we have studied melody and two-voice counterpoint. We now move into the third and final building block of tonal music: harmony. As stated earlier, harmony is most easily viewed as filling in the musical space provided by the counterpoint of two outer voices. The usual format for discussing harmony is the chorale texture: soprano, alto, tenor, and bass. Thus, the soprano and bass provide the outer-voice counterpoint, and the alto and tenor fill in the space between the soprano and bass, creating chords.

Triads Chords that comprise three distinct pitches stacked in thirds are called triads. The lowest pitch is the root and it is this pitch that identifies the triad; the note that is a third above the root is the third, and the note that is a fifth above the root is the fifth (Example 3.1A). There are four qualities of triads above a given root (Example 3.1B). Major and minor triads are consonant triads, since they span a consonant interval (P5). Augmented and

EXAMPLE 3.1A 5th

3rd root of triad

A Triad on C

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Four Types of Triads

EXAMPLE 3.1B

Major triad: M3 + m3

Minor triad: m3 + M3

Diminished triad: m3 + m3

Augmented triad: M3 + M3

EXAMPLE 3.1C

Triad Types

smaller

larger

m3 d5 M3 P5 m3 P5 M3 A5 m3 m3 M3 M3 diminished minor major augmented (d) (m) (M) (A)

diminished triads are dissonant triads: The augmented triad spans an A5, and a diminished triad spans a d5. Only major, minor, and diminished triads are used as harmonic units in common-practice music. Example 3.1C orders the four triad types from smallest intervals spanned (two minor thirds in the diminished triad) to largest (two major thirds in the augmented triad).

Voicing Triads: Spacing and Doubling In Example 3.1 the third and the fifth of each triad are arranged directly above the root. This tight spacing (or voicing) of chordal members—specifically between the three upper voices (soprano, alto, and tenor) of a four-voice structure—is called close position. However, the pitches of a triad do not always appear in close position. Instead, they might be variously distributed in register in order to create a different effect. When this occurs, the triad is in open position. Such spacing is generally wider between the lowest-sounding pitch and the pitches that appear above it because tightly spaced triads in the bass are hard to hear clearly. Listen to the sound of the root-position major, minor, and diminished triads in Example 3.2. Carefully study each example, and label each triad’s members using

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109

EXAMPLE 3.2 Triads in Open Spacing A.

3

B.

C.

D.

E.

F.

G.

H.

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5

1

B Maj.

1, 3, or 5 for root, third, or fifth. Notice that in Example 3.2A, by placing the third above the fifth, a new interval (a sixth) arises between the notes of the upper voices. Composers can thicken the sound of triads by increasing the number of voices and doubling one or more members of the triad. Doubling one member increases the number of sounded notes from three to four. The most stable member of the triad, the root, is the note most often doubled, though doubled fifths and thirds are also common. Example 3.3 illustrates root-position triads in a four-voice texture with one member doubled. Identify the triad type, circle doubled pitches, and label their chordal membership.

EXAMPLE 3.3 Root-Position Triads in Four-Voice Texture A.

B.

C.

D.

E.

F.

G.

H.

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

3rd

C minor

Triad Inversion A triad is said to be in root position if the root is the lowest-sounding pitch, that is, if the root is in the bass. However, the root of a triad need not be the lowest-sounding note. Either the third or the fifth may appear in the bass. When the third or the fifth of a triad appears in the bass, the triad is said to be in inversion. When the third of the triad appears in the bass, the chord is in first inversion. When the fifth is in the bass, the triad is in second inversion. Thus, when triads are in first or second inversion, the root of the chord appears somewhere above the bass. Example 3.4 contains examples of major, minor, and diminished triads in root position, first inversion, and second inversion. It doesn’t matter how the pitches above the bass are distributed; it is only the pitch in the bass that determines root position or an inversion.

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Root-position major and minor triads are stable by virtue of their perfect fifths (perfect consonances), while inverted triads are less stable because they are bound by sixths (imperfect consonances). This results in the listener desiring to hear them move forward toward a cadence, which usually arrives on a root-position triad. When inverted, each type of triad becomes progressively less stable. For example, in first inversion, major and minor triads are less stable than in root position, because they include the intervals of a perfect fourth and a minor or major sixth. This is not true, however, for diminished triads: In root position they are highly dissonant because of the diminished fifth, but in first inversion, only consonant thirds and sixths sound above the bass (the tritone is less audible, because it does not involve the bass). In second inversion, major and minor triads are regarded as dissonant because the perfect fourth is now formed with the bass, which drives the harmony. (Remember that in two voices, the perfect fourth is considered dissonant.) Even in textures of three or more voices (as in the present case), when a perfect fourth is formed with the bass, we hear it as dissonant. Both root-position and first-inversion triads are common in tonal music; however, second-inversion triads, due to their greater instability, occur only in restricted contexts. Thus while triads in root position and first inversion are more or less interchangeable, second-inversion triads are in a class of their own (see Example 3.4).

Triads and Their Inversions

EXAMPLE 3.4 major:

Root position

5 3 1

minor: 1 5 3

3 1 5

1st 2nd inversion inversion

Root position

5 3 1

diminished: 1 5 3

3 1 5

1st 2nd inversion inversion

Root position

5 3 1

1 5 3

3 1 5

1st 2nd inversion inversion

Note WORKBOOK 1 Assignment 3.1

The root is the generating pitch on which a triad is built and the bass is the lowest-sounding pitch in a sonority. For example, in the sonority E –G–C, E  is the bass and C is the root. In order to identify a triad, stack its members in thirds. C G

G E

= E

C

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Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

Figured Bass Many composers who were writing between 1600 and 1800 used a shorthand notation to describe the intervals above bass notes. This type of shorthand, known as figured bass (or sometimes thoroughbass), is a useful way of understanding chordal construction as well as the melodic movement between chords. Today, the lead-sheet symbols of jazz and popular music serve a similar purpose.

Analyzing and Composing Using Figured Bass Figured bass is founded on the fact that the bass, the lowest-sounding voice, is harmonically the most important voice of any texture. A figured bass has two components: 1. A bass note. 2. Numbers, or “figures”—listed under the bass—that indicate the generic intervals formed by the bass and each of the other voices. The numbers are typically listed one below another, from largest to smallest. Figured bass does not indicate which voices have which notes above the bass; it is a catalog of the intervals that occur above the bass, regardless of spacing or doubling. Example 3.5 shows how to represent chords using figured bass. Note that the figures tend to have simple intervals, and the figure “8” is not necessary, since a note one octave above the bass simply doubles the given bass note. Root-position triads yield the figure 53, first inversion 6 6 3, and second inversion 4. Example 3.6 shows how to fill out, or realize, a figured bass to create chords. Performers have a remarkable amount of freedom in the realization of figured bass, deciding the arrangement of the upper voices, as long as the given intervals are sounded with the bass note. For this reason, figured bass works well with improvisatory music. Here we will analyze and

EXAMPLE 3.5

Figured Bass Analysis

chords

figured bass 5 3

6 3

6 4

5 3

6 3

6 4

6 3

5 3

5 3

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THE COMPLETE MUSICIAN

EXAMPLE 3.6 Figured Bass Realization

given figured bass

6 3

5 3

6 4

6 3

5 3

5 3

realization 1

6 3

5 3

realization 2

6 4

6 3

5 3

5 3

6 3

5 3

6 4

6 3

5 3

5 3

realize chords in four-part harmony. Example 3.6 shows two realizations of the same figured bass that result in successions of four-voice chords. The numbers below the bass represent how the chord members would appear in close position. Using this system, a composer writes a bass note with figures, and the performer knows what notes are needed above the bass. The performer builds a chord with the specified intervals while always observing the prevailing key signature.

Additional Figured Bass Conventions: Abbreviations and Chromaticism Because root-position and first-inversion triads are so common, their figured bass notation is often assumed or abbreviated. Normally the 53 symbol is omitted entirely; thus the absence of a figure under a bass note signifies root position. Similarly, 6 by itself is used instead of 63 for first inversion. However, second inversion is always written 64. Example 3.7 shows the bass part from Example 3.5 with standard figured bass abbreviations.

EXAMPLE 3.7 Figured Bass Abbreviations abbreviated figured bass

6

6 4

6

6 4

6

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113

Figured bass follows the given key signature—that is, the notes above the bass follow the given key signature unless the figure is altered. A few common ways to indicate chromatic alterations to notes above the bass include: • If there is an accidental on a pitch above the bass, the same accidental is attached to the corresponding interval in the figured bass (Example 3.8A). • If an accidental occurs on the pitch that is a third above the bass, the number 3 is omitted and only the accidental is written (Example 3.8B). • A plus sign or a slash through a number raises the pitch by one half step (Example 3.8C). • If the bass note is chromatically altered, nothing changes in the figure, since the figure indicates only intervals above the bass (Example 3.8D).

EXAMPLE 3.8 Figured Bass Chromaticism A.

B.

C.

D.

chords

figured bass 6

6

6 4+

6

Figured bass also shows the melodic motion of individual voices, especially voices that move by step. For example, some of the triads that appear in Example 3.9 seem to do so through melodic motion, which is shown in the figured bass: The D-major triad that begins the excerpt moves to a G-major triad on beat 3. However, the melodic motion A–B in the soprano can be shown in the figured bass: The A (a fifth above the bass) moves to B (a sixth above the bass). The figures “5–6” capture that motion, and the dash makes this melodic motion explicit. There are two more of these 5–6 motions in the example. In fact, we can even show dissonant melodic motion in a figured bass, as illustrated by the alto’s G that is sustained past the change to the D chord. The G is a dissonant fourth above the bass, so we label its melodic behavior 4–3. Stepwise motion does not necessarily imply a chord change even it if looks like one based on stacking thirds that may create a different sonority. For example, the opening D-major chord moves by 5–6 melodic motion from A to B in the soprano. However, one could

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THE COMPLETE MUSICIAN

EXAMPLE 3.9 Figured Bass and Melodic Motion

D:

5

6

5

6

5

6

4

3

interpret this as a harmonic change: The A to B motion creates a move from D major to B minor in first inversion. But we do not hear a chord change, only the 5–6 motion, so D major continues and the melodic motion to B only anticipates the following B that is part of a new chord, a G-major (IV) chord. Remember, the ear, not the eye, must inform our analysis. Here is a summary of the most common figured bass symbols for triads, followed by their shorthand abbreviations. Note that there is some redundancy, given that many of these notations are alternate ways to indicate the same thing. • Accidentals that appear next to the figure:  the specified pitch has a flat accidental (this can also have the generic meaning of “lower by a half step”)  the specified pitch has a sharp accidental (this can also have the generic meaning of “raise by a half step”) /, ⫹ raise by a half step  the specified pitch has a natural sign on it • Accidentals appearing alone refer to the third above the bass. • Chromaticism in the bass voice cannot––and need not––be shown in figured bass notation. • The figures do not determine the registral placement of notes in the upper voices. • Chromatic alterations in the figured bass apply only to the pitches that lie directly above the bass—they do not carry through the measure. • The dash (—) indicates that a single voice moves by the intervals indicated on each end of the dash. Example 3.10 shows a sample of figured bass symbols and their realization using F3 and E in the bass, including various transformations of those bass notes. In keeping with the practice of abbreviations, compound intervals larger than a ninth are represented in figured bass notation by their smaller representative (for example, a tenth would be shown as a third). Usually it is not necessary to indicate doublings, and it is never necessary to indicate a chromatically altered octave, since it would be apparent from the given bass pitch (Example 3.11). There are two Ds and one A written above the lowest note of the first chord (F), forming a sixth and a third above the bass. It is 3

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Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

not necessary to account for the duplicate D. This is a 63 chord with D as its root. In the next chord, the lowest note (E) supports the intervals of a fourth, a sixth, and an octave above. Again, we ignore the octave, which duplicates the bass. It is a 64 chord with A as its root.

EXAMPLE 3.10 Figured Bass (FB ⫽ figured bass; CP ⫽ close position; OP ⫽ open position) A.

B. FB

CP

OP

C. FB

CP

OP

D. FB

CP

OP

FB

6

E.

F. FB

CP

OP

CP

OP

I. CP

OP

CP

K. FB

CP

OP

CP

OP

EXAMPLE 3.11 Chromatically Altered Bass Notes

6 4

FB

CP

OP

6 4

L.

FB

—

6

OP

6 —5 4 —3

J. FB

H.

FB

6 4

6

OP

5— 6

G.

FB

CP

FB

6

M. CP

OP

FB

6 4

CP

OP

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EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 3.2–3.3

SOLVED/APP 5

3.1 Figured Bass Practice The following triads are in root position or inversion. For each one, identify the following: • the root • the triad quality (major, minor, or diminished) • the member of the chord that is in the bass—root (1), third (3), or fifth (5) • the complete figured bass symbols. Remember that the figures reflect generic sizes of intervals, not exact sizes, and that they are written with the largest interval above the bass on top and smaller intervals below. Show chromatic alterations (consider there to be no key signature). A.

B.

root:

C

quality:

M

member of chord in bass:

3 rd

figured bass:

6 3

C.

D.

E.

F.

G.

H.

I.

J.

3.2 Triads in Various Spacings The three voices of the following root-position and inverted triads appear in various registers. For each one, identify: • the root • the quality of each • the member of the chord that is in the bass—root (1), third (3), or fifth (5)

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Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

Also provide a complete figured bass analysis that shows any chromatic alterations (consider there to be no key signature). A.

B.

root:

E

quality:

M

member of chord in bass:

3 rd

figured bass:

C.

D.

E.

F.

G.

H.

I.

J.

K.

L.

6 3

Triads and the Scale: Harmonic Analysis Each scale degree of a major or minor scale can support a triad constructed of pitches from that scale. In all major keys, for example, 4 supports a major triad and 2 supports a minor triad. In C, these end up being F major and D minor. In the key of A, they would be D major and B minor. Example 3.12 illustrates which type of triad—major, minor, or diminished—occurs on each scale degree in the major mode. As you learn to recognize the sound of each individual triad, it is also important that you memorize the types of triads generated from each scale degree in major and minor scales. Note that the triads built on: • The tonic (1), the dominant (5), and the subdominant (4) are all major triads. • The supertonic (2), the mediant (3), and the submediant (6) triads are minor. • The leading-tone triad (7) is the only dissonant chord; it is diminished.

EXAMPLE 3.12 Scale Degrees and Triad Types in Major scale degree in major:

1

2

3

4

5

6

7

1

triad type in major:

M

m

m

M

M

m

d

M

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THE COMPLETE MUSICIAN

Because there are various forms of the minor scale (natural, harmonic, and melodic) many more possibilities result from the raised and lowered forms of 6 and 7. Example 3.13 summarizes the most common types of triads that occur in the minor mode. The submediant, 6 usually occurs in its lowered form in the minor scale, thereby affecting the triads in which it is used (that is, triads built on 2, 4, and 6). Although triads built on 5 and 7 are found in both their lowered and raised forms, the most common forms incorporate the leading tone. In minor scales: • Triads built on the tonic (1) and the subdominant (4) are minor. • Triads built on the mediant (3), the dominant (5), the submediant (6), and, occasionally, the subtonic (or lowered form of 7) are major. • Diminished triads result from chords built on the supertonic (2) and the leading tone (raised 7).

EXAMPLE 3.13 Scale Degrees and Triad Types in Minor occasional

occasional

scale degree in minor: 1

2

3

4

4

5

5

6

7

7

1

triad type in minor:

d

M

m

M

m

M

M

M

d

m

m

Roman Numerals Individual pitches can be represented using scale degree numbers that identify their function within a given scale. Similarly, triads are represented by roman numerals that indicate the scale degree on which they are built. For example, a B-major triad in the key of F major is written as IV to show that it is built on the fourth scale degree in that key. Uppercase roman numerals are used for major triads; lowercase roman numerals are used for minor triads. Diminished triads are represented by lowercase roman numerals, with the addition of a small degree sign, “º.” Example 3.14 shows the triads that occur on each scale degree for the keys of D major and D minor, with the appropriate roman numerals. Note that, given the various forms of the minor scale, it is possible to build two different triads on both 4 and 5 and two different triads (with two different roots) on 7.

Introduction to Harmonic Analysis A complete harmonic analysis combines roman numerals and figured bass: • We use a roman numeral to identify the root (by scale degree) and quality of a chord. • We use the figure from figured bass (usually without accidentals) to identify the inversion of the chord and melodic motion (such as 5–6 or 4–3).

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Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

EXAMPLE 3.14 Roman Numerals in Major and Minor major:

I

roman numerals:

ii

iii

minor:

roman numerals:

IV

V

vi

occasional

i

ii

III

iv

IV

v

vii

I

occasional

V

VI

VII

vii

i

Here is a step-by-step procedure to follow: 1. Determine the key of the exercise, because the key signature alone implies two possible keys: either the major or the relative minor. A helpful hint is provided by chromatic alterations of pitches that often indicate leading tones in minor. 2. Write out the letter name of the key, immediately followed by a colon, at the beginning of the exercise, under the bass staff. Use uppercase letters to represent a major key and lowercase to represent a minor key (except for C major and minor, for which you will write “C maj.” and “c min.” 3. Identify triad roots, using roman numerals under each harmony. Note that in most cases, you do not have to calculate the quality of a chord; most of the diatonic chords have one distinct quality (e.g., IV in major usually appears as a major triad; review Example 3.14). In minor keys, chords with 6 and 7 have different forms; you must determine which quality of chord is being used. 4. Do not renotate the roman numeral if a chord is immediately repeated; you can simply draw a horizontal line that indicates the harmony is repeated. 5. If the triad is in root position, you need do nothing more. If the triad is inverted, supply a figured bass. Use the abbreviation “6” for the figure “63” Example 3.15 shows sample harmonic analyses. While roman numerals relate harmonies to a tonic (and can be considered a hierarchical analytical system), figured bass reveals how intervals connect one harmony to another (and is considered to be a highly context-sensitive analytical system). See Example 3.16 for a complete harmonic analysis.

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EXAMPLE 3.15 STR EA MING AUDIO

A.

a:

B.

W W W.OUP.COM/US/LAITZ

i

i6 (3)

V

5 3

V

6 (3)

Brahms, “Gunhilde,” German Folk Songs, vol. 1 In ruhigem Zeitmaß und teilnehmend erzählt

Gesang

1. Gun

hil 2. zog 3. hil

de lebt gar stil le und fromm in ih rem Klo ster bann, mit ihr wohl durch leb ten in Saus und Braus; die Welt, sei mes Weib, Gun hild, was fängst du de ach, du ar an?

Pianoforte

G:

C.

V

vii 6

I

I6

V

IV

vii 6

I

Brahms, “Es wohnet ein Fiedler,” from German Folk Songs, vol. 6 Lebhaft, doch nicht zu rasch

(PT)

Gesang

1. Es 2. Du

woh buck

net ein Fied lich ter Fied

ler zu Frank ler, nun fied

furt am Main, le uns auf,

Pianoforte

a:

i

V

i

ii 6

i

i6

V

Harmony and the Keyboard Keyboard style is a four-voice texture in which three notes (voices) are played in the right hand, within the space of one octave, and one note (voice) is played in the left hand. The notes in the right hand are labeled (from highest to lowest) soprano, alto, and tenor. The

Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

121

EXAMPLE 3.16 Complete Harmonic Analysis

6 6 4—3 B : I V4 I V

I

bass is played with the left hand. This helps to emphasize the outer voices, and is the most common hand position we will use. Further, on occasion you will be writing in keyboard style, although most of our writing will place the upper two voices (soprano and alto) in the treble clef and the lower two voices (tenor and bass) in the bass clef, a distribution called chorale style. Example 3.17 shows the harmonic progression I–V–I in both keyboard style and chorale style.

EXAMPLE 3.17 Four-Voice Styles Keyboard style:

Chorale style:

soprano

soprano

alto tenor

alto

bass

tenor bass

I

V

I

I

V

I

EX ERCISE INTER LUDE W R ITING 3.3 Writing Triads Complete the following tasks on manuscript paper. Write odd-numbered exercises in treble clef, even-numbered exercises in bass clef. A. Notate root-position major triads based on the following pitches: 1. A SOLVED/APP 5 2. B 3. D 4. F

WORKBOOK 1 Assignments 3.4–3.5

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THE COMPLETE MUSICIAN

SOLVED/APP 5

SOLVED/APP 5

SOLVED/APP 5

SOLVED/APP 5

SOLVED/APP 5

SOLVED/APP 5

5. B  6. F B. Notate root-position minor triads based on the following pitches: 1. C 2. B 3. G 4. E  5. B  C. Notate root-position diminished triads based on the following pitches: 1. D 2. E 3. B  4. F 5. B D. Given the triad quality of one member of the triad (root, third, or fifth), notate the complete triad in root position. 1. C is the third of what major triad? the fifth of what minor triad? 2. A  is the third of what major triad? the fifth of what diminished triad? 3. E is the third of what minor triad? the fifth of what major triad? 4. G is the third of what diminished triad? the fifth of what diminished triad? 5. F is the third of what minor triad? the fifth of what minor triad?

A NA LYSIS 3.4 Each of the following triads appears in root position or inversion. Identify the root of the chord, quality (major, minor, or diminished), and the member of the chord that appears as the lowest and the highest pitch (root [1], third [3], or fifth [5]).

SOLVED/APP 5

A.

B.

root:

D

quality:

m

highest:

5

lowest:

1

C.

D.

E.

F.

G.

H.

I.

J.

K.

L.

Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

123

S E V E N T H C HOR D S Sonorities with four notes that can be stacked in thirds are called seventh chords. Listen to the chords in Example 3.18A and then play them on the piano. Identify the different pitch classes in each chord. Describe the sound quality of these chords and their effect in terms of stability and instability. Only the first and last chords are triads. The majority of the remaining chords contain four different pitches, which can be stacked in thirds. The few three-pitch class sonorities are not triads, but they can still be stacked in thirds, although there is a “gap” between the second and third pitches (see Example 3.18B, which stacks each of the chords in thirds, with the root as the lowest pitch). Finally, all but the first and last chords contain the dissonant interval of a seventh (again, see Example 3.18B). Because the chord spans the interval of a seventh, we call it a seventh chord. Because a seventh is a dissonant interval, all seventh chords are dissonant—though to varying degrees, as we shall see.

EXAMPLE 3.18 A Progression with Seventh Chords A. 1

2

3

4

5

6

B. 1

2

3

4

5

6

Definitions and Types We label seventh chords by their two most audible features: the type of triad (major, minor, diminished) and the type of seventh above the root (major, minor, diminished). Composers use five important types of seventh chords, though, like the triad types, they are not used with equal frequency. Seventh chords are named according to the quality of the triad and the size of the seventh: 1. major-major seventh chord (MM 7th), called a major seventh chord 2. major-minor seventh chord (Mm 7th), called a major-minor seventh chord 3. minor-minor seventh chord (mm 7th), called a minor seventh chord

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4. diminished-minor seventh chord (dm 7th), called a half-diminished seventh chord 5. diminished-diminished seventh chord (dd 7th), sometimes called a fully diminished seventh chord but most often simply called a diminished seventh chord Example 3.19 shows an example of each type of seventh chord built on the root C.

EXAMPLE 3.19 Five Types of Seventh Chord STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

major 7th (MM 7th) M

major-minor 7th (Mm 7th)

M

M

m

minor 7th (mm 7th) m

half-diminished 7th (dm 7th) m

d

m

diminished 7th (dd 7th) d

d

Musical Characteristics of Seventh Chords • The major-minor seventh chord (Mm 7th) is the most common seventh chord used in tonal music. It can be found regularly in music written from the early seventeenth century, and it is commonplace in popular music to this day, particularly the blues. The Mm 7 is often called the dominant seventh chord because it so regularly appears on the dominant scale degree (5). For example, in the key of C major, V7 is G–B–D–F. • The major seventh chord (MM 7th), with its major seventh, is more strident than the major-minor seventh chord. It appears occasionally in common-practice music but more regularly in twentieth-century popular music and jazz. • The minor seventh chord (mm 7th), on the other hand, is a very soft-sounding chord, because its minor seventh creates a less dissonant sound than that of the major seventh. • The half-diminished seventh chord (dm 7th, or ø7) is a mix of effects. The dissonant triad is balanced with a less dissonant minor seventh. The chord occurs in both common-practice music—especially in Romantic vocal music, where it is often associated with anguish—and twentieth-century popular music. • The diminished seventh (fully diminished) chord (dd 7th, or º7) is the most dissonant of these seventh chords. It is found in late-Baroque works and throughout the Classical and Romantic eras. In addition, the diminished seventh chord is an asset to silent movie scores, where it often signals trouble, such as the train quickly approaching the maiden tied to the tracks. It is the only seventh chord that contains all the same types of thirds and fifths: three minor thirds and two diminished fifths.

Inverted Seventh Chords Seventh chords often appear in inversion. Example 3.20 shows the three inversions of a major-minor (Mm) seventh chord with the root F. For each inversion, both the full and the abbreviated figures are given.

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Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

EXAMPLE 3.20 Seventh Chord in Root Position and Inversion A.

B.

C.

D.

Root position (Root in bass)

First inversion (3rd in bass)

Second inversion (5th in bass)

Third inversion (7th in bass)

R

R

R

R full version

7 5 3

6 5 3

6 4 3

6 4 2

abbreviated version

7

6 5

4 3

4 2 or simply 2

Analytical Tips Determining the root of an inverted seventh chord is not difficult if you look first for the seventh—the defining interval of the chord—or its inversion, the second. The root of the chord will be the lower note of the seventh or the upper note of the second. For example, in Example 3.20A, the lower note of the seventh F–E is the root. In Example 3.20C, the upper note of the major second (E–F) is the root. As the chords move from root position up through the inversions, their numbers steadily decrease: 7–6–5–4–3–2 (7 ⫽ root position; 65 ⫽ first inversion; 43 ⫽ second inversion; 2 ⫽ third inversion). Composers writing root-position seventh chords may omit the chord’s fifth and double the stable root for reasons such as ease of singing (this occurred in Example 3.18A). When composers write inverted seventh chords, however, they almost always use complete harmonies, with no doubled pitches. Example 3.21 shows various notated seventh chords with their figured bass notation. Play and study each chord. Try playing three of the four voices and singing the fourth voice.

EXAMPLE 3.21 Seventh Chords in Root Position and Inversions A.

B.

C.

D.

E.

F.

G.

H.

I.

mm 7

Mm 7

dm 7

Mm 4 2

6 Mm 4 3

Mm 6 5

dd 7

MM 6 5

6 mm 4 3

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Seventh Chords and Harmonic Analysis All five principal types of seventh chord arise in the major and minor scales, and, just as with triads, particular seventh-chord types are associated with particular scale degrees. As you listen to progressions within the context of a key, you should be able to identify instantly the quality of each chord and the scale degree from which each is built. When analyzing seventh chords using roman numerals, follow a procedure similar to that used for analyzing triads: • Mm and MM seventh chords require uppercase roman numerals. • mm, dm, and dd seventh chords require lowercase roman numerals. • dd seventh chords also require a degree sign (º) to indicate a diminished triad and seventh. • dm seventh chords require a slash through the degree sign (ø) to indicate that the sonority is half diminished. Example 3.22 shows the most common types of seventh chords that occur in major and minor keys. Example 3.23 demonstrates the harmonic analysis of seventh chords in root position and inversion.

EXAMPLE 3.22

Seventh Chords in Major and Minor Keys

major keys; scale degree:

1

2

3

4

5

6

7

type of seventh chord:

MM

mm

mm

MM

Mm

mm

dm

roman numeral:

I7

ii 7

iii 7

IV 7

V7

vi 7

minor keys; scale degree:

type of seventh chord: roman numeral:

7

vii ∅ 7

1

2

3

4

5

6

7

mm

dm

MM

mm

Mm

MM

Mm

dd

i7

ii ∅ 7

III 7

iv 7

V7

VI 7

VII 7

vii 7

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Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

EXAMPLE 3.23 WORKBOOK 1 Assignments 3.6–3.8

G:

I

V7

V 65

I

I

V43

I6

V42

I6

EX ERCISE INTER LUDE A NA LYSIS STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1.

3.5

Aural and Visual Analysis of Root-Position Seventh Chords A. Identify the root and the type of root-position seventh chord, choosing among Mm (major-minor), MM (major), mm (minor), dm (ø7), and dd (º7). Identify the chord member in the soprano (1, 3, 5, or 7). Circle the chordal seventh in each example. 2.

B.

1.

3.

4.

5.

6.

7.

8.

Listen to and study the following series of root-position seventh chords that are written in open position. Identify the type of seventh chord from among the choices listed in part A. Circle each chordal seventh.

2.

3.

4.

5.

6.

7.

8.

W R ITING 3.6 Writing Seventh Chords Complete the following tasks on a separate sheet of manuscript paper. Write evennumbered exercises in treble clef, odd-numbered exercises in bass clef. A. 1. Notate root-position Mm seventh chords with the following roots: A, D, E

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2. 3. 4. 5. B.

Notate root-position mm seventh chords with the following roots: G, B, D Notate root-position dd (º7) seventh chords with the following roots: C, F, A Notate root-position MM seventh chords with the following roots: B, E, B Notate root-position dm (ø7) seventh chords with the following roots: G, F, A, G

1. F is the third of which Mm seventh chord? the fifth of which Mm seventh chord? the seventh of which Mm seventh chord? 2. D is the third of which dd seventh chord? the fifth of which mm seventh chord? the seventh of which MM seventh chord? 3. B is the third of which mm seventh chord? the fifth of which Mm seventh chord? the seventh of which MM seventh chord?

3.7 More Seventh-Chord Writing On a separate sheet of manuscript paper, construct seventh chords according to the following instructions. For example, given D as the third of a major-minor seventh chord, you would write B–D–F–A. Another example: Given D as the fifth of a half-diminished seventh chord, you would write G –B–D–F. A. Spell seventh chords in which E functions as the: 1. root of a dd seventh 2. fifth of a mm seventh 3. seventh of a Mm seventh 4. third of a MM seventh B. Spell seventh chords in which A functions as the: 1. seventh of a mm seventh 2. third of a dd seventh 3. fifth of a Mm seventh 4. seventh of a MM seventh 5. fifth of a dm seventh C. Spell seventh chords in which F functions as the: 1. fifth of a Mm seventh 2. third of a MM seventh 3. seventh of a MM seventh 4. third of a dm seventh 3.8 Inversions of Seventh Chords On a separate sheet of manuscript paper, construct the required seventh chords. For example, given the bass note D and the instruction to spell a Mm 65, you will write D–F–A–B. You know this because the third of the chord is in the bass in first-inversion chords; and since a major third occurs between the bass and the root of a Mm 65 chord, then B is the root. A. With a given bass note of C, spell the following chords: 1. a MM seventh chord 2. a mm 65 chord 3. a dd seventh chord 4. a Mm 42 chord B. With a given bass note of F, spell the following chords: 1. a Mm 65 chord 2. a MM seventh chord

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Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

3. a mm 43 chord 4. a dm 42 chord C. With a given bass note of E , spell the following chords: 1. a dd seventh (º7) chord 2. a Mm 43 chord 3. a mm 42 chord 4. a MM 65 chord

A NA LYSIS

SOLVED/APP 5

3.9 Identify root, type, and inversion of each of the following seventh chords. Circle each chordal seventh. A.

B.

C.

D.

E.

G.

H.

I.

J.

root type inversion

F.

root type inversion

3.10 Distinction Between Scale Degrees, Figured Bass, and Chordal Members In each of the examples, determine the following: 1. full figured bass 2. type of seventh chord 3. member of chord that is circled 4. member of chord in the bass 5. scale degree in the bass A.

SOLVED/APP 5

full figured bass

F:

7 5 3

type of 7th chord

MM

member of chord that is circled

3

member of chord in the bass

1

scale degree in the bass

4

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THE COMPLETE MUSICIAN

M U S IC A L T E X T U R E So far we have explored triads and seventh chords in their most simple form: as simultaneously sounding vertical sonorities. Vertical alignment is but one of many ways that composers distribute the members of a chord. Texture refers to many elements of music, including register and timbre of instrumental combinations. But in particular, texture refers to music’s density (e.g., the number of voices and their spacing). Tonal music has many types of texture, but we can group them into three basic categories, each of which is distinguished by the way the melody is projected. The following excerpts from the literature illustrate the three basic textures: monophonic, polyphonic, and homophonic. Monophonic texture is defined as a single-line melody with no accompaniment. Both a cantus firmus and a tune you whistle are monophonic textures. Schubert’s last symphony begins monophonically with horns that play the primary melody of the first movement (Example 3.24). Note that a texture can be monophonic even though it might be played (e.g., in octaves) by more than one instrument.

EXAMPLE 3.24 Schubert, Symphony no. 9 in C major, Andante STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

2 Corni in C

Polyphonic, or contrapuntal, texture is the combination of two or more melodies so there is no clear distinction between melody and accompaniment. Example 3.25, taken from one of Bach’s fugues, illustrates this second texture type. Although polyphonic texture features greater independence of voices, even such transparent textures as the two-voice counterpoint we studied in Chapter 2 are considered polyphonic because two independent melodies were combined.

EXAMPLE 3.25 Bach, Fugue in G minor, Well-Tempered Clavier, Book 1, BWV 861 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

131

EXAMPLE 3.25 (continued) 4

Homophonic texture is a cross between monophonic and polyphonic textures, given that there is usually a clear melody accompanied by additional voices. The accompaniments can be highly varied; this richness of possibilities is why homophonic texture is the most widespread of the three texture types in common-practice music. The vertical, blockchord chorale texture we have been studying is one of the simplest types of homophonic textures, given that the accompanying voices are rhythmically aligned with the primary voice, which usually appears in the highest register (Example 3.26A). In most homophonic textures, however, single harmonies are spread out over time, with their chordal members distributed over one or more beats, measures, or even multiple measures, as shown in Example 3.26B, where the pulsing F-major triad holds forth for three measures.

EXAMPLE 3.26 A.

Hassler, “O Haupt voll Blut und Wunden” (Harmonization by J. S. Bach)

Soprano What Who

e’er may friend less

vex will

or not

grieve leave

thee, thee,

What Who

e’er may friend less

vex will

or not

grieve leave

thee, thee,

What Who

e’er may friend less

vex will

or not

grieve leave

thee, thee,

What Who

e’er may friend less

vex will

or not

grieve leave

thee, thee,

Alto

Tenor 8

Bass

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

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THE COMPLETE MUSICIAN

EXAMPLE 3.26 (continued) B.

Mozart, Piano Concerto in C major, K. 467, ii, Andante Con Sordino

Violino I. Con Sordino

Violino II. 3

3

3

3

6

6

6

6

6

6

6

6

Con Sordino

Viola 3

3

3

3

Violoncello e Basso. F

C.

Mozart, Piano Sonata in C major, K. 545, Allegro Allegro

G Mm 4 3

C

D.

C

C

Schubert, Impromptu in G major, op. 90, no. 3, D. 899 Andante

6

E.

F6 4

6

Chopin, Etude in A major, op. 25, no. 1

G Mm 6 5

C

Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

133

Analytical Method The harmonies in Example 3.26C unfold at a leisurely pace, given that there are only seven chords in four measures. Depending on the composer, style period, and type of piece, chords may change slowly or quickly. The rate of harmonic change is called harmonic rhythm. The preceding clunky analysis is improved by a more concise and informative roman numeral analysis. (Note values that correspond to the duration of each harmony reveal the harmonic rhythm.) mm:

1 I (

2 V43 I  

3 IV64 I  

4 V65 I  )

Mozart is able to write such a slow harmonic rhythm because of the rhythmic interest created by the accompanimental figures, which—along with the tune—contain each of the chord members. The broken-chord accompanimental pattern in Example 3.26C, called an Alberti bass, is common in the Classical style. The Alberti bass and other such accompanimental patterns are effective because our ears collect the individual pitches of the broken-chord figure into a single harmony. Examples 3.26D and E illustrate some of the variety possible in homophonic textures that involve accompanying a single melody. The Schubert Impromptu opens with a harmonic rhythm of one chord per measure, while Chopin’s is even slower: a single A-major triad extends for both of the excerpt’s measures. The larger noteheads differentiate the principal melody from accompanimental voices and registral and metric accents together articulate the bass voice.

Distribution of Chord Tones and Implied Harmonies Very often the members of a chord in a homophonic texture are distributed between various registers (and therefore clefs) and different instruments. In such cases, we need to examine each part in order to get a complete harmonic picture. Often, however, you will be able to determine the harmony even if you see only one or two chordal members, because the harmonic implications are clear from the musical context. Beethoven’s Piano Trio provides a simple illustration (Example 3.27). The piano—which moves in a basic 2:1 (second-species) motion—contains most, but not all, of the chord tones for each harmony. The first sonority is the perfect fifth E/B. However, we have strong suspicions that it implies a root-position E-major triad (rather than, say, a C mm seventh chord in 65 position) given that the key is E major and the piece is just starting. Our suspicions are corroborated by a glance at the violin part, which presents the missing third (G). Similarly, the incomplete V7 harmony in the piano in m. 1 (B–D–A) is completed by the violin’s F, which provides the fifth of the chord. Further, since the violin carries the melody, and melodies move primarily by step, Beethoven must consider voicing, doubling, register, and instrumentation in order to distribute most effectively this opening tonic triad in this homophonic texture.

Fluency Harmonic analysis of homophonic textures requires that you group members of a harmony quickly. In order to do so, you must be able to read pitches fluently in both bass and

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THE COMPLETE MUSICIAN

EXAMPLE 3.27 Beethoven, Piano Trio in C minor, op. 1, no. 3, ii, Andante cantabile STR EA MING AUDIO W W W.OUP.COM/US/LAITZ sempre

sempre

E :

I

ii 6

V7

I

treble clefs and attain a solid working knowledge of both alto and tenor clefs. The ability to scan music quickly and identify patterns and repetitions is a crucial skill. For example, the thirty-second notes and rests in Example 3.28 certainly look intimidating. However, with a quick scan of the excerpt we discover: (1) a straightforward broken-chord texture (rather than a complicated multivoiced contrapuntal texture), one in which we can easily identify underlying harmonies; (2) that some chords are repeated within a measure or even for an entire measure (e.g., in m. 26 a root-position F-minor triad controls the harmony); (3) if the literal position of the chord (i.e., inversion) is not maintained, there are relations by inversion, such as the D harmony in m. 28, which begins in first inversion, moves to second inversion, and in beat 3 lands on root position; and (4) revoicings of the same chord (such as in m. 25) show us that harmonic motion is not as fast as we might have initially thought.

EXAMPLE 3.28 Beethoven, Violin Sonata no. 3 in E  major, op. 12, no. 3, Adagio con molto espressione STR EA MING AUDIO W W W.OUP.COM/US/LAITZ 25

perdendosi

perdendosi

g Ø6 5

4 3

C

f

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Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

EXAMPLE 3.28 (continued)

A 42

D

6

6 4

5 3

An analysis of the chord types and inversions of the first four measures appears below the score.

Harmonic Reduction Often it is helpful to simplify dense homophonic and polyphonic textures by notating the underlying harmony in close position on a piece of manuscript paper. Such “reductions” capture harmonic motions and repeating patterns, and in time you will be able to negotiate these reductions in your head. This ability is invaluable not only in your theory and analysis but also in sight-reading and learning pieces. For example, the first section of Mozart’s “Catalogue Aria” from Don Giovanni contains a sixteenth-note passage, which can be rendered easily if reduced to its harmonic outline

EXAMPLE 3.29 Mozart, “Madamina,” Don Giovanni, act 1, no. 4 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

77

tà! rage,

A:

d’o All

gni a

for rouse

ma, his

d’o gal

gni e lant

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THE COMPLETE MUSICIAN

EXAMPLE 3.29 (continued)

tà! rage,

d’o All

gni for a rouse

ma, his

d’o gal

gni e lant

tà! rage!

cresc.

(Example 3.29). First, we scan the passage for patterns and repetitions and note that the left hand contains repeating chords (e.g., m. 77 contains two E-major triads) and that the right hand contains an ascending broken-chord figure that outlines the same chords as in the left hand. Further, the right-hand descent is identical to its ascent. Next, notate the bass notes (there is no need to notate the entire left-hand chord since it is easy to see its structure) and the right-hand chord, omitting pitch repetitions and, if possible, maintaining the highest pitch (the soprano), which is structural. The reduction in Example 3.30 shows this procedure and includes two kinds of analysis: the chord names (with uppercase letters indicating major triads and seventh chords that contain major triads, and lowercase letters indicating minor triads and seventh chords that contain minor triads) and inversions, and roman numerals. The bracket indicates that the progression is grouped into two parts; the first ends on vi, and the repeated second progression closes on the tonic.

EXAMPLE 3.30 Reduction of Mozart

A:

E V

A I

f vi

b ii 65

E V

f vi

E V6

A I

f vi

b ii 65

E V7

A I

Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

137

EX ERCISE INTER LUDE WRITING WORKBOOK 1 Assignments 3.9–3.10

3.11 Close and Open Position Notate the triads and seventh chords that are represented by the roman numerals that follow. Write each chord twice, first in close position and then in an open position. Use complete chords and key signature. Be aware that in minor both V and V7 require a chromatic alteration in order to create a leading tone. Sample solution: G major: V7

c

G:

A. D major: vi D. f minor: iv7 G. E major: iii7

o

V7

B. c minor: V7 E. A  major: V7 H. e  minor: V7

C. B  major: ii7 F. b minor: iv7 I. f  minor: vii° 7

T ER MS A ND CONCEP TS • chord versus triad • chromatic alterations • close position and open position • consonant triad • dissonant triad • doubling • figured bass, figured bass realization • harmonic analysis • harmonic rhythm • inversion, triadic—root position, first inversion (63); second inversion (64) • keyboard style versus chorale style • quality • roman numerals • root position (53) • root, third, fifth • seventh chords (types, inversions, and analysis) • spacing, voicing (open position, close position)

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• texture • homophonic • polyphonic (contrapuntal) • monophonic • triad

CH A PTER R EV IEW 1. List the three qualities of triads that can be built using diatonic thirds (that is, major and minor thirds) and their single-letter abbreviations.

2. Define close position versus open position. Why are wider intervals often used between the lowest two notes of a chord?

3. Describe the difference between the root and the bass.

4. List the two components that make up figured bass.

5. List the full (not abbreviated) figured bass numbers that correspond to: 1. root position: 2. first inversion: 3. second inversion:

6. Complete the table below for the major scale: SCALE DEGREE OF ROOT TRIAD T Y PE ROM A N NUMER A L

1

2

3

4

5

6

7

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Chapter 3 Musical Density: Triads, Seventh Chords, and Texture

7. Compare and contrast keyboard and chorale style. Three slots are completed for you. K E Y B OA R D S T Y L E

C HOR A L E S T Y L E

OPEN OR CLOSED POSITION FOR UPPER THR EE VOICES (SOPR A NO, A LTO, TENOR)

open position

SA above, TB below

DISTRIBUTION ON STAV ES RIGHT HA ND PL AYS

tenor and bass

LEFT HA ND PL AYS

8. List the five types of seventh chords. The first one is done for you: • major seventh (MM7) • • • •

9. List the full and abbreviated figured bass numbers for seventh chords. (Note that these numbers apply to all five qualities of seventh chords.) RO O T P O S I T ION FULL V ERSION ABBR EV IATED V ERSION

10. Define harmonic rhythm.

FIRST I N V E R S ION

S E C ON D I N V E R S ION

THIRD I N V E R S ION

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S U M M A R Y OF PA R T 1 You now possess the basic knowledge that is the foundation of tonal music. The terminology and concepts you have learned are the basis for exploring the rich and varied compositional techniques of the music written over nearly four centuries. Tonal music is a complex art form in which single pitches are combined in a carefully regulated fashion that is dictated by the way humans tend to perceive stimuli.

PA R T 2

MERGING MELODY A ND HA R MON Y

N

ow that we have completed our study of fundamentals, we can begin to apply this knowledge to the common-practice repertoire. This part begins to develop new analytical techniques that illuminate the hierarchical nature of music and that will help you develop a basis for making critically informed interpretations about musical structure. We will work with ever-larger musical units and will eventually compose in the common-practice style by combining small harmonic progressions, which are the building blocks of larger musical forms. We’ll discover firsthand how melody, counterpoint, and harmony are interdependent, to the point of being inseparable. And we’ll see that not all chords are created equal. Despite the large number of possible triads and seventh chords, composers of common-practice music tend to use some chords more than others. Indeed, the tonic and dominant triad or seventh chord are the most important harmonies. These two chords form the harmonic axis of practically every phrase of tonal music. However, very little music includes only root-position tonic and dominant chords, and in Part 2 we explore ways in which composers use these and other chords, in both root position and inversion, to create harmonic variety and thus to increase musical interest. Variety, however, does not come at the expense of musical coherence, and so we also learn how these new chords and inversions relate to the underlying tonal axis. What we’ll discover is that each of these larger functions can be embellished over time with other chords, which thereby “expand” or “prolong” the axial harmonies. Thus we shall proceed systematically, introducing how melody and harmony are dependent on one another, the role of rhythm and meter, and the resulting hierarchy.

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CH A PTER 4

When Harmony, Melody, and Rhythm Converge

OV E RV I E W

This chapter shows how to interpret larger stretches of music. We will explore the meaning of tonal hierarchy and musical events unfolding at different levels. We will see how musical works emerge from the process of embellishing melody. We will study how composers create melodic fluency by using recognizable patterns of tones. Finally, we’ll show how melodies suggest an underlying harmony. CHAPTER OUTLINE Tonal Hierarchy in Music ......................................................................................... 144 Embellishing Tones .................................................................................................... 146 Neighboring Tones, Chordal Leaps, and Arpeggiations .................................. 146 Analysis: Distinguishing Between Chord Tones and Embellishing Tones ... 147 The Importance of Context in Analysis ................................................................ 148 Analytical Interlude.................................................................................................... 151 Another Example of Long-Range Pitch Structure ............................................ 152 Reflections on “Clementine” and “God Save the King”.................................. 153 Melodic Fluency .......................................................................................................... 154 Cognition and Perception .................................................................................... 154 Analytical Application: Relying on Instincts and Human Perception ........... 155 The Arch and Nested Lines .................................................................................. 157 Melody as Harmony ................................................................................................... 159 Terms and Concepts ................................................................................................... 163 Chapter Review ........................................................................................................... 164 143

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T H I S C H A P T E R P ROV I D E S a bridge that leads from our study of fundamentals to

our exploration of harmony and form. Fundamentals included the terminology and concepts for the basic building blocks of tonal music (including notation, scales, rhythm, intervals, and melody). In our studies of two-voice counterpoint, triads, and seventh chords, we learned the importance of intervallic consonance and dissonance. In this chapter we begin to extend these concepts so that we will comprehend not only the note-to-note behavior of pitches, but also how certain pitches connect to others despite the fact that there are intervening pitches. These steps are crucial because they not only pave the way for subsequent chapters, but also inform our approach to the music we play and sing.

T O N A L H I E R A RC H Y I N M U S IC Musicians spend a great deal of their practice time weighing the relative importance of individual musical events and how these events interact with one another. Given that music unfolds in time and that we must fill that time with the most effective and dramatic rendering of a piece, we ask questions like “Is this cadence as important as the next one?” and “Which pitches in this melody carry more structural weight?” In addition to considering general issues such as musical accent (which was discussed in Chapter 1A), we are particularly attuned to whether a musical event participates in a motion toward or away from a climactic event. One of the most helpful criteria we use to determine musically important moments is whether an event is dissonant (unstable, initiates motion toward consonance) or consonant (dissipates the dissonance’s instability). Of course, the distinction between consonance and dissonance is not ironclad but depends on the immediate musical context. For example, the minor sixth C–A in Example 4.1A is consonant if either F or A appears below it (creating an F-minor triad or an A-major triad; Example 4.1B), but is unstable if C appears in the bass (the sixth yearns for resolution to the perfect fifth; Example 4.1C). With E in the bass, both pitches comprising the sixth require resolution down by step (Example 4.1D).

EXAMPLE 4.1 A.

B.

m6

F or A

Intervals in Context: Minor Sixth C.

STR EA MING AUDIO

D.

C

W W W.OUP.COM/US/LAITZ

E

Another example could be drawn from the perfect fourth—which we viewed as a dissonance in our counterpoint studies. Indeed, the F above C in Example 4.2A is dissonant; as an active pitch, the F strives toward resolution to a consonance by falling a step. However, when the bass voice does not participate in the formation of the perfect fourth, the interval

Chapter 4 When Harmony, Melody, and Rhythm Converge

145

becomes consonant, as seen in Example 4.2B, where the addition of either A or A below the fourth creates a first-inversion triad. And by adding another F below the C, the upper F becomes stable, since it is now consonant with the bass, as part of an implied F-major or -minor triad (Example 4.2C).

Intervals in Context: Perfect Fourth

EXAMPLE 4.2 A.

B.

P4

M3

C.

F/f

6 3

F/f

5 3

Dissonant intervals—with their harmonic and melodic instability—provide musical tension and energy. Only through resolution can this energy be discharged. Example 4.3 illustrates where perfect consonances (labeled PC ), imperfect consonances (labeled IC ), and dissonances (labeled D) occur within a descending major scale over a sustained bass note. The label P indicates which pitches are passing between, and therefore subordinate to, more important notes.

EXAMPLE 4.3 Consonances and Dissonances

PC

P

P

D

IC

P

PC

D

P

IC

D

PC

Of course, the interval of the octave is completely stable. The dissonant major seventh (B over C) meanwhile requires resolution. Depending on the direction of the line, 7 will either ascend to 8 or descend to 6 where, in the latter case, it forms a consonant sixth with the bass. Yet is the sixth really an arrival? Yes, but not a particularly strong one; as an imperfect consonance, it is less stable than the perfect fifth that results when 6 in turn passes to 5. We can see that the dependence between various intervals establishes a hierarchical relationship between consonance and dissonance. The strident sound of the dissonant

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THE COMPLETE MUSICIAN

seventh is only relatively resolved by the sixth, itself an imperfect consonance. It is the fifth, a perfect consonance, which provides stability. As we have already seen, the passing tone 4, forming a dissonant fourth with the bass, also has a strong need to resolve, and it does so to 3, which forms a major third with the bass. However, because this imperfect consonance is not completely stable, 3 descends via the dissonant passing tone 2 to 1, which forms an octave with the bass. Thus the notes that are consonant with the bass note C in Example 4.3 are C, E, G, and A. If we ranked these consonances, C and G would be the most stable, followed by E. A is the least stable consonance because it has a tendency to fall to G. Therefore, the major tonic triad is a stable entity that is surrounded by unstable forces, as we heard in Bach’s Violin Partita in E major in Chapter 1A.

E M B E L L I S H I N G T ON E S If we view this scale as a crude melody, we now see that the passing tones B, A, F, and D (7, 6, 4, and 2) appear between and therefore connect the stable pitches C, E, G, whose combination results in a triad. Since these passing tones are not members of the underlying C-major triad, which is implied by the sustained C in the bass, we call them nonchord tones. Thus passing tones tend to create tension that requires resolution by chord tones.

Neighboring Tones, Chordal Leaps, and Arpeggiations If we turn the C-major scale into a melody with a more interesting contour, as in Example 4.4, another type of nonchord tone is created: the neighbor tone (also called auxiliary tone, or simply neighbor). Neighbors that lie above a stable pitch are called upper neighbors (UN), whereas those that lie below are called lower neighbors (LN). Since it modifies a single pitch, a neighbor-tone figure is more static (i.e., less dynamic) than the more fluid passing tone, which moves to a new pitch that lies a third above or below the original pitch. Neighbor tones can be dissonant or consonant. An example of a dissonant neighbor occurs between mm. 1 and 2 of Example 4.4; F, which is a fourth above the bass, resolves down to E, a third. A consonant neighbor occurs on beats 2 and 3 of m. 2; A, which is a sixth above the bass, resolves down to G, a fifth. The sixth and the fifth are the only adjacent intervals that are consonant above a bass, and this unique, and therefore privileged,

EXAMPLE 4.4

Neighbor Tones and Arpeggiations double neighbor

arpeg

giatio

n

lower neighbor consonant upper neighbor consonant neighbor leap lower neighbor arpeggiation arpeggiation

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relationship has huge compositional ramifications that we first discovered in our studies of second-species counterpoint (Example 2.15), but which we will encounter regularly in our later studies. For now we will simply refer to it as the 5–6 technique. Dissonant neighbors form intervals of a second, fourth, or seventh above the bass. Finally, a double neighbor results from the combination of the upper neighbor and lower neighbor in m. 2. The melody in Example 4.4 also contains leaps that are consonant with the bass note, C. We refer to leaps that are members of the underlying harmony as consonant leaps or chordal leaps. [In our study of counterpoint in Chapter 2 we distinguished between leaps of thirds (called skips) and larger leaps; we will now refer to all nonstepwise motions interchangeably as either leaps or skips.] If all tones from the same harmony appear in succession, they form an arpeggiation (ARP). We already learned in our counterpoint studies that leaps are permitted only if they are consonant with the cantus. Similarly, triadic skips and leaps are possible as long as they are members of the underlying harmony. Because we have encountered both consonant embellishments (including the chordal leap and arpeggiation) and dissonant embellishments (the dissonant passing tone and neighbor tone), we will not use the term nonharmonic tone, given that the consonant embellishments are members of the underlying harmony and therefore are chord tones. Rather, we refer to all melodic embellishments generically as embellishing tones, and you may add the prefix consonant or dissonant depending on their function within the specific musical context.

Analysis: Distinguishing Between Chord Tones and Embellishing Tones There is very little tonal music written whose texture is characterized by a single sustained bass note and rambling melody above it, as shown in Example 4.4. In fact, as we learned in Chapter 3, much tonal music is homophonic, and, given the strong harmonic underpinning that is usually characteristic, it is not difficult to separate dissonant embellishing tones from consonant embellishing tones. Indeed, composers are careful to clarify the dissonant and consonant status of melodic pitches. For example, in Vivaldi’s Sonata in C minor for oboe (Example 4.5), the Allegro’s harmonic structure is made explicit by the underlying chordal accompaniment. Given that

EXAMPLE 4.5

Vivaldi, Sonata in C minor for Oboe and Basso Continuo, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Allegro

3

C

3

3

3

3

3

3

3

3

3

3

3

3

G

C

∅

d 65

G

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C-minor triads control mm. 1–2, we then know that the oboe’s second pitch, F4 (m. 1), is not a member of the chord. Since F descends from G and immediately returns to G, we understand it to be a dissonant neighbor note, just as we understand the D on beat 3 of m. 1 that fills the space of a third between two chordal members—E5 and C5—to be a dissonant passing tone. However, these same pitches (E5 and C5) in the oboe part of m. 3 have become dissonant passing tones, given that the underlying harmony has changed to the dominant (G–B–D–F) chord. Thus, if we identify underlying harmony (consonance), then we can distinguish between melodic tones that are members of chords and those that are embellishments (just as we did in our 2:1 contrapuntal studies, where, for example, passing tones connected two consonances).

T H E I M P OR TA N C E OF C O N T E X T I N A N A LY S I S We have learned that the tonic pitch and its accompanying triad are central to tonal music. But do composers always give priority to 1, 3, and 5? That is, can we always assume that the tonic triad primarily controls melody? And might we be able to study melody without having to consider the implied harmony or the supporting voices? Listen to an excerpt from one of Schubert’s songs (Example 4.6; for the complete score, see the Anthology no. 50).

EXAMPLE 4.6

Schubert, “Der Lindenbaum,” from Winterreise, D. 911 (melody only) STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

10

7

Am Brun By the

nen vor dem To fountain near the

3

re, gate,

da steht There stands

ein Lin a lin

den baum; den tree;

Because “Der Lindenbaum” (“The Linden Tree”) is in E major, we might assume that E, G, and B are the primary structural tones and that the remaining pitches will be embellishments of the tonic triad. To be sure, the vocal line opens with an arpeggiation of the tonic. The following F4 (m. 11) appears to be a dissonant passing tone that leads to G4, and A4 would then be viewed as an upper neighbor to the stable G4, as shown in Example 4.7. Now listen to the excerpt again, this time with the accompaniment (Example 4.8). The underlying chords in mm. 9 and 10 are, indeed, all tonic. Because the harmony changes in m. 11 to a dominant harmony (B–D–F), however, the E4 in the right-hand accompaniment is not a chord tone but merely delays D 4. Similarly, the F 4 that begins m. 11 in the vocal line is not a dissonant passing tone at all. Rather, it is a member of

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Chapter 4 When Harmony, Melody, and Rhythm Converge

EXAMPLE 4.7

Schubert, “Der Lindenbaum,” from Winterreise, D. 911 (melody only) P?

10

7

Am Brun

nen vor dem

To

N?

P? 3

re,

da

E

steht

E

ein Lin

den baum;

?

the B-major triad and thus is consonant. The following G4, which we originally said was related to the E-major triad, instead turns out to be a dissonant passing tone, since it is not a member of the underlying B-major harmony. Finally, the A4 that we labeled as an upper neighbor to G4 turns out also to be a chord tone; it is the seventh of the dominant harmony, B–D–F–A. Our initial analysis of “Der Lindenbaum” was incorrect. Because we did not consider the underlying harmonic support or the rhythm, we had no standard to measure a pitch’s function within a musical context. As a result, we confused a pitch’s consonant or dissonant status.

EXAMPLE 4.8 Schubert, “Der Lindenbaum” (with accompaniment) STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

7

Am Brun

E:

P

10

nen vor dem To

re,

da steht

B

E

B

V7

I

V

P 3

ein Lin

den baum;

E V7

I

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EX ERCISE INTER LUDE A NA LYSIS 4.1 Harmonic and Melodic Analysis (I) Given are short excerpts of various homophonic textures. Complete the following tasks:

WORKBOOK 1 Assignments 4.1–4.2

1. Circle each harmony, and label the root, the type of harmony (for triads: Maj, min, dim; for seventh chords: MM, Mm, mm, dm, dd), and the inversion, if any (for triads: 6 6 6 4 4 3, 4; for seventh chords 5, 3, 2).

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

SOLVED/APP 5

A.

2. Label each embellishing tone in the melody; use the following abbreviations: passing tone: P; neighbor tone: N; chordal leap: CL; arpeggiation: ARP.

Vivaldi, Sonata in C minor for oboe

6

3

3

3

3

3

3

3

3

3

3

3

3

10

3

3

3

3

3

3

3

3

3

B. Corelli, Sonata no. 11 in F for two flutes, after Violin Sonata in E major, op. 5, Allegro

5

3

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A N A LY T IC AL I N T E R L U DE Let’s develop our understanding of the hierarchy of melodic tones by exploring how they are used in two familiar melodies. Sing the opening of the well-known ballad “Clementine” (Example 4.9). The piece is in F major, and the first phrase begins on 1. The controlling harmonies for each measure are represented by bass pitch and roman numeral. The lengthy pause on G4 in m. 4, which provides a natural place to breathe, divides the eight measures into two four-measure units that we will call phrases and that we will explore in depth in the following chapter. The first phrase consists mostly of disjunct motion. Through a series of consonant skips and leaps, the melody leisurely ascends to the C5 (5) on the downbeat of m. 3. The descending leaps at the beginning of the first two measures are subordinate to the larger arpeggiation of the tonic triad (F4–A4–C5) heard on the strong beats of mm. 1–3. After attaining the melodic high point, the melody quickly descends to the G4 (2) in m. 4, completing the melodic shape of an arch. The stepwise descent, with the B4 in m. 3 acting as a passing tone between C5 and A4, stops short of returning to the tonic F4, thus giving rise to a phrase ending that is somewhat unsettled because it ends on 2. The second phrase begins as the G4 on the third beat of m. 4 ascends by step to B4 via the passing tone A4. Another passing A4 traces the descent from B4 to G4 in m. 5. The consonant skips of the first phrase return in mm. 6–7: first A4 falls to F4, then G4 falls to C4, C4 skips up to E4, and finally E4 skips up to G4. As in the opening phrase, the emphasized downbeats in mm. 5–8 reveal a melodic pattern—this time a stepwise descent from B4 (m. 5) to F4 (m. 8). The F4 at the end of the second phrase “resolves” the G4 “left hanging” at the end of the first phrase. These larger motions are revealed in the structural analysis in Example 4.10.

EXAMPLE 4.9

“Clementine” STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

P

1. In 2. Light

a cav she was

F:

ern, and

mine nine,

V

a a

can fair

yon, y,

Ex And

ca her

vat shoes

ing for were num

I P

4

in like

P

dwelt a mi Her ring box

V7

ner, es

for with

ty ni out top

I

ner ses

and san

his daugh dals were

V

ter for

Cle Cle

men tine. men tine.

I

a ber

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Structural Analysis of “Clementine”

EXAMPLE 4.10 2

4

6

G left hanging

G resolves to F

phrase 1

phrase 2

The notation in Example 4.10 reflects the relative importance of pitches. The most important notes have stems and beams, and the less important notes consist only of noteheads. The slurs either connect less important notes to more important notes (as in a neighbor) or connect one member of a chord to another member.

Another Example of Long-Range Pitch Structure Having analyzed the long-range pitch structure of “Clementine,” it may be illustrative to compare it to “God Save the King” (Example 4.11). This piece is also in the key of F major and has two phrases (once again, harmonic changes are represented in the bass); the first phrase contains six measures, the second phrase contains eight. For the most part, the melody moves in stepwise motion, using passing and neighbor tones. However, the G4 in m. 1 is neither a passing tone nor a typical neighbor. Since G4

EXAMPLE 4.11 “God Save the King” IN

1. God 2. O 3. Thy

save Lord choic

our and est

P

gra God gifts

N

cious King, a rise, in store

God And Long

save make may

the them he

King! fall. reign!

Send Con May

him found he

vic their de

to pol fend

our his be

live ter him

sequence

P

5

Long Scat On

no en pleased

ble King, e mies, to pour,

P

ri ous, i tics, our laws

Hap Frus And

py trate ev

and their er

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Chapter 4 When Harmony, Melody, and Rhythm Converge

(continued)

EXAMPLE 4.11 P

10

glo knav give

ri ous, ish tricks, us cause

Long On To

N

P

to Thee sing

reign our with

P

o hopes heart

ver us, we fix, and voice,

broader

God God God

P

save save save

the King! the King! the King!

neighbors F4 but does not return to F, it is called an incomplete neighbor. This particular type of incomplete neighbor—which is approached by step but is then leapt from in the opposite direction to a chord tone—is called an “escape tone” or “échappée.” The E4 in m. 2 leads through the passing tone F4 to G4. Since the G4 sets the end of the first line of text (“King”) (note the comma in the text) and leads to the A4 that is the focal pitch in mm. 3 and 4, we may consider G to be a slower-moving passing tone, which connects the F of m. 1 with the A of m. 3. B4 is an upper neighbor to the A4 in m. 3. There is a quick descent through G4, which again functions as a passing tone and leads back to F4. The phrase continues, and closure occurs in m. 6. Given that the more important stepwise descent from A4 to F4 occurs only in mm. 4–6, we can view the A4 that begins m. 4 as being extended by a subordinate stepwise descent to F4. In the same manner, we can view the G in m. 5 to be extended by a subordinate stepwise descent to E4. Thus, the same slowly unfolding passing motion that opens the song on F4–G4–A4 (mm. 1–3) is mirrored at the close of the first phrase with A4–G4–F4 (mm. 4–6). The second phrase begins on C5 (5) in m. 7. The passing tone B4 connects C5 to A4 in m. 8, and mm. 9 and 10 imitate mm. 7 and 8 by repeating the material down the interval of a second. This immediate restatement of a musical idea on different scale degrees is called sequence. The A4 returns to C5 in mm. 11 and 12, and the melody ends with a consonant skip from D5 to B4, followed by a stepwise line that descends from A4 through G4 to F4.

Reflections on “Clementine” and “God Save the King” Once again, let’s step back and collect our observations (refer to Example 4.12). The first phrase of the melody (mm. 1–6) begins on F (1), ascends to A (3, m. 3), and returns to 1. The second part of the song descends from C (5) to F (1). If we compare “Clementine” and “God Save the King,” we see that both tunes contain two phrases. More importantly, both first phrases arpeggiate the tonic triad, F4–A4–C5, and both second phrases bring the C5 back to its resting place on 1 through long stepwise descents. These two analyses function as a preview of the sort of contextual and interpretive analysis that will be developed in the text. Our analyses will always go deeper than simply labeling surface events, for it is these deeper relationships that actually control the surface events.

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EXAMPLE 4.12 Structural Analysis of “God Save the King” 3

5

7

11

13

P (n)

phrase 1

phrase 2

M E L ODIC F L U E N C Y We have seen that melodies share particular attributes. For example, melodies often rise from a stable initiating point (usually 1), ascend to a climax, and descend to a point of repose. Melodies move primarily by step, and any large leaps are balanced by stepwise changes of direction. One such melody is heard in Example 4.13, where a rapid ascent to 5 is followed by a long neighbor note on 6 that returns to 5. The following leisurely stepwise descent convincingly closes on 1.

EXAMPLE 4.13 Smetana, “Moldau,” from My Country, mm. 40–47 STR EA MING AUDIO 5

upper neighbor

W W W.OUP.COM/US/LAITZ

6

A given melody (e.g., a cantus firmus) or harmony provides a standard against which we can measure dissonance and consonance. Such a foundation allows us to embellish the given melody with both consonant and dissonant embellishing tones. Conversely, by pruning away, or reducing, these embellishing tones, we discover structural lines and these nonadjacent stepwise pitches provide the underlying skeleton of the piece. We also learned that analysis reveals similar underlying melodic trajectories in works with very different musical surfaces, such as “Clementine” and “God Save the King.” We invoked a single criterion to support our findings: that a pitch’s function depends entirely on the context in which it appears. That is, all scale degrees are not created equal, and subordinate scale degrees embellish more-important scale degrees.

Cognition and Perception Step motions, occurring below the embellished surface of a melody, are central to tonal music. Indeed, they are reflections of a larger human preoccupation to elaborate and dramatize forms of discourse and communication. For example, nothing particularly

Chapter 4 When Harmony, Melody, and Rhythm Converge

155

interesting is learned when someone is described as balding and middle-aged. However, when these generic attributes are augmented by the mention of prominent scars and tattoos, a curious gait, and that third thumb, the listener’s interest is certainly piqued. The same desire to embellish music is age old, as we can see from the highly decorated portions of thousand-year-old chant to classical theme and variations, to jazz and contemporary commercial music. Further, all humans possess the basic desire to make sense of the myriad stimuli presented to them in their day-to-day activities and, therefore, subconsciously to group these stimuli into meaningful shapes. In order to accomplish this, we must ignore superfluous and confusing stimuli, give priority to the most logical, clear, and useful bits of information, and fill in incomplete yet necessary pieces, all in order to create an entity that makes the most sense. The rise of Gestalt psychology in the 1920s and its flowering in the second half of the twentieth century is predicated on the specific ways humans make sense of a world of nonstop stimuli. Composers and performers instinctively invoke these rules, which include various types of balance, expectation, and realization (e.g., the buildup toward a climax and the subsequent release) and the thwarting of expectations, surprise, ambiguity, and so forth. We have already invoked several of these Gestalt principles in our discussion of musical accent in Chapter 1A, and we now encounter a few additional types in the following discussion of below-the-surface step motions. Melodic fluency refers to underlying scalar patterns that support the infinite variety of melodic embellishments that lie on the music’s surface. Most likely you intuitively sense these lines and use them to guide your interpretations of phrases; you might even choose to project them in performance. Indeed, composers guide our ears by aurally “marking” these underlying melodic lines in a variety of ways. Recall from Chapter 1B that we equated marking with “accent” and that there are many ways to accent a musical event, including duration, metric placement, dynamics, articulation, harmonic and contour changes, and so on. Powerful goal-oriented motions arise when accented musical events are coordinated with hierarchical pitch structures (such as the tonic triad).

Analytical Application: Relying on Instincts and Human Perception As you listen to Example 4.14, ask yourself whether or not the melody’s register and general contour are static, or whether there is an ascent or descent over the course of the excerpt. The melody begins on B and slowly descends during the phrase to close a fifth lower on E. That you heard this descent is noteworthy, given that many of the pitchto-pitch melodic gestures actually ascend (e.g., the piece opens with a leap up to E and ascending gestures occur in mm. 3, 5, and 7). By tracing the metrically and durationally accented pitches in this phrase, we understand why you heard the underlying descent (see Example 4.14B): B, which holds forth in mm. 1–2, falls first to A and then to G (m. 4). G, like the preceding B, is a member of the tonic triad that is sustained in m. 5. G then falls to F (which is extended in mm. 6–7) and on to E. Each of these pitches is accented in specific ways: B by duration and metric placement, and A by metric placement and the fact that as 4 it is inherently predisposed to function as a passing tone between the more stable 5 and 3. Further, A is counterpointed by the unstable leading tone, D, which creates a dissonant diminished fifth: D fulfills its responsibility to ascend to E as A in turn falls to G. The following G, F, and E are either metrically accented, durationally accented, or both.

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EXAMPLE 4.14 Melodic Fluency A.

STR EA MING AUDIO

Donizetti, Lucrezia Borgia, act 1, no. 3

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5

B.

Donizetti, Lucrezia Borgia, act 1, no. 3 (reduction) 5

Donizetti uses specific embellishments to elaborate the fifth descent. A chordal leap of a fourth in m. 1 (from B to E) is filled in as the fourth retraces itself by stepwise motion. We have learned that changing direction after a leap is an important means of creating melodic balance. The specific procedure of filling in a leap is called gap-fill, another Gestalt principle that is predicated on the listener’s expectation that a melodic leap will eventually be filled in by stepwise motion in the opposite direction. Notice that the change of harmony to V7 (B–D–F–A) in m. 2 renders the melodic D and B chord tones, with C a weak-beat passing dissonance. In fact, this falling passing motion characterizes mm. 4 and 6. We have, of course, encountered gap-fill in our previous counterpoint studies. But it is a crucial component of successful composition, as we can see in the Chopin excerpts in Example 4.15A–D, each of which begins with a leap that opens a musical space that is immediately filled in—and in contrary motion to the leap.

EXAMPLE 4.15 Gap-Fill in Chopin’s Nocturnes STR EA MING AUDIO

A. In F major, op. 15, no. 1

semplice e tranquillo 3

sempre legato

3

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3

Chapter 4 When Harmony, Melody, and Rhythm Converge

157

EXAMPLE 4.15 (continued) B. In F minor, op. 55, no. 1

C. In E minor, op. posth. 72, no. 1

D. In G minor, op. 15, no. 3

languido e rubato

The Arch and Nested Lines Composers, of course, also create rising structural lines. Placed in the first half of phrases, such lines produce a subtle tension that is balanced and discharged by the later cadential falling (see Example 4.16). The phrase divides into two two-measure units. The second unit is a transposition (up a step) of the first. Further, the rising and falling passing figures that pervade each measure reflect the gradual rise in the line from E to G: E is embellished by the ascending third, while F in m. 2 is embellished by the falling third (A–G–F). In the modified transposition in mm. 3–4, where the F from m. 2 is picked up in m. 3, the line closes on G. Notice that these measure-to-measure thirds reflect the larger ascending third, E–F–G, that spans the entire excerpt. Thus, a slow structural ascent from E to G in the first phrase (mm. 1–4) is embellished by various thirds (E–G, F–A, B–G), with a single neighbor motion (B–C–B) in m. 4 embellishing the high point of the phrase. The descending stepwise contour of the second phrase (mm. 5–9) nicely balances the ascending stepwise contour of the first phrase: The downbeat of m. 5 restates the first phrase’s highest pitch, C, from which the descent unfolds from C back to the passage’s opening pitch, E.

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EXAMPLE 4.16 Beethoven, Piano Trio in G major, op. 1, no. 2, Largo, con espressione STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Many phrases exhibit archlike contours, in which both ascending and descending subsurface lines occur. In Example 4.17A, each member of the stepwise ascending fourth line (from C to F) appears on the accented downbeat. The arrival on F is followed by an equally clear descent in the second half of the excerpt. Notice also that within the web of pitches in each measure (composed mainly of upper and lower neighbors) one hears miniature ascending thirds that mimic the larger passing motion in the line, a phenomenon called “nesting.” For example, Mozart embellishes the structural C that begins the movement with a rise of a third C–D–E in m. 1, the same pitches that occur over measures 1–3. Arches that ascend and then descend are not the only possible types; composers often employ a descent followed by ascent, as shown in Example 4.17B. Notice that Chopin parallels the melodic contour in the bass.

EXAMPLE 4.17 Phrases with Archlike Contours A.

Mozart, Symphony no. 41 in C major, “Jupiter,” K. 551, Andante cantabile

B. Chopin, Etude in A, op. posth.

3

3

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Chapter 4 When Harmony, Melody, and Rhythm Converge

M E L ODY A S H A R MON Y Finally, single-line melodies alone often present explicit or strongly implied harmonic underpinnings. Harmonic underpinning is not limited to multivoiced textures. In fact, even solo instrumental music consisting of but a single line often unfolds within a strong, albeit implied, underlying harmonic context that still allows us to distinguish consonant and dissonant embellishing tones. For example, Bach’s Presto in G minor (Example 4.18) opens with a cascading G-minor broken-chord figure that unfolds over five measures. In m. 6 a V7 (D–F–A–C) chord succeeds the tonic, but only for two measures before G minor returns in m. 8. The acceleration of harmonic rhythm continues, with chord changes at least once per measure: m. 9 contains a C mm7 chord, m. 10 a B MM7, and m. 11 an A dm7 chord, all of which lead to the V7 in m. 12 and back to tonic in m. 13. Notice that mm. 5, 7, and 12 contain pitches that are not members of the underlying harmony within that measure. For example, in m. 5, the C5 and A4 are not members of the G-minor triad but, rather, are passing tones; and in m. 7, B4 is a passing tone within the D7 chord (the parenthetical E5 and, in m. 12, the G5, are embellishing tones that we’ll discuss at a later point). In each case, these nonchord tones function identically to the dissonances encountered in our counterpoint studies.

EXAMPLE 4.18 Bach, Sonata for Solo Violin in G minor, Presto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Presto

P

P

g minor

6

P

D Mm7

g minor

c mm 7

B MM7

11

a dm7 7

D Mm7

g (minor)

As might be expected, such works also depend on the concept of melodic fluency (see Example 4.19). The first step in grappling with this excerpt is to determine the underlying harmonies. It is also helpful to find patterns in the speed of harmonic change (the harmonic rhythm), since composers will usually continue an established pattern, whether it be the texture, the mood, or the rate of harmonic change, yet another Gestalt principle, referred to as good continuation. This knowledge—combined with the fact that changes

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EXAMPLE 4.19 Bach, Sonata no. 2 for Solo Violin in A minor, BWV 1003, Allemande STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

44

47

in harmony usually coincide with metric accents—provides a powerful standard of measurement that guides analysis. Most likely you heard two harmonic changes in each measure. The incomplete first measure establishes the two-beat harmonic rhythm. Example 4.20 presents a harmonic verticalization of the chords, from which we can see the steadily rising chromatic line that begins on C (C–C–D–D–E) and eventually arrives on F (m. 48). Notice that given the pattern of rising half steps, we expect it to continue from the E5 in m. 47, even though E is sustained for one and a half measures. This expectation arises because E is a member of the E-major, A-minor, and A-major harmonies that control the second half of m. 46 and all of m. 47. That the pattern is not continued creates a dramatic moment, and listeners are rewarded for their patience: F arrives over the D-minor harmony. Note that we are able to hear the retention of the previous E and its ascent to F in spite of 25 intervening pitches, given that we expect the previously established pattern to continue. The attentive performer will most likely exploit such a moment in performance.

EXAMPLE 4.20 Harmonic Verticalization of the Chords in Bach’s Sonata no. 2 for Solo Violin 44

45

C

A Mm7

46

d

B Mm7

47

E

a 63

48

A63

d

Another method that composers use to delay ascending and descending lines is momentarily to change a line’s direction, which postpones and even thwarts what listeners assume will happen. The longer the postponement, the more dramatic its effect. This process, called expectation/fulfillment in Gestalt psychology, is central to the unfolding

Chapter 4 When Harmony, Melody, and Rhythm Converge

161

of a musical work. Listen to Example 4.21. The clear stepwise fifth descent from A to D accelerates, so four of the five pitches of the descent occur in mm. 3–4. The descent is postponed, however, by the upper-neighbor A–B–A that follows the initial descending arpeggiation in m. 1. Notice that the upper-neighbor B is consonant, given that it is supported by the tenth, G.

EXAMPLE 4.21 Corelli, Sonata no. 7, op. 5, Sarabande in D minor upper neighbor postpones descent

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Our final example (4.22) traces a third descent and provides a notational means to illustrate such descents. Haydn presents a two-measure tune that is sequentially repeated down a second in mm. 3–4. The D5 from m. 1 moves via passing tone E5 to F5 and via arpeggiation to B4 in m. 2, generating a B triad. Haydn balances the ascending motion in m. 1 with the descent in m. 2. This can be seen at X in Example 4.23. When the idea is repeated in m. 3, D5 is the passing tone that links C5 and E5. The stepwise-third descent that occurs over the four measures from D5 through C5 to B4 can be seen at Y in Example 4.23.

EXAMPLE 4.22

Haydn, String Quartet in B , op. 33, no. 4, Allegretto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

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EXAMPLE 4.23

Structural Analysis of Haydn, Allegretto Y

D

X

C

B

Analysis is not a casual, prescriptive endeavor. It must reflect what actually takes place in the music and what you, the analyst, bring to that music in terms of your own instincts. We must consider an entire musical texture, because harmony provides a foundation that allows us to understand what is stable and what is unstable in the melody.

EX ERCISE INTER LUDE A NA LYSIS STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

WORKBOOK 1 Assignments 4.3–4.4

4.2 Melodic Fluency, Harmony, and Embellishing Tones The florid soprano melody of each of the following examples depends on slower-moving stepwise lines that emerge when we listen to and study the examples. Complete the following tasks: 1. Listen to each example, and circle and stem each note of the structural stepwise line; then beam them together. 2. Identify harmonies using roman numerals for those bass notes with answer blanks beneath them. 3. Label the type of embellishing tone for each soprano pitch beneath an arrow.

A. Haydn, String Quartet in E  major, op. 50, no. 3, Allegro con brio Violino I

Violino II

Viola

Violoncello

Chapter 4 When Harmony, Melody, and Rhythm Converge

SOLVED/APP 5

B. Rameau, Rondino

C. Beethoven, Piano Concerto no. 1 in C major, op. 15, Allegro con brio (Strings)

6

T ER MS A ND CONCEP TS • arpeggiations • chordal leaps (consonant leaps) • embellishing tones • embellishment versus reduction • 5–6 technique • Gestalt concepts: expectation/fulfillment, gap-fill, good continuation • hierarchy • melodic fluency

163

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• neighbor tone (auxiliary tone or neighbor) • upper neighbor, lower neighbor • incomplete neighbor, complete neighbor • consonant neighbor, dissonant neighbor • nonchord tones • passing tones • phrase • resolution • transposition

CH A PTER R EV IEW 1. A pitch that does not belong to the given harmony is a ______________________________.

2. Embellishing tones that lie above a stable pitch are called ____________________________.

3. Embellishing tones that lie below a stable pitch are called ____________________________.

4. Arpeggios (Arp) and chordal leaps (CL) are always [consonant/dissonant].

5. Why it is essential to consider the underlying harmony when analyzing the last two bars of Schubert’s “Der Lindenbaum”?

6. The immediate restatement of a musical idea on different scale degrees is called a ________.

7. Define melodic fluency.

8. The procedure of filling in a leap using the law of recovery is called a ________________.

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9. The Gestalt principle of maintaining established patterns in harmony, melody, and rhythm is referred to as __________.

10. Two words that describe the momentary delay of an established pattern are _____________.

CH A PTER 5

Tonic and Dominant as Tonal Pillars and Introduction to Voice Leading

OV E RV I E W

In this chapter, we will learn that tonic and dominant are the backbone of music and that they are powerful enough by themselves to create entire phrases. We will then discuss how to connect these sonorities to one another, through use of the cadence and voice leading. CHAPTER OUTLINE Characteristics and Effects of V and I ................................................................... 167 Stability of the Tonic ............................................................................................ 168 Instability of the Dominant ................................................................................. 168 Tonic and Dominant Combined......................................................................... 169 Closure on the Dominant .................................................................................... 170 The Cadence ................................................................................................................. 171 Mozart’s Rondo...................................................................................................... 171 Introduction to Voice Leading ................................................................................ 174 Texture and Register ............................................................................................. 174 Notating Four-Voice Textures.......................................................................174 Vocal Registers................................................................................................176 Three Techniques to Create Voice Independence Within a Four-Voice Texture ........................................................................... 176 Technique 1: Smoothness...............................................................................177 (continued)

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Technique 2: Registral Independence ...........................................................177 Technique 3: Contrapuntal Independence...................................................178 Creating the Best Sound: Incomplete and Complete Chords, Doubling, and Spacing..................................................................................... 179 Omitted Chord Tones ...................................................................................179 Doubled Chord Tones ...................................................................................179 Spacing and Voicing ......................................................................................180

Summary of Voice-Leading Rules and Guidelines............................................. 182 Move the Voices as Little as Possible When Changing Chords ...................... 182 Maintain the Independence and Musical Territory for Each Voice ............... 182 Construct Chords Logically ................................................................................. 182 Tips for Avoiding Problems ................................................................................. 182 Terms and Concepts ................................................................................................... 183 Chapter Review ........................................................................................................... 184

TO N I C A N D D O M I N A N T C H O R D S provide the harmonic foundation of tonal music, and can define a key. When used in conjunction with other chords, these two pillars create a sense of arrival and departure. Compositions and the phrases they comprise generally begin with the tonic chord and progress through nontonic chords. Eventually the harmonies lead to the dominant and then on to the concluding tonic. The tonic stated at the opening of a phrase or piece need not progress to any particular chord, but the dominant inevitably leads back to the tonic.

C H A R AC T E R I S T IC S A N D E F F E C T S OF V A N D I In the V chord, melodic and harmonic functions work together to create a powerful expectation of the tonic’s return (see Example 5.1). The dominant’s tendency to resolve to tonic stems from the relationship between its chordal members and those of the tonic.

EXAMPLE 5.1

C:

7

8

2

3

5

1

V

I

The V Chord: Harmonic and Melodic Functions

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The V harmony contains active scale degrees, called tendency tones, that are less stable than those of the tonic triad. 7 and 2 are melodic tendency tones: 7 wants to ascend to 1, and 2 can move to either 1 or 3. Although 5 is stable as a member of the tonic harmony, it is unstable as the root of the dominant harmony and has a tendency to return to 1. Although the progression I–V–I is simple, it is the basis for much great and imaginative music and can create different psychological effects when used in isolation.

Stability of the Tonic

An E-major triad slowly emerges out of the sustained E at the beginning of Wagner’s Das Rheingold (Example 5.2). The chordal fifth is added in m. 5, and the chordal third does not enter until m. 18. This introduction (less than one-tenth of which is reproduced in Example 5.2) contains a single sonority: the tonic triad of E major. Note that the single stable sonority does not create the expectation that it needs to move on to another harmony, in spite of the growth of the triad through register and textural changes; forward motion is achieved instead by rhythmic means.

Instability of the Dominant Now listen to Example 5.3, the climactic passage from the last movement of Beethoven’s Eroica Symphony. Beginning with the arrival of the B-major triad in m. 328, dominant

EXAMPLE 5.2

Wagner, Das Rheingold, Prelude STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Ruhig heitere Bewegung

E :

8va basso

13

(sehr zart)

8va basso

23

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harmony unfolds over the remainder of the excerpt. Compared with Example 5.2, this passage sounds much less stable, because the dominant gives rise to a powerful expectation to resolve to tonic harmony, which occurs after the fermata. Further destabilizing the passage is the addition of the dissonant minor seventh (A), heard first in m. 330 but then incessantly from m. 336 to m. 348, which turns the dominant triad into a dominant seventh chord and creates an even more powerful impulse to resolve.

Tonic and Dominant Combined Lengthy passages of a single harmony have specific rhetorical meaning and are not the norm in tonal music. The following examples juxtapose the two harmonic forces of tonic

EXAMPLE 5.3 Beethoven, Symphony no. 3 in E  major, “Eroica,” op. 55, Finale STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

325

E :

V

331

337

342

8va

8

8va

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and dominant. The forceful opening of the last movement of Beethoven’s Fifth Symphony (Example 5.4) is created by the simple alternation of tonic and dominant harmonies. Here the tonic harmony supports the opening arpeggiation (1–3–5 in mm. 1–2) in the melody, after which I and V7 alternate as the melody descends through the scale back to 1 and tonic harmony (mm. 2–4) and I–V–I supports a scalar ascent to 3 (mm. 4–6). The changing harmonic rhythm is correlated with the rhythm of the melody and the use of V7 chords (as opposed to V triads) to create a sense of both breadth and vigor. That is, after the broad statement of the opening tonic, Beethoven changes chords every beat from the end of m. 2 to the beginning of m. 4 and uses the less stable V7 chord to propel the music forward. Beginning in m. 4, both melody and harmonic rhythm broaden again, and Beethoven’s choice of the dominant triad in m. 5 underscores the grand ascent to 3 over the tonic.

EXAMPLE 5.4

Beethoven, Symphony no. 5 in C minor, op. 67, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1

C:

3

5

I

4

3

2

1

2

1

2

3

V7

I

V7

I

V7

I

V

I

Closure on the Dominant Although the tonic is the ultimate goal of all tonal motions, small yet important arrivals often occur on the dominant; this heightens the musical drama and propels the music forward. Listen to the opening of Beethoven’s Sixth Symphony (Example 5.5). The fourmeasure phrase leads from the tonic to the dominant, creating the effect of a musical question that needs an answer.

EXAMPLE 5.5

Beethoven, Symphony no. 6 in F major, “Pastorale,” op. 68, Allegro ma non troppo STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

I

V

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Chapter 5 Tonic and Dominant as Tonal Pillars and Introduction to Voice Leading

T H E C A DE N C E A cadence is a point of arrival that occurs at the end of a phrase. We first encountered cadences in our exploration of two-voice counterpoint. The preceding examples show that a sense of closure occurs, regardless of whether or not an example ends on I or V. This is because the forward motion of the music often stops on these chords, given the changes in the rhythm and the completion of larger metrical patterns. Further, specific soprano scale degrees are coordinated with these harmonic arrivals so that the entire musical fabric of melody, harmony, counterpoint, rhythm, and meter participates in this phrase-defining moment.

Mozart’s Rondo Mozart’s Rondo contains examples of the two structural cadences used in tonal music (see Example 5.6). The Rondo can be divided into two parallel four-measure phrases. Harmonic as well as melodic motion is necessary to create a phrase. The first phrase closes on the dominant of C major (m. 4), and the second phrase closes on the tonic (m. 8). The melody begins on the downbeat 5, arpeggiates a tonic triad (G5–E5–C5), and arrives in m. 4 on the correspondingly accented 2. At this point, another shorter arpeggiation unfolds, this time on the dominant (D5–B4–G4). The opening idea on I returns in m. 5. When the tonic occurs in m. 8, the soprano strengthens the arrival by firmly stating 1. Notice how changes in the harmonic rhythm help articulate each phrase. In the first phrase, after three measures of tonic harmony, the dominant arrives in m. 4, supporting the arpeggiated D4– B3–G3 in the melody. Leading to the final cadence, the harmonic rhythm speeds up even more noticeably as the chords change every dotted half note beginning in m. 7.

EXAMPLE 5.6

Mozart, Rondo in C major STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

phrase 1 1

5

C:

5

3

1

2

I

7

V phrase 2

5

5

I

1 3

5

2

I

V

1

I

5

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Mozart’s example illustrates the two main types of cadences in tonal music. Authentic cadences, or full cadences (labeled AC), close V–I (dominant to tonic in root position). Half cadences (labeled HC) close on a root-position dominant. Authentic cadences are graded in strength based on the outer voices. In a perfect authentic cadence (labeled PAC) the soprano moves 2–1 or 7–8, while the bass moves 5–1 (see Examples 5.7A–B). An imperfect authentic cadence (labeled IAC) has the soprano close on 5 or 3 (see Examples 5.7C–D). Any bass motion other than 5–1 (such as 7–8 or 2–1) also creates a special type of IAC called a contrapuntal cadence. Contrapuntal cadences, so named because of their relation to the cadences we used in our contrapuntal studies, are harmonically weaker than the more common leaping bass motions of 5 to 1 (see Examples 5.7E–F). In contrast, no formal terms are in use to distinguish different types of half cadences, although the root-position dominant usually supports 2 in the soprano. Examples 5.7G–I show common HCs. In minor, two common chromatic alterations occur. First, the dominant will be a major triad, so 7 must be raised to create a leading tone (Example 5.7J). Second, the tonic harmony that closes a piece will sometimes contain a raised third to form a major triad (Example 5.7K). This idiom is called a Picardy third.

EXAMPLE 5.7 A.

Perfect and Imperfect Authentic Cadences; Half Cadences B.

C.

D.

E.

F.

2

1

7

8

5

5

2

3

2

1

7

8

5

1

5

1

5

1

5

1

7

8

2

1

PAC

PAC

G.

IAC

H.

IAC

I.

IAC IAC (contrapuntal cadences)

J.

K.

3

2

8

7

5

5

7

8

2

3

1

5

3

5

1

5

5

1

5

1

HC

HC

HC

PAC (in minor)

IAC (in minor with Picardy third)

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EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignment 5.1

5.1 The following excerpts employ only tonic and dominant triads in root position. Listen to each example; then locate and label the cadence that closes each excerpt. Provide roman numerals for the remaining chords, and label passing and neighbor tones in the soprano.

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

SOLVED/APP 5

B.

C.

Vivaldi, Violin Sonata in F major, Ryom 176 (Allegro)

75

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THE COMPLETE MUSICIAN

SOLVED/APP 5

D. Clara Schumann, “Les Ballet des Revenants,” from Quatre pièces caractéristique, op. 5 Although the melody occurs in the left hand, the harmony should be clear from the metrically accented notes and the chords in the right hand.

I N T RODUC T IO N T O VOIC E L E A DI N G Using only what we have examined thus far—the tonic and dominant—it is possible to write satisfying music with smooth and logical homophonic progressions. The remaining harmonies can be incorporated once they have been introduced later in this text. You will discover that when we strip away the surface of compositions written in various styles throughout the common-practice period, a small core of tonal principles occurs over and over. These principles are not limited to so-called “serious” or “art” music but extend to popular and commercial music heard today. The idea of an underlying harmonic foundation includes both the permissible chords (harmonic vocabulary) and the order in which chords appear (harmonic progression). The connection between chords must be smooth; therefore, you should focus on how members of one chord connect to members of the following chord. Voice leading refers to the way individual voices move. Voice-leading rules are derived from the principles that we learned in Chapter 2 concerning two-voice counterpoint.

Texture and Register Tonal music of the common-practice era was generally conceived in four voices, although not every piece of tonal music literally uses four voices at every possible moment. Rather, a four-voice framework underlies compositions that may have many more than four voices, such as works for large forces, including the symphony and the concerto, or those that have fewer than four voices, such as solos, duets, and trios in which the framework is implicit. The four-voice texture represents a happy medium because it nicely accommodates the triads and seventh chords, which make up tonal harmony.

Notating Four-Voice Textures To accommodate different vocal ranges, singing is divided into four voices that are ordered from highest to lowest: soprano, alto, tenor, and bass (SATB). Composers notate these four voices in one of three ways: In open score (or full score), each voice appears on its own staff, and clefs specific to each voice are used (Example 5.8A). A short score is notated on two staves, with the women’s voices (SA) in the treble and the men’s voices (TB) in the bass. The soprano and tenor pitches always have upward stems; the alto and bass always have downward stems (Example 5.8B1). Another type of short score is created by reducing an instrumental work (e.g., a symphony) to its “essence,” omitting pitch doublings and compacting the voices into a single register (approximately three octaves).

Chapter 5 Tonic and Dominant as Tonal Pillars and Introduction to Voice Leading

EXAMPLE 5.8 Four-Voice Frameworks A.

Bach, “O Welt, ich muss dich lassen” from St. Matthew Passion (open score: chorale style)

Soprano O

World,

I

now must

leave

thee,

O

World,

I

now must

leave

thee,

O

World,

I

now

leave

thee,

O

World,

I

leave

thee,

Alto

Tenor 8

must

Bass now

must

B1.

Bach, “O Welt, ich muss dich lassen” (short score: chorale style)

B2.

Beethoven, Symphony no. 9 in D minor, Adagio molto (short score)

C.

Keyboard Style

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An example of this type of short score appears in Example 5.8B2, in which Beethoven’s massive Ninth Symphony is reduced to a texture that is playable by a single pianist. We refer to open score and short score as chorale style. The third method of notation is keyboard style, which uses bass and treble staves but places soprano, alto, and tenor in the treble staff and the bass alone in the bass staff (Example 5.8C). The three upper voices should fit within an octave in order to be comfortably played by the right hand. In keyboard style, the soprano stems point upward, alto and tenor stems point downward; the bass voice follows general stem-direction rules of melody writing. In our writing you will rely almost exclusively on the two-stave short-score format.

Vocal Registers Voices, like most instruments, are limited to particular registers. A vocal range is the total span of pitches that a voice can sing; this covers roughly the interval of a twelfth. Composers utilize this “unrestricted range” when writing for solo voice (see Example 5.9). Of course, the entire range of one’s voice is not called for at all times; rather, composers set the majority of a vocal part in a more comfortable register, referred to as its tessitura. This “optimal range” is much better suited to accommodate four voice parts sounding simultaneously. Ambitus refers to the specific range of a melody (as opposed to the range of the instrument playing the melody). Example 5.9 shows both the range and the tessitura for each of the four vocal parts. When writing for four voices, you should observe the narrower tessitura spans. A helpful rule of thumb is to write for a voice’s midrange and restrict its tessitura to about a sixth or a seventh for the upper voices. Note that the bass’s register is usually approximately one octave below the alto, and the tenor’s register is usually one octave below the soprano. The leaps in a soprano melody should be fewer and smaller than those in a bass line. Tenor and alto lines contain even fewer skips than a soprano line. The larger range of the bass voice reflects its dual function as both melodic line and guiding force of the harmonic progression.

EXAMPLE 5.9 Vocal Ranges and Tessituras ranges Bass

Tenor

Alto

Soprano

tessituras

Three Techniques to Create Voice Independence Within a Four-Voice Texture Composers face a continual paradox between maintaining the melodic and independent nature of individual voices and making sure voices work well with each other. In this section, we’ll examine three techniques for reaching this goal. Example 5.10 presents two

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EXAMPLE 5.10 Voice Leading in Four-Part Texture STR EA MING AUDIO

A.

W W W.OUP.COM/US/LAITZ

B.

four-voice examples that use only tonic and dominant harmonies, yet they sound different. Listen carefully to each one. Which do you prefer? Why? What criteria are you using to support your opinions?

Technique 1: Smoothness The first example is unique because of its overall smoothness; the upper three voices in Example 5.10A move primarily by step and never leap more than a third. (The bass moves by leap because it is limited, for now, to the roots of the tonic and the dominant harmonies.) The tenor is remarkably static, because the tonic and dominant share 5 (the fifth of the tonic and the root of the dominant). However, given that our chief concern is for minimal movement of voices, this stasis is an asset. Always try to maintain common tones between chords by either tying or repeating them in a single voice. Example 5.10B reveals melodic lines that are angular and disjunct. Smooth melodic motion is a primary requirement when connecting chords.

Technique 2: Registral Independence Each voice must be independent and should be given a consistently comfortable tessitura. Independence is created in several ways, including maintaining a specific register for each voice, as shown in Example 5.10A. Note how the tenor elegantly controls the area just above and below C4. Now compare this with the tenor line of Example 5.10B, which not only contains unnecessary leaps of fifths and sixths but forces the voice into an exceptionally low register. Excessive leaping and registral shifting within a vocal line usually has very serious consequences, as illustrated in Example 5.10B. Problems start as early as the third beat of m. 1, where the alto intrudes into the soprano’s tessitura by hopping up a sixth to C5, and actually extends beyond the soprano’s previously established A4. Such intrusions are called voice overlaps; additional examples occur between the tenor and alto in m. 2 as well as between the bass and tenor in mm. 3 and 4.

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Voice crossing, another kind of registral intrusion, occurs on the first beat of m. 3. The alto appears below the tenor C4. Crossed voices occur again in the last chord of m. 4, where the tenor C4 is higher than the alto A3. Avoid overlapping and crossing voices.

Technique 3: Contrapuntal Independence The rules of counterpoint aim for contrary and oblique motion, when possible. However, parallel motion in thirds and sixths is perfectly acceptable, as seen in Example 5.10A, where the soprano and alto move primarily in parallel thirds. Notice that all the other intervals in Example 5.10A are approached by contrary or oblique motion. Further, in each case of similar motion, at least one voice moves smoothly by step. Example 5.10B presents the most serious of voice-leading errors: Pairs of voices move in parallel octaves in every measure, creating the effect of one or more voices dropping out of the texture. Further, the soprano and bass move in parallel fifths in m. 2. Parallel motion by perfect fifths and octaves is inherently weak; avoid parallel motion by perfect consonances (unisons, fifths, and octaves) between any pair of voices. You can avoid clumsy vocal lines that contain excessive leaping, intrusion of one voice into another’s musical space, and parallels by following a single rule: Move the voices the shortest possible distance when changing chords. The appearance of leaps of fifths, or even fourths, particularly when you see leaps in two voices simultaneously is an indication that there may be something wrong in your voice leading. Often you can just switch the pitches in the two voices to smooth out the individual lines and correct voice leading between the lines. Example 5.11 shows corrections for two instances of faulty voice leading. In A1, the awkward tenor forms parallel fifths with the bass; in A2, correct voice leading results by switching tenor and alto. In B1, we encounter parallel octaves between alto and bass, and the awkward alto and tenor diverge to create a very wide spacing; in B2, the problem is easily solved simply by maintaining the common tone G in the alto and resolving the tenor’s leading tone (7) up by step.

EXAMPLE 5.11 Correcting Errors in Voice Leading A.

parallel 5ths and skipping voice corrected by swapping tenor and alto voices

1

2

P5

B.

parallel 8ths and two leaps corrected by swapping tenor and alto voices

1

2

P8

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Creating the Best Sound: Incomplete and Complete Chords, Doubling, and Spacing Omitted Chord Tones In general, write complete chords. This is easy, since you have four voices in which to include the three members of a triad. If you must write an incomplete chord for the sake of smooth voice leading or the requirements of dissonance treatment, you may only omit the fifth; all chords must contain a root and a third. Example 5.10A contains an example of an incomplete chord on beat 4 of m. 3: Here, the fifth (E) is missing and the root (A) has been tripled in order to avoid a leaping alto (A–E–G). Because the alto remains on A4, stepwise voice leading is maintained in the upper voices. Example 5.12 shows the two versions.

EXAMPLE 5.12 Incomplete Versus Complete Chords A.

B. incomplete chord: can permit smooth voice leading

complete chord: can create angular voice leading

incomplete

complete

Instances of “illegal” incomplete chords abound in Example 5.10B. For example, there is no third in the first chord of m. 1, and the following chord has three thirds. How many more examples of chords with missing thirds can you identify?

Doubled Chord Tones Most of the time when we write for four voices, we must double one of the triad members. In general, double the root, since it is the most stable member of a chord. (Later, when we use new chords and inversions of chords, we will learn other doublings.) Again, however, if the voice leading is smoother, you may double the fifth and, as a last resort, the third. In Example 5.10A, the first chord in m. 4 contains a doubled fifth (B), which allows the tenor in the following chord to move a half step from C to B and then maintain the B in the next chord. If the root was doubled in the chord, the tenor would then skip from the preceding C up to E and then down a fourth to the B. Example 5.13 shows the two versions. Tendency tones are aurally marked and therefore usually require special treatment. Do not double them because (1) they are already aurally prominent and inherently unstable, and (2) correctly resolving both instances of them will necessarily result in parallel octaves.

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EXAMPLE 5.13 Doubling the Fifth A.

B. doubled fifth doubled root can permit smooth can create angular voice leading voice leading

doubled fifth

doubled root

EXAMPLE 5.14 Leading Tone May Descend When in Alto or Tenor

& ˙˙

# ˙˙

˙ ? ˙

7ˆ

{

i

ww 5ˆ

˙ ˙

ww

V

i

For example, 7 is the most important tendency tone for now. Harmonized by V, it has a strong tendency to resolve to 1 (harmonized by I). As a rule, never double the leading tone. There is one exception to resolve 7 to 1: when the leading tone occurs in the inner voices (tenor or alto) it may fall to 5 to create a complete tonic chord (Example 5.14).

Spacing and Voicing There is one more problem in Example 5.10B. The sound seems muddled in m. 3 as the tenor falls to C. This places the chordal third next to the root in a low register. To avoid this sound, keep adjacent upper voices (i.e., soprano, alto, and tenor) within one octave of one another. As we already know, we can pack the three upper voices within a single octave such that it is not possible to insert additional chord tones between any voice, a spacing referred to as close position. For a chord to be in close position, we consider only the upper three voices and not the bass, which must necessarily leap more than the upper voices, given that it is entrusted with defining the harmony. When the total spacing of the upper voices is an octave or more, we call this open position. It is a good idea to begin an exercise in close position; to accomplish this, keep the inner voices relatively high. Then, as you continue, it is perfectly acceptable to move the upper voices to open position, which results in a fuller, nicely contrasting sound. Try to return

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EXAMPLE 5.15 Benefits of Close Position

A.

no 3rd (illegal incomplete chord) no 5th diss. leap B. (legal incomplete chord)

P5

P4

P5

to close position, however, because in open position one can more easily write problematic parallels, which are more difficult to detect than when writing in close position. For example, parallel fifths are more easily avoided if you use close position, because potential parallel fifths will be rendered as harmless perfect fourths (see Example 5.15). It is common to repeat a harmony within a measure. When this happens, you may change a chord’s voicing by maintaining close (C) or open (O) position, as in Example 5.16A. You also may shift from open to close position, or vice versa, as in Example 5.16B.

EXAMPLE 5.16 Revoicing Repeated Harmony; Parallel Motion A.

B. C

C

O

O

O

C. C

P8

P5

parallels involve motion

not parallel (no motion)

Note that in Example 5.16B the tenor and soprano voices have exchanged the notes C and E in the revoicing that moves from open to close position; this exchange is marked by the diagonal lines that form an X. This swapping is called a voice exchange. In such cases, two or even all three of the upper voices may leap. Note that the sustained perfect fifth (C–G) in the bass and the alto voices is perfectly acceptable and isn’t considered a parallel. Parallels occur only when a pair of voices moves from one perfect interval to the same perfect interval on different pitches, as in Example 5.16C.

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S U M M A R Y OF VOIC E - L E A DI N G RU L E S A N D G U I DE L I N E S The following voice-leading rules and guidelines will remain in effect for our entire study of harmony. Voice-leading rules cannot be broken; guidelines are suggestions, based on style and aesthetics. Many of these rules were first introduced in the counterpoint studies in Chapter 2.

Move the Voices as Little as Possible When Changing Chords RULE 1 Resolve tendency tones (7, chordal dissonances, or chromatically altered tones) by step.

Exceptions: The leading tone, 7, does not need to resolve up to 1 when it is in an inner voice, or as part of the falling line 8–7–6–5.

Guideline 1 Retain common tones, and move upper voices mostly by step. Guideline 2 Avoid melodic leaps involving dissonant intervals.

Maintain the Independence and Musical Territory for Each Voice RULE 2 A pair of voices cannot move from one unison, octave, or perfect fifth to another interval

of the same size in parallel or contrary motion. RULE 3 Tendency tones cannot be doubled. They are aurally marked and often require special treatment. RULE 4 Keep adjacent upper voices (S-A and A-T) within an octave of each other.

Guideline 3 Avoid voice crossings and voice overlappings. A voice overlap occurs when a part leaps above (or below) a higher (or lower) part’s previous pitch, infringing on that part’s territory, so to speak. A voice crossing, on the other hand, occurs when a part is above (or below) a higher (or lower) part’s current pitch, swapping places with the adjacent part. voice overlap voice overlap

voice crossing

Guideline 4 Avoid direct octaves and fifths between the soprano and bass (unless the soprano moves by step, especially in perfect authentic cadences).

Construct Chords Logically Guideline 5 In general, write complete chords. If you must write an incomplete chord for the sake of smooth voice leading or the requirements of dissonance treatment, you may omit only the fifth; all chords must contain a root and a third. Guideline 6 In general, double the root of a chord. However, you may double the fifth (and, as a last resort, the third) if it makes the voice leading smoother.

Tips for Avoiding Problems Guideline 7 Write the outer voices first. Their counterpoint controls everything.

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Guideline 8 Move the upper voices in contrary motion (and, if possible, by step) to the bass. Guideline 9 Begin part-writing exercises with a complete chord in close position, and try to maintain close position as much as possible. Guideline 10 If any pair of upper voices leaps simultaneously by more than a third, try revoicing a chord to smooth things out.

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 5.2–5.5

SOLVED/APP 5

5.2 Review of Analysis and Voice Leading 1. Identify the key and label the harmonies with roman numerals. 2. Identify cadence types (PAC, IAC, or HC). 3. Label the soprano pitches using scale degree numbers. 4. For parallel motions between voice pairs, label the generic interval. Sample solution: 7

1

A.

B.

C.

D.

F.

G.

H.

I.

6

C: E.

V

I

T ER MS A N D CONCEP TS • ambitus • cadence • contrapuntal • imperfect authentic • perfect authentic • common tone

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• contrapuntal framework • doubling • half cadence • harmonic rhythm • hidden (or direct) intervals • parallel intervals • Picardy third • position • close • open • range • tendency tone • tessitura • voice • crossing • exchange • overlap

CH A PTER R EV IEW 1. Define cadence.

2. Complete the following table. Some sections are completed for you. E N DI NG H A R MON Y I N ROM A N NUMER A LS: PER FECT AUTHENTIC CADENCE (PAC)

V–I

IMPER FECT AUTHENTIC CADENCE (IAC)

V–I

CONTR APUNTA L CADENCE

V–I, with bass in an inversion

E N DI NG S OPR A NO I N S C A L E DE G R E E S :

E N DI NG B A S S I N S C A L E DE G R E E S :

5–1

[not specified]

3. Notation using a grand staff with the women’s voices (SA) on the treble clef and the men’s voices (TB) on the bass clef is called ________________________________________________.

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4. Notation with the upper three voices (SAT) on the treble clef and the bass voice (B) on the bass clef is called ___________________________________________________________________.

5. The particular range of a part that is most consistently exploited, as opposed to the total range or compass of such a part, is called the: a. tessitura

b. ambitus

6. The total range or compass of a part is called the: a. tessitura

b. ambitus

7. If you omit the fifth, which chord tone is usually best to double? ________________________

8. As a rule, never double which scale degree? ____________________________________________ Explain why, in a sentence or two.

9. In general, keep the upper three voices within the interval of a(n) _______________________.

10. Usually, it is best to begin an exercise in [close/open] position.

CH A PTER 6

The Impact of Melody, Rhythm, and Meter on Harmony; Introduction to V 7; and Harmonizing Folk-Type Melodies

OV E RV I E W

In this chapter, we will discuss how melody, counterpoint, and rhythm determine how we perceive harmony. We will examine how the upper voice can be embellished by adding harmony beneath it. We will then show how reduction reverses this process to highlight the underlying structural tones. We will introduce the concept of dissonant chords— particularly the V7 chord— and the role they play in harmonic structure. Finally we will show how to harmonize some folk-type melodies. CHAPTER OUTLINE The Interaction of Harmony, Melody, Meter, and Rhythm: Embellishment and Reduction ........................................................................... 187 Embellishment ....................................................................................................... 188 Distinguishing Between Structural and Embellishing Harmonies: Second-Level Analysis ...............................................................................190 Elaborating Structural and Embellishing Tones .........................................190 Reduction ............................................................................................................... 192 (continued)

186

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Levels of Embellishment ...................................................................................... 193 Application of Second-Level Analysis ...........................................................193 Final Interpretation ......................................................................................195 Interpretive Analysis ......................................................................................195 The Deepest Level ..........................................................................................195 Summary................................................................................................................. 196

The Dominant Seventh and Chordal Dissonance ............................................. 197 Derivation and New Melodic Possibilities......................................................... 198 New Harmonization Possibilities........................................................................ 200 Part Writing the Dominant Seventh Chord ...................................................... 201 V 7 and I Chords ..................................................................................................... 201 Incomplete V 7 ................................................................................................201 Incomplete I ...................................................................................................201 Both V 7 and I Are Complete ........................................................................201 Unequal Fifths.............................................................................................. 202 Analytical Interlude............................................................................................... 202 Harmonizing Folk-Type Melodies ......................................................................... 204 Step 1: Identify Cadences ..................................................................................... 204 Step 2: Identify Harmonic Rhythm.................................................................... 205 An Example from Classical Music ...................................................................... 206 Summary ....................................................................................................................... 207 Terms and Concepts ................................................................................................... 209 Chapter Review ........................................................................................................... 209

I N T H I S C H A P T E R W E explore three topics. The first revisits tonal hierarchy, this time through the lens of harmony. The chapter explores how the melodic, contrapuntal, rhythmic, and metric domains determine how we perceive harmonic flow and its impact on harmonic rhythm. The second topic, an introduction to chordal dissonance, details the ramifications of adding a seventh to the dominant triad. Finally, we learn to identify implied harmonies within a melody in order to create a fuller texture.

T H E I N T E R AC T ION OF H A R MON Y, M E L ODY, M E T E R , A N D R H Y T H M : E M B E L L I S H M E N T A N D R E DUC T IO N Tonal music—a composite of harmony, melody, rhythm, meter, dynamics, and register—is crafted through a series of checks and balances. The bass (or harmonic foundation) often contains large leaps that are a result of the alternation of root-position tonic and dominant harmonies. These leaps are, in a sense, compensated for and balanced by a soprano line that moves primarily by step. Meter and rhythm help to coordinate all this activity. Not

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only is harmony governed by the ebb and flow of weak (unaccented) and strong (accented) beats, but the counterpoint between bass and soprano is also dependent on meter and rhythm. Harmonic rhythm is intimately tied to and helps reinforce the meter. Sometimes you will need to make a choice between using one chord or another. For example, when deciding whether to harmonize 5 with tonic or dominant harmony, you must consider its metric placement, since a change to a new harmony creates an accent, and such harmonic accents usually align with metric accents. In general, it is advisable to change chords when moving from a weak to a strong beat (see Example 6.1A). Avoid a syncopated harmonic rhythm (Example 6.1B).

EXAMPLE 6.1 A.

Coordination of Harmonic Rhythm with Rhythm and Meter

1

2

3 4

i

1 2 3 4

V

i

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B.

(coordinated)

1 2 3 4

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(not coordinated)

1 2

3 4

1 ?

1 2 3 4

3 4

1 2

3 ?

1

i

V

i

i

2 ?

V

C. 1

2

(coordinated)

1

i

2

3

1

V

2

3

1

2

i

3

1 2 3

1

2

V

i

i

V

3

1 2 3

i

In è you will often encounter a harmonic change on beat 3, creating the familiar accentual pattern of long–short, which helps to underscore the triple meter (Example 6.1C1). One exception to avoiding a syncopated harmonic rhythm occurs in è at a cadence, when the dominant enters on beat 2 and is sustained through beat 3 (Example 6.1C2). The outer-voice (soprano and bass) framework is another aspect of pitch organization that is dependent on meter and rhythm. This contrapuntal relationship is quite important: For every change of harmony (bass note), there is a single, primary soprano note, just as we learned in our study of first-species counterpoint. We now place the outer-voice framework in a rhythmical-metrical context, one that is fleshed out with complete chords and textural embellishments. Such embellishments are much like the leaves on a tree, which can decorate but not obscure the structural branches on which their existence depends.

Embellishment To embellish a basic outer-voice structure, begin with a single implied harmony, the tonic, which supports 1 (Example 6.2A). We can elaborate this soprano pitch with embellishing tones to create a melody of sorts; one dissonant neighbor and two passing tones

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appear in Example 6.2B. The hierarchy is clear, since not only are the embellishing tones dissonant, but they also fall on unaccented beats or parts of beats. We can also stabilize these embellishing tones by harmonizing them with chords that render them consonant. Since the neighbor (B) and passing tones (D) are members of the dominant harmony, simply place the root of the dominant, G, in the bass (Example 6.2C). While it’s true that each soprano pitch is now consonantly harmonized, you can still distinguish aurally between the more important melody notes that are members of the tonic triad (the soprano C and E) and the subordinate embellishing tones (the neighbor [B] and passing tones [D]). Both the contour of the soprano line and the weak metric and rhythmic placement of the dominant harmony strongly prioritize the tonic. Indeed, these less important melodic and harmonic events let you hear the underlying tonic harmony: the neighbor B extends the flanking C, and the passing Ds provide a bridge that connects

Stages of Embellishment

EXAMPLE 6.2 A.

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I

C.

D. LN

I

V

P

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P

V

I

V

LN

I

I

V

P

I

I

V

I

V

I

V

I

PAC

E.

LN

I

V

P

I

V

I

V

I

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EXAMPLE 6.2

(continued)

F.

LN

V

c: i

i

PT

V

i

V

i

the C and the E. The D5 in m. 1 is perhaps less important than the D5 in m. 2 because the second D5 is a member of the perfect authentic cadence.

Distinguishing Between Structural and Embellishing Harmonies: Second-Level Analysis To illustrate this hierarchy in harmonic analysis, we label every chord and then consider their function within the context by adding a second-level analysis (with roman numerals) that reveals our interpretation of the underlying harmonic progression. (See Example 6.2D.) The first five chords embellish tonic, and the last two chords are part of a PAC. Notice the absence of the P (passing) over the final soprano D, which indicates that this pitch and the accompanying harmony are interpreted as very important, since the V chord is part of the structural authentic cadence and the soprano D is not just another harmonized embellishing tone.

Elaborating Structural and Embellishing Tones You can repeat the procedure of adding embellishing tones and then harmonizing them; done enough times, we could generate an actual piece of music. For now, we merely embellish Example 6.2D twice more with embellishing tones to show that neighbors, passing tones, chordal leaps, and one or two other embellishing tones can be used to create examples in contrasting styles. In Example 6.2E, notice how the E5 on beat 2 in m. 2 delays the arrival of the D5 by a sixteenth note just as the D5 on beat 3 displaces the C5 by a whole beat. Understanding of the harmony once again helps us to interpret melodic features.

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Although Example 6.2F preserves both the harmony and the outer-voice counterpoint of the original model, the surface of the music in this example is even more altered than in Example 6.2E. Cast in the parallel mode of C minor, with each chord change occupying an entire measure rather than a single beat, Example 6.2F is in a freer texture. The arpeggiated figuration creates a seamless flurry of sixteenth notes that is punctuated by the sparse upper-neighbor figure on the third beat of mm. 1–3. Example 6.2 demonstrates how a soprano voice can help distinguish structural from ornamental harmonies, and how a basic two-voice structure might be ornamented—a process called embellishment. Embellishment takes many forms, including the simple process of sustaining and revoicing a tonic harmony that leads to a dominant chord (Example 6.3A). By adding a recurring eighth-note rhythmic figure we energize the texture (Example 6.3B). Finally, with a few passing tones, we have the opening of “Spring” from Vivaldi’s The Four Seasons.

EXAMPLE 6.3

Building a Piece STR EA MING AUDIO

A. Tonic Harmony Revoiced

I

B.

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V

Eighth-Note Figures Added

I

C.

V

Passing Tones Added: Vivaldi, The Four Seasons, “Spring”

I

V

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Reduction Reduction reverses the embellishment process by using the harmony as a means of distinguishing structural tones from embellishing tones, essentially reversing the process in Example 6.2. This process reveals the underlying two-voice contrapuntal framework of a musical passage. Listen to Example 6.4. On the downbeat of m. 8, the musical unit sounds relatively complete, as if closure had been achieved. There are two reasons why we hear a strong arrival in m. 8. First, the eight measures can be subdivided into two symmetrical harmonic and metrical units of four measures each. Given the change to dominant harmony in m. 4 (following three measures of tonic), we expect a similar change to occur in the corresponding spot four measures later, and indeed it does. At the end of m. 4, the addition of the high G in the melody creates a V7 chord that destabilizes the dominant and sends it forward into the next musical unit, which reverses the harmonic process of mm. 1–4: Three measures of dominant seventh harmony lead to one measure of tonic. The return to tonic in m. 8 is what creates the sense of resolution.

EXAMPLE 6.4

Beethoven, Piano Sonata in D minor, “Tempest,” op. 31, no. 2, Allegretto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1

i

5

V

V7

i

Second, the relationship between the melody and the harmony enhances the effect of closure. The opening D5 (1) over tonic harmony repeats on the downbeats of mm. 2 and 3, after which E5 (2) arrives over the dominant on the downbeat of m. 4. Thereafter, E5 is similarly emphasized over a repeated V7 chord until it ascends to F5 (3), coinciding with the return of tonic harmony in m. 8. Thus, a sense of harmonic arrival is balanced by the forward motion of the melody: Tonic harmony returns at the moment the melody dramatically attains 3. Example 6.5 is a reduction of Example 6.4. Literal repetitions of patterns are not shown. • Vertical stems indicate structural pitches: those pitches that help create the crucial bass/soprano structure. • Ties illustrate restatements of important pitches, such as the two Ds and the three Es. • Slurs convey the dependency of less important melodic pitches (e.g., passing and neighboring tones) on the important ones.

Chapter 6 The Impact of Melody, Rhythm, and Meter on Harmony; Introduction to V 7

EXAMPLE 6.5 1

Structural Analysis of Beethoven, Allegretto 2

m. 4

d:

i

193

V7

3

m. 8

i

Notice that the pitches aligned with a slur’s beginning and ending points are members of the underlying harmony: The notes D, F, and A begin and end slurs over the tonic harmony, and the notes A, E, and G begin and end slurs over the V7 harmony. In Example 6.5, we can view the E in mm. 4–7 (at a deeper melodic level) as a largescale passing tone that connects D and F. This motion is represented by the beamed pitches, which are supported by the bass voice as in previous chapters. This large-scale melodic ascent (1–2–3) is reflected in reverse order within the right hand’s sixteenth-note figuration in Example 6.4.

Levels of Embellishment Supermetrical figurations are embellishing figures (like the large-scale melodic passing figure D–E–F) whose durations extend beyond the value of the beat. These figurations are always made consonant by the supporting bass notes, as seen in the harmonization of the passing figure with the bass D–A–D, creating the overarching i–V7–i progression.

Application of Second-Level Analysis Understanding the important roles played by meter, rhythm, melody, harmony, and their contrapuntal combinations provides a standard by which to measure the relative strength and weakness of certain chords. Even when they appear in root position, shown in previous examples, we can distinguish between structural and ornamental harmonies. Example 6.6A reminds us to postpone interpretive decisions until carefully considering the musical context. Tonic harmony usually falls on strong beats within a measure. But is this true for Example 6.6A? Tonic and dominant harmonies alternate on two levels: on the downbeat of each measure (level 2A) and within each measure (level 1). Tonic does indeed control m. 1 since the dominant appears on a weak beat and is outnumbered by the tonic harmonies that flank it on beats 1 and 3. The D5 is a harmonized passing tone that connects E5 and C5. Since D occupies one metrical unit (in this context one beat), we call it a metrical passing tone. Metrical figurations are any figurations whose duration occupies one metrical unit. Note that for an embellishing tone to occupy an entire metrical unit, it must be rendered consonant. Thus, metrical figurations are harmonized. The relationship between the tonic and the dominant is reversed in m. 2: Tonic harmony helps to extend the dominant, with C5 as a harmonized passing tone between B4

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EXAMPLE 6.6A

Two Levels of I–V Harmonies

P

level 1: I level 2A: I level 2B: I

V

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I

V V V

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I I I

V

I

V V

I

V V

and D5. And given its identical function as the passing tone D5 in m. 1, it too can be labeled as a metrical figuration (again, harmonized). The eighth-note passing tone A4 (in the alto) is called a submetrical passing tone. Submetrical figurations are any figurations whose duration occupies less than one metrical unit. That A4 is not harmonized is common for submetrical figurations, although submetrical figurations may be harmonized. Although m. 3 begins and ends with tonic harmony, it differs in two important ways from the previous measures. First, rather than a single harmony between the flanking chords, as in mm. 1 and 2, there are three root-position harmonies between the two flanking tonics. Second, accented beat 3 is occupied by a different harmony from that on the downbeat of the measure. For the first time, deciding which harmony is most important within the measure is more difficult. For example, if metrically accented harmonies are more important than unaccented harmonies, then we can assume that the dominant on beat 3 is more important than the tonic on beat 4. This would mean that the tonic on beat 4 (and the C5 in the soprano) becomes a passing tone between the dominant chord on beat 3 and the dominant arrival in the next measure. This interpretation is reflected in level 2B. If, however, we view the two tonic harmonies that begin and end the measure as important, then the dominant on beat 3 extends the tonic by harmonizing the lower neighbor B4, in spite of the neighbor note’s metric prominence. This interpretation is shown in level 2A. These are two very different, yet plausible, readings that carry important performance implications. For example, the level 2A interpretation takes into account patterns established in the preceding measures. Since a single harmony controlled each of the preceding two measures, and a pattern of alternation of harmonies was established (i.e., m. 1 begins on I, m. 2 begins on V, and m. 3 begins on I), the listener may expect a continuation of the pattern. Thus, a performer would interpret it the same way as mm. 1 and 2, with the tonic controlling m. 3. Since this interpretation postpones the dominant arrival until m. 4, the performer will shape m. 3 accordingly and play down the importance of the dominant chords. Alternatively, the interpretation in level 2B, with the greater rhythmic complexity of m. 3, breaks the pattern of the repeated rhythm in mm. 1–2. Given that surface changes create an accent, the listener is drawn to this moment, and the performer would highlight the dominant’s control that would begin midway through m. 3.

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Final Interpretation Consider the harmonic changes on the eighth notes in m. 3. We will adopt interpretation 2A (in which tonic governs all of m. 3) because of the strength of pattern continuation over expected change. The soprano’s B would be labeled a neighbor; given its strong metric placement, we call it an accented neighbor note. Further, since the neighbor is made consonant by the V, it is a harmonized accented neighbor note, analogous to the harmonized passing tones discussed earlier. Finally, given its short duration, this accented neighbor note is a submetrical embellishing tone.

EXAMPLE 6.6B

Second-Level Analysis of Example 6.6A

PT

I

V I

PT

I

V

I

N

V

V

I

V

N

I

I I

V

I

V

V

I

V V

Example 6.6B summarizes our analysis so far. Notice two things. First, the soprano pitches in each measure, which are subordinate to more structural pitches, are now circled and labeled as harmonized passing tones (PT) and harmonized neighbor tones (N). Second, each chord is labeled with a roman numeral, and the bracketed groups indicate the larger harmonic units with the controlling harmonies labeled beneath the brackets.

Interpretive Analysis Multileveled analysis, a reduction that uses counterpoint and harmony to distinguish structural harmonies and melodies from embellishments, is called second-level analysis. Second-level analysis is also referred to as interpretive analysis, given that the deeper you understand the function of counterpoint and harmony within a passage, the more it becomes a matter of interpretation. Finally, depending on the number of musical events, there may be more than one level of reduction required. For example, in m. 3 the submetrical I–V–I harmonies that occur on beats 1 and 2 require their own interpretation before it is possible to analyze the entire measure.

The Deepest Level If we consider the possibility of a melodically fluent large-scale soprano controlling the entire passage, we can view the E5 in m. 1 moving to the C5 in m. 3 through a large-scale supermetrical passing tone in m. 2 (see Example 6.6C). Finally, our attention will be naturally drawn to the opening E. Given the extension of the tonic over mm. 1–3 and the

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EXAMPLE 6.6C

Structural Analysis of Example 6.6A

PT

I I

V

I

V V

accent created by the change to the dominant harmony on the half cadence in m. 4, our ears might connect the opening E to the final D in the melody. Such deep-level melodic fluency is a feature of musical unity, one that composers are well aware of.

Summary As we have just seen, the harmonies in a progression are not always of equal structural value. There are many musical contexts in which I and V, chords that are usually viewed as structural, may become subordinate to each other and to other harmonies. The key to hearing and analyzing music is being sensitive to the musical context, especially the meter, the rhythm, and the counterpoint between bass and soprano. Think of analysis as a musical triangle; each side is intimately connected with and dependent on the other two sides. rhythm and meter

harmony

melody

Taking these elements into account makes analysis a creative enterprise and informs musical interpretations and therefore performance.

EX ERCISE INTER LUDE A NA LYSIS STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

6.1 Provide a two-level roman numeral analysis of each of the following examples. Only rootposition I and V are used. In order to derive your second-level analysis, in which either tonic or dominant controls one or more measures, you will need to consider metric placement (i.e., whether or not the harmony occurs on a metrically stressed beat) and the

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soprano (whether the chord provides consonant support of a soprano passing tone or neighbor tone). Sample solution: N

I I (optional) I

V I

N

V

I

V

V neighbor in soprano

I I

V I

V

I

V

I

V

I

SOLVED/APP 5

A.

B.

SOLVED/APP 5

C.

T H E D OM I N A N T S E V E N T H A N D C HOR DA L DI S S ON A N C E The seventh is a dissonant interval, and chords that contain the seventh are dissonant. Just as dissonant intervals resolve to consonant ones, dissonant chords seek resolution to consonant chords. Dissonant chords create tension and heighten expectation in tonal music. In the opening measures of Beethoven’s Fourth Symphony, the repeated V7 chord that

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links the end of the slow introduction with the following Allegro vivace provides a powerful springboard to the eventual tonic that arrives seven measures later (see Example 6.7).

EXAMPLE 6.7

Beethoven, Symphony no. 4 in B  major, op. 60, Adagio/Allegro vivace STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Allegro vivace 35

5

5

cresc.

trem.

B :

V

7

3

40

I

Derivation and New Melodic Possibilities

Chordal sevenths are generated from a passing motion, in which 4 (the seventh of the dominant) fills the space between 5 and 3. • Example 6.8A is a basic model, showing a I–V–I progression with G4–G4–E4 (5–5–3) in the soprano voice.

EXAMPLE 6.8 A.

C:

I

Passing Seventh B.

V

I

I

C.

P

V8–7

I

I

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V7

I

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• Example 6.8B is nearly identical, except that the skip from G4 to E4 in the soprano voice has been filled in by a passing F4. Notice how the “8–7” in the figured bass acknowledges the voice leading of the soprano voice over the bass G: The octave G moves to a passing seventh. Notice further that the F4 is introduced inconspicuously on a weak beat, in the same way we wrote passing dissonance in second-species counterpoint. • In Example 6.8C the seventh now enters the harmonic domain and appears on a strong beat. Melodic motion remains intact; F4 still passes between G4 and E4, but now it is accented. Chordal sevenths can also participate in neighboring motions. • In Example 6.9A, F—the seventh of the V7 chord—functions as a neighbor to the surrounding Es. • The treatment of the chordal seventh in Example 6.9B significantly differs from the preceding examples: F is not preceded by step. Rather, it enters by leap (from C) and then falls by step, creating an incomplete-neighbor motion in the soprano. For V7, the approach to the dissonance (its preparation) can occur in different ways. But there is only one way to leave the dissonant seventh (its resolution): by descending step. Preparation by step from above is the preferred method to use. The unprepared entrance of the seventh in Example 6.9B is not very common; avoid it.

EXAMPLE 6.9 A.

C:

N

I

V7 I

Neighboring Seventh B.

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V7 I

Schubert’s song “Wasserfluth,” from the song cycle Winterreise (Example 6.10), demonstrates how V7 works within a musical context. Note how the tonic controls mm. 4–5, and the vocal line mostly arpeggiates the F-minor triad. Dominant harmony enters in m. 6 and returns to the tonic in m. 7. In m. 6, C5 in the vocal line descends by step to B4, the dissonant seventh, which resolves appropriately to A4. Thus, B4 functions as a passing tone that connects C5 and A4. Once again, we label the figured bass “8–7” to show the voice leading, with respect to the bass C, of the passing seventh from the octave. The dash connecting the two numbers means that this voice leading takes place in a single voice. Note also how the V7 chord can participate in an authentic cadence (here, the IAC in mm. 6–7);

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EXAMPLE 6.10 Schubert, “Wasserfluth” (“Torrent”), Winterreise, op. 89, no. 6, D. 911 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

4

5 4

3

Man Many

f

3

che Thrän’ tears

aus mei from my

3

3

nen Au gen Eyes

i

ist ge fal have fal

V

len in len on

den Schnee; the snow;

8 – 7

i

the addition of a seventh only enhances the dominant triad’s tendency to resolve to tonic. Therefore, always use the dominant triad (and not V 7) at a half cadence.

New Harmonization Possibilities

With the addition of the V 7 chord to our harmonic palette, we add 4 to the soprano scale degrees that can be harmonized by the chords discussed thus far: 1, 2, 3, 4, 5, 7. Using 4 opens up the possibility of harmonizing a complete descending-fifth soprano melody from 5 to 1 (Example 6.11). The passing motion from 5 to 3 in the soprano is imitated in the tenor over the last three chords. You can add the seventh to V and create a V 7 chord, but you can’t go from V 7 to V; to do so would contradict the natural drive to the tonic chord when the tritone is created by the addition of the seventh.

EXAMPLE 6.11 Harmonizing the Falling Fifth: 5–1 STR EA MING AUDIO

resolution 5

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4

3

2

1

(7

5)

7th

I

V I resolution

7th

I

V

7

7

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201

Part Writing the Dominant Seventh Chord 1. Connect the upper voices of V 7 to the preceding chord (for now, I) by step. 2. Resolve the chord’s tendency tones as follows: • the chordal seventh (4) always descends in any voice (as a dissonant tendency tone there are no other options) • the leading tone (7) always ascends when it occurs in the soprano. These two members of the V 7 chord create a tritone, either a diminished fifth or an augmented fourth, which resolves to I by moving in contrary motion: The diminished fifth contracts to a third, and the augmented fourth expands to a sixth. Tritones and their resolutions occur in the upper voices of Example 6.12.

EXAMPLE 6.12 Resolving the V 7 chord A.

B.

C.

4

7

4

°5 contracts °5th 3rd

7

+4 expands +4th 6th

4

complete incomplete incomplete complete

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7

5

complete complete

V 7 and I Chords

Incomplete V 7

Incomplete chords occur frequently in V 7–I progressions, often due to the resolution of tendency tones. The only member of a triad or a seventh chord that you can omit is the fifth. In Example 6.12A, the V 7 chord is complete, and the tonic triad is incomplete. The tendency tones in the soprano and alto resolve as expected, and the bass moves from 5 to 1. The tenor cannot create a complete C-major triad; to do so would require a jump to G, which would cause consecutive perfect fifths in the bass and tenor. Instead, the tenor moves by step and triples the root, omitting the fifth of the C-major triad.

Incomplete I In Example 6.12B, it is the I chord that is complete. The soprano and alto again have the two tendency tones of the V 7 chord, and the tenor cannot complete the V7 chord with a D. If the tenor were to take the D in the first chord, parallel fifths would occur between the bass and tenor. Instead, the tenor doubles the root of the V 7 chord and omits the fifth. Generally, a complete V 7 resolves to an incomplete tonic, and an incomplete V 7 resolves to a complete tonic.

Both V 7 and I Are Complete There is one way to have both the V 7 and I chords complete. When the leading tone is in an inner voice, it can move down to 5 instead of resolving to 1 (Example 6.12C). This

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THE COMPLETE MUSICIAN

exception to the rule that the leading tone must ascend by step to 1 is permissible because the leading tone occurs in an inner voice, where its skip to 5 is less audible than it would be had it occurred in an outer voice.

Unequal Fifths The final part-writing issue concerns I moving to V 7, where the perfect fifth in I moves to the diminished fifth in V 7 (see Example 6.13). These fifths are not parallel perfect fifths, but rather unequal fifths, and they are permissible as long as the diminished fifth resolves to a third. Note that the reverse—a diminished fifth moving to a perfect fifth—is generally not permitted, since it contradicts the natural tendency of the diminished fifth to resolve to a third.

EXAMPLE 6.13 Approaching the V 7 Chord STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

P5

5

3

Analytical Interlude Beethoven’s “Tempest” Sonata provides an analytical model for the accompanying exercises (Example 6.14). Listen for the context in which the dominant seventh chord appears, and how it intensifies the musical drama and enriches the voice leading.

WORKBOOK 1 Assignments 6.1–6.3

EXAMPLE 6.14 Beethoven, Piano Sonata in D minor, “Tempest,” op. 31, no. 2, Allegretto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1

2

3

m.5

d:

i

V

V

7

i

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203

As we saw in Examples 6.4 and 6.5, this excerpt is built out of two four-measure units; the second unit mirrors the first in its 3 ⫹ 1 harmonic rhythm:

mm. 1–4: i–i–i–V

mm. 5–8: V 7–V 7–V 7–i

The dominant seventh chord that appears in the upbeat to m. 5 (G5 in the soprano) intensifies the sound of the dominant triad in the beginning of m. 4. The harmonic motion is i–V→|V7–i. The V provides the musical glue that binds the two units to create a single phrase. Above the staff of Example 6.14, the long beam connects the three pitches of the largescale melodic ascent in the right hand from D5 via E5 to F5. The reverse of this melodic line (F5–E5–D5) occurs in sixteenth notes in mm. 1–3 and is answered by another filled-in third, G5–E5, in each of mm. 4–7. The imperfect authentic cadence in m. 8 spotlights the all-important arrival on the soprano’s F5, because this pitch is a point of arrival that is simultaneously secured from both above and below. E5 rises to F5, and G5—the crucial seventh of the dominant harmony—falls to F5. See the summary in Example 6.15.

EXAMPLE 6.15 Beethoven, Piano Sonata in D minor (reduction) UN

PT

d:

i

V7

i

Notice that the seventh, G, does not resolve to the sixteenth-note F that immediately follows it in each of mm. 4–6. The harmony at this point is still dominant and the F is a passing tone between G and E. Resolution of G occurs only in m. 8, where the F has the support of the underlying tonic harmony. Given that the basic soprano motion of the example is an ascent from D5 to F5, we view both E and G as supermetrical embellishing tones. A second example of supermetrical passing motion is given in Example 6.16. It is generally unproblematic to identify submetrical and metrical figurations. Supermetrical figurations can be more difficult to perceive. If, however, you locate the entrance and resolution of the seventh (recall that the resolution always requires a chord change), then you should be able to trace the deeper-level passing or neighbor motion.

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EXAMPLE 6.16

Mozart, Eine Kleine Nachtmusik, K. 525, Trio STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5

4 (PT)

3

I

V7

I

sotto voce

H A R MO N I Z I N G F OL K-T Y PE M E L ODI E S Up to this point we have harmonized melodies in chorale style, a procedure in which every soprano pitch is harmonized. Such settings resulted in very fast harmonic rhythm, with four or even more chord changes within each measure. However, composers regularly slow the harmonic rhythm to only one chord change in each measure or even in a group of measures. The listener hears the single underlying harmony that controls the span (whether it be part of a measure, an entire measure, or a group of measures) and the underlying pattern of harmonic changes expressed in the harmonic rhythm. The vast body of folk songs is an important repertoire that relies on a few basic harmonies—such as I, V and V 7—to accompany countless melodies. What follows is a simple method to harmonize these tunes.

Step 1: Identify Cadences Example 6.17 presents the popular tune “Simple Gifts.” Begin by singing the tune, noting the key and where cadences (and thus phrase endings) occur. The key is F major, and melodic repetitions, sustained pitches, and particularly the underlying four-measure “feel” of musical units reveal four-measures phrases, with cadences in mm. 4, 8, 12, and 16. We can determine the type of cadences as follows: Measure 4 ends on C (5), and while this could be harmonized with a I chord, such a weak authentic cadence would not be as common as a half cadence, implying V. In addition, m. 4 arpeggiates a V chord and there is no sign of F anywhere. The choice of dominant harmony is supported by the beginning of the next phrase (m. 5), which—given that it starts on F—strongly implies a I chord.

Chapter 6 The Impact of Melody, Rhythm, and Meter on Harmony; Introduction to V 7

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EXAMPLE 6.17 “Simple Gifts” STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

’Tis a

gift

to be sim ple ’tis a

gift

to be free, ’Tis a

gift

to come down to

where we ought to be,

And

5

when we find our

selves in the place

When

true

sim

turn,

turn,

just

right,

’Twill be

in the val ley

of

love

and

de light.

9

plic

i

ty

is gained,

To

bow

and to bend

we

won’t

be

a shamed. To

13

will

be

our de light

’Til

by

turn

ing and turn ing we

come

a round right.

An authentic cadence is implied in m. 8, given the strong repeated Fs. Measure 12 again suggests a HC and m. 16 an authentic. Notice the pattern of cadences:

mm. 1–4 HC

mm. 5–8 PAC

mm. 9–12 HC

mm. 13–16 PAC

Step 2: Identify Harmonic Rhythm Finish by identifying the harmonies that begin each phrase and then look for an underlying harmonic rhythm. In order to determine the controlling harmony for a span, look at accented pitches, which will be stressed in a variety of ways, including metrically, durationally, and by repetition. Be aware which scale degrees can be harmonized with which harmony: 1–3–5 implies a I chord, and 5–7–2 and often 4 imply a V(7) harmony. The greater the number of stressed scale degrees that belong to a single harmony, the greater the chance that that harmony will work best for that span. The accented pitches in m. 1 are F (on beat 1) and A (on beat 3), which imply a tonic harmony. Because this is the first full measure of the piece, we can almost assume it will be tonic. Further, the upbeat eighth notes (on C) imply a dominant harmony, and chords generally change from a weak beat to a strong beat. Using this method, the following summarizes the harmonies that begin and end phrases:

Phrase 1: mm. 1–2–3–4 I HC

Phrase 2: mm. 5–6–7–8 I PAC

Phrase 3: mm. 9–10–11–12 I HC

Phrase 4: mm. 13–14–15–16 I PAC

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THE COMPLETE MUSICIAN

Examining melodic patterns and starting to feel the implied harmonic changes, shows that the harmonies change no more often than once per measure. Phrase 1 contains harmonic changes every two measures. Phrases 2 and 4 share the same harmonic rhythm: two measures of tonic, one measure of dominant, and cadence on tonic. Phrase 3 has three measures of tonic and one measure of dominant.

Phrase 1: mm. 1–2–3–4 I V

Phrase 2: 5–6–7–8 I V I

Phrase 3: 9–10–11–12 I V

Phrase 4: 13–14–15–16 I V I

An Example from Classical Music Of course, the folk song is but one type of music that depends on a relatively slow rate of harmonic change and the use of only a few basic chords (see Example 6.18). This analytical method shows that there are two phrases, the first of which implies a HC and the second a PAC. The remaining harmonies are clearly implied, given that most of the melody is composed of chordal leaps. Thus, mm. 37–38 are tonic harmony, mm. 39–40 are dominant, and m. 40 is the HC. Measures 41–42 are dominant, with m. 42 adding A, the seventh of the chord. Measure 42 begins with A, implying a V7 chord, and the rest of the measure could certainly be harmonized all by V7 (the embellishing tones are strongly accented and therefore obscure the implied harmony).

EXAMPLE 6.18 Haydn, String Quartet in E  major, op. 64, no. 6, Trio (melody only) STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Trio

37

40

dolce

Examine how Haydn actually harmonizes these eight measures, with special attention to m. 43 (Example 6.19). Haydn has indeed followed the hints in the melody and harmonized at least most of it the way we might have imagined. However, he fools us a bit in m. 43: He begins the measure with a I chord, treating the downbeat A as a dissonant embellishing tone. Only at the very end of the measure does he move to the expected V chord.

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207

EXAMPLE 6.19 Haydn, String Quartet in E  major, op. 64, no. 6, Trio STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

37

40

dolce

SU M M A RY The central point of this chapter has been to show that tonal music is hierarchical. That is, certain events are more important than others. And what is remarkable is that these events need not be literally sounding in order for them to control a musical passage. For example, an underlying tonic may guide a tonal progression even if the actual tonic triad is not present. This notion of hierarchy can trickle down so that chords that help to extend a harmony may themselves be more important than surrounding harmonies, a process that can continue to the surface of the music. How composers extend more important contrapuntal and harmonic events with those that are less important is one thread we will follow in Chapters 7 and 8.

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 6.4–6.5

6.2 The following excerpts demonstrate I, V, and V7. 1. Listen to each example and complete a two-level harmonic analysis. Be sure you are able to distinguish between V and V7. 2. As you analyze each example, note if the sevenths are prepared (not a requirement) as a common tone or by step. Draw a line from each seventh to its resolution.

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THE COMPLETE MUSICIAN

A.

B.

Schubert, Waltz in B major, from 36 Originaltänze, op. 9, no. 24, D. 365

C. Schubert, Minuet in A minor, from 20 Minuets, D. 41, no. 8, Trio The dissonant notes in the sixteenth-note figure found in mm. 2, 3, 6, and 7 are upper and lower neighbors around the chord tones. Together they constitute a double-neighbor figure.

4

Chapter 6 The Impact of Melody, Rhythm, and Meter on Harmony; Introduction to V 7

209

Mozart, Cosi fan tutte, act 1, scene 5

D.

Soprano

Alto

O, wie schön, Bel la vi

Sol dat ta mi

zu li

sein, tar,

o, wie schön, bel la vi

Sol dat ta mi

zu li

sein! tar!

Ein Sol O gni

dat dì

O, wie schön, Bel la vi

Sol dat ta mi

zu li

sein, tar,

o, wie schön, bel la vi

Sol dat ta mi

zu li

sein! tar!

Ein Sol O gni

dat dì

Tenor

8

Baß

T ER MS A ND CONCEP TS • analysis: descriptive versus interpretive • embellishment/figuration: metrical, submetrical, supermetrical • chordal dissonance • dominant seventh chord • 8–7 • preparation and resolution • unequal fifths

CH A PTER R EV IEW 1. Define embellishment.

2. Define reduction.

3. How are embellishment and reduction related?

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THE COMPLETE MUSICIAN

4. What is another name for second-level analysis?

5. True or False: Always use V, not V 7, at a half cadence.

6. In a V 7 chord, the chordal 7th (4) always: a. descends

b. ascends

7. In a V 7 chord, the leading tone (scale degree 7) always: a. descends

b. ascends

8. The only member of a triad or a seventh chord that you can omit is the _________________.

9. Generally, a complete V 7 resolves to an ________________________ tonic, and an incomplete V 7 resolves to a _________________________ tonic.

10. Unequal fifths (perfect fifth moving to diminished fifth) are permissible if: _____________.

CH A PTER 7

Contrapuntal Expansions of Tonic and Dominant: Six-Three Chords

OV E RV I E W

In this chapter we study first-inversion tonic, dominant, and leadingtone triads. These allow the bass to participate in melodic motion rather than hopping between root-position tonic and dominant chords. Some of the techniques we will examine include chordal leaps in the bass part; neighboring tones in the bass (V6); passing tones in the bass; tonic expansion; and combining first-inversion chords. CHAPTER OUTLINE Chordal Leaps in the Bass: I6 and V6 ..................................................................... 212 Neighbor Tones in the Bass (V6) ............................................................................. 216 Another Neighboring Motion ............................................................................. 217 Second-Level Analysis................................................................................................ 218 Passing Tones in the Bass: vii°6 ............................................................................... 221 Tonic Expansion the Long Way: Descending a Sixth from 1 to 3 ................ 223 IV 6 as Part of Arpeggiation.................................................................................. 223 Dominant Expansion with Passing Tones: IV 6 .................................................. 224 Combining First-Inversion Chords ....................................................................... 225 Summary ....................................................................................................................... 226 Demonstration that Harmony Is a By-Product of Melody ............................. 226 Terms and Concepts ................................................................................................... 229 Chapter Review ........................................................................................................... 229 211

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THE COMPLETE MUSICIAN

I N T H I S C H A P T E R W E explore how specific first-inversion triads enrich musical struc-

ture by elaborating the tonic–dominant axis within a phrase. Because inverted triads are less stable than their root-position counterparts, they allow for greater harmonic nuance. And by using inversions, composers turn the bass line into a melody.

C HOR DA L L E A P S I N T H E B A S S : I 6 A N D V 6 The progression I–V–I (shown in Example 7.1A) can be expanded by simply repeating the first chord: I–I–V–I (Example 7.1B). One could also revoice the upper parts for added interest (Example 7.1C). But a more dramatic and contrapuntally interesting way to expand the tonic is to use the tonic in first inversion: I–I6–V–I (Example 7.1D). Instead of the leap of a fifth from 1 to 5, the bass first skips by chordal leap to another note in the tonic chord. The I6 chord is less stable than the root-position I chord, which helps to push the music forward. (See Example 7.2.)

EXAMPLE 7.1 Embellishing Tonic with First Inversion A.

C:

B.

I

V

I

D.

C.

I

I

V

I

I

I

I I

V

I

I6

I

V

I

I

EXAMPLE 7.2 Relative Stability of Root-Position and Inverted Triads sixth above bass makes the chord less stable

C:

I stable

I6 less stable

fourth above the bass is dissonant

I 46 unstable

Whereas root-position and first-inversion triads can often be interchanged, secondinversion triads are not an effective substitute for either root position or first inversion, given their dissonant fourth above the bass. Triads in second inversion function quite differently from those in root position and first inversion.

Chapter 7 Contrapuntal Expansions of Tonic and Dominant: Six-Three Chords

213

The folk song excerpt in Example 7.3A can be harmonized exclusively by means of tonic and dominant chords. Indeed, the chordal leaps and single weak-beat passing tone in m. 3 imply a harmonic rhythm of one chord per measure, with an alternation of rootposition tonic and dominant chords (see Example 7.3B). The excerpt closes with a half cadence. Although this is a passable harmonization, it is not very inspiring, given the predictable bass. More problematic is the rather heavy and static sound created by the consistent root-position harmonies. Indeed, the half cadence sounds less like an arrival and more like just another dominant harmony.

EXAMPLE 7.3 “Vom verwundeten Knaben” STR EA MING AUDIO

A. “Vom verwundeten Knaben” (“Of a wounded boy”) (German Folk Song)

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B.

Root-Position Setting

a:

C.

V

i

Brahms’s Setting of “Vom verwundeten Knaben,” op. 14, no. 2

Es

D.

i

wollt

ein

Mäd

chen

früh

auf

stehn

6

10

10

8

10

6

5

i6

i

V6

V

i

i6

V

auf

stehn

Brahms, with Voice Exchanges Andantino

Es

wollt

ein

Mäd

chen

früh

V

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THE COMPLETE MUSICIAN

In Example 7.3C, Brahms restricts the harmonies in his setting to the very tonic and dominant chords heard in the previous example. But rather than relying exclusively on root-position triads, he includes their first-inversion counterparts. This change aurally alters the piece so that it is now buoyant and strongly directed toward the half cadence. First-inversion chords energize phrases because they render the bass more melodic. A brief look at the lowest voice in Brahms’s setting reveals a melodic arch created by the opening descent of a sixth from C to E and the following ascent of an octave to the half cadence. The bass plays multiple roles, fusing harmonic function with melodic interest, as it becomes a counterpart to the soprano, with which its underlying counterpoint controls the flow of events. The downbeat intervals of the root-position harmonization in Example 7.3B reveal an octave, a fifth, a tenth, and a fifth; only the tenth is active. Now compare this with Brahms’s setting in Example 7.3C. Not only are the downbeat intervals all active (sixths and tenths, except for the half cadence’s fifth), but so are nearly all of the weak-beat intervals. Note that the piece begins with tonic in first inversion, as does the second measure, where the leading tone, G, is prominently displayed in the bass’s V6 chord. The relationship between bass and soprano is intensified by the fact that the intervals in mm. 1 and 3 are inverted, and the pitches are swapped, creating voice exchanges (the voice exchange in m. 2 occurs between the piano’s bass and alto parts). Example 7.3D shows these voice exchanges. Moving between a chord’s root position and first inversion is analogous to revoicing the upper voices of a harmony. There is no harmonic change, but rather, the extension or prolongation of a single harmony. That this can occur in the bass simply makes the change more dramatic. Example 7.4 presents common bass and soprano settings for motions between I and I6, all of which are applicable to expanding V with V6 (as shown in Example 7.4A2). Notice that the motion both to root position from first inversion and from first inversion to root position involves at least one and often two imperfect consonances (thirds and sixths). The fluid nature of the inverted chords helps propel a phrase. Therefore these chords are best

Expanding I and V with 63 Chords

EXAMPLE 7.4

STR EA MING AUDIO

A. Voice Exchange A1.

C:

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A3. Schubert, Impromptu in B major, Thema, Andante

A2.

I6

I I

V

I

V6

V V

I

B :

I

6

Chapter 7 Contrapuntal Expansions of Tonic and Dominant: Six-Three Chords

EXAMPLE 7.4 B.

(continued)

Similar Motion

5

C:

C.

6

Parallel Motion

10

I6

I

215

10

I6

I

I

I

used within a phrase rather than at the beginning or end of a phrase, where the stability of root-position chords is desired [although Brahms began his song in this very way (see Example 7.3), with a i6 chord!]. Just as 1 in the soprano is most often harmonized by the tonic, 3 in the bass overwhelmingly appears as part of the tonic triad. The pitches retained through the voice exchange make it clear that a single harmony, the tonic, has been extended by chordal leaps, which we saw earlier breaks the bass leap of a fifth from 1 to 5 into two smaller thirds: 1–3–5. The contrary-motion voice exchange is one of many possible outer-voice configurations. Example 7.4B shows a similar-motion outer-voice counterpoint, and Example 7.4C shows parallel-tenth motion. Not only are these chordal leaps reversible (53 → 63 or 63 → 53), but they can work in tandem, their combination creating entire phrases, as shown in Example 7.5. Telemann draws exclusively on I, I6, V, and V6, reserving two root-position V7 chords for the cadence.

EXAMPLE 7.5

Telemann, “Domenica,” from Scherzi Melodichi, Vivace STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Violino

Viola

Continuo

D:

V

I6 I

V

I6

V6

6

V7 I

V7 I

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THE COMPLETE MUSICIAN

N E IG H B OR T O N E S I N T H E B A S S ( V 6 ) We have seen that a harmony can be ornamented with a neighbor tone; in Example 7.6A, the B in the bass is a neighbor tone that ties together the surrounding root-position tonic chords. However, the “clunky” and out-of-place dissonant B is not a member of the tonic harmony. By harmonizing the B, it is rendered consonant, for it becomes the third of a V6 chord (Example 7.6B). Although the V6 chord only embellishes or extends the flanking tonic chords, we view it as a neighboring chord, given its melodic generation through neighboring motion.

EXAMPLE 7.6 Stabilizing Neighbors A.

B. N

I

(N)

I I

V6 N

I

Often 5 is prominently displayed in the soprano when V6 extends I, because this common tone secures their kinship. In addition, the musical drama is intensified because the outervoice perfect fifth of the tonic harmony (1 in the bass and 5 in the soprano) is destabilized by the sixth of the first-inversion dominant harmony. Beethoven takes advantage of this effect in the first sonorities of the slow movement from his seventh symphony (Example 7.7A). A different effect is created when the soprano begins on 3, joining the bass in its

EXAMPLE 7.7 Examples of Stabilizing Neighbors A.

Beethoven, Symphony no. 7 in A major, op. 92, Allegretto ∧ 5

3

5th

a:

ten.

i

6th

V6

V 53

i

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

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217

EXAMPLE 7.7 (continued) B.

Schubert, Piano Sonata in A major, D. 959, Andantino

f :

V6 (N)

i

V6 (N)

i

i

own neighboring motion; the result is the gently rocking pair of lines moving in parallel tenths. Schubert opens one of his slow movements in just this way (Example 7.7B).

Another Neighboring Motion The V6 can also be used as an incomplete neighboring chord. The most common type of incomplete neighbor occurs when i6 is followed by V6, which then returns to i (see Example 7.8A). In minor, the bass leap from 3 to 7 forms a diminished fourth, which is permitted given its extreme pathos and the leading tone is immediately resolved. See Example 7.8B, in which Corelli presents a dramatic diminished-fourth leap from E (the bass of i6) to B (bass of V6).

EXAMPLE 7.8 Incomplete Neighboring Chord A.

B. Corelli, Concerto Grosso no. 8 in G minor, Allegro no. 2 P

C:

i6

V6 (IN)

i

i

C:

i6 i

V6 (IN)

i

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THE COMPLETE MUSICIAN

S E C O N D - L E V E L A N A LY S I S We learned in Chapter 6 that harmonic analysis is a two-stage process. • The first stage (or first-level analysis) identifies each sonority with roman numerals and figured bass; such labeling represents the descriptive analysis of the progression. • The second stage—or second-level analysis—is interpretive and reflects the functions of the sonorities. • Level 2A distinguishes harmonies that are structural from harmonies that are ornamental. Structural harmonies are progressional because they indicate movement from one harmonic function (such as tonic) to another (such as dominant). Structural harmonies keep their roman numerals in second-level analysis. Ornamental harmonies—such as the neighboring chord in Example 7.8—help to extend or prolong a single structural harmony, and are thus called prolongational. In level 2A analysis, prolongational chords are labeled by melodic function, as the following chart shows. • Level 2B analysis contains only structural harmonies, usually only I and V (at least at this point in your studies). Merely labeling each harmony with a roman numeral does not constitute an analysis; it is more of a description. An analysis with the sole aim of placing roman numerals beneath

Summary of Structural and Ornamental Harmonies Structural harmonies . . . Ornamental harmonies . . . • are progressional • have harmonic function (tonic, dominant) • are usually on strong beats • are usually in root position • are part of a harmonic progression • keep their roman numerals in second-level analysis

• are prolongational • have melodic function (chordal leap, neighbor tone) • are usually on weak beats • are usually in inversion • are part of a contrapuntal progression • are labeled as ornaments (“N,” “CL”) in second-level analysis

EXAMPLE 7.9 Examples of Doubled Unisons and Octaves

A.

doubled unison

B.

doubled unison

C.

neutral position

doubled root

6

6

6

or

doubled fifth

6

Chapter 7 Contrapuntal Expansions of Tonic and Dominant: Six-Three Chords

219

every chord is a mechanical and dull exercise, one that is doomed to fail. As we proceed, you will see the merits of multilevel analysis. Analysis is a creative, thought-provoking activity whose goal is to penetrate deep into the musical structure to reveal important correspondences between the surface and the underlying structure of a composition.

Voice-Leading and Doubling Rules for I6 and V6 • Keep common tones (unless you use a voice exchange, which often requires movement in multiple voices). • When possible, double the root (you can double the third or fifth if it smooths the voice leading). • Never double the leading tone, 7 (the third of a dominant chord). • If the bass is not doubled, choose one of the following spacings for first-inversion triads: • Doubled unison: Two voices share the same pitch at the unison (Example 7.9A–B). • Neutral position: Two voices share the same pitch at the octave (Example 7.9C). • Subordinate harmonies, especially those that neighbor, usually appear on metrically weak beats or parts of beats.

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignment 7.1

7.1 Each excerpt contains one or more first-inversion chords that expand tonic or dominant. Analyze each example using a first- and second-level (2A and 2B) analysis.

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SOLVED/APP 5

B. Mozart, String Quartet in D minor, K. 173, Menuetto

C. Mozart, String Quartet in C major, K. 157, Andante 119

Coda.

123

W R ITING 7.2 In four-voice chorale style, set the following soprano scale degree fragments and bass scale degree fragments in the keys listed. Each progression must contain a tonic expansion. Some progressions, however, may contain both a tonic expansion and a cadence. Use only I (i), I6 (i6), V, V6, V7. Soprano scale degrees: SOLVED/APP 5

• In A minor: 1–2–3 • In F major: 3–1–5–4–3 • In B minor: 3–2–1–7–1

Bass scale degrees: SOLVED/APP 5

• In C minor: 1–7–1–2–3 • In E major: 1–3–7–1 • In A major: 3–1–7–5–1

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PA S S I N G T ON E S I N T H E B A S S : v i i° 6 Example 7.10 shows common settings of vii°6 with both first- and second-level analysis. Again, each of the contrapuntal chords occurs on a metrically unaccented beat, while the underlying harmony that is expanded usually occurs in a metrically accented position.

EXAMPLE 7.10 Common Settings of vii°6 the soprano and bass motion in tenths makes the direct fifths acceptable in this progression

A.

C:

B.

I I

vii 6 (P)

I6

I I

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C.

vii 6 (P)

I6

I

vii 6 (P)

I6

I

The vii° in first inversion—rather than ii in root position—is used when harmonizing the bass passing tone 2. The ii is a strong harmony that draws attention away from the tonic and therefore is not a suitable contrapuntal chord. By contrast, vii°6 is a perfect passing chord because: • It is an unstable diminished sonority and demands continuation to a more stable sonority, such as I6. • It shares notes with V and V 7, which work well as passing chords (we call vii°6 a dominant substitute). • It is in first inversion and therefore is more likely to be a contrapuntal chord. In addition to the contrapuntal expansions that depend on neighbors and chordal leaps in the bass, the passing tone is particularly important. The most common form fills the third between 1 and 3. Example 7.11 presents the opening of one of Handel’s flute sonata movements. Each of the tonic’s bass tones (1 and 3 in m. 1 and the reverse in m. 2) is harmonized by rootposition and first-inversion triads; in m. 1 a voice exchange is created between the bass and flute Bs and Ds. Additionally, Handel has harmonized the bass and soprano passing tones C (2) with first-inversion chords built on vii°. Because vii°6 harmonizes the passing tone C, it is called a passing chord, as shown below the example in the second-level analysis. Similar to neighboring embellishing chords, passing chords usually fall on metrically weak beats or parts of beats. Before we leave the Handel example, notice in m. 3 that the

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tonic harmony first appears on a weak part of the beat, sandwiched between two dominant harmonies and harmonizing D, a weak-beat passing tone in the flute. The tonic chord is an incomplete neighbor that helps to extend the dominant that began its control on the second beat of m. 2 and that remains in force until the strong-beat arrival of tonic at the end of the excerpt. We might even assign the extended V6 chord a neighboring function, given that it is flanked by the opening and closing tonic chords in root position.

EXAMPLE 7.11 Handel, Flute Sonata in B minor, HWV 367b A tempo di Minuet

Figured bass: Descriptive level: i

vii

Interpretive levels:

(P)

6

i6

i6

vii

6

i

V6

(P)

V7

i

V6

i

(IN)

i

V6

i

(N)

i

Voice Leading for vii°6 • Never double the leading tone, 7. • Try to double the third of the chord (2), which may move to either 1 or 3 (you may double 4 but only to make the voice leading smoother). • If possible, resolve the tritone (as you did with V7)—but it is common not to resolve the tritone if: • It leads to a complete tonic triad (Example 7.10A, B, and C). • It does not involve the bass (Example 7.10A and B). This is especially true if the tritone is expressed as an augmented fourth (rather than a diminished fifth). • The bass and soprano move by parallel tenths (Example 7.10C).

When we write vii°6 in the minor mode, there is one addition to our figured bass vocabulary. We must raise the sixth above the bass of a vii°6 chord—this is 7—in order to create a leading tone. Example 7.12 presents the figured bass you will encounter for vii°6 in major and minor modes and, below that, the harmonic analysis that you should use.

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EXAMPLE 7.12 Voice Leading and Analyzing vii°6 A.

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figured bass:

6

harmonic analysis:

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6 6

I6

i6

6 or 6 vii

6 i6

6

T ON IC E X PA N S ION T H E L ON G WA Y: DE S C E N DI N G A S I X T H F ROM 1 T O 3 We know that I6 expands I, with the bass ascending by a third (from 1 up to 3). Sometimes, the bass moves from I to I6 by falling a sixth, from 1 down to 3 as in Example 7.13A. Notice the large-scale voice exchange that results in the process: The soprano uses a passing figure (3–2–1), and the bass uses an arpeggiation (1–5–3). See Example 7.13B. The resulting V chord is subordinate to the surrounding tonic chords.

IV6 as Part of Arpeggiation

The large leap of a sixth is often split into the arpeggiation 1–6–3 by the addition of a new chord: IV6 (Example 7.14). Notice the stepwise ascent, 3–4–5 in the soprano; this ascent of 4 to 5 provides an important contrast to its more usual descent, as the dissonant

EXAMPLE 7.13 Handel, “Comfort Ye,” from Messiah, HWV 56: V Breaks Up the Span of the Falling Sixth from I to I6 STR EA MING AUDIO

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I6

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EXAMPLE 7.13 (continued) B. 3

2

1

PT

I6

I

EXAMPLE 7.14 Haydn, Symphony no. 101, “Clock,” Finale: IV6 Breaks Up the Span of the Falling Sixth from I to I6 3

4

5

IV 6 (ARP)

I6

Violino I

Violino II

Violoncelloe Contrabasso D:

I I

seventh in dominant harmony. Composers commonly double 1 (the third above the bass) when writing IV6, but you are free to double any member of the chord since smooth voice leading must always take priority over doublings.

D OM I N A N T E X PA N S IO N W I T H PA S S I N G T O N E S : I V 6 Just as tonic may be expanded with a passing vii°6 chord, so too may the dominant be expanded by a first-inversion IV6 chord. Observe in Example 7.15 how V–IV6–V6 is used in major and minor keys.

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EXAMPLE 7.15 IV6 Expands V A.

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I6 I

6

V

IV 6 (P)

V6

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V

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i6 i

6

V

IV 6 (P)

V6

V

i i

Voice Leading for V–IV6–V6 • In minor keys, 6 must be raised to avoid an augmented second between 6 and 7—this results in a major IV6 chord. • Avoid parallel fifths and octaves in IV6–V6 by moving the upper voices in contrary motion to the bass.

C OM B I N I N G F I R S T- I N V E R S IO N C HOR D S Extended prolongations of tonic are common, and they often involve combinations of the first-inversion chords we have discussed (I6, V6, vii°6, and IV6). Example 7.16 shows how a neighboring V6 and vii°6 create a double-neighbor figure in the bass and in the soprano. Example 7.17, from one of Telemann’s flute sonatas, opens with an expansion of the G-minor tonic using the same chords as Example 7.16: V6 and vii°6. However, V6 is now an incomplete neighbor and vii°6 passes between I and i6.

EXAMPLE 7.16 Multiple Expansions of Tonic N

I

V6 (N)

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I

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EXAMPLE 7.17 Telemann, Sonata for Flute in B  major, Dolce STR EA MING AUDIO P

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Violin or Flute

Continuo

g:

i

V (CL)

i

vii 6 (P)

i6

V6 (IN)

i

vii (P)

6

i6

i

SU M M A RY This chapter continued our exploration of two basic types of harmonies: structural (which control the underlying harmonic flow of the music) and embellishing (which ornament and extend the structural harmonies through their derivation as by-products of melodic and contrapuntal events). Considering melody, harmony, and the resulting two-voice counterpoint, provides a powerful standard by which to interpret each harmony.

Demonstration that Harmony Is a By-Product of Melody The importance of determining the function of each harmony is underscored in our secondlevel analysis, which carries with it performance implications. To be sure, composers did not create their artworks because of some burning desire to insert a I6 or vii°6 chord. Rather, their choice of harmony came from artistic efforts to make their pieces goal-directed and integrated. They accomplished this in a variety of ways, including sharing the same melodic figures (such as passing and neighbor tones), and passing them from one instrument to another to create recurring gestures or motives. When they fleshed out the harmonies implied by the melodic lines, the result was a tightly knit and organic structure. The two Corelli excerpts in Example 7.18 reveal this process. If labeling each chord with a roman numeral (m. 1: (i)–V–i–vii°6; and m. 2: i6–V6–i–etc.) were to be the limits of analysis, one would have missed the “point,” or premise, of these pieces, because the harmonies are actually the by-products of a compositional process. In Example 7.18A, Corelli has simply transferred the melodic figure of F–B–C–D–A–B from violin 1 to the keyboard. The same process is seen in Example 7.18B, where the I–IV6–I6 progression is the result of the transfer of the violin’s tune to the keyboard. (A glance back at Example 7.17 reveals that Telemann, too, had the same idea in mind.)

Chapter 7 Contrapuntal Expansions of Tonic and Dominant: Six-Three Chords

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EXAMPLE 7.18 Harmony as the By-Product of Imitative Lines Corelli, Violin Sonata in B minor, op. 2, no 8, Tempo di Gavotta

A.

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Violino I

Violino II

Cembalo

Corelli, Violin Sonata in F major, op. 5, no. 4, Grave

B.

Violino

Cembalo

Example 7.19 graphically summarizes the way tonic and dominant functions are elaborated by means of first-inversion triads.

EXAMPLE 7.19 Chart of Chords

Expanding tonic

(N) V6

V

(P) IV6

V6

Expanding dominant

I

(P) vii° 6 IV6 (ARP)

I6

I6

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EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 7.2–7.5

SOLVED/APP 5

7.3 Each given analytical snapshot contains tonic expansions and includes one or more of the first-inversion triads I6, V6, vii°6, and IV6. Analyze each example using two levels where appropriate. A.

Johann Jacob Bach, Flute Sonata in C minor, Allegro 30

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6 SOLVED/APP 5

B.

6

6

Haydn, String Quartet in D minor, op. 76, no. 2, Andante o piú tosto allegretto ten. ( )

mezza voce pizz.

pizz.

pizz.

C.

Beethoven, Violin Sonata no. 8 in G major, op. 30, no. 3, Minuet Be aware of both the key and the mode. cresc.

3

3

3

cresc.

Chapter 7 Contrapuntal Expansions of Tonic and Dominant: Six-Three Chords

229

D.

T ER MS A N D CONCEP TS • descriptive versus interpretive analysis • dominant substitute • harmonic versus contrapuntal progression • incomplete neighboring chord • neighboring chord • passing chord • passing motion • structural harmonies versus embellishing harmonies • voice exchange

CH A PTER R EV IEW 1. Why aren’t second-inversion chords effective substitutes for either root-position or firstinversion chords?

2. When two voices swap pitches over the interval of a third, this is called a __________________________________________________________________________________.

3. Whereas a neighboring chord is approached and left by step, an ________________________ neighboring chord has one leap and one step.

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4. Fill in the table. S T RUC T U R A L H A R MON I E S . . .

OR N A M E N TA L H A R MON I E S . . .

5. Summarize the voice-leading and doubling rules for I6 and V6.

6. Roman numeral vii°6 often replaces V or V7; we therefore called it a _____________________.

7. Summarize the rules for voice leading vii°6.

8. Summarize the rules for voice leading V–IV6–V6.

CH A PTER 8

More Contrapuntal Expansions: Inversions of V 7, Introduction to Leading-Tone Seventh Chords, and Reduction and Elaboration

OV E RV I E W

This chapter concludes our study of tonic and dominant expansions using inverted seventh chords built on V and vii. Further, we will tie the complementary processes of analytical reduction and compositional elaboration to performance. CHAPTER OUTLINE V 7 and Its Inversions .................................................................................................. 232 V65 ............................................................................................................................. 233 Passing Seventh in V65 ............................................................................................ 233 Neighboring Seventh in V65 .................................................................................. 234 V43 ............................................................................................................................. 235 V42 ............................................................................................................................. 236 Voice-Leading Inversions of V 7 ........................................................................... 237 Combining Inversions of V 7 ................................................................................ 237 (continued)

231

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THE COMPLETE MUSICIAN

Leading-Tone Seventh Chords: vii°7 and viiø7 .................................................... 240 Relationships Between vii°7 and V 7.................................................................... 241 Voice Leading for vii°7 .......................................................................................... 241 Analytical Interlude............................................................................................... 243 viiø7 .......................................................................................................................... 244 Compositional Impact of Contrapuntal Chords ............................................... 246 Summary of Contrapuntal Expansions ................................................................ 248 Reduction and Elaboration: Compositional and Performance Implications ............................................................................................................ 250 Reduction ............................................................................................................... 250 Elaboration ............................................................................................................. 253 Terms and Concepts ................................................................................................... 257 Chapter Review ........................................................................................................... 258 Summary of Part 2...................................................................................................... 259 T H I S C H A P T E R E X P LO R E S T H E compositional possibilities of inverting V 7 and

vii°7 chords. These unstable chords are used primarily to expand tonic. We also examine the more limited functions of viiø7.

V 7 A N D I T S I N V E R S ION S Root-position V 7 generally does not expand the tonic. It is a progressional harmony that often signals a cadence and should be used sparingly. Inverted chords are inherently unstable and give rise to the kind of motion that is needed within a phrase. The inversions of V 7 are ideal embellishing chords. The voice leading for inverted V 7 chords is identical to root-position chords reviewed in Example 8.1: The chordal third (7) rises (to 1), and the chordal seventh (4) resolves down by step (to 3).

EXAMPLE 8.1

Tendency Tones and V 7

the leading tone must resolve up in the soprano . . .

C:

I

V7

I

but the leading tone can fall to ^ 5 when in an inner part

I

V7

the seventh of the V7 chord always descends by step

I

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Chapter 8 More Contrapuntal Expansions

V 65 V 65 (first inversion) places the leading tone and chordal third (7) in the bass; thus it is usually a neighboring chord (like its first-inversion triadic cousin, V6). The single difference between V6 and V 65 is the presence of the chordal seventh (4) in the latter, which often appears in the soprano.

Passing Seventh in V 65 Example 8.2 presents the derivation of the V 65 chord from the V6. The soprano in Example 8.2A skips down a third (from 5 to 3). The third is filled with the unaccented passing seventh in Example 8.2B. In Example 8.2C, the passing seventh is metrically accented. Example 8.2D illustrates the smooth entrance of the seventh: Mozart’s movement begins on tonic, with B (5) prominently stated and then repeated as a dramatic octave leap. The sustained B accompanies a harmonic change to a neighboring V6 chord, which prepares the weak-beat passing seventh (A) that leads to the return of tonic in m. 3. Finally, V 65 can also follow V or V6 (as shown in Example 8.2E) because the addition of the seventh intensifies a triad.

EXAMPLE 8.2 A.

Passing Sevenths in V 56 B.

CL 3

5

C.

P

5

4

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3

5

4

3

I

I

V 65 (N)

I

chordal 7th

I

V6 (N)

I

I

D.

I

6

V 6—5 (N)

I

I

Mozart, Piano Sonata in E major, K. 282, Allegro 5

4

I I

V 66 (N)

5

3

I

the seventh of the V65 chord always descends by step

E. 1

2

(P)

V V

V 65 (CS)

(P)

I

V6

I

V6

V 65

I I

the bass of V 65 , which is the leading tone, always resolves up by step

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THE COMPLETE MUSICIAN

Neighboring Seventh in V 65 The seventh often appears within a neighboring configuration, where it mirrors the neighboring bass in contrary motion, as shown in Example 8.3A and B. With the anchoring neighbor motion of the fifth in an inner voice, a number of creative soprano lines are possible, one of which is shown in Example 8.3C, in which Mozart counterpoints the first violin and cello in parallel tenths.

EXAMPLE 8.3

Neighboring Seventh in V 65 STR EA MING AUDIO

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V 65 (N)

I

I

I

B.

Beethoven, Symphony no. 7 in A major, Assai meno presto UN

dolce

D:

col

I

V6 (N)

I

I

C.

Mozart, String Quartet in B major, K. 159, Rondo Allegro grazioso

^ 5

10

B :

I

as

anchor

10

10

V 65

I

V

(N) I

V

V 56 I (N)

V V

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Chapter 8 More Contrapuntal Expansions

V 43

EXAMPLE 8.4 A1.

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10

?

V 43 within Passing and Neighboring Motions

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j œ j œ œ j œ œ œ œ œ œ œ œ J mp ? b 43 ‰ œ œ œ œ 10œ œ œ œ œ œ œ 10 œ ˙™ ˙™ ˙™ ˙™

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V43 (second inversion) places the chordal fifth (2) in the bass. Since 2 also appears in the bass of vii°6, V43 functions in much the same way—as a neighboring chord to I (i) or, more often, as a passing chord between I and I6 (i and i6). Example 8.4A shows this passing motion as V43 connects i and i6. The soprano moves in parallel tenths with the bass. In Example 8.4B1, the contour is reversed: V43 is part of an ascending line, connecting I and I6. Notice that the chordal seventh (F) ascends to G instead of resolving normally to E. This exception to the rule that chordal dissonance must resolve by step descent is permitted because the strong parallel-tenth motion between bass and soprano overrides the normal resolution of the seventh. Schubert’s song “Des Müllers Blumen” opens in just this way, with the outer voices of the accompaniment tracing the parallel-tenth motion (Example 8.4B2).

Schubert, “Wasserflut,” from Winterreise 3

3

3

i i

V 43 (N)

i

V 43 (N)

i

V

i

V

i

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THE COMPLETE MUSICIAN

V43 may also prolong the tonic by neighbor motion, as shown in Example 8.4C1 and C2.

V 42 V42 (third inversion) places the chordal seventh (4) in the bass. Given the prominent placement of the seventh, V42 is the least stable of the inverted dominants. Example 8.5A presents a setting of V42 in which it participates in a tonic expansion from I to I6 that includes a voice exchange. Composers often soften the effect of V42 by preparing the seventh as a passing tone, as shown in Example 8.5B. It is also possible to use V42 as an upper neighbor to I6, which creates a less stable, more fleeting prolongation of the tonic (see Example 8.5C).

V 42

EXAMPLE 8.5 A.

B.

P

I

V 42 I 6 (IN)

I

P

V

4 2

I6

(PT)

I

C.

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I

Mozart, Piano Sonata in C major, K. 545, Allegro

14

I6

V 24 (UN)

4 3

4 D1. D1. Tonic TonicExpansion Expansionand andTypical TypicalPAC PACD2. D2.V42Vin EvadedCadences Cadences 2 in D1. Evaded

I6 I6

vii (P)

6

I

I6

V8

7

V7 PAC

I

I6

I

I6

vii (P)

6

I

I6

V

4 2

I6

NO PAC (evaded cadence)

Chapter 8 More Contrapuntal Expansions

237

Finally, placing the passing seventh in the bass at a cadence destabilizes dominant and transforms it into part of a tonic prolongation. Example 8.5D1 shows a tonic expansion and typical PAC (with passing seventh in the alto). Example 8.5D2 presents the passing seventh in the bass, creating an evaded cadence.

Voice-Leading Inversions of V 7 There are no new voice-leading rules for writing the inversions of V7, but remember these tenets of good part writing that have already been discussed. 1. Move most, if not all, of the voices by step or common tone when leading to and from inversions of V7. 2. Use complete chords for inversions of V7. 3. Place inversions of V7 on metrically unaccented beats so they connect tonic triads, which usually tend to fall on strong beats. 4. Resolve tendency tones: 7 (the leading tone) must ascend when it occurs in an outer voice (but may fall to 5 when it occurs in an inner voice). 4 (the seventh of V7) must descend to 3 (except in the progression I–V 43 –I6, harmonizing a 3–4–5 soprano).

Combining Inversions of V 7 Extended prolongations of tonic are common, and they usually involve two or more inverted V7 chords. A Donizetti aria (reproduced in Example 8.6A) opens with a tonic expansion using both V 43 and V 56. These expanding inverted dominant sevenths link the two-measure subphrases by creating the overall effect of double neighbors, as shown in the second-level analysis. Notice how Donizetti moves from an inversion with a less active tone in the bass (2) to one with an active tone (7), and not the reverse (i.e., V 56–V 43). The melodically fluent soprano line, B–A–G, enhances the connection between the two subphrases.

EXAMPLE 8.6 A.

Multiple Expansions of Tonic STR EA MING AUDIO

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V 43 (UN)

V 65 (LN)

3

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(continued)

EXAMPLE 8.6 B.

Mozart, Piano Sonata in F, K. 280, Presto 5

4

3

2

1

C

B

A

G

F

G V 43 (N)

F I

B V 42 (N)

A I6

(I) I

C.

Beethoven, Symphony no. 5 in C minor, Allegro

i

V 43 (P)

i6

V 56 (IN)

i

I

Example 8.6B shows how V 43 and V 42 expand the tonic in the opening of a Mozart Presto. Notice that their contrapuntal functions are made clear in the melodic swapping of the two-note pairs B–A and G–F. Single-pitch swappings are called voice exchanges; multiplepitch swappings are called part exchanges. The part exchanges in the upper voice are members of a longer stepwise falling fifth from the opening C down to F. Example 8.6C shows how Beethoven expands the tonic by moving from i to i6 through V 43 and then dramatically leaps by a diminished fourth from 3 to 7 and back to 1 through a neighboring V 56 chord.

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 8.1–8.3

8.1 Analytical Snapshots Each of the following short excerpts contains expansions of the tonic and the dominant using inversions of V7. Expect to encounter vii°6 and V6 as well. Analyze each, using two levels where appropriate.

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Chapter 8 More Contrapuntal Expansions

A. Schubert, “Morgengruss,” from Die schöne Müllerin

B.

Gu ten

Mor

gen, schö ne

Mül

Good

Mor

ning, fair

Miller

le rin! maid!

wo steckst

du

why do you

avert your head?

gleich das

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Mozart, String Quartet in B  major, K. 172, Allegro assai

29

C.

Beethoven, Violin Sonata no. 3 in E  major, op. 12, no. 3, Adagio con molta espressione

D.

Brahms, Horn Trio, Andante (What harmony is prolonged in mm. 1–4?)

dolce espress.

dolce

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THE COMPLETE MUSICIAN

Thomas, Gavotte, from Mignon Allegretto

Allegretto

W R ITING 8.2 Spelling Inversions of V 7 Given here are unordered inversions of V7 chords. The first boldfaced pitch is the bass. Determine the major key in which each chord functions as V7, and, using figured bass, provide the inversion based on the given bass note. Example: Given: G–D–B–E Answer: A major: V 56

SOLVED/APP 5

SOLVED/APP 5

SOLVED/APP 5

A. B. C. D. E. F. G. H. I. J.

F–D–B –A  C–A –E –G  F–B–D–G A –F–D –C  D–G –E–B A–F–C–E  A–D–C–F A–D –F–B G –C –E –B E –C –G –B 

_____________________________ _____________________________ _____________________________ _____________________________ _____________________________ _____________________________ _____________________________ _____________________________ _____________________________ _____________________________

L E A DI N G -T O N E S E V E N T H C HOR D S : v i i° 7 A N D v i i

Ø

7

A glance at the bass line of Gluck’s Orfeo in Example 8.7 reveals contrapuntal expansions of the tonic similar to inversions of V7. However, when you listen to the example, you will hear that each neighboring and passing sonority is a form of vii°7. The vii°7 and its inversions are much more dissonant than V7 and its inversions. This is because vii°7 contains the interval of the diminished seventh as well as two tritones (in C minor, B–F and D–A). Further, V7 shares one common tone with the tonic (5), while vii°7 does not share any common tones with the tonic (7, 2, 4, 6).

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Chapter 8 More Contrapuntal Expansions

Gluck, Orfeo, act 1, no. 1

EXAMPLE 8.7

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Thou

hast

P

him

quite

for

sak

N

press

N

left

up

on

en;

N

him;

N

Come,

N

IN

then,

Care

and

sor

row

N

come,

set him free

from dis tress.

IN

Relationships Between vii° 7 and V 7 The vii°7 and its inversions function the same way as V7 and its inversions because they share three pitches (7, 2, and 4). vii°7 and V7 are interchangeable, as follows: • vii°7 behaves just like V 56—it is a neighboring chord to root-position tonic. • vii°56 behaves like V 43—it is a passing chord between i and i6. • vii°43 behaves like V 42—it is a passing chord between V and i6, or it is a neighboring chord to i6. • vii°42 is rare and usually is a neighboring chord to root-position V7. The diminished seventh chord appears more often in minor-mode compositions because the chord appears without requiring chromatic alteration in the harmonic form of the minor scale. Finally, the diminished seventh provides support of 6. Example 8.8A shows the contrapuntal functions of vii°7 and its inversions. Example 8.8B compares V7 with vii°7; unfilled noteheads show common tones, and filled noteheads show the pitch difference between V7 and vii°7. Composers often take advantage of this subtle semitone shift between 5 and 6, as we will see. Finally, Example 8.8C compares and contrasts V7 and vii°7 in chart form.

Voice Leading for vii°7 The best way to approach writing vii°7 is first to think of the inversions of V7 and then to substitute 6 for 5. Note: Correct resolution of vii°7 and its inversions to tonic usully results

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THE COMPLETE MUSICIAN

EXAMPLE 8.8 Contrapuntal Functions of vii°7 and Its Inversions STR EA MING AUDIO

A.

c:

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i

vii (N)

7

i

i

i

vii (P)

6 5

i6

i6

i

vii (N)

4 3

i6

V

vii 42 V7 i (N) i

vii

4 2

V

i

B.

V65

vii

V43

7

vii

6 5

V42

vii

4 3

V7

C. vii°7 chords . . .

V7 chords . . .

• expand tonic

• expand tonic

• occur in minor keys

• occur in major and minor keys

• have 7–2–4 plus 6

• have 7–2–4 plus 5

• share no notes with tonic

• share one note (5) with tonic

• are highly unstable because they have two tritones, 7–4 and 2–6

• are somewhat unstable because have they have one tritone, 7–4

in a doubled third. Since all notes in vii°7 are tendency tones, the following is a guide to resolving the vii°7 chord to tonic (see Example 8.9): • Prepare 6—approach by step or with a common tone. • 6 moves down to 5. • 4 moves down to 3. • 2 usually moves up to 3 (resulting in the common doubled third in the tonic chord), or it can move down to 1. • 7 moves up to 1. Example 8.10 demonstrates these voice-leading guidelines. Example 8.8 confirms that these guidelines are consistent regardless of inversion. Alternatively, consider the resolution of vii°7 and its inversions from the perspective of chord-tone pairs and their resolution. For example, the interval of the diminished seventh (or augmented second when the chord is inverted) between 7 and 6 must resolve by

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Chapter 8 More Contrapuntal Expansions

Resolving the vii°7 Chord to Tonic

EXAMPLE 8.9

6ˆ 5ˆ

4ˆ

3ˆ doubled 2ˆ 1ˆ 7ˆ vii

7

i

EXAMPLE 8.10 Voice Leading vii°7 and Its Inversions

prepare 6 6 goes to 5

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7 goes to 1

4 goes to 3

4 goes to 3 or to 5 prepare 6 6 goes to 5

doubled 3rd

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doubled 3rd

7 goes to 1

c:

i i

vii (N)

7

i

i i i

vii 65 (P)

i6

contrary motion to 1 and 5. Further, resolve the tritones normally: A diminished fifth contracts and an augmented fourth expands. (Remember that resolution to tonic chords with doubled thirds is common.) Just like V7 and its inversions, vii°7 and its inversions often appear in combination, not only with one another but also with V7 and its inversions. Example 8.11 presents vii°7 as part of an expansion of tonic (in m. 4). In m. 5, vii°43 moves to vii°7 and on to V7 before resolving to tonic. However, beginning in m. 5 and continuing until m. 8, the dominant holds forth, with viio7 as its substitute.

Analytical Interlude

A compelling example of vii°7 occurs in Mozart’s E-major symphony (Example 8.12). Each of the four possible positions of vii°7 occurs, with tonic playing a subordinate role in the passage. Beginning with the highly unstable vii°42 and falling through 43, 56, and finally 7,

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EXAMPLE 8.11 Jean-Marie Leclair l’aîné, Sonata in G minor for Two Violins and Basso Continuo, op. 4, no. 5, Andante STR EA MING AUDIO W W W.OUP.COM/US/LAITZ 5

Violine I

Violine II

Klavier Basso continuo (Violoncello)

i

i

i

vii 7 i (N)

vii

4 3

vii

7

7

vii

7

V7

i

V7

i

inversions of the tonic (C) occur as passing chords that help to extend the dramatic vii°7, which functions as an upbeat gesture that leads eventually to the arrival on C minor in m. 75. Notice that the outer voices move in contrary motion, each spanning the interval of the diminished seventh (B–A). Since the initial interval is an augmented second (A–B) and the final interval a diminished seventh (B–A), a voice exchange results (Example 8.12B).

viiø7 The leading-tone seventh chord in major is a half-diminished seventh chord (e.g., B–D–F–A in C major). The minor seventh between 7 and 6 is much less dissonant than the diminished seventh found in the fully diminished seventh chord. However, because of its less goal-oriented tendencies, the viiø7 chord in major occurs much less often than its minor-mode counterpart. In fact, composers often import the fully diminished seventh chord from minor into their major-mode works by borrowing 6 from the parallel minor, a technique discussed in Chapter 21.

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Chapter 8 More Contrapuntal Expansions

EXAMPLE 8.12 Example of vii°7 in Mozart

A.

Mozart, Symphony in E major, K. 132, Andante

B.

Reduction

71 3

3

vii

4 2

c:

6 5

4 3

7

7

i

i

Example 8.13 illustrates viiø7 used to expand the tonic. Here, viiø7 appears as part of a larger neighboring process that unfolds in the melody: The line B–C–B (in which C is harmonized by V 65) is transposed up a third to D–E–D. Because no inversion of V7 contains 6, Mozart must use the viiø7. Notice also the unusual treatment of the seventh of the rootposition V7 chord in m. 28: It rises, rather than falls, in order to pass up to the D in m. 29. The viiø7 appears much more often in root position than in any of its inversions. Follow the part-writing rules for vii°7.

WORKBOOK 1 Assignments 8.4–8.5

EXAMPLE 8.13 Mozart, Symphony in D major, K. 97, Trio STR EA MING AUDIO W W W.OUP.COM/US/LAITZ 3

N

5

25

N

P (ascending 7th!)

I

V7

I

V7

I

vii ø7

I

V7

I

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C OM P O S I T IO N A L I M PAC T OF C O N T R A PU N TA L C HOR D S The wide variety of different chords that expand tonic and dominant function in only three settings: passing, neighboring, and chordal leaps. Indeed, bass passing tones between 1 and 3 come in many colors, including vii°6, V 43, and vii°65. Composers’ choices depend on the level of dissonance they desire and other issues of musical taste. What is important is that these compositional models, or harmonic paradigms, are crucial to the unfolding of all music written in the common-practice periods (including the Baroque, Classical, and Romantic periods and the late nineteenth century) as well as the commercial and popular music of today. You should be able to recognize these paradigms immediately no matter what the key, the mode, the meter, the instrumentation, the texture, or the like. Consider two excerpts by Chopin, a Romantic composer credited with expanding the Classical harmonic palette by experimenting with unusual sonorities and progressions. However, he still relied heavily on these paradigms at the surface as well as the deeper levels of his works. Listen to the excerpts in Example 8.14.

EXAMPLE 8.14 Harmonic Paradigms in Chopin A1.

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Chopin, Etude in F major, op. 10, no. 8, BI 42

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veloce

F:

I

3

V65 6

cresc.

I

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Chapter 8 More Contrapuntal Expansions

(continued)

EXAMPLE 8.14 A2. 1

4

8

I

V 65 (N)

I

I

B1.

Chopin, Impromptu no. 1 in A major, op. 29, BI 110 3

3

3

legato

3

3

A :

3

3

3

3

3

3

V 43

I

3

3

3

V 43

I

3 3

3

3

3

3

3

I6

3

3

(ii 65 as pre-dominant)

3

3

3

3

3

3

3

V7

B2.

I I

V 43 (N)

I

V 43 (P)

I6

ii 56

V (HC)

ii65

V

The progression in the etude is simple: an eight-measure phrase that consists entirely of tonic in root position, a neighboring V 65 that extends the tonic, and a return to tonic. In Example 8.14B, the tonic is also prolonged by linear chords. In mm. 1–3, two instances of V 43 help prolong the tonic—the first as a neighboring chord, the second as a passing

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THE COMPLETE MUSICIAN

chord. The cadential dominant arrives in the second half of m. 4. Indeed, these crucial harmonies are the skeleton that composers from various stylistic periods flesh out with their own distinctive figurations.

S U M M A R Y OF C ON T R A PU N TA L E X PA N S ION S Example 8.15 presents a summary of the various contrapuntal expansions of tonic and dominant that involve chordal skips, passing, neighboring, and their combinations. These involve the following chords:

I and I6

V7, V 65, V 43, and V 42

V and V6

vii°6, vii° 7 (viiø7), vii°65, vii°43, and vii°42

IV6

Summary of Contrapuntal Expansions

EXAMPLE 8.15 A. I 6 – V6 1

2

I

6

I

3

V

V

6

V6 expands I

I

I6

I I

6

I

V6

I

(IN)

I

B. vii

6

(2 in bass)

passing tones

passing chord

P

P

1

P I

6

I I

neighboring tones

2

neighboring chord

N

N

P vii 6 I6

N I

I I

neighbor and passing tones

3

passing chord with neighboring soprano

N

N

N vii 6 I

P I

I I

passing tone passing chord with incomplete with incomplete neighbor tone neighboring soprano

4

IN

IN

P vii 6 I 6

P I

I I

P vii 6 I 6

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Chapter 8 More Contrapuntal Expansions

(continued)

EXAMPLE 8.15 C. V 65

vii

7

(7 in bass)

Note: examples show V 56 . For vii 7, substitute 6 (A in minor only) for 5 (G). For vii , substitute 6 (A in major only) for 5. neighboring chord

neighboring tones

1

N

passing

N

N

chordal leap and passing tone

2 tone

P

P

N

I

I

6

V 65

I

I

I V

I

8

7

I

6 5

V

I

D. V 43

vii neighboring tones

1

6 5

(2 in bass)

2

N

N

N

V 43 + 65 soprano (N) bass (P)

neighboring chord

P

I I

I

passing chord

P

P

P

P

P

I I

passing tones

3

N

N

N V43

passing chord and neighboring soprano

V43

I I

6

I

6

I

6

double neighbors

Note: bass and soprano in 10ths

I I

6

V43

4

1

vii

4 3

as bass passing tone

DN I

I

6

(4 in bass) neighboring

2 tones

neighboring chord

incomplete neighbor chord with passing tone

incomplete

3 neighbor with passing tone

N

N

N P V

4 2

I6 I6

I6

I6

N V42

P

P

IN I6 6

I I

6

I

IN V42

DN

DN

6

E. V 42

double neighbor chords

I6 6

I I

DN V 43 V 65 I

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THE COMPLETE MUSICIAN

EXAMPLE 8.15

(continued)

F. IV6

(6 in bass)

1

2 6

IV extends I

6

P

IV extends V

P

ARP I

6

I

IV 6 I 6

V P V 56

I

I ARP I 6 I

V

I

V

IV6 V 65 I

V

P

V

V 65 I

R E DUC T IO N A N D E L A B OR AT ION : C OM P O S I T IO N A L A N D PE R F OR M A N C E I M PL IC AT ION S This chapter and Chapters 5–7, have explored the complementary processes of reduction and elaboration. To illustrate reduction, a florid example from the literature was simplified so that only the essential outer-voice counterpoint and homophonic inner voices remained. In the example of elaboration, a skeletal two-voice counterpoint or four-voice homophonic texture was embellished with florid accompaniments, embellishing tones, and the like. We now begin to apply these concepts to your specific instrument, particularly melodic instruments (i.e., winds, brass, and strings). Internalizing and transferring this knowledge to your own repertoire is the ultimate goal of these exercises. The elaborating process lets you be creative and encourages you to improvise your solutions. The reductive process lets you apply your analytical and aural skills to discover the melodic, contrapuntal, and harmonic commonality in tonal pieces.

Reduction To see how the reduction process can be applied to a melody instrument like the violin, consider the orchestral excerpt in Example 8.16. With its seven staves, three different clefs, dense texture, and highly varied rhythmic complexity, this excerpt looks formidable. However, following a specific procedure will let you tackle any score and find its basic harmonic structure and voice leading. • First, determine the key. This is necessary because an example may not be taken from the opening of a movement but may be from an interior portion of the movement, where a key other than the main key of the movement occurs. In the Mozart

Chapter 8 More Contrapuntal Expansions

251

EXAMPLE 8.16 Mozart, Symphony no. 28 in C major, K. 200, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

26

Oboi

Corni in C

Trombe in C

Vln I

Vln II

Vla

'Celli/basso 29

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excerpt, we see that G major is the key because of the introduction of the accidental (F) and the emphasis on dominant and tonic harmonies. • Second, we determine the function of each harmony, beginning with the harmonic rhythm, which seems to change once per measure. Focus on the accented bass notes, which are usually the lowest-sounding pitches. Large scores often use a great deal of pitch doubling, especially between the strings and the woodwinds. So it is usually easiest to focus on the four string parts (violins 1 and 2, viola, and cello/bass) and merely glance at the winds to confirm that they are doubling the strings. You must then reduce out the embellishing tones, including dissonant as well as consonant types. Here the chords unfold as follows: V 65 (two measures)–I–IV6–I6. This contrapuntal progression expands I (G major), first with a neighbor figure (F–G in the bass) and then with a descending arpeggiation (G–E–B in the bass). • Third, find the spacing of the upper voices and determine how these voices lead from one chord to another. Begin with the soprano in order to establish the outervoice counterpoint, and notice a lot of activity around C in both the first violin and the upper winds (Example 8.17). C is the seventh of the dominant; as such, it should resolve by descending to B, the third of the tonic chord, just as the bass F (as the leading tone) must resolve to 1. Indeed, Mozart follows the standard voice leading. Continue this process to see that the main soprano pitches, doubled in high strings and winds, are C–D, as shown in Example 8.17. This very same counterpoint was presented earlier (e.g., Example 7.14).

EXAMPLE 8.17 Mozart, Symphony in C major (reduction)

G:

V 65 (N) I

I

IV 6 (ARP)

I6

• Fourth, add the inner voices. But first review the outer-voice counterpoint in order to have a general idea of what pitches are missing in the chord and, therefore, what to expect to find in the actual composition. Given that the root (D) and the fifth (A) are missing in the outer-voice counterpoint of the V 65 chord, you should expect those pitches to be prominent in the remaining instruments. Indeed, the missing A appears immediately beneath the soprano’s C in winds and strings, and the root, D, appears on the downbeat in four other instruments. Now trace the voice leading from one chord to the other, as shown in Example 8.18 (note that the upper voices are notated one octave lower).

Chapter 8 More Contrapuntal Expansions

253

EXAMPLE 8.18 Adding Inner Voices to the Mozart Reduction

V 65

I

IV 6

I6

Mozart’s surface embellishments have now been reduced to the generating four-voice structure; you should play it on the piano. However, this chordal structure cannot be played on a melody instrument, so, we must “horizontalize” the homophonic chords, as shown in Example 8.19, by playing them as arpeggiations. Note, however, that the strict four-part voice leading in Example 8.18 is maintained. You need not play your arpeggiations within the meter, and you should find a register that suits your instrument (e.g., the viola’s range would accommodate the music in Example 8.19, but the violinist would need to transpose the excerpt at least a semitone higher). When you reduce an embellished score from the literature, you must be flexible, since you will need to omit embellishing tones, normalize the registers of pitches, infer the existence of missing pitches, etc.

EXAMPLE 8.19 “Horizontalizing” a Chorale Texture for Performance on a Melody Instrument

Elaboration The elaboration process involves three types of models: a four-voice chord progression, a soprano melody (with or without given roman numerals), and a figured bass (with or without a given soprano). Example 8.20 provides the third type of model, a figured bass (without a given soprano). Example 8.20A contains five bass notes and figures that could be the opening of a progression. Again, use a multistage procedure to bring this figured bass to life.

Step 1 (Example 8.20B). Determine the chord progression based on the figures, and add a soprano voice. Again, we encounter an expansion of the tonic, one that begins with a neighbor and then passes up to i6 (i—V 65—i—vii°6—i6).

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THE COMPLETE MUSICIAN

Step 2 (Example 8.20C). Add the inner voices to create a four-part structure. Step 3 (Example 8.21). Horizontalize the progression into broken chords at this performing stage. However, whereas this was the end of the exercise when reducing the score, the arpeggiation of the chords marks the beginning of the elaboration process. There are many ways to play these arpeggiations. • In Example 8.21A, only an ascending arpeggiation occurs.

EXAMPLE 8.20 Stages in Embellishing a Figured Bass A.

C.

B.

6 5

6

6

6 5

i

6

V 65 (N)

i

vii (P)

6 6

i

i6

V 65 (N)

i

vii 6 (P)

i6

i

i

EXAMPLE 8.21 Performing a Horizontalized Figured Bass A.

B.

e:

C.

D.

etc.

E.

F. pizz.

N

P

P

arco CL

etc.

Chapter 8 More Contrapuntal Expansions

255

• In Example B, changes of direction are incorporated that align with the strong beats. • In Example C, a mix of directions is possible. • In Example D, triplets replace the sixteenth notes. Note that if you choose to use triplets, you need to leave out one of the chord tones in the seventh chords, even if they are inverted. For example, in the V7 chord (m. 1, beat 2), only the third, the root, and the seventh occur. • In Example E, an alternation of arco and pizzicato differentiates the bass and the upper voices. • In Example F, shorter note values increase the possibilities not only of contour, but also for the addition of embellishing tones (in this case neighbors and passing tones). Finally, you can increase the duration of each chord to slow the harmonic rhythm to two or even more times its length. Particularly expansive examples of slowing the harmonic rhythm occur in many of Corelli’s concerto grossi; an excerpt of one in the key of D major is given as Example 8.22. Note the single tonic harmony that unfolds over eight measures. (For a full score of another concerto grossi by Corelli, see the Anthology no. 1.)

EXAMPLE 8.22 Corelli, Concerto Grosso in D major, op. 6, no. 7, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

31

Vln

Vln

Vla

Cello

I

I

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THE COMPLETE MUSICIAN

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 8.4–8.5

8.3 Analytical Snapshots Each of the following short excerpts contains expansions of the tonic using vii°7 and viiø7. Expect to encounter other chords that expand tonic, including vii°6, V6, and inversions of V7 as well. Analyze each, using two levels where appropriate. Sample solution: Mozart, Rondo, in F major, K. 494

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51

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3

3

A.

i

V 43

i

i

V 43

(P)

i

(N)

V 65

vii vii

After Strauss, “Ach lieb, ich muss nun scheiden,” op. 21, no. 3

SOLVED/APP 5

B.

Johann Helmich Roman, Flute Sonata in B minor, op. 1, no. 6, Grave

4 3 4 3

i6

vii

i

(P)

6

i6

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Chapter 8 More Contrapuntal Expansions

SOLVED/APP 5

C.

Haydn, String Quartet in G minor, op. 74, no. 3, ii, Largo assai Largo assai

ten.

ten.

ten.

ten.

ten.

ten.

ten.

ten.

mezza voce

mezza voce

mezza voce

mezza voce

D.

Wagner, Das Rheingold, scene 1 WOGL.

Hei a ja hei a! Hei a ja hei a!

hei a ja hei a! hei a ja hei a!

wal la la la la la lei wal la la la la la lei

a ja a ja

hei! hei!

Rhein Rhine

gold! gold!

Rhein Rhine

gold! gold!

hei a ja hei a! hei a ja hei a!

wal la la la la la lei wal la la la la la lei

a ja a ja

hei! hei!

Rhein Rhine

gold! gold!

Rhein Rhine

gold! gold!

hei a ja hei a! hei a ja hei a!

wal la la la la la lei wal la la la la la lei

a ja a ja

hei! hei!

Rhein Rhine

gold! gold!

Rhein Rhine

gold! gold!

WELLG.

Hei a ja hei a! Hei a ja hei a!

FLOSSH.

Hei a ja hei a! Hei a ja hei a!

T ER MS A ND CONCEP TS • elaboration and reduction • evaded cadence • harmonic paradigms • part exchange

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THE COMPLETE MUSICIAN

CH A PTER R EV IEW 1. Complete the table for the inversions of V 7. The first box is complete for you. Notice that, in general, the numbers move from highest to lowest from left to right. INVERSION ABBREVIATE FIGURED BASS SYMBOL

Root position

First inversion

Second inversion

Third inversion

7

2. Summarize the four guidelines for “Voice Leading Inversions of V7.”

3. Short compositional models, often comprising as few as three chords, are called __________.

4. Fill in the table, comparing the two types of dominant harmonies. v i io 7 C HOR D S . . .

V 7 C HOR D S . . .

5. List the roman numerals with inversions that have been introduced thus far in the text.

6. Summarize the four-step process of reduction.

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259

7. List the three textural models for elaboration. Be specific about each one.

8. Summarize the three-step process for elaborating a figured bass line.

S U M M A R Y OF PA R T 2 In Part 2, you have learned that a great deal of music can be made from tonic and dominant harmonies. In addition to their use as vertical harmonic pillars, their contrapuntal expansion allows them to participate in melodic construction. Melodic passing tones and neighbor tones in the outer voices, when harmonized, become passing and neighboring chords. In a similar manner, the succession of these chords is often dependent on melodic processes. We saw that dissonance and consonance still regulate musical flow and that inverted triads, derived from melodic passing and neighboring motions, are effective means for creating musical drive. The six-three chord is a versatile sonority often used to expand the tonic or the dominant function, or to lead from the tonic to the dominant, or vice versa. We also used seventh chords, including those built on 5 and 7, both of which served to expand the tonic. We discovered that these underlying tonal principles and processes are not limited to any one style period but can be found in musical examples written by composers over three centuries. Our examples have been taken from the music of Bach, Mozart, Beethoven, Schubert, Chopin, and Brahms.

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PA R T 3

A NEW HA R MONIC FUNCTION, THE PHR ASE MODEL, A ND A DDITIONA L MELODIC A ND HA R MONIC EMBELLISHMENTS

I

n Part 3 we will explore how composers incorporate the third and final harmonic function, the pre-dominant. This harmonic function introduces a new way of enhancing the listener’s expectations through the “phrase model” and also new ways of fulfilling or even thwarting those expectations. You will also learn new techniques for elaborating both melodic lines and harmonic functions, as well as techniques composers use to drive their pieces forward and unify them. Finally, you will learn about a new type of melodic figuration predicated on metric accent and chromaticism.

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CH A PTER 9

The Pre-Dominant Function and the Phrase Model OV E RV I E W

In this chapter we explore the third and final harmonic function: the pre-dominant, whose role is to lead from the tonic to the dominant. We will define and discuss the subdominant, the supertonic, pre-dominants and the stepwise ascending bass, and part writing for and extending the pre-dominant. With this function added, we introduce the phrase model, which provides the foundation for all phrases in the common-practice era. CHAPTER OUTLINE The Pre-Dominant Function ................................................................................... 264 The Subdominant (IV in Major, iv in Minor) ................................................... 264 The Phrygian Half Cadence .........................................................................265 The Supertonic (ii in Major, ii° in Minor)......................................................... 267 ii( 6) and ii°6 ................................................................................................. 267 Pre-Dominants and the Stepwise Ascending Bass ............................................ 268 Part Writing Pre-Dominants ............................................................................... 268 Extending the Pre-Dominant .............................................................................. 272 Chordal Skip................................................................................................. 272 IV–ii Complex.............................................................................................. 272 Introduction to the Phrase Model ......................................................................... 273 The Phrase Model’s Flexibility ............................................................................. 273 Analytical Interlude: Stylistic Diversity Within the Constraints of the Phrase Model.......................................................................................... 276 Terms and Concepts ................................................................................................... 279 Chapter Review ........................................................................................................... 279 263

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THE COMPLETE MUSICIAN

T H E PR E - D OM I N A N T F U N C T ION Whereas tonic and dominant functions are sufficient to create coherent musical passages, a third harmonic function adds a new dimension to our sense of harmonic tension and resolution. Each excerpt in Example 9.1 contains independent sonorities that act as connective tissue between the tonic and the dominant. We call these chords pre-dominants because they precede the dominant. The most important pre-dominant chords are IV and ii, which we see in Example 9.1. Listen to the intensified harmonic drive that results from these pre-dominant chords. Note that we now add the symbols T, PD, and D to represent the three functions of “tonic,” “pre-dominant” and “dominant” in the second-level analysis.

The Subdominant (IV in Major, iv in Minor) Composers frequently choose the subdominant as the pre-dominant chord because the I–IV motion proceeds by descending fifth (the most convincing root motion in tonal music) and the bass’s ascent from 4 to 5 creates a smooth motion to the dominant (Example 9.2). As the bass ascends by step, the upper voices usually descend, to avoid voice-leading

EXAMPLE 9.1 The Pre-Dominant in Context A.

STR EA MING AUDIO

Meyerbeer, “Se non ti moro allato,” Sei canzonette italiane, no. 5

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dolce

Ad Fare

E:

B.

di well

o

mia my

I T

vi li

ta, fe,

mia vi my li

IV PD

V D

ta, fe,

ad di o, Fare well,

I T

Foster, “Beautiful Dreamer” Beau ti ful dream

E :

I T

er,

wake un to me,

ii 6 PD

Star light and dew drops are wait ing for

V7 D

thee;

I T

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Chapter 9 The Pre-Dominant Function and the Phrase Model

EXAMPLE 9.1 (continued) C. Verdi, Overture to La forza del destino

3 3

3

a:

3

i T

3 3

3

3

3

3

3

3

iv

V7

i

PD

D

T

EXAMPLE 9.2 Outer-Voice Contrary Motion in Progressions Involving IV to V A.

B.

C:

D5 A2

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C.

D5 A2

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D5 A2

problems. Example 9.3 shows how IV can move to V 7. Note in Example 9.3 that the soprano’s 4 prepares the seventh of the upcoming dominant.

The Phrygian Half Cadence Approaching V from below (i.e., 4 up to 5 in the bass) is not the only way to incorporate a pre-dominant IV within a progression. Motion from IV6 to V, allowing the bass to fall from 6 to 5, is very useful, especially in the minor mode, where the powerful falling half

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EXAMPLE 9.3 Part Writing IV STR EA MING AUDIO

note how 4 prepares the seventh of V 7 Major Minor

A.

G:

3

4

3

I T

IV PD

V D

7

I T

B.

g:

3

4

i T

iv PD

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3

V D

IAC

7

i T

IAC

step intensifies tonal motion to the dominant. This resulting special type of half cadence, in which iv6 moves to V, is known as a Phrygian half cadence (Example 9.4A). Listen to the characteristic sound of the Phrygian half cadence in Example 9.4B, and note how the upper voice moves from 4 to 5 against the bass’s descent from 6 to 5. Given the musical tension of the Phrygian half cadence, Baroque composers were predisposed to closing slow inner movements of multimovement works with this cadence, leaving the listener with a strong expectation of tonic to follow in the opening of the next movement. See Example 9.4C.

Phrygian Half Cadence

EXAMPLE 9.4 A.

Phrygian Half Cadence 4

g:

i T

B. Bach, “Wo soll ich fliehen hin,” Cantata no. 5, BWV 5

5

6

5

iv 6 PD

V D

Phrygian HC

g:

i T

i

V6 i (N)

4

5

6

5

iv 6

V

PD D Phrygian HC

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Chapter 9 The Pre-Dominant Function and the Phrase Model

EXAMPLE 9.4 C.

267

(continued)

Corelli, Violin Sonata in A minor, op. 1, no. 4, Presto/Adagio

a: i

V

6

6

i6

V6

T

4

5

6

5

6 i

iv6 PD

V D

Phrygian HC

The Supertonic (ii in Major, ii° in Minor) The supertonic is the most common pre-dominant chord. There are three main reasons why composers consider the supertonic to be an effective pre-dominant: 1. The progression ii–V proceeds by descending-fifth motion, the strongest root motion in tonal music. 2. It introduces a striking sonority and modal contrast in progressions: a. In major keys, ii is minor. I and V are major. b. In minor keys, ii° is diminished. i is minor and V is major. 3. The progression ii–V–I is often set to 2–7–1 in the soprano, versus the less dynamic 1–7–1 when IV functions as the pre-dominant. This melodic motion encircles the upcoming 1, making the cadence especially powerful (Example 9.5).

ii( 6) and ii° 6 Composers write ii and ii6 in the major mode, but they almost always use the first-inversion ii°6 chord in the minor mode. This is because ii° is a dissonant diminished triad, and (as with vii°) any root-position diminished triad has an unsettling effect, given its exposed tritone between the bass and an upper voice. The tritone is softened when first-inversion ii°6 is used and 4 occurs in the bass (Example 9.6).

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EXAMPLE 9.5

Soprano Converges on 1 in ii6 –V–I STR EA MING AUDIO

G:

3

2

7

1

I T

ii PD

V D

I T

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EXAMPLE 9.6 Part Writing ii and ii°6 A.

B.

ii 53 ok in major because of P5

C.

ii 35 not ok in minor because of 5 with bass

STR EA MING AUDIO use ii 6 in minor to avoid 5 with bass

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+4 P5

I

5

ii

V

I

i

ii

V

i

i

ii

6

V

i

no!

The use of ii in first inversion raises an important issue. Recall that root-position ii lacks the smooth melodic step progression to V in the bass that is enjoyed by IV (Example 9.3). The first-inversion supertonic (ii6) embodies the best attributes of ii and IV: the modal contrast from ii, the descending-fifth root relation of ii–V, and the smooth bass voice leading of 4–5 from IV. See Example 9.7.

Pre-Dominants and the Stepwise Ascending Bass

When we first used V 7, we harmonized stepwise motions between 1 and 5 in the soprano (see Chapters 6 and 8). With the addition of pre-dominants, you can now write a stepwise line in the bass that ascends from 1 to 5. Thousands of musical phrases, from the early Baroque to today’s popular music, feature this bass line, as shown in Example 9.8. The ascending bass line has an especially powerful effect in major-mode pieces, given that the bass of I6 (3) lies only a half step from the pre-dominant on 4.

Part Writing Pre-Dominants Keep the following in mind when writing pre-dominants. 1. Pre-dominants move to V: tonic→pre-dominant→dominant→tonic. The supertonic (ii) never moves to tonic.

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Chapter 9 The Pre-Dominant Function and the Phrase Model

EXAMPLE 9.7 Haydn, String Quartet in F minor, op. 20, no. 5, Hob III.35, Allegro moderato STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1

2

3

2

7

1

Violin I

Violin II

Viola

Violoncello

f:

V65

i

i

ii

(N)

T

6

PD

V7

i

D

T

EXAMPLE 9.8 Chopin, Nocturne in F minor, op. 48, no. 2 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

57

3

4

5

5

10

6

10

5

10

10

1

2

3

V43

I

I6

4

IV

(P) T

PD

61

( )

( )

5

5

5

V7 D IAC

I

V7

T

D

I T PAC (as echo)

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EXAMPLE 9.9 Pre-Dominant Part-Writing Summary A.

B. 1

7

4

C.

D.

2

4

5

E. 2

7

2

F. A2

7

avoid

C:

IV

V

IV

c:

V

iv6

V

C: ii

V

ii6

V

good

good

c:

+2 because

G.

6 rises to 7

par. 5th (or doubled leading tone) 5

( )6 falls to 5

approach 7 from above

5

iv

V

no!

iv

V

ok

2. When the bass of a pre-dominant chord approaches the dominant by step (4–5 or 6–5), the soprano moves in contrary motion with the bass (Example 9.9A–E). 3. Try to double the root of pre-dominant chords that are in root position (Example 9.9D). 4. Try to double the bass (4) when writing a ii6 chord (Example 9.9E). 5. In a Phrygian half cadence (iv6 –V), the bass moves from 6 to 5, the soprano usually moves from 4 to 5, and the other voices double 1 to avoid errors in voice leading (Example 9.9C). 6. When writing in a minor key, approach the leading tone (7) in the V chord from above. Examples 9.9F and G show both problematic and good voice leading.

EX ERCISE INTER LUDE W R ITING WORKBOOK 1 Assignments 9.1–9.2

9.1 Brain twister: Complete the tasks that follow on a separate sheet of manuscript paper. A. In no more than five chords in A major incorporate a tonic expansion, a PD, and a half cadence.

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Chapter 9 The Pre-Dominant Function and the Phrase Model

B.

Provide three different harmonic settings in G minor for the following bass line (you need add only the roman numerals, not pitches): G–F–G–A–B –D. C. Incorporate both iiø6 and iv6 in a five to seven chord progression in B minor.

A NA LYSIS

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9.2 Snapshots Listen to and study the following excerpts. Identify the harmonic rhythm. When do chords change? Identify the tonic, pre-dominant, and dominant parts of each excerpt. Some chords may be ornamented with nonchord tones. Provide a two-level harmonic analysis.

Sample solution: Beethoven, Piano Sonata in G major, op. 14, no. 2, Andante

I

V 43

T

(P)

I6

V6 (IN)

I

ii 6

V

PD

D

A.

Mozart, Piano Sonata in D major, K. 284, “Variation VII, Minore”

B.

Haydn, String Quartet in B minor, op. 64, no. 2, Hob III.68, Adagio ma non troppo

mezza voce

mezza voce

mezza voce

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Extending the Pre-Dominant Just as the tonic and the dominant functions may be extended by embellishing chords, so too may the pre-dominant. Following are two techniques that extend the pre-dominant function.

Chordal Skip The first technique involves the use of a chordal skip in the bass, moving from ii to ii6 or vice versa. Example 9.10 illustrates this simple technique. Notice the resulting voice exchange between the outer voices.

EXAMPLE 9.10 Beethoven, Piano Concerto in G major, op. 58/I, Allegro moderato STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

dolce

I

V (ARP)

T

I

6

ii PD

6

V D

IV–ii Complex The second technique is subtler, yet is often considered to be more important. Progressions whose roots move by step (e.g., IV–V) are especially vulnerable to parallel perfect intervals in voice leading, especially when the outer voices move in the same direction (Example 9.11A). In order to avoid poor voice leading, you can use a voice-leading chord, which breaks up the parallels. In Example 9.11B, the soprano quarter-note motion creates a contrapuntal 5–6 motion above the bass that anticipates the dominant pitch G and avoids the parallel fifths seen in Example 9.11A. Though it appears that the IV moves to ii6, we interpret this motion as a subtle melodic shift (IV5–6) rather than as a functional chord change, and we refer to the process as the IV–ii complex. This interpretation is reflected in the second-level analysis, which groups the IV–ii under a single functional heading: PD. In Example 9.11C the bass falls from 4 to 2, yet even this apparent chord change (IV to ii) is still motivated by the same voiceleading concerns as in Example 9.11B. Note that the goal-oriented melodic motion in the succession IV–ii(6) is very common but that the weaker motion of ii–IV is not. Example 9.11D1, from Mozart’s “Haffner” Symphony, shows how the pre-dominant, IV, moves to V 7 using the IV–ii complex. Keenly aware of effective voice leading, Mozart would never move in parallel fifths from IV to V (as shown in Example 9.11D2). Rather, he shifts the upper note of the fifth, D, by step up to E, creating a consonant sixth and a resulting ii6 chord. E is sustained as the bass raises to A (the root of the V), where it functions as the fifth of the chord (Example 9.11D2).

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Chapter 9 The Pre-Dominant Function and the Phrase Model

EXAMPLE 9.11 The IV–ii Complex STR EA MING AUDIO

A. Parallel Fifths 5

D1.

—

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B. Parallels Avoided with 5–6 Motion

C. Parallels Avoided with Individual Chords

anticipation

5

I

IV

V7

I

I I

IV ii 6 IV 5 – 6

V7

I

I

IV

T

PD

D

T

T

PD

D

T

T

PD

ii

V7

I

D

T

Mozart, Symphony 35 in D major, “Haffner,” K. 385, Menuetto 5

5

6

5

I

IV

T

6

(ii) PD

5

V7

I

D

T

D2. Parallel Fifths Corrected by the IV/ii Complex 5

becomes:

5

5

5

6

5

IV

V

IV

(ii)

V

I N T RODUC T ION T O T H E PH R A S E MODE L Complete musical statements can rely exclusively on tonic and dominant chords. Called phrases, these musical units are always punctuated by strong closing gestures called cadences. Although many examples of phrases built exclusively on tonics and dominants exist, most phrases incorporate the pre-dominant function to create a richer harmonic progression. The harmonic motion of tonic (T), through pre-dominant (PD), to dominant and tonic at the cadence (D or D-T) guides a phrase from its beginning to its cadence and is called the phrase model.

The Phrase Model’s Flexibility Although the phrase model can occupy any number of measures, four measures (or some multiple of four) is common, as seen in Example 9.12. Here, a balanced motion is clearly felt

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THE COMPLETE MUSICIAN

EXAMPLE 9.12 Haydn, String Quartet in D major, “The Frog,” op. 50, no. 6, Hob III.49, Menuetto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

D:

I

IV

V7

T

PD

D

I

PAC

as the harmonic rhythm shifts once every measure. There is much room for variation in this model, however, and while the order of presentation of harmonic functions (T–PD–D–T) remains the same, their relative durations may vary considerably. For instance, the opening tonic often occupies at least as much time as the pre-dominant and dominant combined. Example 9.13 extends the tonic for three and a third measures, with the PD and D occupying barely more than one beat. (Notice that the bass and soprano begin at the interval of a tenth; then, in parallel motion, they descend by step together and then return to the rootposition tonic harmony, making the expansion of tonic explicit.) In Example 9.12 the phrase model closed with an authentic cadence. Example 9.13 closes with a half cadence. These two basic models are represented schematically in

EXAMPLE 9.13 Mozart, Piano Sonata in A major, K. 331, Andante grazioso STR EA MING AUDIO 3

A:

I T

3

2

ii 6

V

PD

D

HC

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Chapter 9 The Pre-Dominant Function and the Phrase Model

Example 9.14. Models 3 and 4, which close with a half cadence, are as grammatically complete as the first two models, yet their harmony implies that the piece will eventually resolve the tension of the dominant.

EXAMPLE 9.14

Four-Measure Phrase Models measures:

1

2

3

4

cadence

model 1:

T

PD

D

T

authentic

model 2:

T

D

T

authentic

model 3:

T

PD

D

half

model 4:

T

PD

PD

D

half

Notice how in models 2–4 it takes much more time for the tonic to move to the predominant than for the pre-dominant to move to the dominant. It is common for the tonic to occupy two or even three times more time than the pre-dominant. Example 9.15 (closely resembling model 3) illustrates a four-measure phrase with five and a half beats of tonic and one and a half beats of dominant, but only half a beat of pre-dominant.

EXAMPLE 9.15 Schubert, Violin Sonata no. 2 in G minor, D. 408, Andante STR EA MING AUDIO W W W.OUP.COM/US/LAITZ dolce

E :

I6 T

I

V 34

V7

I

6

IV

V

PD

D HC

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Final Checklist for Pre-Dominant Function • • •

The T–PD–D–T order is not reversible. Use contrary motion in the outer voices when writing I–ii, IV–V, or ii6–V. In minor, 6 must descend to 5, and 7 must be approached from above.

Analytical Interlude: Stylistic Diversity Within the Constraints of the Phrase Model Although the phrase models shown in Example 9.14 might seem to constrain a composer’s creativity, they actually generate unlimited compositional possibilities. Composers from the Baroque era through the late nineteenth century, writing in very different styles, employed these models tirelessly. For example, listen to the two excerpts in Example 9.16. Both excerpts share the same harmonic structure, but because of their different figurations on the musical “surface,” they could not sound more different. • Each contains a single phrase (example A is four measures and example B is eight). • Each begins with a tonic expansion (i–V6 (or V 65)–V7–i). • This is followed by a pre-dominant on ii, ornamented with strong-beat upper-voice dissonances. • This is followed by a half cadence (also embellished by strong-beat dissonances). • Note the identical 5–6–5– 4–5 motive in both examples, which helps to extend the tonic.

EXAMPLE 9.16 A.

Diversity in the Phrase Model STR EA MING AUDIO

Mendelssohn, Lieder ohne Worte (“Songs Without Words”), op. 19, no. 5 5

Poco agitato

f :

i T

6

5

4

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5

V6

7

i

ii 6

V

PD

D HC

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Chapter 9 The Pre-Dominant Function and the Phrase Model

EXAMPLE 9.16 B.

(continued)

Mendelssohn, Lieder ohne Worte (“Songs Without Words”), op. 30, no. 2 Allegro di molto

b :

dim.

6

5

5

i T

cresc.

4

5

V65

7

i

ii 6

V

PD

D HC

EX ERCISE INTER LUDE

WORKBOOK 1 Assignments 9.3–9.4

A.

9.3 Error Detection Each short progression contains a minimum of three part-writing and spelling errors. To develop fluency, study each progression for no more than one minute, adding roman numerals and labeling each error. B.

C.

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THE COMPLETE MUSICIAN

D.

E.

F.

A NA LYSIS

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9.4 Determine the cadence, harmonic rhythm, and pre-dominant (ii, ii6, or IV) for each of the following excerpts. Also, answer the following questions for each excerpt. 1. How is the tonic expanded? 2. Is the pre-dominant expanded (e.g., using the IV–ii complex)? Circle and label each PD harmony. 3. What phrase model does each example most resemble?

A.

Mozart, Piano Sonata in B  major, K. 333, Allegro

SOLVED/APP 5

B.

After Handel, Concerto Grosso, op. 6, no. 9, Largo

Violino I. conc. e rip. Violino II.

Viola.

Tutti Bassi.

Chapter 9 The Pre-Dominant Function and the Phrase Model

T ER MS A ND CONCEP TS • IV–ii complex • four-measure phrase model: with perfect authentic cadence and with half cadence • helping chords (or voice-leading chords)

• • • • •

Phrygian half cadence pre-dominant use of IV use of ii phrase model

CH A PTER R EV IEW 1. What are the two most important pre-dominant chords?

2. How does the bass approach 5 in a Phrygian half cadence?

3. Summarize the “Part Writing for Pre-Dominants” list given in this chapter.

4. The IV–ii complex belongs to which functional category? a. tonic

b. pre-dominant

c. dominant

5. The phrase model places the three functions mentioned above in what order?

6. Which functional category is often prolonged the longest?

7. In general, does harmonic rhythm tend to speed up or slow down when approaching a cadence?

8. Summarize “Final Checklist for Pre-Dominant Function.”

279

C H A P T E R 10

Accented and Chromatic Embellishing Tones

OV E RV I E W

We complete our study of embellishing tones by focusing on three distinct types: 1. Non-chordal embellishments that appear on beats (accented), rather than between beats (unaccented) 2. Chromatic embellishments that are accented and unaccented 3. Leaps to non-chordal embellishments CHAPTER OUTLINE Unaccented Tones of Figuration ............................................................................. 281 Accented Tones of Figuration .................................................................................. 282 Specifics of Unaccented and Accented Tones of Figuration ............................ 282 Accented Embellishing Tones .................................................................................. 283 The Accented Passing Tone (APT) ......................................................................... 283 The Chromatic Passing Tone (CPT) ...................................................................... 284 Metric Placement and Contour........................................................................... 285 Sample Analysis ..................................................................................................... 285 The Accented Neighbor Tone (AN) ........................................................................ 286 Metric Placement and Contour........................................................................... 286 The Chromatic Neighbor Tone (CN) .................................................................... 287 Analytical Interlude............................................................................................... 287 The Appoggiatura (APP) .......................................................................................... 288 (continued)

280

281

Chapter 10 Accented and Chromatic Embellishing Tones

The Suspension (S) ..................................................................................................... 289 Characteristics of Suspensions............................................................................. 289 Components of Suspensions ................................................................................ 290 Suspensions in Four Voices .................................................................................. 290 Labeling Suspensions ............................................................................................ 291 Writing Suspensions.............................................................................................. 292 Additional Suspension Techniques ..................................................................... 293 The Anticipation (ANT)............................................................................................ 295 The Pedal (PED) ......................................................................................................... 296 Summary of the Most Common Embellishing Tones....................................... 297 Terms and Concepts ................................................................................................... 301 Chapter Review ........................................................................................................... 301

E M B E L L I S H I N G TO N E S E N H A N C E M U S I C ’ S motion, grace, and drama. Their presence on the immediate surface of the music means that they are the first events to which the listener’s attention is drawn. Embellishing tones flesh out the basic harmonic and contrapuntal structures in infinite ways, and, finally, composers use them in specific ways, to the degree that they provide stylistic fingerprints and helpful cues for performance practice.

U N AC C E N T E D T O N E S OF F IG U R AT IO N So far we have encountered three types of melodic embellishments: chordal leaps, passing tones, and neighbor tones. The Corelli excerpt in Example 10.1 contains examples of each of these types of embellishments: (1) Chordal leaps are heard in the first two beats of m. 9.

EXAMPLE 10.1 Corelli, Sonata for Two Violins in E  major, op. 2, no. 11, Giga CL

9

PT

CL

N

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IN

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Vln 1 PT

CL

CL

P

Vln 2

root:

E

B

c

G

c6

F7

G

c

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THE COMPLETE MUSICIAN

(2) Passing tones occur in beat 3 of m. 9. (3) The upper-neighbor figure G–A–G on beat 2 in m. 10 is followed by an incomplete neighbor in violin 1 and a passing tone on beat 3 in violin 2. All dissonances are metrically unaccented; as such, they create a light and buoyant sound.

AC C E N T E D T O N E S OF F IG U R AT IO N Now listen to Example 10.2, taken from the slow movement of another Corelli sonata. Again, the letter names of chord roots appear below the score. Compare Corelli’s use of embellishing tones in this example with their use in the previous example. The embellishing tones in Example 10.2 are much more striking than those heard in Example 10.1. This is because the dissonances occur on accented beats or parts of beats. Most seem to arise through a rhythmic delay or anticipation, and are shown with arrows. For example, in m. 29 the chordal seventh, G, extends into the following measure, where it forms a dissonance against the D-major harmony. However, one beat later, G falls by step to F, where it functions as the third of the D-major chord. Another type of dissonance occurs in m. 31: The second violin plays an accented neighbor figure C–D–C over the F triad. The appearance of this dissonant neighbor on a beat rather than between beats makes it much more striking.

EXAMPLE 10.2 Corelli, Sonata for Two Violins in E minor, op. 2, no. 4, Preludio STR EA MING AUDIO 29

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31

Violin I

Violin II

root:

A7

D

A

F

6

b

6

c

6 5

F

b

S PE C I F IC S OF U N AC C E N T E D A N D AC C E N T E D T O N E S OF F IG U R AT IO N We group embellishing tones into two categories, based on their rhythmic placement. The first category, called unaccented embellishing tones (Example 10.1), includes metrically unstressed embellishing tones. We have already studied the most important of these, including the chordal leap, the passing tone, and the neighbor tone (both complete and

283

Chapter 10 Accented and Chromatic Embellishing Tones

incomplete). We further categorized the unaccented embellishing tones into those that are consonant (chordal leaps) and those that are dissonant (most passing tones and neighbor tones). Consonant embellishing tones may appear without preparation or resolution. However, dissonant embellishing tones must be carefully controlled, nearly always occurring between consonances and moving by step.

AC C E N T E D E M B E L L I S H I N G T ON E S Embellishing tones that belong to the second category, called accented embellishing tones (Example 10.2), occur in metrically stressed contexts (e.g., on, rather than between, beats). Accented embellishing tones are some of the most emotive elements of music; recognizing them can influence your performance significantly. In fact, given that Baroqueand Classical-period composers expected performers to add various types of embellishing tones to their published scores, it is desirable for the modern performer to enhance the music’s drama with ornamentation. Accented dissonances occur in many forms, but the most important are: • The accented passing tone (APT) • The accented neighbor tone (AN) • The suspension (S) • The pedal (PED) • The appoggiatura (APP) Since embellishing tones often fill the space between chordal members, then, by extension, chromatic embellishing tones fill the smaller intervallic space that occurs between stepwise motions. We also explore such unaccented and accented chromatic figures.

T H E AC C E N T E D PA S S I N G T ON E ( A P T ) Just like a passing tone, an accented passing tone (APT) fills in a melodic third; however, the APT occurs on, rather than between, beats. The usual metric positions of consonance and dissonance are reversed with the APT.

EXAMPLE 10.3 Unaccented and Accented Passing Tones A.

B.

C

I

I6

IV

I

PT

D

C.

PT

C

I6

D

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APT

C

D

IV

I

APT

C

D

I6

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APT

C

D

IV

C

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Example 10.3A shows an unelaborated SATB progression; Example 10.3B elaborates the progression with unaccented PTs. Note that consonance is aligned with metrical stress and that dissonance is reserved for the metrically weak offbeat. Example 10.3C demonstrates accented passing tones; dissonance is highlighted because it occurs on the beat, whereas the consonance now occurs on the offbeat. Accented passing tones impart a new level of tension, since consonance and metrical accents do not align. Accented passing tones most often occur in descending lines, and they usually are part of either a 7–6 or 4–3 contrapuntal motion against the bass voice. Example 10.4A presents the opening of Schumann’s song “Am leuchtenden Sommermorgen,” in which the accented passing tone A at the downbeat of m. 4 forms a dissonant fourth with the E harmony before resolving to the chordal third. Imagine if Schumann had instead written the more mundane unaccented passing tone, as shown in Example 10.4B.

EXAMPLE 10.4 APTs and PTs in Context A.

Schumann, “Am leuchtenden Sommermorgen,” from Dichterliebe, op. 48

2

APT

Am leuch

B.

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ten den Som

mer

mor gen

geh’ ich im Gar

ten her

um.

ten her

um.

Schumann, “Am leuchtenden Sommermorgen,” from Dichterliebe (modified)

2

PT

Am

leuch

ten den Som

mer mor gen

geh’ ich im Gar

T H E C H ROM AT IC PA S S I N G T ON E (C P T ) Chromatic passing tones fill the space between two diatonic pitches. Most often, the diatonic pitches are separated by a major second, creating a series of half-step motions. Example 10.5A1 illustrates how the diatonic passing tone E fills the space between

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Chapter 10 Accented and Chromatic Embellishing Tones

D and F. Example 10.5A2 illustrates the chromatic passing tone E, which fills the space between the major second E to F. Less often CPTs can fill the space between diatonic pitches a third apart, as in Example 10.5A3.

EXAMPLE 10.5

Chromatic Passing Tones STR EA MING AUDIO

A.

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PT

PT CPT

1

2

I

B.

6

CPT

APT

3

I

6

4

I

I

6

PT

ACPT

5

6

I

6

Mozart, Piano Sonata in B, K. 570, Allegretto CPT

CPT

APT (double)

1

I

V 43

I6

(P)

V6

I

V 43

(P)

I T

I

6

V6

I

(IN) V

V6 I

ii 6 V

(N) I PD D (HC)

Metric Placement and Contour Like diatonic passing tones, chromatic passing tones occur in both unaccented and accented contexts. They are more common than those that descend because ascending CPTs create miniature leading tones to the pitch they precede, thereby intensifying the melodic direction. Example 10.5A4 illustrates a diatonic APT, and Example 10.5A5 illustrates a chromatic APT (ACPT). Notice how all of the five passing tones in Example 10.5A increase their aural prominence as they move along a continuum from unaccented and diatonic to accented and chromatic.

Sample Analysis Example 10.5B presents the opening phrase of a Mozart piano sonata that contains both unaccented and accented CPTs. We’ll begin with m. 3, where two unaccented CPTs (B4 and C5) fill the space between B4 and D5 (1 and 3). Because these CPTs are unaccented, our ears are not nearly as drawn to them as they are to the accented CPT E5 that occurs on—rather than between—the strong part of beat 2 in m. 1 and that fills the space between E and F. Notice that Mozart has written a two-note slur, indicating that E is to receive an emphasis (both dynamic and articulative), whereas the unaccented CPTs in m. 3 are

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marked as the second pitches in two-note slurs, indicating that dynamic stress should be given to the first pitch in a two-note slur and that the second pitch is released and played without emphasis. Mozart’s phrase unfolds in the standard phrase model: T is prolonged for the vast majority of the excerpt, over three measures, until the PD enters for only an eighth-note duration and leads to D, on which the phrase closes with a half cadence. The strong, double APTs (B4 and D5) at the end of m. 4 (Example 10.5B) postpone and therefore draw the listener’s attention to the HC (both B and D lead to the chord tones A and C of the dominant). Notice that the tonic prolongation is made clear by the soprano’s line that falls a third from D to B (3–2–1) and ascends to recapture D. The counterpoint with the bass creates two voice exchanges (B–D). D finally falls to C (2) in the HC.

T H E AC C E N T E D N E IG H B OR T ON E ( A N ) While not nearly as common as accented passing tones, the accented neighbor tone occurs with some frequency, especially in nineteenth-century music. Example 10.6A presents a neighboring expansion of the tonic without melodic embellishment. Example 10.6B contains an unaccented neighbor (G–A–G) and passing tone (G–F–E). In Example 10.6C, the neighbor A4 is metrically accented, since it sounds on the beat. The second accented event occurs when F4, as passing seventh of the dominant harmony, becomes an APT (4–3) over tonic harmony.

Metric Placement and Contour Just as unaccented upper neighbors are more common than unaccented lower neighbors, so too are accented upper neighbors more common than accented lower neighbors. Finally, notice that the displacement (postponement) of the soprano’s G in the V6 chord results in what might be mistaken for some altered form of a seventh chord. This interpretation ignores the nonharmonic—and therefore aurally marked—function of the soprano’s A and instead views it as the chordal seventh. This analytical error has performance repercussions, for the nonchord tone A begins a pattern of implied two-note slurs that carries over into the next beat of the soprano’s line, where F clearly displaces E.

EXAMPLE 10.6 Unaccented and Accented Neighbors A.

B. N

figured bass:

6

harmonic analysis: I

V6

5

I

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C.

I

6

6 6

V 65

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P

AN

5

7

I

I

V6

APT

6

4

I

3

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Chapter 10 Accented and Chromatic Embellishing Tones

T H E C H ROM AT IC N E IG H B OR T ON E (C N ) The chromatic neighbor is highly dissonant yet very beautiful. Example 10.7 recasts the diatonic neighbors from Example 10.6 as chromatic neighbors.

EXAMPLE 10.7 Chromatic Neighbors A.

B. CN

figured bass:

6

harmonic analysis: I

V6

5

I

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C.

I

6

6 6

V 56

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P

CAN

5

7 6

I

I

V6

APT

6

4

3

I

Analytical Interlude One frequently encounters accented and chromatic passing and neighboring tones in variation sets written in the late Classical and Romantic periods, where such variation and intensification of rhythmic and diatonic regularity provide contrast and drama. For example, Schubert’s Impromptu in B is cast as a theme followed by a series of variations. The theme (Example 10.8A) opens with a simple alternation of tonic and dominant, each of which is elaborated by inversion. Variation 1 (Example 10.8B) is characterized by a broken-chord figure in which the melodic third D–B from the theme is filled by the APT C5, creating a 7–6 contrapuntal motion with the bass.

EXAMPLE 10.8 Schubert, Impromptu no. 3 in B , D. 935 STR EA MING AUDIO

A.

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Thema Andante

B :

I

6

V 43

7

I

ii 65

(V 65 /V )

V (HC)

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EXAMPLE 10.8 (continued) B.

C.

Variation 1 legato

19

APT

7

55

APT

6

I6

I

Variation 3

7

b :

i6

i

6

D. Variation 2 AIN

37

CN

AIN

4

B :

I

CPT

ACPT

ACN

I

6

3

V 43

V7

I

Variation 3 (Example 10.8C) contains the same APT figure in the right hand, but this variation is cast in the parallel minor, so the 7–6 figure is more dissonant, given that the seventh is major and more intense than the minor seventh found in Variation 1. The upper part of the left hand contains faster-moving chromatic, unaccented neighbors that together form a larger, double-neighbor figure. Variation 2 (Example 10.8D) contains nearly every possible type of embellishment, including chromatic neighbors (both unaccented and accented), examples of which occur in m. 1. The variation opens with the complete neighbor D–C–D. This variation also presents something new, the accented incomplete neighbor (AIN). Incomplete neighbors move by step to a chord tone in only one direction; that is, rather than moving from a diatonic pitch and returning to the same pitch, incomplete neighbors usually leap from a diatonic pitch and move by step (up or down) to a different diatonic pitch. For example, in m. 37 beat 3, G is an incomplete upper neighbor: It leaps down a third from the chord tone B and then falls by step to the chord tone F as its incomplete upper neighbor. An incomplete lower neighbor is heard near the end of the example, where A leaps from F and resolves in neighbor fashion to B.

T H E A PP O G G I AT U R A ( A PP) The appoggiatura is a striking type of embellishment. Different than passing tones and complete neighbor tones (which are flanked by chord tones), appoggiaturas enter by leap and are dissonant and accented. They are related to other embellishing tones only in that

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they resolve by step to a chord tone (and usually in the direction opposite of their leap in order to balance the melodic contour; a number of important exceptions exist, such as the “Maria” motive from Leonard Bernstein’s West Side Story). Thus, the appoggiatura behaves very much like the accented incomplete neighbors we encountered in Example 10.8. We will tend to refer to accented incomplete neighbors as appoggiaturas. Example 10.9 illustrates appoggiaturas and their labeling.

EXAMPLE 10.9 Appoggiaturas 4 — 3

APP

V

4 — 3

9 — 8

V7

9

—

8

9

APP

APP

APP

i

4 — 3

APP

APP

VI

V7

iv

—

8

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i

T H E S U S PE N S ION (S)

Characteristics of Suspensions Listen to Example 10.10A, which presents a two-voice example that we’ll consider to be the outer voices of the implied progression whose roman numeral analysis is given. Example 10.10B presents a modified version of Example 10.10A; in four instances the soprano voice is sustained, where it intrudes into the following implied chord change. The

EXAMPLE 10.10 Suspensions in Two Voices STR EA MING AUDIO

A.

a:

B.

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i

V 42

P

S

7

i

V 42

figured bass: harmonic analysis:

i6

vii

R

P

S

6

6

i6

6

R

7

vii

i

V

P

S

i

V

6 6

i

R

4

i

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accented dissonant pitch creates a great deal of musical tension, which is then discharged, or resolved, as it falls by step to a chord tone. We refer to such expressive embellishments as suspensions; they are the most important type of accented embellishing tones, one found consistently in music from the fifteenth century to today’s commercial and popular music.

Components of Suspensions The contrapuntal setting and metric placement of suspensions is prescribed and cannot be altered. Suspensions are composed of two pitches that are governed by a three-stage process. The first pitch progresses through two of the stages: a weak-beat preparation (P) followed by a strong-beat suspension (S). The second pitch participates in the third stage: a weak-beat resolution (R). Each suspension in Example 10.10B illustrates the two-note figure and the three stages. In m. 1, for example, the two pitches of the suspension figure are C and B. The first pitch, C, participates in the two stages of preparation and suspension. The second pitch, B, participates in stage 3: resolution. Details of each stage follow. • Stage 1, preparation: C is initially consonant (a tenth above the bass) on the weak beat (beat 2) so that it prepares for its transformation into a dissonance. • Stage 2, suspension: The prepared pitch is held, by means of a tie or a dot, as the bass moves to the implied V 42. The C is now transformed from a third (tenth) above the bass into a seventh above the bass. • Stage 3, resolution: This stage occurs when the dissonant seventh falls by step to the chord tone B, resulting in the interval of a sixth above the bass.

Suspensions in Four Voices Example 10.11 demonstrates the most common types of suspensions within a four-voice musical context. Listen to the example, which contains five suspensions. Once again, the three stages are labeled P, S, and R. • Suspension 1 occurs in m. 1 as the harmony expands the tonic by moving from i to i6 using a passing vii°6. The motion in the soprano to its lower neighbor is delayed past the onset of beat 2 as C5 in the soprano is suspended over the changing chord to create a seventh above the bass (D3). The resolution to B occurs on the following weak-beat eighth note. • Suspension 2 occurs in m. 3, as the soprano’s D5 from m. 2 is suspended over the tonic chord in m. 3 to form a ninth above the bass; it resolves on the weak third beat. • Suspension 3 appears in the bass in m. 4, as C3 is sustained from m. 3 to the downbeat of m. 4, thereby delaying for one beat the B2 (as chordal third of V6). Note: The figured bass numbers in the bass suspension increase rather than decrease in size. This is because as the bass resolves down, the intervals between it and the upper voices increase. • Suspension 4 appears in the soprano voice between mm. 4 and 5. Given its aural prominence, it coincides with, and thus highlights, the change from T to PD. Here, E5 is suspended and forms a dissonant seventh before resolving to the chord tone D, the root of ii°6. Notice that the pre-dominant harmony appears to be an incomplete iv7 chord, given the pitches F–A–E. As we discussed in relation to Example

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Chapter 10 Accented and Chromatic Embellishing Tones

EXAMPLE 10.11 Suspensions in Four Voices STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

#1 P

S

#4

#2 R

P

S

R

P

S

R

#5 P

P

S

R

5 2

6 3

S

R

#3 7

figured bass: harmonic analysis:

i i

vii (P)

6

6

6

7

i6

V7

6

7

i

V

T

9

i i

8

V6 (N)

7

i i

6

7

4

ii

6

V7

i

ii

6

V7

i

D

T

PD

10.6, context must determine function: Given the example’s pattern of suspensions, the tie, and the fact that ii6 is a far more common pre-dominant chord than iv7, we interpret E5 as a nonchord tone that resolves to D. • Suspension 5 occurs in m. 6: The tenor finally gets a chance to suspend, imitating the soprano. A dissonant fourth (F4) against the bass (C3) is created as the tenor holds F4 and the bass moves to C2; the tenor resolves down to E4 on the final beat of the excerpt.

Labeling Suspensions We use figured bass numbers to label the melodic motion of the suspension and resolution stages of the suspension figure. The names of the four upper-voice suspensions in Example 10.11 are based on the intervallic content of the suspended voice reckoned with the bass. Thus, the figured bass indications are 7–6, 9–8, 7–6, and 4–3, respectively. We label compound suspending intervals by their reduced, noncompound forms (an 11–10 suspension is called a 4–3, for example). By convention, however, the 9–8 suspension retains its compound label. The 2–1 suspension, while possible, is uncommon, given that the dissonance is sounding immediately adjacent to its resolution. The 2–3 suspension in Example 10.11 (mm. 3–4) is the figured bass label given to the most common bass suspension. Note that the suspension in the bass voice is represented by “2–3”; but in a four-voice texture, there is always another voice that creates the “5–6” motion above the suspending bass. In mm. 3–4 of Example 10.11, the alto and tenor G4 create the 5–6 motion against the bass’s C–B. In bass suspensions the numbers increase in size because the upper voices remain stationary, whereas the bass, in its descending resolution, naturally increases the size of the interval.

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We place the figured bass numbers immediately below the moving pitches, and we show the melodic motion by using the dash so as not to confuse the suspensions with inversions of chords. For example, a “7” appearing by itself indicates a root-position seventh chord; thus the “7” is a chord member. However, a “7–6” indicates a 7–6 suspension (such as in m. 1 of Example 10.11) in which the seventh displaces the sixth of a first-inversion chord. That is, the second chord is not ii7; rather, it is a vii°6 chord with a suspended seventh. Conversely, the V7 in m. 5 indicates that the dominant includes a chordal seventh above the bass. Depending on your teacher’s preference, you can represent suspensions (and other accented embellishing tones) within a figured bass analysis (immediately below the bass staff ), or you can incorporate them in your roman numeral analysis.

Writing Suspensions The most common upper-voice suspensions are the 9–8, 7–6, and 4–3. In the bass, it is the 2–3. The following guidelines will help to write suspensions. 1. Suspension figures logically work best with chords whose intervals contain the interval of resolution. For example: • 7–6 suspensions work well with 63 chords, given that all first-inversion chords contain the interval of a sixth and that chords with a sixth above the bass are most often first-inversion chords (e.g., vii°6, V6, and I6). • Similarly, 4–3 and 9–8 suspensions work best with root-position chords. • The bass suspension (2–3) works best with a 63 chord (especially in the progression I–V6). 2. Suspensions may occur in any voice at any time as long as the voice is moving down by step to the next chord tone. For example, in the chord progression in Example 10.12A, the three upper voices in the first chord all lie a second above the corresponding voice in the second chord, which means that the resolution is already set up. Now we consider the second chord in order to find an appropriate voice to suspend. Given that the second chord is a first-inversion sonority, the 7–6 suspension would work best (see Example 10.12B). Study Examples 10.12A and B to see how suspensions are generated. 3. If the voice in which you want to write a suspension is moving up by step, consider inserting an ascending chordal leap, which would allow for the preparation and resolution of the suspension downward. For example, say that you wanted to insert a soprano-voice suspension, as in Example 10.12C. However, F4 lies below G4, which prevents the use of a suspension. A chordal leap from F4 to A4 solves the problem, since the A4 can now resolve to G4 in a 7–6 suspension. 4. Make sure that the resolution pitch is not doubled in any other voice, for if it were, it would be sounding against the dissonant suspension and thus would anticipate the suspension’s tone of resolution and ruin its intended effect. The one exception to this rule is the 9–8 suspension, which falls to the octave, because the dissonance is far enough away from the sounding note of resolution. Finally, the duration of the dissonant suspended note should be at least as long or longer than the preparation and the resolution.

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EXAMPLE 10.12 Adding Suspensions in Four Voices STR EA MING AUDIO

look for descending steps (shown by arrows)

A.

I

vii

6

I6

IV

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V

4 2

I6

4

3

5 2

V6

I

B.

7

C.

6

7

6

9

8

6 3

9

8

Ascending Chordal Leap Prepares Suspension P S R

⇒ 7

6

Additional Suspension Techniques Having learned the basics of suspensions, it is easy to spot variations on suspension technique in musical works. There are six common modifications of the basic suspension pattern that we will encounter in our analyses. Example 10.13, which is an elaboration of Example 10.11, illustrates each of these suspension modifications. 1. Embellished suspensions, as seen in mm. 1, 4, and 6, use submetrical figurations to embellish the dissonant note. 2. Suspensions with a change of bass, as seen in m. 1, involve a bass leap to another consonance at the same time that an upper-voice suspension resolves. Since the bass is changing, this often results in a harmonic change. The figured bass notation for change-of-bass suspensions follows our established rules. Make sure you include the horizontal dash in order to make clear that the dissonance resolves (as seen in the 7–3 in the example).

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EXAMPLE 10.13 More Suspension Possibilities STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Restruck susp. Double susp.

Embellished susp. P

S

R

P

S

P

7

figured bass:

3

6

7

Change of bass

R

S

P 9 4

Double susp. P

S

R

8 3

R

P

S 5 2

R 6 3

Embellished susp.

7 6 4

Retardation P

S

R

S

5

7 4

R

8

Double susp. Embellished susp.

3. Restruck suspensions, as seen in m. 2, omit the tie, permitting the suspended note to be resounded at the point of dissonance. 4. Double and triple suspensions, as seen in mm. 2–3, 4–5, and 6, involve two or three simultaneous dissonances, each of which resolves correctly. 5. Retardations (upward-resolving suspensions), as seen in m. 6, are common in Classical music, especially in the works of Mozart. We will use only one type, 7–8, and only in perfect authentic cadences. 6. The suspension chain is a patterned series of suspensions that interlock. An example can be derived from a series of falling 63 chords (Example 10.14A), which in the hands of Haydn has been transformed into a suspension chain in Example 10.14B. In the reduction of Example 10.14C, we see how such motions are much more contrapuntal and melodic than harmonic. With all the submetrical

EXAMPLE 10.14 Suspension Chains A.

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Parallel Six-Three Chords 5

6 3

5

6 3

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6 3

6 3

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Chapter 10 Accented and Chromatic Embellishing Tones

295

EXAMPLE 10.14 (continued) Haydn, Piano Sonata no. 37 in E major, Hob XVI.22, Tempo di Menuetto

B.

63

C.

Reduction

10

10

10

10

10

10

change of bass

G:

5

vi

6

7

6

7

6

7

6

7

3

ii 7

V7

I

figuration removed, Example 10.14C reveals outer-voice parallel tenths that descend by step, which provide an outer frame for the suspensions that occur in the alto voice. Haydn begins the series of 7–6 suspensions in m. 63 by moving the fifth of the E-minor chord, B4, up to C5. This is an effective preparation that creates a sixth that is tied over the bar to become the suspended seventh in the next measure. The 7–6s continue until m. 67, where Haydn uses a change of bass to create a V7 harmony that intensifies the cadence on G major. Had he maintained the suspension pattern, the less conclusive vii°6 chord would have occurred as the cadential chord. Notice how the parallel fifths in the alto and soprano of Example 10.14A are disguised by Haydn.

T H E A N T IC I PAT ION ( A N T ) The anticipation is an unaccented nonchord tone, but, given that it can be considered the “mirror opposite” of the suspension, it is included at this point. The anticipation appears before the chord to which it belongs actually sounds, usually creating a dissonance with the already-sounding chord. Because it occurs on a weak beat and is premature, it can be viewed as an embellishing tone that functions in the exact opposite manner of the suspension, which is an accented tone that delays a chord tone’s resolution. It is most effective at cadences, when the final chord is strongly expected. Example 10.15 presents an example of a double anticipation: The Phrygian cadence (iv6–V) is intensified by the entrance of C and A (members of V) prematurely, while iv6 is still sounding. This example also contains a hemiola and another double suspension.

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EXAMPLE 10.15 Corelli, Violin Sonata no. 11 in D minor, op. 1, Adagio 6

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ANT

5

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4

hemiola:

1 2

1

2

1 2 iv 6

1 V

Phrygian cadence

T H E PE DA L ( PE D) A sustained pitch or harmony that sits motionless during multiple harmonic changes is known as a pedal or pedal point. Derived from the organ’s ability to sustain a pitch indefinitely, the pedal tone usually occurs in the bass and almost always is a tonic or dominant scale degree, which slows down the harmonic motion and firmly grounds the music on one static harmony. Pedals often occur in cadential situations (Example 10.16), in which harmonic successions can unfold over a single held note. As the two levels of analysis in the Bach excerpt show, such harmonic successions (usually labeled as though they were in root position) are subordinate to the pedal.

EXAMPLE 10.16 Bach, Fugue in C minor, from The Well-Tempered Clavier, Book 1, BWV 847 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

29

c:

Ped. i

T

iv

vii 7

(PED)

(PED)

i

vii 7

(PED)

I

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Chapter 10 Accented and Chromatic Embellishing Tones

S U M M A R Y OF T H E MO S T C OM MO N E M B E L L I S H I N G T O N E S

EXAMPLE 10.17 A.

CL (diss.)

B. ANT

CL

ARP

CL

ARP

CL

C.

N (lower)

N (consonant upper)

DN (double neighbor)

IN (incomplete neighbor)

V

I

I

V

V7

I

D.

6 5

CN (chromatic neighbor)

I

E. PT

AN

APT CPT

6

APP

APP

(S)

APT

APT CPT

CPT

I

ACN

V 34

6

I

V

I

7

6

Unaccented Anticipation (ANT): dissonant, premature entrance of a member of an upcoming chord (Example 10.17A). Arpeggiation (ARP): successive chordal leaps that occur in a single direction and that include all members of the triad or seventh chord (Example 10.17B). Chordal leap (CL; called consonant leap in contexts such as sixteenth-century counterpoint) 1. A leap from one chord tone to another within a single harmony (Example 10.17B). 2. Dissonant leaps are permitted if the pitches are members of V7 (e.g., the tritone between scale degrees 7 and 4) (Example 10.17B). Neighbor tone (N, IN, DN, CN) 1. Stepwise ascent or descent from a chord tone, followed by a change in direction and return to the initial chord tone (N) (Example 10.17C). 2. Incomplete neighbor (IN): a leap to a note that neighbors a chord tone, followed by resolution to that chord tone by step (Example 10.17C). 3. Double-neighbor figure (DN): stepwise ascent or descent from a chord tone, followed by a balancing motion to the opposite neighbor and return to the initial chordal tone (Example 10.17C). 4. Chromatic neighbor (CN): includes one or more nondiatonic pitches (Example 10.17C).

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Passing tone (PT) 1. Stepwise motion in a single direction that fills in an interval of a chord, most often a third (Example 10.17D). 2. Chromatic passing tone (CPT): fills the space between two diatonic tones a major second apart (or between two chord tones a third apart) (Example 10.17D). Accented Accented neighbor note (AN) 1. A three-note figure identical to the unaccented neighbor but occurring on accented beats (Example 10.17E). 2. Accented chromatic neighbor (ACN): A three-note figure identical to the chromatic neighbor but occurring on accented beats (Example 10.17E). Accented passing tone (APT): a dissonant member of a passing figure that occurs on an accented beat. Usually occurs in descending lines. Most common intervallic structure is 7–6 and 4–3 (Example 10.17D and E). Appoggiatura (APP): unprepared dissonance occurring on a strong beat; essentially an accented incomplete neighbor. Resolves by step, usually in the direction opposite that of its leap; 4–3 and 9–8 are most common (Example 10.17E). Pedal (PED) 1. A sustained pitch, most often in the bass, with tonic or dominant function; surface harmonic succession usually unfolds above. Suspension (S) 1. Most important accented embellishing tone, in which a stepwise melodic descent is temporarily postponed and that creates a dissonance before the line continues (Example 10.17E). 2. Unfolds in three stages: a. preparation (P): weak-beat consonance (chord tone). b. suspension (S): sustained preparation note continues into strong-beat chord change. In this environment it is a nonchord tone (usually dissonant). c. resolution (R): sounding dissonant suspension falls by step on a weak beat to a chord tone. 3. Three common upper-voice types: 9–8, 7–6, 4–3. 4. One common bass-voice type: 2–3 (9–10).

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 10.1–10.4

10.1 Suspensions Analyze the given excerpts. Include the following: 1. Circle and label each component of the suspension (P, S, and R).

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Chapter 10 Accented and Chromatic Embellishing Tones

2. Figured bass that specifies the melodic motion of the suspension. 3. Roman numerals. STR EA MING AUDIO

Sample solution: Mozart, String Quartet in B  major, K. 172, Adagio

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P

S

7 I

A.

P

R

6

V 34

V7

V 42

Beethoven, Symphony no. 1 in C major, op. 21, Finale

56

SOLVED/APP 5

B. Haydn, Piano Sonata in D major, Hob XVI.4, Menuetto (Do not include roman numerals.) 3

3

SOLVED/APP 5

C.

Giardini, Six Duos for Violin and Cello, no. 2 Adagio

S

R

7

6

I6

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THE COMPLETE MUSICIAN

10.2 All Embellishing Tones Circle and label all embellishing tones. Add roman numerals when specified. Be aware of accented and unprepared dissonances. STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

SOLVED/APP 5

A.

Schubert, Waltz in C  minor, no. 27, from 36 Original Dances, D. 365 (Add roman numerals.)

SOLVED/APP 5

B. Mozart, Variations on “Ah vous dirais-je, Maman,” K. 265 VAR. I.

legato

C. Haydn, String Quartet in G major, op. 33, no. 5, iii Allegro Violino I.

Violino II.

Viola

Cello

Chapter 10 Accented and Chromatic Embellishing Tones

301

T ER MS A ND CONCEP TS • accented dissonances (accented embellishing tones) • accented neighbor, accented chromatic neighbor note • accented passing tone • appoggiatura • pedal • suspension • unaccented dissonances (unaccented embellishing tones) • anticipation • neighbor • passing tone • chromatic dissonances • chromatic neighbor • chromatic passing tone • suspension • preparation, suspension, and resolution • suspension chains • suspension patterns • double and triple suspension • embellished suspension • suspension with change of bass • retardation • restruck suspensions

CH A PTER R EV IEW 1. Thus far in the text, we have encountered chordal leaps, passing tones, and neighbor tones. Until now, these embellishing tones have always been [accented/unaccented].

2. List the five most important accented dissonances below, with their abbreviations.

3. Which kind of embellishing tone fills in the space between two neighboring chord members?

4. Appoggiaturas (APP) enter by [step/leap], are [consonant/dissonant], and [accented/ unaccented].

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5. List the three stages of a suspension.

6. List the four most common types of suspensions, identifying each by a pair of numbers (e.g., 6–5). Which one occurs in the bass?

7. Define each type of suspension as briefly as possible. 1. Embellishing suspensions 2. Suspensions with a change of bass 3. Restruck suspension 4. Double and triple suspensions 5. Retardation 6. Suspension chain

8. Anticipations (ANT) are [accented/unaccented] and [consonant/dissonant].

9. A pedal point is usually in the [bass/soprano] and is usually one of which two scale degrees?

C H A P T E R 11

Six-Four Chords, Revisiting the Subdominant, and Summary of Contrapuntal Expansions OV E RV I E W

In this chapter we complete our study of contrapuntal expansions by taking up the final triad type: six-four chords. We also extend these expansion techniques to other scale degrees so longer spans of music may be created using not only the tonic, but also the dominant and the pre-dominant. CHAPTER OUTLINE Unaccented Six-Four Chords................................................................................... 304 Pedal ........................................................................................................................ 304 As Passing Tones ........................................................................................... 304 Passing..................................................................................................................... 306 Arpeggiating ........................................................................................................... 307 Accented Six-Four Chords in Cadences ................................................................ 308 Cadential Six-Four Chord as a By-Product of the Suspension ....................... 308 Cadential Six-Four Chord as a By-Product of the Accented Passing Tone ... 309 Preparing Cadential Six-Four Chords ................................................................ 310 Additional Uses of Cadential Six-Four Chords ................................................. 310 As Part of Half Cadences ..............................................................................310 Preceding V 7 ..................................................................................................311 Within a Phrase.............................................................................................311 Evaded Cadences: Elision and Extension ....................................................312 Triple Meter ...................................................................................................314 Writing Six-Four Chords ..............................................................................315 (continued)

303

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THE COMPLETE MUSICIAN

Revisiting the Subdominant ................................................................................ 316 Contrapuntal Expansion with IV ................................................................316 IV in Two Very Different Contexts..............................................................317 Plagal Cadence ..............................................................................................317

Summary of Harmonic Paradigms......................................................................... 318 Harmonizing Florid Melodies................................................................................. 318 Terms and Concepts ................................................................................................... 322 Chapter Review ........................................................................................................... 323

Y O U M I G H T H AV E N OT I C E D that we have not discussed any six-four (64) chords in

our studies (save for their simple definition in Part 1). This is because they occur much less often than root-position and first-inversion chords, given their dissonant interval of a fourth that lies above their bass; root-position and first-inversion triads contain only consonant intervals (octaves, thirds, fifths, and sixths). While their intervals stack into secondinversion triads, they rarely function as do their root-position and first-inversion cousins. We will see that six-four chords are often only apparent harmonies resulting from the coincidence of passing and neighboring tones in two or more voices. Therefore, six-four chords require careful contextual analysis and writing. Six-four chords occur in either unaccented or accented contexts; their discussion here will follow in that order.

U N AC C E N T E D S I X- F OU R C HOR D S

Pedal Unaccented six-four chords usually occur on weak beats within a measure or on weakly accented measures in four-measure groups. Listen to the short excerpt in Example 11.1, noting the six-four chord’s function. You probably heard the opening of this famous Christmas carol as a single prolonged tonic harmony. If so, you would have interpreted the two IV64 chords as sonorities that elaborate the much stronger-sounding tonic chords, rather than as some sort of structural chords. These six-four chords arise when the bass holds B and the inner voices ascend from D4 and F4 to E4 and G4, followed by a return to D4 and F4. Thus, the apparent IV64 arises through a neighbor figure exhibited simultaneously in two voices. Given the sustained bass over which the neighbor figure appears, we assign the name 5–6–5 pedal six-four chord. We label pedal six-four chords as Ped64 or, with figured bass, 3–4–3 . Pedal six-four chords can prolong not only tonic, but also the dominant, as shown in Example 11.2. It is crucial to recognize that the apparent tonic harmony (I64) in m. 3 arises as the by-product of two upper neighbors that move in parallel motion.

As Passing Tones So far, we have seen how pedal six-fours can arise out of upper-voice neighboring motion. Pedal six-four chords can also arise from passing motion. The expansion of V(7) is often accomplished through a pedal six-four, with the upper voices ascending or descending a third (from 7 to 2 and 2 to 4), as shown in Example 11.3.

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Chapter 11 Six-Four Chords, Revisiting the Subdominant

EXAMPLE 11.1 Pedal Six-Four Chords Extend Tonic: Gruber, “Stille Nacht” (“Silent Night”) neighbors above pedal

.

B :

6– I 53 –––– –––– 4 –

*

5 3

I 53

I

– –

6 – 5 4 –3

I

Ped64

T

EXAMPLE 11.2 Pedal Six-Four Chords Extend Dominant: Schubert, Minuet in D major, D. 41 Ped 64

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1

D:

I

V

T

D

5 – 6 – 5 3 – 4 – 3

EXAMPLE 11.3 Pedal Six-Four Chords Within Passing Motion: Mozart, Symphony in A major, K. 385, Menuetto/Trio STR EA MING AUDIO

Passing tones above pedal

A:

I

V 75

T

D

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– 6 – 5 – 4 – 3

&

Ped64

T

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THE COMPLETE MUSICIAN

Passing We learned that pedal six-four chords derive their name from a sustained bass and uppervoice motion. The passing six-four chord (P64) derives its name from the bass passing motion that fills the interval of a third. Listen to Example 11.4 and locate the passing six-four chord. Measures 17–21 act as a tonic prolongation from i to i6 featuring an archshaped bass line (A–B–C–D–C). Within the arch, the passing six-four chord occurs in m. 18, where it connects root-position tonic with first-inversion tonic by the stepwise bass line A2–B2–C3. Notice that this passing six-four chord functions identically to the passing vii°6 chord, which also fills the space between the tonic and its first inversion. On the second level of analysis, we label the chord P to reflect its passing function. Here, it is important to consider how this P64 is unaccented. Unlike that of Example 11.2, which occurs on a weak beat, this chord occurs on a weak measure within a quickly moving four-bar group. Similarly, in very slow tempos such chords may occur on weak parts of beats.

EXAMPLE 11.4 Passing Six-Four Chord: Beethoven, Piano Sonata in C major, op. 2, no. 3, Trio STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

17

3 3

3

a:

3

3

3

3

6

i

3

3

3

3 3

4

i6

V4

V2

(P)

T

(N) (S)

21

( )

3 3

i6

3

3

ii

6

PD

3

3

3

V 57 D

3

6 4

3

5 3

i T

Passing six-four chords may be used to connect any five-three chord with its sixthree inversion. Example 11.5 demonstrates a passing six-four to extend both the tonic (D minor) and the subdominant (G minor). The Allegro opens with a series of restruck suspensions; once we remove them from the texture in Example 11.5B, we easily see the implied passing six-fours connecting i to i6 and iv to iv6.

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Chapter 11 Six-Four Chords, Revisiting the Subdominant

EXAMPLE 11.5 Passing Six-Four Chords A.

STR EA MING AUDIO

Beethoven, Piano Sonata in D minor, op. 31, no. 2, Largo/Allegro Largo

Allegro

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5

cresc.

6

d:

V5

6

i

V4 (P)

i6

T

B.

6

iv

i4 (P)

iv 6

V

PD

D

Reduction

iv i64 iv 6 PD (P)

V 64 i 6 T (P)

d:

i

V D

Arpeggiating Emerging from figurated textures and accompanimental patterns, the arpeggiating sixfour chord (Arp64) is common in marches, waltzes, and folk tunes and is sometimes referred to as a waltz six-four chord (Example 11.6). In both the Schubert and Beethoven

EXAMPLE 11.6 Arpeggiating Six-Four Chords A.

STR EA MING AUDIO

Schubert, Ländler, D. 734, op. 67, no. 16

Arp 6

G:

4

I

IV

I

Arp 64

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Arp 64 V

7

I

IV

I

Arp 64

V7

I

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THE COMPLETE MUSICIAN

EXAMPLE 11.6 (continued) B.

Beethoven, Symphony no. 3 in E major, op. 55, III, Trio

167

E :

I I

6 3

Arp64

5 3

Arp 64

6 3

5 3

V 53 V

6 4

5 3

examples, the six-four chords that appear are consonant and are merely part of arpeggiations of the harmony that controls each measure. In pieces such as waltzes, where one could easily imagine the first (low) bass note sustained through the entire measure, the (higher) apparent six-four chords are heard as completing a root-position harmony. Thus, when analyzing arpeggiating six-fours, you need not label the actual chords; it is sufficient to draw a dash after the initial roman numeral. This analytical method can be seen at work in Example 11.7, where the “filler” six-four chords on beats 2 and 3 of mm. 1 and 3 are effectively ignored. Example 11.7 contains not only the arpeggiated six-four (which occurs on the weak beats of mm. 1 and 3) but also a pedal six-four (m. 2), which expands the flanking tonic harmonies in mm. 1 and 3 through neighboring motion (see the left hand).

EXAMPLE 11.7 Schubert, Waltz in A minor, from 12 Grazer Walzer, D. 924, no. 9 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

a:

i T

5 3

6 4

5 3

V7 D

AC C E N T E D S I X- F OU R C HOR D S I N C A DE N C E S

Cadential Six-Four Chord as a By-Product of the Suspension We will explore only one type of accented six-four chord, which is usually found at cadences. For that reason, we call it the cadential six-four chord (Cad64). The cadential sixfour chord was an outgrowth of two metrically stressed dissonant events: the suspension

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Chapter 11 Six-Four Chords, Revisiting the Subdominant

and the accented passing tone. Example 11.8 provides a possible evolution of the cadential six-four chord from the suspension. • In Example 11.8A, the progression is I–I6–V–I; each harmonic function occupies one measure. The tied G4 in the alto shows the common tone between the dominant and the tonic. • In Example 11.8B, the progression is ornamented by a 4–3 suspension, as the soprano C5 sustains into a measure of dominant harmony. • In Example 11.8C, the tenor voice links up with the soprano voice by suspending 6–5 into the next measure of dominant harmony and creating a 4–3 double suspension. The sixth then falls to a fifth and the fourth falls to a third. • Example 11.8D revoices the upper voices so that the suspended 3 appears in the soprano voice. • Example 11.8E adds the PD function by incorporating a IV chord, since 1, the chordal fifth, continues to serve as preparation for the suspension.

EXAMPLE 11.8 Cadential Six-Four Arising from the Suspension STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

B.

I

6

T

C.

V

I

I

D

T

T

6

V4 D

3

I

I

T

T

D.

6

V 64 D

5 3

I

I

T

T

6

V64 D

5 3

I T

E.

I

IV

V 64 –– 53

I

T

PD

D

T

Cadential Six-Four Chord as a By-Product of the Accented Passing Tone Example 11.9 presents an evolution of the cadential six-four chord through the second type of dissonant event: the accented passing tone. Recall that a melodic gap occurs in the soprano between 2 and 7 (see Example 11.9A) or between 4 and 2 (see Example 11.9B) when moving from ii(6) to V. The cadential six-four chord fills this gap of a third as a

310

THE COMPLETE MUSICIAN

powerful accented passing tone that intensifies the motion to 7 or 2. The IV chord, with 4 in the soprano, also works well in this situation.

EXAMPLE 11.9 Cadential Six-Four Arising from the Accented Passing Tone

A. 3

2

7

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filled

gap

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APT 1

3

2

1

7

1

5 V 64 — —3

I

D

T

⇒

B.

I

ii 6

V

I

I

ii 6

T

PD

D

T

T

PD

filled APT

gap 5

4

2

1

5

4

3

2

1

5 V 64 — —3 D

I T

⇒ I T

ii 6 PD

V D

I T

I T

ii 6 PD

The cadential six-four chord, then, is a root-position dominant harmony whose chordal fifth and third are temporarily postponed by an accented dissonant fourth and sixth.

Preparing Cadential Six-Four Chords These upper-voice, nonharmonic tones are resolved by step down. Preparation occurs in one of two ways: 1. Preparation by common tone (as suspensions) occurs when I precedes the cadential six-four (given that 1 and 3 appear in tonic and become the double suspensions in the cadential six-four). The IV chord (with 1 in the soprano) works well, too. (See Example 11.8C and D.) 2. Preparation by step (as accented passing tones) is used when a pre-dominant harmony precedes the cadential six-four (Example 11.9A and B).

Additional Uses of Cadential Six-Four Chords As Part of Half Cadences Not only do cadential six-four chords occur in authentic cadences, but they also intensify the dominant at half cadences, given the accented strong-beat dissonance that draws

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Chapter 11 Six-Four Chords, Revisiting the Subdominant

attention to the chord. Example 11.10 shows cadential six-four chords in half and authentic cadences. The first phrase closes in m. 4 with a HC that includes the cadential six-four. This permits a full measure for the horn to move from D through the accented passing tone C and eventually on, to resolve to B. The second phrase closes with an acceleration of the harmonic rhythm: Both the cadential six-four and the tonic occupy m. 8 as the horn balances the previous falling motion with a rise to 1.

EXAMPLE 11.10 Cadential Six Fours in Half and Authentic Cadences: Mozart, Concerto in E  for Horn and Orchestra, K. 447, Larghetto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

APT

1

)

I

6

V5 (N)

I I

4

I6

V3 (P)

T

ii 6 PD

6

V4

5 3

D HC APT

8vb

5

I

6

V5

V7

(N)

(CL)

T

I

6

ii 5 PD

8

V6 4

7 5 3

D

I T

PAC

Preceding V 7 Notice that the cadential six-four in m. 8 of Example 11.10 leads not to a triad on V but, rather, to V7: E (the root of V7) appears as part of a melodic 8–7 motion above the bass.

Within a Phrase Just as V7 may occur within a phrase, so too do accented six-four chords. Example 11.11 presents an example. The six-measure phrase closes with a half cadence that is strengthened by a cadential six-four. However, Haydn peppers his phrase with sustained dominants, the first of which (m. 1) contains a 4–3 suspension, while the second example intensifies the single suspension with two suspensions, creating the characteristic cadential six-four.

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EXAMPLE 11.11 Cadential Six-Four Chords Within the Phrase: Haydn, Piano Sonata in G minor, Hob XVI.44, Allegretto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

4

i

V 4–

i

V 6–5 4–

i6

ii 6

V 42

T

i6

V 56

i

V 64

5

D HC

Evaded Cadences: Elision and Extension We have seen that composers can thwart a listener’s expectations of a strong cadence by changing the direction of the line at the last second. For example, a root-position V chord setting up an authentic cadence can be weakened by the addition of the chordal seventh in the bass (resulting in a V 42 chord), as we saw in Example 8.5D2. This common procedure of circumventing a cadence is called an evaded cadence. Evading the cadence occurs even more often when the most powerful dominant, the cadential six-four chord, intensifies as the dominant. Indeed, the addition of a simple passing seventh in the bass effectively dissolves a strong cadence, given that this seventh must resolve to the far-weaker I6 chord rather than to a root-position tonic. There are two common reasons why composers would want to evade a cadence when using a cadential six-four chord: 1. They wish to hide the seams between two independent phrases in order to create one large phrase, a technique called elision. 2. Or they wish to intensify a cadence by repeating certain elements of it, including the pre-dominant function and the dissonant, first part of the cadential six-four chord, before finally stating the authentic cadence— a technique called cadential extension. Listen to Example 11.12 for an example of phrase elision using V42. Mozart creates a single expansive eight-measure phrase rather than two four-measure phrases by converting the cadential six-four (m. 12) into a V42. Indeed, the required resolution to I6 averts the potential HC and thus covers any seam between mm. 12 and 13. Notice that the final cadence includes another cadential six-four, this one, however, participating in the PAC. Cadential extension using V42 dramatically intensifies the listener’s desire for closure and sets up what amounts to a harmonic crescendo that heralds the impending structural cadence. Example 11.12B illustrates how Mozart is able both to suspend and to intensify

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Chapter 11 Six-Four Chords, Revisiting the Subdominant

EXAMPLE 11.12 Evaded Cadences and Cadential Six-Four Chords A.

9

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12

V 65

I A:

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Phrase Elision: Mozart, Symphony in A major, K. 114, Allegro moderato

V 64

ii 6

I

5 3

V 42

I6

IV

ii 6

I

as PT link

T

PD

V 46

5 3

I

D

T

PAC

B.

Cadential Extension: Mozart, Quintet “Hm! Hm! Hm!” from The Magic Flute, act I

frie hap

den pi

heit ness

ver and

mehrt, mirth,

wird to

Men hap

schen glück ness pi

ver and

frie hap

den pi

heit ness

ver and

mehrt, mirth,

wird to

Men hap

schen glück pi ness

ver and

frie hap

den pi

heit ness

ver and

mehrt, mirth,

wird to

Men hap

schen pi

glück ness

ver and

frie hap

den pi

heit ness

ver and

mehrt, mirth,

wird to

Men hap

schen pi

glück ness

ver and

I6

ii 6

V 46

1st attempt

4 2

I6 2nd attempt

ii 6

V 64

4 2

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THE COMPLETE MUSICIAN

EXAMPLE 11.12 (continued)

mehrt, mirth,

wird to

Men hap

schen glück pi ness

ver and

mehrt. mirth.

mehrt, mirth,

wird to

Men hap

schen glück pi ness

ver and

mehrt. mirth.

mehrt, mirth,

wird to

Men hap

schen glück ness pi

ver and

mehrt. mirth.

mehrt, mirth,

wird to

Men hap

I6

ii 6

V 64

schen pi

glück ness

ver mehrt. and mirth.

7 5 3

I

3rd attempt PAC

an expected cadence. In the close of a quintet from his Magic Flute, we hear the powerful cadential six-four chord lead not to a five-three chord, but rather to V42, which necessarily leads to I6 and another attempt to close the phrase. In the second attempt, the cadential six-four is extended, lasting almost two measures (rather than two beats, as in the first attempt). It is only in the third attempt, that the V 64 finally resolves to the root-position V7 chord and moves on to tonic.

Triple Meter In triple meter, the cadential six-four chord may appear on either beat 1 or beat 2, since both are metrically stronger than beat 3. The last movement of Mozart’s B major Bassoon Concerto in #$ often emphasizes beat 2, through durational accents (see Example 11.13). Yet again, the first appearance of a cadential six-four moves to V42. However, different than in Example 11.12, we still hear two phrases, given the parallel melodic construction. Nonetheless, Mozart smooths the seam between the two phrases. Notice that the cadential six-four chord (m. 7) appears on beat 2 and falls to five-three on beat 3.

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Chapter 11 Six-Four Chords, Revisiting the Subdominant

EXAMPLE 11.13 Cadential Six-Four Chords in Triple Meter: Mozart, Bassoon Concerto in B , K. 191, Rondo, Tempo di Menuetto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1

Violino I.

Violino II.

Viola.

Violoncello e Contrabasso. B :

I ( T

)

ii 6 PD

V 64 53 D

4 2

I6 T

HC

(

)

I

V64 35

I

D

T PAC

Writing Six-Four Chords Based on the models of unaccented and accented six-four chords, we can now summarize their functions and formulate writing rules. 1. Unaccented six-four chords are embellishing chords that prolong another harmony, usually the tonic. These include the pedal (Example 11.14A), passing (Example 11.14B), and arpeggiating six-four chords (Example 11.14C). 2. The one type of accented six-four chord we have learned is the cadential six-four. The cadential six-four occurs over the root-position dominant and is formed by two nonchord tones above the root of V: the sixth and the fourth postpone the chordal fifth and third. The cadential six-four chord: a. may be used at either a HC or an AC (Example 11.14D). b. is usually immediately preceded by a pre-dominant, although sometimes by a form of the tonic, but not by another dominant-function chord (e.g., vii°6 or vii° 7) since it weakens the impact of the Cad64 arrival. c. occurs on a metrically accented beat (beat 1 in duple meter, beat 1 or 2 in triple meter, beat 1 or 3 in quadruple meter). d. participates in a HC or an AC. e. may be used within a phrase or between phrases (use V42 to elide phrases by weakening cadential motion). 3. Approach and leave six-four chords by step or common tone. 4. Double the bass in six-four chords.

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THE COMPLETE MUSICIAN

EXAMPLE 11.14 Summary of Six-Four Chords A. Pedal

I 35

B. Passing

6 4

T

V 64 I 6 (P)

I I

5 3

C.

T

D. Cadential

Arpeggiating

I 64 I 6 (Arp) T

V

I

V 64 –– 53

D

T

D

Revisiting the Subdominant Contrapuntal Expansion with IV The subdominant harmony can function in two very different ways: WORKBOOK 1 Assignment 11.1

• In its root position or first inversion (as part of the Phrygian cadence) it occurs as a strong harmonic function: the pre-dominant. • In its first inversion, it regularly occurs as a weak contrapuntal chord that expands either I or V. (Recall that IV6 participates in tonic expansions as part of a bass arpeggiation [1–6–3] and as dominant expansions as a passing chord between V and V6.) We now see how IV in root position may be used to expand tonic. Remember that the pedal six-four chord contains the same pitches as the subdominant, yet we refrained from labeling it a IV harmony because of its neighboring motion in the upper voices. Consider the situation in Example 11.15. The central sonority in Example 11.15A clearly acts as a pedal six-four chord. The central chord in Example 11.15B looks

EXAMPLE 11.15 IV as an Embellishing Chord A.

B.

I 53

6 4

5 3

I IV

(Ped) T

C. Haydn, Divertimento, “St. Anthony Chorale”

(EC) T

I

I IV64 I (Ped) T

IV (EC)

I

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

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Chapter 11 Six-Four Chords, Revisiting the Subdominant

similar, yet the neighbor notes (G and E) are less dissonant. In fact, the chord is a stable root-position triad on IV since the bass leap to E renders G and E in the upper voices temporarily consonant. Therefore, even though IV appears in root position, we still hear tonic controlling the example, and we label the IV an embellishing chord (EC). Example 11.15C illustrates Haydn’s use of IV to expand tonic.

IV in Two Very Different Contexts As we do with every musical event, we must consider the context in which the subdominant appears and interpret it accordingly. For example, the Menuetto from Mozart’s Symphony no. 39 opens with multiple statements of the IV chord (Example 11.16). It appears as a pre-dominant in mm. 3–4, leading to the dominant function in m. 5–6. However, in m. 2, IV prolongs I through a neighboring motion.

EXAMPLE 11.16 Mozart, Symphony no. 39 in E  major, K. 543, Menuetto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Allegretto

E:

I T

5

I 6 IV I 6 IV expands I

IV

V

I

D

T

IV as PD PD

Plagal Cadence IV can embellish the tonic at the end of a piece immediately following an authentic cadence. In Example 11.17, IV participates in closing the hymn. The two-chord motion IV–I is called a plagal cadence (because it often appears in church music, it is also known as the “amen cadence”). However, notice that the plagal cadence immediately follows an authentic cadence, almost as if it were tacked on to the end of the piece. The plagal cadence is often a cadence in name only, since a strong authentic cadence usually precedes it. This plagal motion is much weaker than the authentic cadence because the motion of IV to I is not nearly as goal-directed as the motion from V to I heard in the authentic cadence. Whereas the authentic cadence contains the tonally defining descending-fifth root motion coupled with the equally strong melodic resolution of 7 to 1, the plagal cadence has only a descending fourth in the bass and a static common tone above, 1. Therefore, IV is peripheral to the harmonic motion and instead extends the tonic through double upperneighbor motion.

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THE COMPLETE MUSICIAN

EXAMPLE 11.17 Dykes, “Holy, Holy, Holy” STR EA MING AUDIO

Plagal

PAC

God in three Per sons, bless ed Tri ni ty. Which wert, and art, and ev er more shalt be. Per fect in power, in love, and pu ri ty.

W W W.OUP.COM/US/LAITZ

A men

S U M M A R Y OF H A R MO N IC PA R A DIG M S We have now completed our study of contrapuntal expansions. Although we have focused exclusively on ways that such embellishments expand the tonic and the dominant, we will see in later chapters that the principles can be applied to all of the other harmonies. Example 11.18 summarizes neighboring, passing and leaping bass motions, the possible contrapuntal chords used to harmonize them, and common soprano pitches used in setting these contrapuntal expansions. Progressions occur in major and minor, except those that involve vii°7, which (for now) occur only in minor.

H A R MON I Z I N G F L OR I D M E L ODI E S Now that the pre-dominant function has been added to your harmonic palette, we can harmonize tunes with slower harmonic rhythm much more effectively than we could using only tonic and dominant functions. Further, this chapter’s discussion of six-four

EXAMPLE 11.18 Summary of Bass and Soprano Harmonic Paradigms Neighbor: 1

2

1

Passing: 5

6

5

3

4

3

3

2

3

5

4

Stationary: 3

3

2

1

1

2

3

5

5

5

6 ) ( only V(5)

(only vii 7 )

Neighboring bass on 1:

I

6 I V(5)

vii 7

319

Chapter 11 Six-Four Chords, Revisiting the Subdominant

EXAMPLE 11.18 (continued) Neighbor: 1

7

Passing:

1

5

6

5

3

(only vii 65 )

4

Leaping:

3

(no V43 )

(no P 46 )

Passing bass on 1 or 3:

I

(no P 64 )

6 I6 vii (5)

(no P 64 )

6 ) ( only V(5)

indicates reversible progression

V43

(1 2 3

P64

3 2 1)

Other Bass Motions: 1

7

1

1

2

1

5

5

5

5

(only V 42 )

Neighboring bass on 1:

I

6

V42

I

6

5

7

7

1

5

1

5

I

V42 I

7

1

7

Passing bass

6

on V:

V42

V

2

1

I

6

vii 4

3

2

1

(only vii 7 )

vii 4 3

7

3

3

4

I

5

IV 6 I 6

5

6

5

I

3

IV

4

I

vii 4

3

5

4

4

V IV V 65 I

3

6

3

Incomplete neighbor Arpeggiating bass

Leaping bass

Passing bass

from 1

chords and the use of IV to expand I allows us to add these sonorities to our vocabulary and use them when harmonizing florid melodies. For example, in “My Gentle Harp” (also called “Danny Boy”) (Example 11.19), we see how a IV chord in m. 2 embellishes the tonic harmonies that extend from mm. 1–3.

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THE COMPLETE MUSICIAN

Note the possible addition of either a root-position IV or a pedal six-four chord in m. 3 to embellish the eighth-note A. The first phrase closes with a HC in m. 4. A single V chord will work well here, although the falling line in the bass allows a stepwise motion back to tonic in m. 5, and it nicely harmonizes the upbeat figure in the tune. The second phrase opens the same as the first phrase but closes with a strong predominant (IV) and cadential six-four chord that is part of a PAC. Recall that in previous chapters we harmonized tunes with implied chord changes only once each measure or even less often. Such melodies contrast vividly with those whose harmonic changes accompany each melody note.

EXAMPLE 11.19 “My Gentle Harp” 1

My gen tle Then who can

V

4

harp, ask

once for

more notes

I

poco rit.

strain, thine?

HC

wak pleas

en ure,

The sweet ness of My droop ing harp,

I (6)

IV (as EC)

thy slumb from chords

’ring like

IV I 6 or Ped 64

a tempo

In tears our last A las, the lark’s

V42 I 6 vii6 I

V

I of

fare well gay

was tak morning meas

en, And now in ure As ill would

IV (as PD)

tears suit

we meet a the swan’s de

V 64

5 3

gain. cline.

I

PAC

We review and elaborate the working method that was presented in previous chapters. 1. Begin by singing the tune, noting the key and locations of cadences, since cadences imply the ends of phrases. • Phrases that end 2–1, 7–1, 4–3, or 2–3 imply authentic cadences. • Phrases that end on 2 or 7 imply half cadences. • Cadences on 5 usually imply a half cadence, but they can imply an authentic cadence; you will need to consider the preceding pitches and implied harmonies before making a decision. 2. Identify harmonies that begin each phrase, and determine the pattern of harmonic rhythm. In order to determine the controlling harmony for a group of pitches, focus on accented pitches. Recall that accented musical events take many forms, but the most important are metric (i.e., they fall on accented beats) and durational (i.e., they are longer notes) and are repeated.

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Chapter 11 Six-Four Chords, Revisiting the Subdominant

Keep in mind what scale degrees can be harmonized with what harmony, because the greater the number of stressed scale degrees that belong to a single harmony, the more chance that that harmony will work best for that span. In general, change harmonies on strong beats rather than on weak beats. 3. Keep the phrase model in mind, and remember that T–PD–D (T) is not reversible. T is usually prolonged for the majority of the phrase, and PD–D usually occur together as part of a cadential gesture (either a HC or an AC).

EX ERCISE INTER LUDE

WORKBOOK 1 Assignments 11.2–11.4

11.1 Error Detection Analyze the following error-ridden example with roman numerals and figured bass. Errors are not restricted to six-four chords. Identify errors with numbers keyed to your detailed explanations of what is wrong.

SOLVED/APP 5

A NA LYSIS STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

11.2 Analytical Snapshots of Six-Four Chords and IV Using first and second levels, analyze the following excerpts, which illustrate various types of six-four chords.

SOLVED/APP 5

A. Mozart, “In diesen heiligen Hallen,” from The Magic Flute Larghetto

Sarastro

1. In die sen heil 2. In die sen heil 1. With in these ho 2. With in this ho

gen gen ly ly

Hal Mau por dwell

len ern, tals, ing,

kennt man die Ra che nicht, wo Mensch den Men schen liebt, Re venge re ma ins un known, one lives, er love In broth

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THE COMPLETE MUSICIAN

SOLVED/APP 5

B.

Daniel Gottlob Türk, Serenade Andantino

sempre piano

C.

Beethoven, Piano Sonata in F minor, op. 2, no. 1, Adagio

dolce

5

T ER MS A ND CONCEP TS • cadential extension • elision • embellishing chord • plagal cadence • six-four chord • pedal six-four • passing six-four • arpeggiating six-four (waltz six-four) • cadential six-four

Chapter 11 Six-Four Chords, Revisiting the Subdominant

323

CH A PTER R EV IEW 1. List the four kinds of six-four chords.

2. Which type of six-four chord also functions in half cadences and authentic cadences?

3. List the two most common reasons composers use evaded cadences, and define each term.

4. Summarize the guidelines for “Writing Six-Four Chords.”

5. What two roman numerals make a plagal cadence in the major mode?

6. Explain in a sentence or two why the plagal cadence is weaker than the authentic cadence.

7. Summarize the three steps for “Harmonizing Florid Melodies.”

C H A P T E R 12

The Pre-Dominant Refines the Phrase Model

OV E RV I E W

This chapter focuses on the pre-dominant’s special capabilities to enrich phrases and create variety and depth within the phrase model. We will also explore the possibilities of the phrase model emerging through an additive process, creating phrases of eight, twelve, and even fourteen measures. CHAPTER OUTLINE Nondominant Seventh Chords: IV7 (IV 65) and ii7 (ii65) ..................................... 325 Supertonic Seventh Chords (ii7) .......................................................................... 326 Subdominant Seventh Chords (IV 7) .................................................................. 327 Analyzing Nondominant Seventh Chords: Ear Versus Eye ............................. 327 Embedding the Phrase Model ................................................................................. 329 Phrase Extension ................................................................................................... 331 Contrapuntal Cadences............................................................................................. 332 Analysis and Interpretation .................................................................................. 332 Expanding the Pre-Dominant ................................................................................. 333 1: Passing Chord Between ii and ii6 (or Between ii6 and ii) ............................ 334 2: Passing Chord Between IV and IV 6 (or Between IV 6 and IV)................... 334 3: Passing Chord Moving from IV6 (IV) to ii65 .................................................. 334 4: Restate Tonic Material Up a Step ................................................................... 335 (continued)

324

Chapter 12 The Pre-Dominant Refines the Phrase Model

325

Subphrases .................................................................................................................... 337 Pauses Without Subphrases ................................................................................. 337 Subphrases Without Pauses ................................................................................. 337 Composite Phrases ................................................................................................ 339 Terms and Concepts ................................................................................................... 343 Chapter Review ........................................................................................................... 344 Summary of Part 3...................................................................................................... 344

T H E P H R A S E M O D E L I S central to tonal music. Composed of goal-oriented harmonic progressions and melodic structures, phrases are complete, organic entities. The ordered harmonic functions of tonic, pre-dominant, dominant, and return to tonic—and their accompanying contrapuntal expansions—underlie the musical phrase and provide it with a simple yet remarkably rich and powerful structure on which composers have relied for over four centuries. In this chapter we explore important refinements in the phrase model and will learn that each of the five refinements depends on the expanded role played by the pre-dominant function. We will:

1. Revisit pre-dominant triads to discover that composers enrich them by adding sevenths, which create nondominant seventh chords. 2. Learn how the pre-dominant can partner with the dominant to expand the tonic. Such embedded phrase models add a new level of musical interest, sophistication, and structure to the phrase. 3. See that these same compositional techniques used to expand the tonic can be transferred to structural cadences that close phrases. Such contrapuntal cadences permit a subtler means of musical closure. 4. Explore how the pre-dominant function itself can be expanded in precisely the same ways that tonic and dominant can be expanded: by adding less-important passing and neighboring chords. 5. And finally learn that phrases often complete their dramatic trajectories in a series of stages, a sort of additive process, whereby each component functions as a subphrase. These subphrases often create phrase lengths that far exceed the common four-measure model.

N O N D OM I N A N T S E V E N T H C HOR D S : I V 7 ( I V 65 ) A N D i i 7 (i i 65 ) Just as a diatonic seventh can be added to the V triad to create V 7 in both major and minor keys, so too can a seventh be added to the pre-dominant ii and IV triads. Example 12.1A shows how ii becomes ii7 and IV becomes IV7 in major. Example 12.1B shows how ii° becomes iiø7 and iv becomes iv7 in minor. Example 12.1C shows the first measures of one of Chopin’s nocturnes, in which he presents the cadential progression ii7–V7–I. Notice

326

THE COMPLETE MUSICIAN

the tension created by the abrupt and unprepared entrance of the ii7 chord. Further, the following V7 chord sounds more like a resolution that discharges the tension of the ii7 than a dissonance.

EXAMPLE 12.1 Nondominant Seventh Chords STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A. ii and ii7 in major

&

# ww w

www w

G: ii

ii7(mm)

IV and IV7 in major

B. ii° and ii¯7 in minor

www w

ww w

IV7 (MM)

IV

b b www

ww ww

g: ii°

ii¯7(dm)

iv and iv7 in minor

ww w IV

www w

IV7 (mm)

C. Chopin, Nocturne in B major, op. 62, no. 1 Andante

{

? #### c #

œ œ

œ

œ

œ

œ œ

w ww ww ww w

## & # ## c

w

? #### c #

w

{

w ii7 PD

w ww w w

Ó

œ œ œ œ

œ œ

∏∏∏∏∏

## & # ## c

dolce legato

∑

œ œ œ œ œ œ

œ w

w w

w w

V7 D

I T

These pre-dominant seventh chords fall into a broad category of nondominant seventh chords—the chords in this category do not have a dominant (major–minor) or leadingtone (diminished–diminished) seventh-chord quality. Nondominant seventh chords are widely used throughout the common-practice period; they provide color and contrast and are generally easy to implement.

Supertonic Seventh Chords (ii7) In general, pre-dominant seventh chords occur in all forms and inversions; however, ii65 is the most common type and inversion of nondominant seventh chords. Example 12.2 illustrates ii65 and the root-position ii7 chord. Note how the seventh of the chord is prepared (marked with a P) and resolved (R). Also note that the ii65 chord is complete but that the ii7 chord omits the fifth and doubles the root to avoid parallels with the preceding tonic chord.

327

Chapter 12 The Pre-Dominant Refines the Phrase Model

EXAMPLE 12.2 Part-Writing Supertonic Seventh Chords

A.

B.

seventh must be prepared P

7th

R

P

OR

I

ii 65

V

I

P

7th

R

I

ii 65

V 8–7

I

I

STR EA MING AUDIO

ii7 often omits chordal fifth

W W W.OUP.COM/US/LAITZ

7th R

P

7th

R

ii 7

V7

I

Subdominant Seventh Chords (IV 7) The IV7 chord, not as common as ii7, is a colorful sonority that may occur in root position (Example 12.3A). Pay particular attention to the potential parallel fifths between IV 7 and V. To avoid this part-writing error, IV 7 is often followed by V7 (Example 12.3B) or the cadential six-four chord (Example 12.3C). Doubling the root of IV7 (4) and omitting the fifth not only helps to avoid parallels, but also prepares the seventh of V. Finally, the IV65 chord, shown in Example 12.3D, typically resolves to a V65 chord.

EXAMPLE 12.3 Part-Writing Subdominant Seventh Chords STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

G:/(g):

I

5

5

IV 7

V

B.

I

I

C.

IV7

V7

I

I

D.

IV 7 V 46

5 3

I

I

IV56

V65

I

Analyzing Nondominant Seventh Chords: Ear Versus Eye Composers often highlight nondominant seventh chords by suspending one of their chordal members. However, such suspensions can sometimes be misinterpreted as chord members, thus rendering a roman numeral label incorrect. Consider ii65, a particular favorite of composers to which suspensions can be applied. In Example 12.4A1 the voices of the tonic move simultaneously to form iiø65. Because a form of the tonic usually precedes ii65, 3 is the perfect candidate to suspend, since it displaces

328

THE COMPLETE MUSICIAN

Part-Writing Nondominant Seventh Chords 1. You must prepare the seventh of the chord. The note that becomes the seventh of the chord must be approached (in the same voice) by the same note (called common-tone preparation and the preferred means of preparation) or by the note one step higher. (See Example 12.2A.) 2. You must resolve the seventh of the chord. As with the V7 chord, the seventh of the nondominant seventh chord must step down in the next harmony. 3. Chords in inversion should be complete. Root-position seventh chords can omit the fifth (and double the root) in order to avoid parallels. (See Example 12.2B.)

the chordal root of ii^% , 2, to create a 7–6 suspension, as shown in Example 12.4A2. Notice that this suspended pitch (3) looks like it could be a chordal member not of a ii7 chord, but of a root-position iv7 harmony. However, it sounds like a suspension that resolves correctly to the chord tone D (2). As always, we must interpret music as it sounds and as those sounds fit into the context.

EXAMPLE 12.4

Contextual Analysis of Nondominant Seventh Chords STR EA MING AUDIO

A.

W W W.OUP.COM/US/LAITZ

7 2 ii ø 6 5 not iv

1

i

B.

ii ø 56

7

V

ii ø 65

i

6

V

Schumann, “Winterzeit,” from Album for the Young, op. 68 (S)

C.

(S)

Schumann (Untitled), from Album for the Young, op. 68 Sehr langsam (S)

Das zweite mal

i 6 V 43 i

7

i

ii 6

P

i

6

V7

i

F:

I6

7 5 ii 65

6

329

Chapter 12 The Pre-Dominant Refines the Phrase Model

Examples 12.4B and C illustrate similar situations in two works by Schumann. Note that the suspensions are part of the motivic fabric of each example; therefore interpreting them in one context as chord tones but in another as nonchord tones is problematic. WORKBOOK 1 Assignments 12.1–12.2

E M B E DDI N G T H E PH R A S E MODE L We have seen how musical events can coexist at various hierarchical levels. The tonal progression of the phrase model is no different. Composers often incorporate a mini “T–PD–D–T” model within a larger phrase model. The “mini” model begins and ends on tonic, thereby prolonging the tonic at the beginning of the phrase.

Embedded Phrase Model “mini” model: phrase model:

T

PD

D

T

T ——————

PD

D

T

In order to accomplish this, composers weaken the first PD–D–T progression through the use of inversions so that a listener will not confuse it with the actual cadence of the phrase model. This progression can be seen in Example 12.5, where the tonic expansion includes a mini, noncadential “T–PD–D–T” model.

Cadential and Noncadential Phrase Models

EXAMPLE 12.5

not cadential (PD–D–T part of tonic expansion)

g:

i T T

i6

ii

6

PD

V 42

i6

D

T

cadential (PD–D–T closes the phrase and is independent of tonic expansion)

vii (P)

6

i

6

V7

i

PD

D

T

PD

D

T

ii

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Such mini “T–PD–D–T” models, which we call embedded phrase models (EPMs), may occur anywhere within the tonic prolongation portion of the phrase. Keep the following in mind when analyzing a phrase with multiple T–PD–D–T progressions: A second-level analysis has just one overall T–PD–D–T progression for a phrase. Other occurrences of

330

THE COMPLETE MUSICIAN

T–PD–D–T earlier in the phrase are not cadential—they are EPMs and expand tonic. Example 12.6 shows the following four important settings of EPMs: • Example 12.6A places the dominant in a weak inversion and evades a cadence. • Example 12.6B shows an EPM that affords great stability and balance between outer voices. The example has a neighboring motion in both of the outer voices. It also includes a common and important use of the ii42 chord, whose seventh (1) is prepared and resolved in the bass. • In Example 12.6C, the bass downward leap of a third and stepwise return to 1 contrasts with the upper-voice neighboring motion. • Example 12.6D shows the progression from 12.6C in minor. Note that 6 and 7 are raised to avoid awkward melodic intervals in the bass.

EXAMPLE 12.6 Common EPM Paradigms STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

B.

D.

R

P

C:

C.

I

ii 65 V 42

T

(EPM)

I6

P

I T

R ii 42 V 65 (EPM)

I

I T

IV 6 V 65 (EPM)

I

c: i T

IV 6 V65

i

(EPM)

EX ERCISE INTER LUDE A NA LYSIS STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

12.1 Provide a two-level harmonic analysis for the following excerpts. Next, circle and label the preparation and resolution of nondominant seventh chords.

SOLVED/APP 5

A.

Bach, “O Welt, ich muss dich lassen”

331

Chapter 12 The Pre-Dominant Refines the Phrase Model

B.

Corelli, Violin Sonata, op. 2, no. 3, Preludio, Largo

Largo

SOLVED/APP 5

C.

Mendelssohn, Lieder ohne Worte (“Songs Without Words”), no. 20 in E major, op. 53 Allegro non troppo sehr innig

3

3

3

3

3 3

3

3 3

3

3

3

3

SOLVED/APP 5

D. Corrette, Sarabanda in E minor for Flute and Continuo In m. 1, at the asterisk (*), which chord label is more appropriate for a tonic expansion: ii7 or vii°6? *

Phrase Extension In Example 12.7A, we see a standard four-measure phrase model closing with a half cadence. Tonic and dominant alternate in mm. 1–2, until i6 appears at the end of m. 2 and signals the upcoming pre-dominant, which enters in m. 3 and moves to the embellished HC. This example is a recomposition of what Haydn could have done. In fact, Haydn extends his phrase to six full measures by evading the HC in m. 4 (Example 12.7B). He does so by sustaining the bass pitch (C), which becomes the dissonant seventh in a V42 chord. The chord resolves weakly to i6, thus extending the tonic for two more measures before cadencing on V.

332

THE COMPLETE MUSICIAN

EXAMPLE 12.7 A.

Embedded Phrase Model STR EA MING AUDIO

Haydn, Piano Sonata in G minor, Hob XVI.44 (recomposed)

W W W.OUP.COM/US/LAITZ

Allegretto 1

g:

i T

B.

2

V (EC)

i

3

V (EC)

4

i6

5

6

iv

ii

PD

V D

Haydn, Piano Sonata in G minor, Hob XVI.44 (original) 1

g:

i T

2

V (EC)

i

3

V (EC)

i6

4

5

6

iv

ii

PD

T

5

V 42 D

i6 T

6

V 65 (IN)

i

V D D

C O N T R A PU N TA L C A DE N C E S Structural cadences involve root-position dominant and tonic harmonies. However, composers occasionally close phrases using inverted dominant and tonic harmonies, often in order to save the powerful root-position V until a more dramatic and final-sounding cadence is required. Cadences in which either the dominant or the tonic (or both) are inverted are called contrapuntal cadences. Contrapuntal cadences often involve the very harmonies used in EPMs (e.g., I–IV6–V 65–I) as well as others, including those shown in Example 12.8. Notice that not only V, but also vii°6 participate in the contrapuntal motions.

Analysis and Interpretation Example 12.8C presents the first vocal phrase from Schubert’s song “Die Krähe.” The first three measures that expand tonic are followed by the very weak vii°6–i to close the phrase. Clearly this four-measure excerpt has many of the hallmarks of a phrase: Both melody and accompaniment descend over the course of the excerpt and close on 1 (the voice and piano unisons dramatize the text, showing the crow’s attachment to the tired protagonist

333

Chapter 12 The Pre-Dominant Refines the Phrase Model

by doubling—shadowing—the voice and piano at the unison). In the closing phrase, the relatively weak vii°6 chord (found more often in tonic expansions) could be heard as substituting for—yet functioning as—the dominant. It is also possible to view the four-measure excerpt as merely a tonic expansion and therefore not a phrase, since there is no strong root-position harmonic motion from T through D. Even such apparently simple decisions as whether a musical unit is a phrase or not often can become a matter of interpretation.

Common Contrapuntal Cadences

EXAMPLE 12.8 A.

STR EA MING AUDIO

B. IAC

IAC

I

C.

6

ii 7

V 43

I

W W W.OUP.COM/US/LAITZ

I

IV

vii

6

I

Schubert, “Die Krähe,” from Winterreise 3

Ei A

ne

Krä

he

crow

war

mit

mir

aus

der

Stadt

ge

fol

lowed

me

out

of

the

town

zo

i6

i T

2

1

gen

vii 6

i

D

T

E X PA N DI N G T H E PR E - D OM I N A N T Just as the tonic and the dominant can be expanded, so can the pre-dominant. An obvious way is to move from ii6 to ii, or vice versa, creating a voice exchange, as seen in Example 12.9. Recall the more subtle and important IV–ii complex technique used to expand the predominant described in Chapter 9. Pre-dominants may also be expanded through passing and neighboring chords, in the same ways we have used them to expand the tonic and the dominant. Consider four additional ways the pre-dominant can be expanded.

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THE COMPLETE MUSICIAN

EXAMPLE 12.9 Expanding the PD Through Voice Exchange: Beethoven, Piano Concerto no. 4 in G major, op. 58, Allegro moderato STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

dolce

I

I6

V

ii

ii 6

V

(ARP) I

ii

V

1: Passing Chord Between ii and ii6 (or Between ii6 and ii) I6 is an ideal choice for a passing chord between ii and ii6. This works in exactly the same manner in which vii°6 passes between I and I6. Here, the I6 chord is subordinate to the prevailing pre-dominant, given its weak-beat placement and role as subordinate chord within a voice exchange. See Example 12.10. Note: A weak I6 can be used to expand the supertonic (ii), but the reverse—ii(6) used to expand the tonic—is not possible.

EXAMPLE 12.10 Expanding ii Using I6 as Passing Harmony STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

I6

ii

ii 6

V7

I

D

T

(P) T

PD

2: Passing Chord Between IV and IV6 (or Between IV6 and IV) A passing I64 chord helps to expand the pre-dominant IV. In Example 12.11 a passing i64 chord occurs on a weak beat and is in the middle of the voice exchange.

3: Passing Chord Moving from IV6 (IV 65) to ii65 Expanding the pre-dominant by moving from IV6 (IV 65) to ii65 invokes both pre-dominant harmonies through voice exchange. As you may remember, this technique embodies another expansion of the IV–ii complex. The motion from IV 65 to ii65 typically involves a passing six-four chord and a voice exchange. Notice the smooth voice leading in Example 12.12: three voices move by step, and the fourth holds a common tone.

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Chapter 12 The Pre-Dominant Refines the Phrase Model

EXAMPLE 12.11

b3 &b 8 œ œ œ œ œJ p espr. j ? b b 83 œ œ œ œ

{

i T

Expanding IV using I64 as Passing Harmony: Bach, “Gerne will ich mich bequemen” (“Gladly Will I Take My Portion”), St. Matthew Passion, BWV 244 STR EA MING AUDIO

œœ œœœ œœ œœ ™ œ œ #œ ™ œ œ œ œ œ œ

œ œ

(P) iv6 i64 iv

V PD D

EXAMPLE 12.12

W W W.OUP.COM/US/LAITZ

œœ ™

j œ œ œ œ i T

Expanding PD with 4–6 Voice Exchange STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

i

6 iv(5) i 64

T

PD

(P)

ii

6 5

V8

7

i

D

T

4: Restate Tonic Material Up a Step One other way to expand the supertonic is to restate, up a step, musical material that was initially stated in the tonic. Consider Example 12.13, where the initial material in mm. 1–2 repeats up a step in mm. 5–6, expanding the supertonic (E-minor harmony) in mm. 5–7.

EXAMPLE 12.13

Tonic Material Transposed to the Supertonic: Mozart, Piano Sonata in D major, K. 576, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

V 42

I I T

I6

V6

I

ii 6 PD

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THE COMPLETE MUSICIAN

EXAMPLE 12.13

(continued)

4

V 64

5 3

ii

V

vii of

6

PD

ii 6

V

I

D

T

(The chromatically altered pitch D5 in m. 6 creates a temporary leading tone that belongs to the E-minor scale.) The expanded ii leads to the cadential dominant in m. 7.

EX ERCISE INTER LUDE A NA LYSIS 12.2 WORKBOOK 1 12.2

Analysis of Nondominant Seventh Chords, EPMs, Contrapuntal Cadences, and Pre-Dominant Expansions Provide a two-level harmonic analysis for the following excerpts. Circle and label the preparation and resolution of any nondominant seventh chords. SOLVED/APP 5

A. Bach, “In allen meinen Taten”

C. Bach, “Des heil’gen Geistes reiche Gnad”

B. Bach, “O Haupt voll Blut und Wunden”

Chapter 12 The Pre-Dominant Refines the Phrase Model

337

SOLVED/APP 5

D.

Mozart, Symphony no. 36 in C major, “Linz,” K. 425, Poco adagio

E. Mendelssohn, Lieder ohne Worte (“Songs Without Words”), no. 48 in C major, op. 102

S U B PH R A S E S A complete phrase may comprise two or more smaller units called subphrases. A subphrase is a relatively independent part of a phrase that is marked by a pause (called a caesura) and/or by the repetition and variation of short yet relatively complete melodic gestures. The eight-measure phrase in Example 12.14 divides into three subphrases. The first two subphrases are both two measures long, and each ends with a caesura. The final subphrase is four measures long and ends with a half cadence (thus ending the overall phrase).

Pauses Without Subphrases The presence of a caesura does not guarantee the presence of a subphrase. For example, in the opening of Example 12.15, the vocal line is clearly divided into two gestures. However, a glance at the harmony reveals a single continuous harmonic motion over the four-measure phrase. The V43 harmony in m. 8 functions as a bass passing tone between 1 in m. 7 and 3 in m. 9. This I6 then leads to the pre-dominant–dominant in mm. 3 and 4. The contiguous stepwise-fifth ascent in the bass combined with a goal-oriented harmonic progression and cadence in m. 10 results in a phrase that does not contain subphrases.

Subphrases Without Pauses Conversely, there may be subphrases within a phrase, even if there are no caesuras present. The eight-measure phrase in Example 12.16 moves from the tonic to a half cadence. Despite the nearly continuous movement, the phrase contains three subphrases, the first two are two measures long (delineated by their motivic structure), and the third is four measures long. (Roman numerals reveal the self-contained harmonic motions.)

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THE COMPLETE MUSICIAN

EXAMPLE 12.14 Subphrases: Haydn, Symphony no. 100 in G major, “Military,” Allegretto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Violino I

Violino II

Viola

Violoncello dolce Contrabasso

HC

EXAMPLE 12.15

Continuous Harmonic Motion Overrides Caesura: Schubert, “Des Müllers Blumen” (“The Miller’s Flowers”), from Die schöne Müllerin, D. 795

melodic gesture 1

melodic gesture 2

7

1. Am Bach viel klei ne Blu men stehn, aus (Beside the brook many flowers grow,

hel len, gazing

blau

en Au gen sehn; with clear blue eyes)

1

2

3

4

5

I

V 43

I6

ii 65

V

PD

D

(P) T single harmonic motion

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Chapter 12 The Pre-Dominant Refines the Phrase Model

EXAMPLE 12.16

Independent Harmonic Motions Override Continuous Melody: Schubert, Symphony no. 4 in C minor, “Tragic,” Andante STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Violino I dolce Violino II dolce Viola

Violoncello e Basso

A :

I

V

I

V

I6

V HC

Composite Phrases Phrases that comprise three or more subphrases are called composite phrases. The phrases in Examples 12.14 and 12.16 are both composite. Composite phrases—like all phrases— contain only one structural harmonic progression and one cadence, but they are often longer than common four-measure phrases, usually eight or more measures in length. They give the aural impression of being composed in an additive stage-by-stage process rather than as a single sweeping motion, which is why you need to be aware that these are single phrases—with one cadence—rather than multiple phrases. The two common types of composite phrases are distinguished in the way their harmonic motion unfolds. 1. The harmonic progression unfolds gradually, with each subphrase’s melody supported by a new harmonic function, as illustrated in Example 12.17. This 14-measure phrase contains three subphrases, and a single goal-oriented I–ii6 –V–I progression underlies the entire structure. 2. The harmonic progression stays on the initial tonic through most of the subphrases, changing to PD, D, and T only at the very end of the phrase, as shown in Example 12.18. Projecting this structure in performance enhances the musical drama considerably: • Subphrase 1 ends in parallel tenths, surely a weak conclusion. • Subphrase 2, while featuring a ii–V 7–I ending, still feels more like the beginning of a new phrase that is cut short with a T–PD–D gesture—more a harmonization of the soprano melody 3–4–3 than an actual cadence. • It is only with the deceleration of the melody to quarter notes and the trill that the final subphrase brings the entire structure to a close in m. 8 (Example 12.18).

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THE COMPLETE MUSICIAN

Haydn, String Quartet in B  major, op. 64, no. 3, Hob III.67, Menuetto

EXAMPLE 12.17

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subphrase 1

subphrase 2

X

X

6

I T

ii 6 PD

subphrase 3 7

ii 6

V 46 D

5 3

I T

Notice in Example 12.18 how Haydn balances the varying subphrase lengths with an overall graceful symmetry. The last subphrase brings the melody back down from 5 to its resting place, 3. The symmetrical shape, and the harmonic and melodic structure of the passage, are summarized in Example 12.19. Identification and interpretation of both subphrases and composite phrases is often, if not usually, a subjective enterprise. In fact, the interpretations of Examples 12.14–12.18 are all debatable to some extent, and alternate viewpoints are certainly possible.

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Chapter 12 The Pre-Dominant Refines the Phrase Model

EXAMPLE 12.18 Haydn, Piano Sonata no. 30 in D major, Hob XVI.19, Moderato STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

subphrase 1 3

3

6

I T subphrase 2

I

subphrase 3

V7

ii

I6

I

ii V 7 I

T

PD D T IAC

EXAMPLE 12.19 Haydn Piano Sonata (reduction) ascent 3

I T

4

neighbor 5

3

6

I

4

descent 3

5

6

3

4

ii

V7

PD D

I T

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THE COMPLETE MUSICIAN

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 12.4–12.5

12.3 Subphrases Bracket subphrases and provide a first- and second-level analysis (that includes T, PD, and D).

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A.

Schubert, Symphony no. 9 in C major, Scherzo 4

7

B.

10

Haydn, Piano Sonata no. 29 in E  major, Hob XVI.45, Moderato

343

Chapter 12 The Pre-Dominant Refines the Phrase Model SOLVED/APP 5

C.

Haydn, Symphony no. 92 in G major, “Oxford,” Hob I.92, Adagio

Violino I cantabile Violino II cantabile Viola

Violoncello

Contrabasso

(V 7 of IV)

3

Violino I

Violino II

Viola

Violoncello

Contrabasso

(V7/V)

T ER MS A ND CONCEP TS • caesura • composite phrase • contrapuntal cadence • embedded phrase model • expansion of the pre-dominant • nondominant seventh chord • passing tonic • subphrase

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THE COMPLETE MUSICIAN

CH A PTER R EV IEW 1. Pre-dominant (or nondominant) sevenths by definition never include which two qualities of seventh chords?

2. Summarize the guidelines for “Part-Writing Nondominant Seventh Chords.”

3. Embedded phrase models (EPM) usually prolong which functional category of a phrase?

4. In a contrapuntal cadence, either the tonic or the dominant (or both) are in: a. root position

b. inversion

5. Subphrases are often marked by pauses, also known as ___________________________.

6. Define composite phrase.

S U M M A R Y OF PA R T 3 We explored several new topics in Part 3. First, the pre-dominant function is the third and final harmonic function in tonal music. This intermediate function, which occurs between the tonic and dominant functions, includes either or both the supertonic and subdominant harmonies. Predominants provide contrast between the tonic and the dominant while at the same time become springboards to and aural signals for the upcoming dominant function. The three functions provide a goal-directed motion through the phrase, which we call the phrase model. We also learned that metrically accented and chromatic dissonances provide the phrase with intensity and dramatic forward motion. Further, our discussion of the various six-four chords confirmed the importance of considering harmonies within a musical context, rather than just stacking thirds and adding roman numerals. Finally, we ended Part 3 by returning to where we began: We revisited the pre-dominant function, elaborating it by adding sevenths and, as we’ve done with both tonic and dominant, expanding it with embellishing harmonies. The phrase model reigned supreme, and we saw how the internal components of phrases can be elaborated and how phrases themselves can be extended.

PA R T 4

NEW CHOR DS A ND NEW FOR MS

W

e continue to explore the phrase model in the five chapters of Part 4. First, we complete our study of diatonic harmonies, including the submediant and mediant. We will learn how composers create larger formal structures by combining phrases. We refine our understanding of how music is hierarchical and present new techniques that reveal how harmony and counterpoint are interdependent. We also incorporate more fully the psychological phenomena of expectation and fulfillment. Analysis continues to be an essential activity in learning how subphrases and phrases can be strung together, but other skills also will be necessary. As you are given more creative responsibility, composition and instrumental application exercises will play a more pronounced role. You will learn how to write structures that balance repetition with contrast and stability with motion. The writing exercises depend on a rich and varied background of listening to and making music, since these activities provide a repository of common stylistic traits that can help guide your compositional choices.

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C H A P T E R 13

The Submediant: A New Diatonic Harmony, and Further Extensions of the Phrase Model

OV E RV I E W

This chapter explores the submediant harmony, one of the most versatile and expressive harmonies in tonal music. The submediant chord provides new compositional possibilities and color contrasts. This chapter also demonstrates the importance of listening to, and not merely looking at, a score; in doing so, alternate—and more musical—interpretations arise, and with them, performance interpretations. Finally, the step descent in the bass is introduced, arguably the oldest, most-esteemed, and still current melodic pattern in tonal music. CHAPTER OUTLINE The Submediant (vi in Major, VI in Minor) ........................................................ 348 The Submediant as Bridge in the Descending-Thirds Progression ................ 348 The Submediant in the Descending-Circle-of-Fifths Progression .................. 349 Contextual Analysis ...................................................................................... 349 The Submediant as Tonic Substitute in Ascending-Seconds Progressions ... 351 Deceptive Motion as Part of a Larger Progression ......................................353 The Submediant as the Pre-Dominant ............................................................... 353 (continued)

347

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THE COMPLETE MUSICIAN

Voice Leading for the Submediant ......................................................................... 353 The Descending-Thirds Progression, I–vi–IV ................................................... 354 The Descending-Fifths Progression, I–vi–ii (or I–vi–ii6)................................. 354 The Ascending-Seconds Progression, V–vi ........................................................ 354 Contextual Analysis.................................................................................................... 355 vi Overshadows V .................................................................................................. 355 vi Overshadows I ................................................................................................... 356 Apparent Submediants ......................................................................................... 356 The Step Descent in the Bass ................................................................................... 358 Two Types of Step-Descent Basses ..................................................................... 359 Writing Step-Descent Basses ............................................................................... 360 Terms and Concepts ................................................................................................... 364 Chapter Review ........................................................................................................... 365

T H E N E X T T WO C H A P T E R S introduce the last of the diatonic harmonies: the submediant and the mediant. These chords always provide dramatic color contrast to the prevailing key and play important roles supporting the tonic, pre-dominant, and dominant pillars of the phrase model.

T H E S U B M E DI A N T (v i I N M A JOR , V I I N M I N OR ) In a major key, the submediant harmony is a minor triad (vi). Because IV, V, and I are all major triads in a major key, the introduction of a minor sonority can provide a welcome relief from the prevailing harmonic color. In a minor key, the submediant harmony is a major triad (VI), so again it offers contrast to the minor and diminished harmonies i, iv, and ii°. The harmonic contexts in which the submediant typically occurs are inextricably tied to the three basic root motions of tonal music: • the descending fifth, seen in the authentic cadence, V–I • the ascending second, seen in the progression IV–V • the descending third, to which we now turn

The Submediant as Bridge in the Descending-Thirds Progression Our discussion of the submediant’s first function arises out of the root motion by descending thirds (Example 13.1). Listen to Example 13.2, which demonstrates a progression that characterizes much of the rock and roll music of the 1950s and early 1960s. Take a moment to enjoy the voice leading of that style, which provides a heavy dose of parallel perfect intervals. Example 13.2B illustrates the same progression but places it in the minor mode and uses commonpractice voice leading to connect the chords. In these examples, the submediant is both attained and departed from by means of a descending third: I–vi and vi–IV. Taken together,

349

Chapter 13 The Submediant: A New Diatonic Harmony

EXAMPLE 13.1 Root Motion by Descending Thirds 1ˆ I

Bass: Harmonies:

6ˆ vi

-

-

4ˆ IV

-

the three roots 1–6–4 arpeggiate a triad of sorts. This progression is therefore often called a descending harmonic arpeggiation. The submediant in descending harmonic arpeggiations provides a way station, or bridge, connecting the tonic to the pre-dominant.

EXAMPLE 13.2 Harmonic Arpeggiations of vi STR EA MING AUDIO

A. 3

W W W.OUP.COM/US/LAITZ

3

&c œ œ œ œ œ œ œ œ œ œ œ œ &c œ œ œ œœ œœ œœ 3 ?c œ œ œ œ œ œ

{

3

C:

3

œ œ œ œ œ œ œ œ œ œ œ œ

œœ œœ œœ œœ œœ œœ œœ œœ œœ œ œ œ œ œ œ œ œ œ

œœœ œœœ œœœ œœœ œœœ # œœœ œœœ œœœ œœœ œœœ œœœ œœœ

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

œ œ œ œ œ #œ œ œ œ œ œ œ œ œ œ œ œ #œ œ œ œ œ œ œ

3

I T

vi

IV PD

V D

B.

b 3 & b b 4 ˙˙

œœ

˙˙

? b 43 ˙˙ bb

œœ

˙ ˙™

{

c:

I T

VI

œœ

˙˙

œ

˙ ˙ iv PD

œœ ˙˙ ™™ nœ ˙ ™ œ ˙™ V7 D

i T

The Submediant in the Descending-Circle-of-Fifths Progression Another function of the submediant arises from its participation in descending-fifths progressions. It fits nicely into such a progression, extending the circle-of-fifths progression as seen in Example 13.3.

Contextual Analysis Listen to Example 13.4. The vi chord appears twice, first as part of an embedded phrase model (EPM) that prolongs the tonic and then as part of the phrase’s structural cadence. Both times it is part of a descending-fifths progression.

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THE COMPLETE MUSICIAN

Analytical Note: The submediant often acts in two seemingly contradictory ways within a phrase: 1. As an extension of the tonic, given its two common tones with the I chord that can be seen as arising from a contrapuntal 5–6 motion. 2. As a pre-pre-dominant chord, because it prepares the PD chord. Although vi exhibits both qualities, we tend to analyze vi under “T” at the second level. However, the arrowhead is added to show the bridging function of vi.

EXAMPLE 13.3 vi as Part of Descending-Fifths Motion STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

F:

vi

ii D5

V D5

I D5

EXAMPLE 13.4 vi Within EPM and as Part of Structural Cadence: Beethoven, Violin Sonata no. 5 in F major (“Spring”), op. 24, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Allegro

F:

I T T

vi

ii PD (EPM)

351

Chapter 13 The Submediant: A New Diatonic Harmony

EXAMPLE 13.4 (continued) 10

5

V7

I6

4 2

D

vi

ii

V7

I

PD

D

T

T

In Example 13.5 the vi–ii6 progression blends the strong descending-fifths motion with a new means of obtaining a melodic bass arpeggiation: 1–6–4. In Chapter 9 we praised the qualities of ii6–V motion, in which a convincing descendingfifths root motion combines with smooth 4–5 bass motion. We see the same ii6–V motion in the major-mode progression I–vi–ii6–V–I, as shown in Example 13.5.

The Submediant as Tonic Substitute in Ascending-Seconds Progressions So far we have seen vi appear as a bridging harmony within a descending-thirds progression and as a harmony that initiates a descending-fifths progression. A third functional

EXAMPLE 13.5 I–vi–ii6 as Melodic Arpeggiation: Schubert, “Frühlingstraum” (“A Dream of Springtime”), Winterreise, D. 911, no. 11 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5

träum I

A:

te von bun dreamt

ten Blu men, of colorful ̘ Ž›œ,

so wie œžŒh

sie wohl blü hen im Mai; aœ bloom in May;

1

6

4

I

vi

ii 6

V7

I

PD

D

T

T

352

THE COMPLETE MUSICIAN

possibility is for vi to substitute for the tonic chord in the cadential progression V–I; the resulting progression is a root motion by ascending second (V–vi). This is shown in Example 13.6, where V moves to vi and the bass moves from 5 to 6. Haydn thwarts the arrival of the tonic by moving to vi. This suspenseful drama is intensified by the fermata as well as by the florid ascent in the first violin to a very high register. In general, the progression V–vi is called a deceptive motion (also called evaded cadence), since the listener expects one outcome (V–I) but hears another (V–vi).

EXAMPLE 13.6 Haydn, String Quartet in D minor, “Quinten,” op. 76, no. 2, Hob III.76, Andante o più tosto allegretto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

49

arco

arco

arco

D:

IV 6

I

I6

IV

V 64

PD

D

5 3

vi

(ARP) T

"T"

EXAMPLE 13.7 Mozart, Clarinet Quintet in A major, K. 581, I STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1

4

A: I T T

I6

V7

vi

ii 6 I 6 ii ii 6 (P) PD (EPM)

7

8

V7

vi

IV

D

“T”

I6 (P)

ii 7

V7

I

PD

D

T

PD

D

T

Chapter 13 The Submediant: A New Diatonic Harmony

353

Deceptive Motion as Part of a Larger Progression At the end of Example 13.6, we are suspended on vi and craving the tonic. In general, after a deceptive motion, the incomplete phrase model continues on to the pre-dominant, which is followed by an authentic cadence. Listen to Example 13.7. The dramatic deceptive motion in m. 4 is followed by pre-dominant harmonies, which leads to an imperfect authentic cadence in m. 7.

The Submediant as the Pre-Dominant Occasionally, vi immediately precedes the dominant and, therefore, functions as the pre-dominant chord. Listen to Example 13.8; this famous opening features vi as a predominant. As such, it allows for the motive of a descending second (6–5) to occur in the bass. Given the strong outer-voice counterpoint—10–5–10—that undergirds the progression, composers often use this very progression in their works. See Example 13.8B for Chopin’s setting from 70 years earlier, and in the same key as Mahler’s movement.

EXAMPLE 13.8 vi as Pre-Dominant A.

Mahler, Symphony no. 2 in C minor (“Resurrection”), “Urlicht” 1

2

10

D :

B.

5

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

3

10

vi PD

V D

I T

Chopin, Scherzo no. 3 in C minor, op. 39 leggiero. 8

Meno mosso sosten. 10

D :

I T

5

vi PD

10

V D

I T

VOIC E L E A DI N G F OR T H E S U B M E DI A N T Incorporating the submediant into your compositions is simple, and its color will greatly expand your harmonic palette, which until now involved only the tonic, dominant, and pre-dominant harmonies.

354

THE COMPLETE MUSICIAN

The Descending-Thirds Progression, I–vi–IV

The chords I and vi share two common tones (1 and 3), and the chords vi and IV share two common tones (6 and 1). When writing the descending-thirds progression, I–vi–IV, keep all the common tones; any voice that moves, except the bass, should move up by step (Example 13.9).

EXAMPLE 13.9 Part Writing vi as Descending-Thirds Progressions

OR

G:

I

vi

IV

OR EVEN

I

vi

IV

I

vi

IV 7

The Descending-Fifths Progression, I–vi–ii (or I–vi–ii6)

The chords I and vi share two common tones (1 and 3), so keep all the common tones in the progression I–vi. Since vi and ii share only one common tone (6), you have more freedom in the voice leading.

The Ascending-Seconds Progression, V–vi

To enhance the deceptive effect of the progression V–vi, use 2–1 or 7–1 in the soprano. The voice leading varies slightly for major and minor keys because in the major mode (as part of V) may either descend to 6 or ascend to 1. In minor, however, 7 may only ascend, since falling to 6 would create an augmented second. • In major keys, if the soprano falls 2–1 the remaining upper voices may all descend (as 7 falls to 6; see Example 13.10A) or 7 may rise to 1, in which case there will be a doubled third in the vi chord. See Example 13.10B. • In minor keys, all upper voices move downward, except for the leading tone, which must resolve upward to 1 (to avoid the augmented second between raised 7 and lowered 6). This will always result in a doubled third (1) in the VI chord. See Example 13.10C.

As with the progression V–vi, the voice leading for the progression vi–V varies slightly for major and minor keys. • In major keys, all upper voices move upward against the descending bass. If the third is doubled, then the inner voice will follow the bass in tenths. See Example 13.11A. • In minor keys, the VI chord must have a doubled third (1) to avoid the augmented second. See Example 13.11B.

Chapter 13 The Submediant: A New Diatonic Harmony

355

EXAMPLE 13.10 Part Writing vi in Ascending-Seconds Progressions A.

B. 2

1

C.

2

1

7

1

doubled third in minor to avoid +2 (F –E ) 2

1

doubled third

G: V

vi

V

vi

V

7

1

doubled third

vi

g: V

in major:

VI

V

VI

in minor:

EXAMPLE 13.11 Part Writing vi as a Pre-Dominant A1.

A2. 1

2

1

B1. 2

B2. 1

2

1

7

VI

V

doubled 3rd

G:

vi

V

in major:

vi

V

g: VI

V

in minor:

C ON T E X T UA L A N A LY S I S

vi Overshadows V

WORKBOOK 1 Assignments 13.1–13.2

Although I and V are structural tonal pillars—usually more important than any other harmonies in a key—this is not always the case, because the importance of a harmony depends wholly on the musical context in which it appears. For example, in the progression I–V–vi, the vi chord often overshadows the dominant, which is demoted to being connective tissue between I and vi (Example 13.12). Notice the deceptive motion in mm. 9–10 of Example 13.12. Because V is metrically weak (compared to the strong-beat tonic and submediant), it functions as a weak voiceleading chord (in this context it harmonizes the violin’s G). Thus, the overall progression is I–vi–ii65–V, with vi initiating a descending-fifths harmonic progression. Example 13.12, also shows why we refer to such progressions as deceptive motions rather than as deceptive cadences: Clearly there cannot be a cadence after only three chords of a

356

THE COMPLETE MUSICIAN

EXAMPLE 13.12 Mozart, Violin Sonata in F major, K. 377, Minuet STR EA MING AUDIO

9

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dolce

I T

V7 (EC)

vi

ii 65 PD

V D (HC)

piece (m. 9 is a repetition of the opening), and, most importantly, vi is not an independent entity but, rather, a member of the continuing progression. It leads to the pre-dominant and dominant functions. The caesura on vi merely highlights the chord, but it does not weaken its important role in the overall progression.

vi Overshadows I Not only can vi be more important than V, but it can even outrank the tonic. Listen to Example 13.13. Even though I6 appears prominently at the end of m. 2, one can hear it as not being structural. To see why this is, consider the V6 that occurs on beat 3 of m. 1: It acts as a passing chord between I and vi. Similarly, the I6 on beat 3 of m. 2 is a voiceleading chord linking vi to the pre-dominant, ii65 in m. 3. Recognizing the harmonic motion I–vi–ii65 can influence the performance of this passage. Rather than dividing mm. 1–4 into two-measure units, a performer can use the vi to fuse mm. 1–4 into a continuous idea. One can also hear the I6 outranking the submediant in m. 2. In this interpretation, the first two measures expand the tonic. A performance that considers the weak-beat I6 as more important than the vi might result in a more flexible and lilting rendering of the phrase, especially if the downbeat is not emphasized by the performer.

Apparent Submediants When the submediant occurs as a by-product of voice leading it does not function as an actual harmony. Voice-leading harmonies occur in several contexts, the most important of which is in progressions whose roots lie a second away from one another, such as the progression IV–V. The important 5–6 motion—in which the interval of a fifth above the bass moves to a sixth—allows IV to move to V, since the potential parallel fifths are broken up by the intervening sixth. The result of this 5–6 motion creates the ii6 chord (Example

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Chapter 13 The Submediant: A New Diatonic Harmony

EXAMPLE 13.13 Mozart, String Quartet in B  major, K. 159, Andante 5

B :

4

6

I I

V (P)

6

vi vi

I (EC) E

I

6

P

ii 5 ii 65 M

T

7

V V7

STR EA MING AUDIO

3

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vi vi

IV

I

“T”

IV

I plagal motion

13.14A). This process, the “IV–ii complex,” can occur in any progression where roots progress by an ascending second. In Example 13.14B, an analogous situation occurs when I moves to ii. Again, the 5–6 motion helps to avoid parallel fifths: F moves to G, which is already sounding as the bass rises to create the ii chord. Note that this 5–6 motion creates an apparent vi6 chord; however, there is no “chord change.” Rather the vi6 is a by-product of the voice leading. Example 13.14C presents an example of the apparent vi6 in an aria from Wagner’s The Flying Dutchman.

EXAMPLE 13.14 5–6 Motion Versus “vi6” A. 5–6 motion above bass

B :

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B.

IV5

6

(ii 6 )

V7

I

5–6 motion above bass

I5

6

(vi 6 )

ii 7

V

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THE COMPLETE MUSICIAN

EXAMPLE 13.14 (continued) C. Wagner, “Mögst du mein Kind,” from The Flying Dutchman, act 2

Sieh' Look

die ses Band on these gems,

sieh' look

die se Span on these brace

gen! lets!

Was er be To what he

dolce

5

I

sit, owns,

V7

6

(vi 6 as voice-leading chord)

ii

macht dies ge ring tri fles are these

I

T H E S T E P DE S C E N T I N T H E B A S S The most prevalent harmonic motion in phrases is from the tonic to the dominant. In Chapter 9 we saw a way to embellish I–V motion by means of stepwise ascent in the bass (Example 9.8). It is also possible to move from the tonic to the dominant by descending steps in the bass. Composers have been creating phrases built on bass descents from 1 to 5 since the early seventeenth century. For example, the descending four-note scale segment 1–7–6–5 appears regularly in Monteverdi’s operas and madrigals. Composers use numerous paths of descent, ranging from diatonic (1–7–6–5) to descents that are chromatic (with multiple expressive chromatic passing tones), to descents that even overshoot 5 and then return to the dominant. Some well-known examples include “Dido’s Lament” from Purcell’s Dido and Aeneas and the “Crucifixus” from Bach’s Mass in B minor. Listen first to the diatonic descent in Example 13.15. Schütz’s composition illustrates a characteristic stepwise descent: i→passing v6→iv6→V7. Note that an especially strong

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Chapter 13 The Submediant: A New Diatonic Harmony

EXAMPLE 13.15 Schütz, “Nacket bin ich von Mutterleibe kommen” (“Naked I have come from my mother’s womb”), Musicalischen Exequien, op. 7, SWV 279 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Tenor I 8

Na

cket

wer

cket

wer

de ich

de

ich

wie der um

da

hin

da

hin

fah

7

6

5

hin

fah

fah

ren,

Tenor II 8

Na

wie der um

1

ren,

Bass Na

f :

i T

cket

wer

de ich

wie der um

da 6

v (P)

ren,

iv 6

V7

i

PD

D

T

gravitational pull downward to V is created by the descending melodic minor scale: This feel and the expressive half step 6–5 (D–C in Example 13.15) show why such descents occur more often in the minor mode than in the major. Note that in minor, v6 is used to precede minor iv6 to give the bass line 8–7–6–5; the use of ↓7 avoids the augmented second between ↑7 and ↓6. First-inversion minor v and root-position v do not function as dominants; rather, they are used as passing chords or voice-leading chords.

Two Types of Step-Descent Basses Step-descent basses that fall directly from tonic to dominant (1–7–6–5) are called direct step-descent basses. When direct step-descent basses are cast in the minor mode they are known as lament basses. Lament basses often accompany melancholy texts, which are not historically confined to the seventeenth century. Songs such as “Hit the Road, Jack,” and “Erie Canal” are built on the same formula (Example 13.16A). A quite different approach is taken by Gabriel Fauré in his eloquent Pavane (Example 13.16B). Each step of the lament bass (F–E–D–C) is interposed with a falling-third motion that not only creates beautiful, fleeting seventh chords (shown in Example 13.16C), but this wafting bass motion also provides voice leading that helps to avert the parallels that would have occured had Fauré used only the root-position chords on the downbeats. Step-descent basses are often repeated throughout a piece, providing the composition with a firm harmonic foundation. Such repetitions are called ostinatos, and the pieces based on them are often called ground basses or chaconnes.

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THE COMPLETE MUSICIAN

EXAMPLE 13.16 The Step-Descent Bass in Context STR EA MING AUDIO

A. Traditional, “Erie Canal”

W W W.OUP.COM/US/LAITZ

Moderately

1. I’ve

got

a

mule, her

name is

Sal,

Fif

teen

miles on the

E rie Ca nal

PT i

6 P4

iv6

T

PD

B.

Fauré, Pavane, op. 50

C.

Pavane (reduction)

i

( VI 7 )

V

i

D

T

VII

( v7)

PD

VI

( iv7 )

V

i

D

T

V

Writing Step-Descent Basses The most common harmonic settings of these step-descent basses use the PD iv6, which moves to V (Example 13.17A). Because of the lurking parallels, a root-position VI usually does not lead directly to V (Example 13.17E). Rather, it is first converted into a iv6 chord via a contrapuntal 5–6 motion in order to avoid parallels (Example 13.17B). Also, composers may opt to move 1–7 in the bass while sustaining the tonic harmony; this creates a passing tone in the bass and the passing sonority i42 (Example 13.17C). Finally, two less common variants of the step-descent bass are presented. In Example 13.17D, note how iiø43 substitutes for iv6; in Example 13.17E, note how the major mode may be used for the step-descent bass. There is less danger of awkward voice-leading

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Chapter 13 The Submediant: A New Diatonic Harmony

EXAMPLE 13.17 Voice Leading the Direct Step-Descent Bass STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

B.

C.

common

D.

common

common = CT

E. less common

avoid

P5

5

i

v 6 iv 6 V

i

6

v 6 VI iv

V

i

(P)

(P) T

6

T

PD D

i 42

iv 6 V

III 64 ii

4 3

V

I

V 6 vi V 7

P 64

(P) PD

i

D

intervals for the bass in the major mode than in the minor mode. Therefore, the major V6 can move directly to vi or IV6 (but be aware of potential parallels). The second type of step-descent basses is characterized by passing through the dominant to reach a pre-dominant on 4, which is harmonized by iv or ii6. Such indirect stepdescent basses (1–7–6–5–4 and then back to 5) create a descent by fifth. Composers often harmonize the first 5 with a passing 65 or 64 chord to avoid any feeling of arrival on the dominant (Example 13.18).

EXAMPLE 13.18 Voice Leading the Indirect Step-Descent Bass A.

STR EA MING AUDIO

B.

c:

i

v6

VI

(P) T

III 63 iv

V

i

(P) PD

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v6

iv 6 i 64

(P) D

T

iv

V

(P) PD

D

Descents can assume a number of different guises. Likewise, they can prolong any of the three harmonic functions. See Example 13.19. Bass descent prolongs the tonic and encompasses an entire octave. Notice that the dominant is converted to a V42 that passes on to I6, which expands the tonic in m. 3. The next passing V64 connects I6 with I, closing the octave descent and creating a large-scale tonic expansion. Notice also the problematic parallels between vi and V.

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EXAMPLE 13.19 Tchaikovsky, “Za oknom v teni mel’kajet” (“At the window, in the shadow”), op. 60, no. 10

C:

I

V6

vi

V

I6

V 42

V 64

I

T

EX ERCISE INTER LUDE A NA LYSIS 13.1 The following excerpts include vi in various contexts (as an independent harmony that leads to or functions as the pre-dominant, as a voice-leading chord, and as the lament bass). Analyze each. When you encounter vi, specify the function of vi each time it appears.

WORKBOOK 1 Assignments 13.3–13.4

SOLVED/APP 5

A. Bach, Geistliches Lied, “Beschränkt ihr Weisen” Voice Be

schränkt

ihr

Wei

sen

die

ser

Welt

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Continuo

B. Mozart, Serenade in D major, K. 204

A:

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Chapter 13 The Submediant: A New Diatonic Harmony

SOLVED/APP 5

C. Mendelssohn, Elijah, opening of Part I EINLEITUNG. Grave

ELIAS

bass solo:

So wahr der As God, the

Herr, Lord

der Gott of Is

Is ra els le el liv ra

bet, eth,

vor dem ich ste be fore whom

he: I stand

SOLVED/APP 5

D.

Bach, Flute Sonata in B minor, BWV 1030, Largo

Flöte

Klavier

(Cembalo)

6

6 5

6 4

5

13.2 Each of the given excerpts contains at least one example of the submediant. Specify the function of vi each time it appears: STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

• Is it a “bridge” in a descending-third motion? • Does it start a descending-fifth motion? • Does it substitute for tonic in a deceptive motion? • Is it the PD chord?

Mozart, Violin Sonata in G major, K. 379, Adagio

Piano

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THE COMPLETE MUSICIAN

SOLVED/APP 5

B. Wagner, “Der Augen leuchtendes Paar” (“Those eyes so lustrous and clear”) (Wotan’s Farewell), Die Walküre, act 3, scene 3 (He clasps her head in his hands.)

Denn so kehrt

der Gott

sich

dir ab,

espress. 3

C. Beethoven, String Quartet no. 13 in B  major, op. 130, Alla danza tedesca Describe the curious rhythmic effect in this excerpt. Allegro assai

T ER MS A ND CONCEP TS • bass motion versus root motion • deceptive motion, deceptive cadence • harmonic versus melodic bass arpeggiation • lament bass, step-descent bass (direct and indirect) • tonic substitute

Chapter 13 The Submediant: A New Diatonic Harmony

365

CH A PTER R EV IEW 1. List the three basic root motions of tonal music.

2. What three bass scale degrees comprise a common descending harmonic arpeggiation?

3. State the two possible functional categories for the submediant and describe the contexts of their use. (Remember, there are only three function categories: T, PD, and D.)

4. The V–vi progression, where the submediant functions as a tonic substitute, is called _____________________________________________, or the evaded cadence.

5. Summarize the rules for “Voice Leading for the Submediant,” given under each heading. 1. The Descending-Thirds Progression, I–vi–IV 2. The Descending-Fifths Progression, I–vi–ii (or I–vi–ii6) 3. The Ascending-Seconds Progression, V–vi

6. The 5–6 complex is often placed between which two roman numerals to avoid parallels?

7. When a direct step-descent bass is placed in minor, it is called a _______________________.

8. List two names for pieces that employ a bass ostinato.

9. True or False: Step-descent basses can prolong any of the three harmonic functions.

C H A P T E R 14

The Mediant, the BackRelating Dominant, and a Synthesis of Diatonic Harmonic Relationships

OV E RV I E W

In this chapter, the mediant chord is introduced. While a relative rarity in the major mode, the mediant occurs remarkably frequently in the minor. This chapter also introduces a special function of the dominant, one in which it can either intensify or inhibit a phrase’s motion. The chapter concludes with a summary of diatonic functions, which groups all harmonic motions into three basic categories based on root motion, and follows up with a step-by-step approach to incorporating these concepts into a model composition. CHAPTER OUTLINE The Mediant (iii in Major, III in Minor) ............................................................. 367 The Mediant in Arpeggiations ............................................................................. 367 A Special Case: Preparing the III Chord in Minor ........................................... 369 Voice Leading for the Mediant ............................................................................ 370 More Contextual Analysis: The Back-Relating Dominant .............................. 372 Analytical and Aural Quandary ........................................................................... 372 The BRD at Deeper Levels................................................................................... 373 (continued)

366

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Chapter 14 The Mediant, the Back-Relating Dominant

Synthesis: Root-Motion Principles and Their Compositional Impact ........ 374 Compositional Application .................................................................................. 375 Summary ....................................................................................................................... 376 Terms and Concepts ................................................................................................... 377 Chapter Review ........................................................................................................... 377

T H E M E DI A N T (i i i I N M A JOR , I I I I N M I N OR ) While the mediant harmony occurs less frequently than any other diatonic harmony, the chord is not unimportant. In minor-key pieces the structural significance of III is great— second only to that of tonic and dominant. The mediant harmony provides the same color contrast as the submediant: It is a minor triad in a major key and a major triad in a minor key. Within the phrase, the mediant usually appears in one of the following contexts: (1) ascending-bass arpeggiations and (2) descending-fifth progressions.

The Mediant in Arpeggiations

In Example 7.14, we encountered the ascending-bass arpeggiation 1–3–5 under a I– I6–V progression. The contrapuntal motion of the bass can be filled with passing harmonies to create a stepwise ascent:

Ascending-Bass Arpeggiation Bass:

1 I

2 vii°6 or V43

3 I6

4 IV or ii6

5 V

Although 3 in the bass is most often harmonized by I6, it can also be harmonized by a root-position mediant chord. In this way, iii substitutes for I6 to create a tonic extension, just as vi may substitute for tonic. Example 14.1A illustrates the common tones in I–iii and I–vi progressions. The rest of the example shows some common uses of the mediant within phrases. Just as we label vi’s bridging function from T to PD with an arrow, we also use the arrow to show iii’s bridging function leading from T to PD. • In Example 14.1B, the bass of the pre-dominant IV fills the space between 3 and 5. Note also how the soprano descends stepwise from 1 to 5, with 7 functioning as a downward passing tone rather than a leading tone. • Example 14.1C shows how vi can be inserted between I and iii, resulting in an effective descending arpeggiation. • In many progressions, iii descends to vi, thus extending the descending-fifths progression back yet another notch (Example 14.1D).

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EXAMPLE 14.1 Typical Harmonic Contexts for the Mediant STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

B. As Substitute for I6

A. Common Tones 5

3

3

C:

C. As Part of Descending Arpeggiation (I−vi−iii) Leading to PD

1

7

6

5

1

I

iii

IV

V

I

I

PD

D

T

T

7

6

5

4

3

iii

IV

V6

I

PD

D

T

1

I

iii

I

vi

T

E. As Substitute for I6

D. As Part of DescendingFifths Paern

I T

iii

ii7

vi

PD

vi

(4

1

7

6

5

III

iv

V8 – 7

PD

D

V 64 –– 53

I

i

D

T

T

)

3

8 – 7 – 5 4 – 3

F. As Part of Plagal Motion, Substituting for I 1

7

6

5

i

I

iii

IV

I

T

T

• Example 14.1E recasts 14.1B in the minor mode. Example 14.1F illustrates a prolongation of tonic: iii and IV harmonize passing tones in the soprano (7–6) which leads back to I. The 1960s hit song “Puff the Magic Dragon” harmonizes its descending melody with this very progression (Example 14.2A). Mahler uses iii in his song “Urlicht.” Note how vi also figures prominently in this excerpt (Example 14.2B).

EXAMPLE 14.2A

Yarrow, “Puff the Magic Dragon” STR EA MING AUDIO

1

7

6

5

I

iii

IV

I

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Chapter 14 The Mediant, the Back-Relating Dominant

EXAMPLE 14.2B

Mahler, “Urlicht” (“Primeval Light”), Des Knaben Wunderhorn, no. 12 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Sehr feierlich, aber schlicht durchaus zart

O O

E∫:

Rös - chen red - dest

vi

rot! rose!

V

Nicht schleppen choralmässig

I

I

V I (PED)

7

I

V6

ii

vi

I

iii

IV

,

,

,

,

IV

V

I

A Special Case: Preparing the III Chord in Minor The mediant appears in the minor mode more often than in the major mode. Listen to Example 14.3. The second harmony that appears in all three examples is unfamiliar: a major triad built on 7. We have seen chords built from a leading tone (vii°6 and vii°7) and a passing v6 chord (in the step-descent bass). In Example 14.3, the root-position “VII” chord has a different function: It is the dominant chord of III. To reflect this motion of the V–I sound of B–E, we label the B harmony as “V of III” (or “V/III”), indicating that B is the dominant (V) chord that leads to E (III). This roman numeral symbol represents the sound of the triad built on 7 far more accurately than would the label “VII,” which fails to capture its dominant function at the immediate, local level. V/III often occurs in first inversion as V6/III (Example 14.3B). The use of this inversion prominently places D—the temporary leading tone that leads to E (III)—in the bass, thus intensifying the motion to III. In Example 14.3C, a seventh is added to create V7/III, which further intensifies motion to III (since V7–I is more powerful than V–I). We explore the use of chords such as V/III, which are called applied chords, further in Chapter 18.

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THE COMPLETE MUSICIAN

EXAMPLE 14.3 VII as V/III STR EA MING AUDIO

A.

B.

c:

i

V

/III

i

III ii

6

V 64

III ii

6

V

i

PD

D

T

T

– 5 – 3

— i

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C.

i

V6

III ii 6 V i

i

PD D T

T

/III

T

V7

/III

III

ii

6

PD

V 64

– 5 – 3

i

D

T

Voice Leading for the Mediant Using the mediant with good voice leading is easy as long as you remember these simple guidelines: 1. Try to move the upper voices in contrary motion to the bass when approaching and leaving the mediant (Example 14.4). 2. Use the soprano line 1–7–6 when iii supports the passing tone 7.

EXAMPLE 14.4 Part Writing the Mediant

P5

C:

I

iii

IV

V

I

poor

iii

IV

V

good

EX ERCISE INTER LUDE W R ITING WORKBOOK 1 Assignments 14.1–14.3

14.1 The following exercises contain ascending-bass arpeggiations and descending-fifths motions using the mediant. Choose a meter and write the progressions in four-voice chorale

Chapter 14 The Mediant, the Back-Relating Dominant

371

style. Include a second-level analysis, and label the mediant’s function (use a bracket and label with “arp. prog.” or “fifths prog.”).

SOLVED/APP 5

A. B. C. D.

In C minor: i–V/III–III–ii°6 –V–I (begin soprano on 1) In A minor: i–V65/III–III–iv–V–VI (begin soprano on 5) In D major: I–iii–IV–ii65 –V42 –I6 –V65 –I–vi–ii6 –V7–I (begin soprano on 5) In D minor: i–V/III–III–VI–ii°6 –V–i (begin soprano on 3)

A NA LYSIS

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

14.2 The following excerpts contain the mediant either in the context of an ascending-bass arpeggiation or as part of a descending-fifths progression. Analyze with roman numerals (first-level analysis).

A. Schubert, “Am Frühling,” D. 882 Note the clef in the right hand.

( vii 7/ V) B. Marcello, Sonata in A minor, no. 8, Presto Consider the standard harmonic phrase model as you analyze this example.

SOLVED/APP 5

C.

Schumann, “Armes Waisenkind,” from Children’s Pieces, op. 68, no. 6 Langsam

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THE COMPLETE MUSICIAN

Brahms, Symphony no. 4 in E minor, op. 98, Allegro giocoso

D.

MOR E C ON T E X T UA L A N A LY S I S : T H E B AC K- R E L AT I N G D OM I N A N T We know that a V chord may or may not function as a structural, cadential dominant. For example, for a phrase built on the progression I–V–vi–ii–V–I, the structural dominant is most likely the second one, while the first dominant is only a voice-leading chord that connects tonic and submediant harmonies and helps to avert potential parallels. Another example of a nonstructural dominant occurs in the step-descent bass progression i–v6–iv6–V. The minor v6 in this progression is far removed from its dominant function; it harmonizes the passing tone ↓7, connecting 1 and 6 in the bass. As always, such contextual analysis is essential for understanding how harmony works, and for interpreting which chords are structural and which ones merely embellishing.

Analytical and Aural Quandary Example 14.5A demonstrates another important way in which the dominant may appear in a nonstructural context. Listen to the example while observing the roman numeral analysis. What is unusual about the harmonic progression? Heard as a single phrase, this progression presents us with an analytical dilemma. You know that V does not progress to ii; such a backward motion from D to PD is called a retrogression, which usually sounds awkward and weak. But Bach’s phrase doesn’t sound weak at all. So what is the function of the V that appears in m. 2? Is it the structural dominant, which is prolonged through m. 3

EXAMPLE 14.5 A.

E :

Bach, Prelude in E Major, The Well-Tempered Clavier, Book 2, BWV 876

I

V

ii 7

V

8

—

7

I

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Chapter 14 The Mediant, the Back-Relating Dominant

(continued)

EXAMPLE 14.5 B.

373

Bach, Prelude (reduction)

I

V

ii 7

V7

I

T

(BRD)

PD

D

T

by means of a passing ii? This reading makes abstract sense, yet we probably don’t hear the V in m. 2 as a structural V. Further, doesn’t the ii chord sound as if it plays a harmonic role as a pre-dominant? Listen to the excerpt once again. Ignoring the supertonic harmony is not a reasonable interpretation, because it clearly plays an important role in the excerpt. Given the prominence of ii, the harmonic importance of the first V now seems to wane. The excerpt begins on a soprano B4, but in m. 2—where the problematic V appears— the soprano leaps to E5 and then descends to D5. If we ignore the first dominant, the overall progression is I–ii7–V7–I, and each harmony supports the melodic descent in the soprano (B4–A4–G4). Example 14.5B shows this interpretation. This analysis, which takes account of the phrasing and melodic continuity of the excerpt, reflects the perception of the music much better than viewing the V in m. 2 as structural. The dominant chord in m. 2 prolongs the preceding tonic, but there is no connection between the dominant and the following ii chord. Dominants that prolong a previously sounding tonic without resolving to a following tonic are called back-relating dominants (BRDs). BRDs can be shown only in second-level analysis: 1st-level analysis: 2nd-level analysis:

I V ii T————(BRD)———— PD

The BRD at Deeper Levels Given that the music following a half cadence is a restart of a new phrase model and not a continuation of the previous phrase model, we will view the half cadence as a common and important type of back-relating dominant. The concept of the back-relating dominant can be extended from a single phrase to multiple phrases, where we begin to account for more substantive events within a piece. When considering how it functions at this deeper level, it carries possible performance implications, as Example 14.6 illustrates. The first phrase (mm. 1–4) closes on a half cadence, strongly articulated by the powerful cadential six-four chord that helps to secure the dominant. The next phrase begins on the supertonic (ii). Because Mozart merely transposes the opening material of phrase 1 up a step (from D major to E minor), we can connect the openings of the two phrases

374

THE COMPLETE MUSICIAN

EXAMPLE 14.6 Mozart, Piano Sonata in D major, K. 576, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

D:

V 42

I

I6

V6

ii 6

I

T

PD

T 4

V 64

5 3

(BRD)

ii

vii 6 of ii

ii 6

PD

HC

V

I

D

T

PAC

rather than the end of the first phrase and the opening of the second phrase. Further, since Mozart extends the pre-dominant function, we see a single, large-scale tonal motion over two phrases: I (BRD)–ii–V7–I. Indeed, since the phrase with the HC is left harmonically open, the following phrase completes the incomplete tonal motion of the first phrase. The combination of the two phrases creates a single entity called a period, discussed in the next chapter.

S Y N T H E S I S : RO O T- MO T IO N PR I N C I PL E S A N D T H E I R C OM P O S I T ION A L I M PAC T The phrase model, composed of three ordered harmonic functions (T–PD–D–T), lies at the heart of tonal progressions, and the tonic function usually occupies significantly more time and chords than the other two functions. Further, considering how harmonies function within a musical context—rather than haphazardly scattering roman numeral labels over a score—allows us to see deeper connections. We will apply these global analytical ideas to composition as well. However, we may find ourselves in a situation where we simply can’t figure out which chord could come next. For example, after completing a basic tonic expansion using contrapuntal chords,

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Chapter 14 The Mediant, the Back-Relating Dominant

we might wish to use other diatonic harmonies within the tonic expansion. In general, diatonic harmonies (such as dominants, submediants, supertonics, and mediants) tend to follow one another in one of the following three root motions: 1. by descending fifth (or rising fourth), which we abbreviate D5 2. by ascending second, which we abbreviate A2 3. by descending third, which we abbreviate D3 These root motions may be combined in an infinite number of ways. For example, a series of falling thirds from the tonic, I–vi–IV, may be followed by two successive A2s (IV to V and then, the deceptive motion V to vi). From the submediant, a set of D5 motions might follow, which will return the progression to tonic (ii–V–I). The sum total of all this motion is a large goal-directed progression: I–vi–IV–V–vi–ii–V–I, which may be set in many ways, depending on the progression’s meter and harmonic rhythm. Most musical settings of this progression would likely reflect the following second-level analysis: I–vi–IV–V–vi–ii7 ––V7–I T—————–PD-D–T

Compositional Application Let’s try out some of these ideas by setting ourselves a task and then working through the compositional process. Task: Write a piece for string quartet or vocal ensemble (SATB) that encompasses 12–20 measures and contains three or more phrases. The key (major or minor) and meter are your choice. 1. Begin with a compositional plan, one in which you envision the large-scale harmonic progressions. For example, if you write a four-phrase piece, consider how each phrase will close and how it will relate to succeeding phrases. Example 14.7 presents an example plan for a minor key. 2. Then decide on the length of each phrase; four measures is the most common. Think about the general harmonies that lead to each cadence. You may use all the diatonic harmonies we have discussed, including EPMs, BRDs, and stepdescent basses.

EXAMPLE 14.7 Example Plan for a Four-Phrase Piece in a Minor Key

soprano: harmony:

phrase 1:

phrase 2:

phrase 3:

phrase 4:

5

3

5

2–1

i→HC

i→IAC

i→HC

i→PAC

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THE COMPLETE MUSICIAN

You may wish to lay out controlling harmonies for each measure by writing roman numerals, as in Example 14.8.

EXAMPLE 14.8 Controlling Harmonies

measures: harmonies: second level:

phrase 1: 1 2 3 4 i V43 i6–iv6 V T———–PD D

phrase 2: 5 6 7 8 i VI iv V7–i T———PD D T

phrase 3: 9 10 11 12 i III VI ii°6–V T———PD D

phrase 4: 13 14 15 16 i iv–P46–iv6 V46–53–i T—PD———D T

3. If the tempo is slow and the harmonic rhythm fast, as in the chorale, then you may wish to go so far as to specify every harmony within each measure; their exact rhythmic placement will have much to do with your choice of meter and melodic motives. Example 14.9 presents a detailed plan for the first phrase only.

EXAMPLE 14.9 Detailed Plan for the First Phrase

measures: harmonies: structure: second level:

phrase 1: 1 2 3 4 ø4 6 4 6 4 6 6 V3–i –V2 i –III–iv–iv V i–ii 2–V5–i 4 6 6 i iv V i V3 T—————————————————PD————————D

SU M M A RY

WORKBOOK 1 Assignment 14.4

We have explored phrases containing all diatonic harmonies. Keep in mind, however, that the phrase model—comprised of the three ordered tonal functions [T, PD, D(T)]— relegates all surface harmonies to this overriding structural unit. This hierarchy may always be represented through a multitiered analytical process. In first-level analysis, we describe all vertical sonorities using roman numerals. In second-level analysis, we interpret harmonic functions within the musical context to see larger connections. We can interpret tricky harmonic successions by considering their overall tonal motion and effect (such as the back-relating dominant), and use a second-level analysis to mirror our perception of the music. This type of analysis can significantly influence the way we shape phrases in a performance.

Chapter 14 The Mediant, the Back-Relating Dominant

377

T ER MS A ND CONCEP TS • back-relating dominant (BRD) • iii in: • bass arpeggiations • motions of descending fifths • retrogression • V/III

CH A PTER R EV IEW 1. Name the bass scale degrees that often make up an ascending-bass arpeggiation.

2. Summarize the guidelines for “Voice Leading for the Mediant.”

3. Backward motion from D to PD is called a ___________________________________________.

4. Dominants that prolong a previously sounding tonic without resolving to a following tonic are called ___________________________________________________________________________.

5. In first-level analysis, we [describe/interpret] all vertical sonorities using roman numerals. In second-level analysis, we [describe/interpret] harmonic functions within the musical context to see larger connections.

C H A P T E R 15

The Period

OV E RV I E W

This chapter introduces the musical period, an element of form that is defined as the combination of two or more phrases. An emphasis is placed on how melody and harmony interact. A step-by-step analytical procedure prepares for sample analyses and composition. CHAPTER OUTLINE Form as Process ........................................................................................................... 379 Aspects of Melody and Harmony in Periods ....................................................... 380 Comparisons .......................................................................................................... 380 Contrasts................................................................................................................. 380 Melodic.......................................................................................................... 380 Harmonic ...................................................................................................... 380 Two Other Options ...................................................................................... 383 Sectional ........................................................................................................ 383 Progressive ..................................................................................................... 384 Representing Form: The Formal Diagram ........................................................... 384 Phrases and Periods ............................................................................................... 384 Melody .................................................................................................................... 385 Harmony ................................................................................................................ 385 Period Label ........................................................................................................... 385 Sample Analyses of Periods and Some Analytical Guidelines ........................ 387 Summary for Analyzing Periods .......................................................................... 388 Composing Periods .................................................................................................... 389 Terms and Concepts ................................................................................................... 391 Chapter Review ........................................................................................................... 391 378

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Chapter 15 The Period

F OR M A S PRO C E S S We have seen how contrapuntal and harmonic motions combine to create music: A phrase is not just a random succession of notes and chords, but a carefully balanced, goal-directed motion controlled by the outer-voice counterpoint and the pacing of the phrase model. According to the model, phrases often comprise one or more tonic expansions, a predominant, and either a half cadence or an authentic cadence. Larger musical structures— those composed of multiple phrases—unfold logically as well. If this were not the case, music would move in unconnected, unmotivated chunks rather than in the smooth manner that integrates the opening of the first phrase with the close of the piece. Throughout the tonal era (and beyond), composers have relied on the pattern of incompleteness followed by completeness. Because a sense of incompleteness is crucial to the large-scale organization of tonal music, composers often avoid harmonically closed four-bar units. Instead, they rely on multiple four- or eight-bar phrases that hinge on one another. Listen to Example 15.1, noting how the phrases work together. The first phrase ends on a half cadence with 2 in the soprano; this leaves the listener craving tonic and the resolution of the melody to 1, which is achieved at the PAC of the second phrase. When a weakly conclusive phrase pairs with a stronger, more conclusive phrase, we call the resulting unit a period. The pairing is possible because the harmonic and melodic tensions

EXAMPLE 15.1 Beethoven, Symphony no. 3 in E  major, “Eroica,” op. 55, Allegro vivace: Trio STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

2

Antecedent

I T

V D HC 1

Consequent cresc.

cresc.

I T

V D

I T PAC

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THE COMPLETE MUSICIAN

left hanging at the end of the opening (antecedent) phrase resolve at the end of the final (consequent) phrase. Two phrases make a period only when they relate to each other musically, and the second phrase ends with a strong authentic cadence. Understanding the period allows us to view musical spans of eight or sixteen measures (as in Example 15.1)—or even more measures—as a single musical idea. We will explore how composers manipulate these units, increasing their size and linking them together.

A S PE C T S OF M E L ODY A N D H A R MON Y I N PE R IOD S The cementing of two separate phrases is highly dependent on the interaction of melody and harmony. Listen to the two periods in Example 15.2, focusing on the following melodic and harmonic issues: 1. Do the two phrases in each period have melodies that resemble one another? If so, in what ways? 2. Locate and compare cadences. 3. What does the second-level harmonic analysis reveal about each phrase?

Comparisons

Both periods in Example 15.2 are in the key of B major and divide into two four-measure phrases. Although the examples sound very different, they share several basic melodic features: 1. Both melodies begin with arpeggiations of the tonic triad. 2. Mozart’s melody descends from 5 to 3 to 1 in mm. 1–3; Beethoven’s melody ascends from 5 to 1 to 3 in mm. 1–3 and finally to the upper-octave 5 in m. 4. 3. The same accompanimental neighboring figure (boxed in both excerpts) gives a chromatic twist to each example.

Contrasts Melodic However, there are important melodic differences: The second phrase of the Mozart excerpt begins exactly the same as the first, with only a slight change at the end, while the Beethoven excerpt has no melodic repetition of material from phrase to phrase. When the two phrases begin with highly similar thematic material, as in the Mozart example, we call them parallel periods (aa or aa⬘). Those that are melodically dissimilar, as in the Beethoven example, are called contrasting periods (ab).

Harmonic Although the two periods in Example 15.2 have similar cadences (HC and AC), there is one important harmonic difference. Mozart’s second phrase begins again on the tonic, restating the same melodic idea of the first phrase. It is as if the music restarts after being interrupted at the half cadence. Only in the second phrase does the music push through the cadential dominant to attain the long-awaited tonic in m. 8. A pair of phrases with this related harmonic structure creates an interrupted period. We indicate the interrupted

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Chapter 15 The Period

EXAMPLE 15.2 Two Periods A.

STR EA MING AUDIO

Mozart, Piano Concerto in D minor, K. 466, Andante

W W W.OUP.COM/US/LAITZ

First Phrase (Antecedent)

B :

I

V HC Second Phrase (Consequent)

I

B.

V

I IAC

Beethoven, Piano Sonata no. 11 in B major, op. 22, Menuetto First Phrase (Antecedent)

B :

I

PD Second Phrase (Consequent)

cresc.

V HC

9 V7

I PAC

motion with a double slash. (Note that Mozart’s half cadence does not resolve to the tonic that begins the second phrase; the dominant at the end of the first phrase is a back-relating dominant that extends the first tonic.)

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THE COMPLETE MUSICIAN

Mozart: Parallel Interrupted Period phrase 1_____________________ T D // phrase interrupted

phrase 2____________ T D T starts over → resolves!

Beethoven’s first phrase also has the structure T–PD–D. The second phrase, by contrast, does not begin on the tonic. Instead it begins with a V7 chord, and continues away from the tonic. A pair of phrases with this single, sweeping harmonic motion forms a continuous period.

Beethoven: Contrasting Continuous Period phrase 1____________ phrase 2____________ T PD D____________(D)____________T phrase model continues →

A favorite device of composers here is to lead to a HC in the first phrase but then follow it with the structural pre-dominant to begin the second phrase. In this case, the HC is strongly heard as a back-relating dominant:

Continuous Period With PD in Second Phrase phrase 1____________ phrase 2____________ (BRD) T PD D T phrase model continues

An alternate method of creating a continuous period is to end the first phrase with an authentic cadence on a harmony other than tonic, and then continue the second phrase on the dominant, as shown here:

Continuous Period With PD in First Phrase phrase 1_________ phrase 2__________ ___________ T PAC in ii D______________T T_________________PD_________D______________T phrase model continues ___________→

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Chapter 15 The Period

Again, a single harmonic sweep occurs, as shown by the second-level analysis, which is the same for both models: T–PD–D–T.

Two Other Options Two other harmonic possibilities exist in addition to interrupted and continuous periods. Listen to Example 15.3 and focus on the cadences that close each phrase.

EXAMPLE 15.3 Mozart, Piano Sonata in B  major, K. 281, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

First Phrase (Antecedent)

3

3

3

3

I Second Phrase (Consequent) 5 3

3

3

3

3

ii 6

I IAC

3

_____ 7

V 64 _____ 53

I PAC

Sectional In Example 15.3 even though both phrases close on the tonic, they form a period because the second phrase subtly completes the melodic motion by ending on 1. When two phrases have the cadences IAC and PAC—and each phrase is, in a sense, a closed harmonic section—they form a sectional period.

Sectional Period (Parallel) phrase 1___________________ T PD D T IAC: melody does not close on 1

phrase 2_______________________ T PD D T PAC: melody closes on 1

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THE COMPLETE MUSICIAN

Progressive The cadence in Example 15.4 forms a weak–strong relationship (HC–PAC), but we are struck by the sound of the second cadence, which ends in the key of v.

EXAMPLE 15.4 Beethoven, Piano Sonata in D major, op. 28, Andante First Phrase (Antecedent)

HC

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

cresc.

sempre stacc. d: i

V

6 4

— —

5 3

PAC (in new key)

Second Phrase (Consequent)

cresc.

F:

I

a: ii

6 5

V

8 6 4

— — —

7 5 3

i

If two phrases have a weak–strong cadence relationship and there is a key change during the course of the phrases, they form a progressive period. It does not matter whether the cadences reflect characteristics of any other period (sectional, continuous, interrupted). The “progressive” label trumps all other labels because it indicates a change of key.

R E PR E S E N T I N G F OR M : T H E F OR M A L DI AG R A M Diagramming the relationships of phrases visually captures the sense of how they combine to form periods.

Phrases and Periods Arcs represent phrases, and an overarching curve over two arcs indicates that the phrases combine into a single period.

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Chapter 15 The Period

Melody Letter names represent the melodic relationship between phrases: For phrase 1: a ⫽ melodic material of the first phrase For phrase 2: a⬘ ⫽ melodic material similar to the first phrase b ⫽ melodic material different from the first phrase Compare the following diagrams with the melodic material in Examples 15.2A and 15.2B: Mozart a

Beethoven a⬘

a

b

Harmony Diagrams also capture the harmonic content of a period by listing the initial harmony and the cadence for each phrase. Initial harmony: Typically, the first harmony is listed by roman numeral. Cadence: Use HC, IAC, or PAC to identify the cadence. A double slash (//) after a HC indicates a harmonic interruption—the second phrase restarts with tonic. Consider the diagrams for Examples 15.2A and 15.2B: Mozart a I

Beethoven a⬘

HC ⁄⁄

I

a IAC

I

HC V

7

b PAC

Period Label We label a period with three words: 1. The first word describes the melodic relationship between phrases. The choices are: a. parallel b. contrasting 2. The second word describes the harmonic motion of the period. The choices are: a. interrupted b. continuous c. sectional d. progressive 3. The last word identifies the structure: period.

Period Diagrams and Their Labels Period label

Abbreviation

Interrupted parallel interrupted period

PIP

contrasting interrupted period

CIP

contrasting sectional period

CSP

Progressive parallel progressive period

contrasting progressive period

I

a⬘ HC ⁄⁄

I

a

PSP

contrasting continuous period

386

a

Sectional parallel sectional period

Continuous parallel continuous period

Formal diagram

PAC

b

I

HC ⁄⁄

I

PAC

a I

a⬘ IAC

I

a

PCP

IAC

a HC, or AC somewhere other than tonic

PAC

a⬘ phrase 2 PAC begins somewhere other than tonic

a

a I

HC or IAC

PPP

I

CPP

I

b HC, phrase 2 PAC or AC begins somewhere somewhere other than tonic other than tonic

I

CCP

b

I

I

PAC

a

HC or IAC

a⬘ phrase 2 ends with AC somewhere other than tonic

b phrase 2 ends with AC somewhere other than tonic

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Chapter 15 The Period

As the completed form diagram illustrates, Example 15.2A is a parallel interrupted period and Example 15.2B is a contrasting continuous period. The following diagram represents the parallel sectional period and parallel progressive period of Examples 15.3 and 15.4, respectively. Note that the new key is shown in the progressive period (i.e., “v”). Mozart, Allegro parallel sectional period a I

Beethoven, “Andante” parallel progressive period

a⬘ IAC

I

a PAC

i

a HC

III

v: PAC

S A M PL E A N A LY S E S OF PE R IOD S A N D S OM E A N A LY T IC A L GU I DE L I N E S Listen to Example 15.5 and consider the five questions and answers that follow.

EXAMPLE 15.5 Mozart, Die Zauberflöte (The Magic Flute), K. 620, act I, Finale STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

(plays the flute)

1. Can the excerpt be divided into two or more phrases? Answer: Yes, it can be divided into two four-measure phrases, each of which ends with a cadence. 2. Do these phrases create an antecedent–consequent relationship? Answer: Yes, the first phrase sounds harmonically open (ending on a HC) and melodically open (ending on the leading tone); the second phrase provides satisfying closure, with 2–1 in the melody over a PAC.

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THE COMPLETE MUSICIAN

3. Is the second cadence stronger than the first? Answer: Yes, the HC is less conclusive than a PAC. This forms a period. 4. Are the melodies in each phrase related? Answer: Yes, they are clearly related. The second phrase is nearly identical to the first phrase except for embellishments throughout. Thus, the melodic structure is parallel. 5. What harmonies begin and end each phrase? Answer: Phrase I begins with tonic and ends with a HC. Phrase 2 restarts with tonic and ends with a PAC. Thus, the harmonic structure is interrupted. From the answers to these five questions, we are ready to label the period as a PIP and diagram it in the following manner:

a I

a⬘ HC ⁄⁄

I

PAC

parallel interrupted period

Now let’s try applying the same question-and-answer process to Example 15.6.

EXAMPLE 15.6 Beethoven, Klavierstück, WoO 82 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Moderato

1. Can the excerpt be divided into two or more phrases? Answer: No. Although the excerpt divides into two musical units, they cannot be considered phrases because there is no cadence in m. 4, just a caesura on a dissonant ii65 chord. Because there is only one cadence (m. 8), there can be only one phrase. This excerpt is simply an eight-measure phrase; it is not a period.

Summary for Analyzing Periods The following four steps will assist you in locating and identifying periods. STEP 1 Locate phrases and mark their cadences. STEP 2 Examine the cadence of phrase 1. If it is a PAC in the tonic, it cannot be part of a period. If the first phrase closes with a cadence that is weaker than the cadence found at the end of the second phrase, however, draw arcs and identify phrase lengths.

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Chapter 15 The Period

STEP 3 Analyze the melodies of the phrases for the two possible melodic structures: parallel and contrasting. STEP 4 Analyze the cadences of the phrases and write your answers to the right of each arc. Next, label the harmony that begins each phrase using one of the four possible harmonic structures: sectional, interrupted, continuous, and progressive.

C OM P O S I N G PE R IOD S Writing periods involves creativity and using your ear. For the time being, confine yourself to three period types that end on the tonic. In beginning a composition, start with the large harmonic picture using the following tonal models: Phrase One:

Phrase Two:

• I_____ HC • I_____ IAC • I_____ HC

I_____ PAC or IAC I_____ PAC V(7) ___ PAC

Next, map out the harmonies within each phrase. As a general rule, harmonic changes tend to occur on strong, accented beats (such as downbeats). The following eight-measure structure reveals two potential harmonic solutions for an interrupted period (the first tonal model shown earlier): Phrase One

Phrase Two

Measure:

1

2

3

4

5

6

7

8

Solution 1:

I

vi

IV

V //

I–IV–I

iii–vi

ii–V7

I

Solution 2:

I–I6

V42–I6

ii6

V //

I–iii

vi–IV

ii65 –V7

I

Notice that the consequent phrases in both solutions open with harmonic settings different from their antecedents. Such harmonic contrast permits—in fact, almost demands— these periods to be contrasting melodically rather than parallel. After your harmonic plan is in place, you can then add a melody that provides a good outer-voice counterpoint and exhibits a high degree of motivic consistency and melodic interest.

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 15.1–15.3

15.1 Following the question-and-answer procedure demonstrated earlier, label each of the following examples. The examples may be a single phrase or a period; if an example is a period,

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THE COMPLETE MUSICIAN

provide a formal diagram and period label. Note: You may find it useful to mark up the music to help you with your analysis. Do not analyze every harmony. STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

SOLVED/APP 5

A.

Mozart, Piano Sonata in B  major, K. 333, Allegretto grazioso

3

SOLVED/APP 5

B.

Mozart, Symphony no. 39 in E  major, K. 543, Allegretto 5

C.

Brahms, Waltz in A  major, op. 39, no. 15

D.

Beethoven, Violin Sonata in G major, op. 30, no. 3, Allegro assai Allegro assai

Allegro assai

cresc.

Chapter 15 The Period

391

T ER MS A ND CONCEP TS • period • melodic types • parallel • contrasting • harmonic types • interrupted • continuous • sectional • progressive • phrase • antecedent versus consequent

CH A PTER R EV IEW 1. Two phrases make a period only if two conditions are fulfilled:

2. The name for the weak phrase is ____________________ and the name for the strong phrase is __________________________________________________________________________________.

3. Two phrases that are melodically similar in the pattern [a a] or [a a⬘] are called: a. parallel

b. contrasting

392

THE COMPLETE MUSICIAN

4. Two phrases are melodically dissimilar in the pattern [a b] are called: a. parallel

b. contrasting

5. An interrupted period has an antecedent that ends on [T/PD/D] and a consequent that begins with [T/PD/D].

6. A continuous period has a consequent that begins with something other than [T/PD/D].

7. A sectional period has an antecedent that cadences with a [HC/IAC/PAC] and a consequent that cadences with a [HC/IAC/PAC].

8. A progressive period has a consequent that cadences in: a. the original key

b. a new key (it modulates)

9. Parallel and contrasting are words that describe: a. melody

b. harmony

10. Interrupted, continuous, sectional, and progressive are words that describe: a. melody

b. harmony

C H A P T E R 16

Other Small Musical Structures: Sentences, Double Periods, and Modified Periods

OV E RV I E W

This chapter continues the topic of form by introducing variations of phrases and periods. These include structures that unfold in a proportional manner (the sentence), and larger formal units, such as the combination and modifications of period structures (the double period; modified periods). CHAPTER OUTLINE The Sentence: An Alternative Musical Structure ................................................ 394 The Double Period ..................................................................................................... 400 Modified Periods ......................................................................................................... 402 Terms and Concepts ................................................................................................... 407 Chapter Review ........................................................................................................... 407

H AV E Y O U E V E R L I S T E N E D to the way parents call their children inside on a hot summer evening? There is usually a consistency in their speech pattern, since parents typically need to make their announcement more than once:

“Johnny, it’s time to come in now.” “Johnny, you need to come in now.” “Johnny, I mean it. Get in right now or you’ll be grounded for life.” 393

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THE COMPLETE MUSICIAN

While reading these three statements aloud, notice the pattern and the proportional length of each utterance. The first two declamations are related both in length and content: In eight syllables, each statement communicates that Johnny must come in, although a slight emphasis is made in the second statement by leaning on the word now. The third statement, however, is very different. Not only is it exactly twice as long (16 syllables), but now the parent’s level of insistence is communicated by a threat to the child. One would assume that other factors, such as the pitch and the dynamic level of the parent’s voice, are correspondingly accentuated as well. However, it is often only the third statement—which intensifies the sentiments of the previous two—that is ever successful: Within 15 seconds, the child makes it breathlessly through the door. This threefold process of communication is common in human interaction: a short statement followed by a similar repetition and then an elaboration of the statement that occupies exactly twice as much time. Whenever this formal device of short–short–long (usually in the proportion 1:1:2) occurs within music, it is described as an instance of sentence structure. Many folk and even popular tunes unfold using this pattern. Consider the pacing of “Clementine” (Oh My Darlin’ | Oh My Darlin’ | Oh My Dar—lin’ Clementine). Entire genres of music are based on sentence structure, including the blues, and—not to be left out—composers of art music from the seventeenth century to the present have relied on this time-honored device.

T H E S E N T E N C E : A N A LT E R N AT I V E M U S IC A L S T RUC T U R E Listen to Example 16.1. The phrase contains subphrases articulated by rests that create a breathy and halting effect. The analytical annotations represent the harmonic, melodic, and rhythmic content of each gesture in the excerpt. Measures 1 and 2, which move from I to V, are labeled A; mm. 3 and 4, which transpose the melody up a second, moving from V65 to I, are labeled A. The second contrasting gesture behaves as one continuous unit of four measures and is labeled B. We see in Example 16.1 how Beethoven creates a proportional, additive structure, in which a two-measure musical idea is stated, restated, and then embellished and extended, ending in a cadence. The excerpt is particularly satisfying because it develops so organically: The two two-measure subphrases become, in a sense, an integral part of the consequent unit. Now listen to Example 16.2. This eight-measure excerpt comprises a single phrase that closes with a half cadence. The first half of the phrase contains two distinct yet closely related ideas (labeled A and A); the second four measures seem to combine into a single unit, creating an overall 2  2  4 sentence structure. Yet there is more to this sentence. Examining the harmonic rhythm reveals that the rate of change is relatively slow in the first four measures (two measures of tonic are followed by two measures of a neighboring dominant). The harmonic rhythm speeds up in mm. 4–8, as illustrated here: measure: harmony

1 2 3 4 i V65 rate of harmonic change accelerates

5 i

6 vii°6

7 i6 ii°6

8 V

Chapter 16 Other Small Musical Structures: Sentences, Double Periods, and Modified Periods 395

EXAMPLE 16.1 Beethoven, “Lustig-Traurig,” WoO 54 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1

measure:

2

3

2

4

+

5

2

4

7

+

4

+

4

A⬘

A

I

6

V

6

8

B

6

V5

I

ii 66 V 7

I

I PAC

EXAMPLE 16.2 Beethoven, Piano Sonata no. 1 in F minor, op. 2, no. 1, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A

A

3

3

V 65

i

B

3

3

i

vii

6

i6

ii

6

V HC

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THE COMPLETE MUSICIAN

Notice how Beethoven creates a musical paradox in his sentence: As the initial two-measure units combine and lengthen into a single four-measure unit, the final four measures are fragmented by the acceleration of the harmonic rhythm. Further analysis reveals another layer of complexity: On the first pass, we labeled the melodic ideas in the first four measures A and A, implying a close relationship. However, the melodic content of mm. 5–6 also implies a close relationship, because m. 5 repeats a step higher in m. 6, even though this melody goes by twice as fast as A and A. When the melody of mm. 5–6 (labeled a and a) is followed by the climactic twomeasure gesture of mm. 7–8 (labeled b), we see a miniature sentence develop (1  1  2) within the four-measure B of the larger sentence. This nesting of sentences is reflected in the following diagram. (When nested structures occur within both the A and the B portions of the sentence, new letters (c and d) are assigned to the nested structures in the B portion of the sentence. For example, A’s nested structures would be labeled a, a, b, and B’s nested structures would be labeled c, c, d.) measure: larger sentence: smaller sentence:

1 2 3 4 A (2 mm.)  A (2 mm.)

5 6 B (4 mm.) a (1) a (1)

7

8

b (2)

Beethoven is not the only composer to use these elegant techniques. Examples 16.3A and B present sentences composed by Haydn and Mozart, respectively. Haydn’s sentence illustrates a single four-measure phrase; Mozart’s sentence contains eight measures. Given that phrases are often fashioned into sentence structures, it follows that periods draw on sentence construction. Listen to Example 16.4. The first phrase (mm. 1–4) is also

EXAMPLE 16.3 A.

STR EA MING AUDIO

Haydn, Piano Sonata no. 38 in F major, Hob XVI.23, Adagio

W W W.OUP.COM/US/LAITZ

A

A

dolce

3

3

3

3

3

3

3

3

B

( ) 3

3

3

3

3 3

3

3

3

3

3

3

Chapter 16 Other Small Musical Structures: Sentences, Double Periods, and Modified Periods 397

EXAMPLE 16.3 (continued) B.

Mozart, Violin Sonata in C major, K. 14, Menuetto secondo en Carillon A

A

3

3

3

3

B

a

3

a

3

3

3

3

b

3

a sentence, containing two one-measure ideas that are answered by a two-measure idea that moves to a half cadence. The material repeats in an ornamented form in mm. 5–8 and closes with a PAC. The idea of repeating a phrase with sentence structure is one of

EXAMPLE 16.4

Mozart, Piano Sonata in B  major, K. 281, Rondeau: Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A

A

B

A

HC

398

THE COMPLETE MUSICIAN

(continued)

EXAMPLE 16.4 (A)

A

B

5

PAC

two common techniques for casting a period in sentence structure (Example 16.5A). The second technique, which does not merely repeat the sentence structure, is more dramatic. The first phrase forms the A and A of the sentence; the second phrase comprises the B. Thus, a single sentence structure unfolds over the entire period (Example 16.5B).

Periods Composed of Sentence Structures

EXAMPLE 16.5 A.

Period Composed of a Repeated Sentence:

A (1 m.) A (1 m.)

B.

B (2 mm.)

A (1 m.) A (1 m.)

B (2 mm.)

Period Composed of a Single Sentence:

A (2 mm.)

A (2 mm.)

B (4 mm.)

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignment 16.1

16.1 The following phrases and periods contain sentence structures. Do not analyze with roman numerals; provide only a formal diagram for each. Include period labels, and clearly

Chapter 16 Other Small Musical Structures: Sentences, Double Periods, and Modified Periods 399

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identify sentence structures with brackets. (When you encounter a nested sentence, as in Example 16.2, use uppercase letters for the larger sentence and lowercase letters for the smaller sentence. Further, if both the A and the B of the sentence contain nested structures, assign new letters [c and d] to the nested structures in the B portion of the sentence.) In a paragraph or two, compare or contrast any two examples.

Sample solution: Beethoven, Piano Concerto no. 2 in B , op. 19, Rondo A (2 mm.)

A (2 mm.) 1/2

1/2

1

1/2

1/2

1

a

a

b

a

a

b

(stacc.)

B (4 mm.) 5

1

1

2

c

c

d

(

A.

)

Beethoven, Violin Concerto in D major, op. 61, Rondo: Allegro sul G. ten.

ten.

ten.

Violino principale

Vcl. Violoncello e Basso

SOLVED/APP 5

B. Haydn, String Quartet in B  major, “Sunrise,” op. 76, no. 4, Adagio Adagio

ten.

400

C.

THE COMPLETE MUSICIAN

Schubert, Piano Sonata in A major, D. 959, Trio Un poco più lento m.s.

D. Schumann, “Kind im einschlummern,” Kinderszenen, op. 15, no. 12

SOLVED/APP 5

E.

Chopin, Nocturne in F minor, op. 55, no. 1

T H E D OU B L E PE R IOD In Example 16.6, Beethoven’s Piano Sonata in A major, the first 16 measures contain four distinct cadences, which do not truly comprise two periods. The cadence in m. 8 is not conclusive enough to close a period; it is only a half cadence, which requires a consequent authentic cadence. The necessary PAC does not appear until m. 16, yet the 16 measures do not truly comprise one giant period either. It’s true that mm. 1–8 and 9–16 each subdivide into four-measure antecedent– consequent segments and that the cadences in mm. 8 and 16 are stronger than the

Chapter 16 Other Small Musical Structures: Sentences, Double Periods, and Modified Periods 401

EXAMPLE 16.6 Beethoven, Piano Sonata in A  major, op. 26, Andante STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Antecedent “antecedent”

HC 4

cresc.

A :

HC “consequent”

“antecedent”

HC 8

cresc.

PAC

Consequent HC

“consequent”

PAC

12

cadences in mm. 4 and 12. For example, the half cadence in m. 4 comes about almost as an afterthought. The downbeat sonority of m. 4 is tonic, and the dominant enters only on the weak beat of the measure. The half cadence in m. 8, however, appears to be more confident; here, the bass rings on dominant 5 right from the downbeat. The fact that m. 9 parallels the melody of m. 1 creates a set of expectations for mm. 9–16. We anticipate that this second unit will take eight measures to close on the tonic. And indeed, the melody in mm. 9–16 is similar to the melody in mm. 1–8. The result is a parallel melodic structure, in which the PAC in m. 16 answers the HC in m. 8. The diagram in Example 16.7 summarizes the form of the four phrases. Measures 1–16 appear to be one giant parallel interrupted period, each half of which contains two contrasting phrases. This type of structure—the antecedent and consequent segments divide into antecedent–consequent phrases at a smaller level—is called a double period. (For the full score of this section, see the Anthology no. 41.)

402

THE COMPLETE MUSICIAN

EXAMPLE 16.7 Double Period Structure

measures:

1– 4

harmony:

I

smaller-level melody: large-level melody:

5–8 HC

a A

smaller-level period structure: large-level period structure:

“antecedent” Antecedent

IV6

9– 12 HC ⁄⁄

b

“consequent”

I

13–16 IV6

HC

a A

PAC

b

“antecedent” Consequent

“consequent”

MODI F I E D PE R IOD S Occasionally we encounter periods that do not exhibit the typical antecedent–consequent relationship. Composers alter the standard two-phrase model in many ways; consider the following three: 1. Composers may immediately repeat either the antecedent or the consequent (for example, aab or abb). Example 16.8 presents the opening of a rondo by

EXAMPLE 16.8 Beethoven, Piano Sonata in C minor, “Pathetique,” op. 13, Rondo STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A

B

Allegro

(B) 6

B (echo)

Chapter 16 Other Small Musical Structures: Sentences, Double Periods, and Modified Periods 403

Beethoven that has the structure antecedent–consequent–consequent. This type of period maintains a deeper-level two-phrase symmetry; the repetition of the consequent (which can also be considered an “extension” or “suffix” after the cadence in m. 8) is more of an echo than an independent entity. 2. A series of phrases punctuated by weak cadences—none of which is strong enough to close a passage— does not constitute a period. Rather, it is just a phrase chain, or phrase group. Sometimes a composer writes a series of phrases, each of which contains new material, but the cadences in each, save for the final phrase, are weak or even more like caesuras. Thus, we must consider the strength of the final cadence in order to discriminate a period from a phrase group. Example 16.9 has three distinct four-measure units, but only the third closes with a real cadence. The first unit, which alternates tonic and dominant, barely qualifies as a phrase, and the second unit merely elaborates tonic with a IV–I motion. Yet, given that the final cadence is so strong and brings closure to the

EXAMPLE 16.9 Gruber, “Silent Night”

Si Si

lent night, lent night,

ho ho

Round yon vir Glo ries stream

gin Moth from heav

Sleep Christ

en ly iour is

in heav the Sav

ly ly

er and Child, en a far,

peace, born!

night! night!

Ho Heav’n

Sleep Christ

All Shep

ly ly

is calm, herds quake

In fant so hosts sing

in heav the Sav

ten al

en ly iour is

all at

is bright, the sight!

der and mild le lu ia;

peace. born!

404

THE COMPLETE MUSICIAN

previous “phrases,” one could interpret the piece as a two-phrase period, with the middle unit acting as an extension of phrase one: A–extension–B. 3. Occasionally, composers write periods comprising an uneven number of distinct phrases, which create three-phrase, five-phrase, or even seven-phrase periods. We call these asymmetrical periods. Example 16.10 is an example of a threephrase asymmetrical period (abc) that includes repeated phrases creating the pattern aabcc: a b c ||: I_______HC :|| V_______HC ||: I_______PAC :|| phrase 1 phrase 3 phrase 4 phrase 2 phrase 5

EXAMPLE 16.10 Haydn, String Quartet in C major, “Emperor,” op. 76, no. 3, Hob III.77, Poco adagio; cantabile STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A

A

dolce.

dolce.

dolce.

dolce.

B 10

C

Chapter 16 Other Small Musical Structures: Sentences, Double Periods, and Modified Periods 405

EXAMPLE 16.10 (continued) C 20

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignment 16.2

16.2 Analysis of Periods and Sentences Analyze each of the following periods by providing a formal diagram. Do not add a roman numeral analysis. Note that you may encounter sentences, double periods, and asymmetrical periods.

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A. Mozart, Piano Sonata in D major, K. 284, Theme: Andante

406

THE COMPLETE MUSICIAN

SOLVED/APP 5

B.

Brahms, Intermezzo in A minor, op. 116, no. 2

3

3

SOLVED/APP 5

C.

Mozart, Piano Sonata in D major, K. 576, Allegretto Allegretto

D. Tchaikovsky, “Sweet Reverie,” Children’s Pieces, op. 39, no. 21 Explain why this excerpt could be interpreted as containing a sentence structure. dolce cantabile

Chapter 16 Other Small Musical Structures: Sentences, Double Periods, and Modified Periods 407

poco più

cresc.

T ER MS A ND CONCEP TS • asymmetrical period • double period • nesting of sentences • phrase group • sentence • sentence structure

CH A PTER R EV IEW 1. Describe the proportions that make up sentence structure using ratios.

2. When one or both phrases of a sentence use sentence structure, this is called _____________.

408

THE COMPLETE MUSICIAN

3. Draw a diagram, showing melodic relationships (a, a, etc.) and phrase lengths in measures, that illustrates a sentential period.

4. Draw a diagram, showing melodic relationships (a, a, etc.), cadences (HC, PAC, etc.), and antecedents/consequents, that illustrates a double period.

5. List and briefly describe the three types of modified periods.

C H A P T E R 17

Harmonic Sequences OV E RV I E W

This chapter presents a musical technique so widespread that it would be unusual not to encounter it in a tonal work written from 1680 to this day. The technique, called sequence, combines harmony and rhythm by repeating a small two-chord pattern on different scale degrees. Sequences increase the length of phrases, accelerate the harmonic rhythm, and intensify musical drama. CHAPTER OUTLINE Components and Types of Sequences ................................................................... 412 The Descending-Second (D2) Sequence ............................................................ 413 The Descending-Second Sequence in Inversion ...........................................414 The Descending-Third (D3) Sequence ............................................................... 414 The Descending-Third Sequence in Inversion .............................................415 The Ascending-Second (A2) Sequence ............................................................... 416 Another Ascending-Second Sequence ................................................................ 417 Sequences with Diatonic Seventh Chords ......................................................... 421 Sequences with Inversions of Seventh Chords .................................................. 422 Writing Sequences ...................................................................................................... 423 Terms and Concepts ................................................................................................... 429 Chapter Review ........................................................................................................... 430 Summary of Part 4...................................................................................................... 431

409

410

THE COMPLETE MUSICIAN

D I ATO N I C H A R M O N I E S I N B OT H major and minor keys participate in the phrase

model. Though each harmony may appear in a variety of musical contexts, its behavior is strictly regulated by counterpoint and the hierarchy of the phrase model. The three ordered harmonic functions, and their expansion through contrapuntal chords, rarely incorporate more than just a few diatonic harmonies within any phrase. In this chapter, we explore how composers can employ all of the diatonic harmonies to fill a single phrase. Listen to Example 17.1A, which presents the end of one phrase followed by a complete four-measure phrase. Example 17.1B presents the same structure as Example 17.1A, except the final phrase of Example 17.1B contains twice as many measures. The added measures, bracketed and labeled in the example, are interpolated between the i6 that begins the final phrase and the ii°(6)–V65–i that closes the phrase. However, the added chords fit nicely within the phrase and serve both to prolong the tonic function and to connect

EXAMPLE 17.1 Inserting a Harmonic Sequence STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A. Vivaldi, Violin Concerto in C minor, “Il Sospetto,” RV199, Allegro (sequence omitted) 14

iv 6

4 2

V

i6

PHRY

B. Vivaldi (original) 14

iv 6

4 2

V

i6

PHRY 19

ii

6

V6

5

i

ii

6

V6

5

i

Chapter 17 Harmonic Sequences

411

the tonic to the pre-dominant. Such patterns, called harmonic sequences, form seamless, goal-directed musical units that do not draw attention away from the underlying harmonic progression. Sequences first appeared during the Renaissance period (ca. 1450–1600), but they played a much more important role in the Baroque (ca. 1600–1750) and in successive musical periods, including the popular and commercial music of today. Sequences embody a paradox. Given their rapid harmonic rhythm, they provide the impression of intense musical motion. Yet, given their repetition, predictability, and subordination to harmonically functional chords, they actually serve to slow harmonic motion. Sequences are comparable to some of the art of M. C. Escher, whose paintings, such as Ascending and Descending (1960) (Example 17.2), represent constant goal-directed motion. Following the course of these busy monks through their journey, only brings an observer back to the beginning point.

EXAMPLE 17.2 M. C. Escher (1898–1972), Ascending and Descending

412

THE COMPLETE MUSICIAN

C OM P ON E N T S A N D T Y PE S OF S E QU E N C E S One can divide a sequence into two parts: the model and its copies (which “copy and paste” the model at different pitch levels). The model presents the basic contrapuntal/ harmonic pattern—this is usually two chords in length. Any melodic or motivic figuration used in the sequence will first appear in the model and will be repeated in each successive copy. Sequences typically have two or three copies of the model. Sequence types are determined from harmonic and contrapuntal voice-leading patterns. Although there are many types of sequences, they fall into two categories: descending and ascending sequences. Consider Example 17.3.

EXAMPLE 17.3 Sequence Terminology A.

model

a

–5

b

copy

+4

copy

copy

B.

c

C: I

I D2 (– 5/+4)

The sequence label indicates the distances between the chord roots that comprise the repeating pattern: 1. The first distance to consider is the root distance from chord a to chord c—the amount that the model moves each time it makes a new copy. In this example, the distance from the C-major chord to the B-diminished chord is a descending second (D2). 2. We now determine how the model is copied down a step (in this case). A. determine the distance from chord a to chord b (C down to F is a fifth [⫺5]) B. Then determine the distance from chord b to chord c, F up to B, which is a fourth (⫹4). Notice that chord-to-chord motions are labeled with negative numbers to indicate descent and positive numbers to indicate ascent. 3. The labeling system makes sense since it describes both the overall intervallic motion from the model to copy (here, down a second) and it reveals how this was accomplished: by descending a 5th and then rising a 4th, the net result is being a 2nd below where we began. 4. Only the first and last chords in a sequence receive roman numerals, because only they participate in the harmonic progression of the phrase. (See Example 17.3B.) The complete label for this sequence is D2 (⫺5/⫹4). We will now examine two sequences that descend and two sequences that ascend.

413

Chapter 17 Harmonic Sequences

The Descending-Second (D2) Sequence The D2 (⫺5/⫹4) sequence, as in our example, is called the descending-second sequence. It is also called the sequence with descending circle-of-fifths progression, because the root motion from chord to chord follows the circle of fifths. We began our harmonic discussion with V–I. Each time we added a new harmony, we backed up one harmony on the circle of fifths. The complete diatonic pattern of fifths is I–IV–vii°–iii–vi–ii–V–I. Range limitations preclude using descending fifths exclusively; therefore, a descending fifth is typically answered with an ascending fourth, as illustrated in the previous example. Of course, composers might begin their D2 sequences by rising a fourth and then falling a fifth. For simplicity any sequence whose roots fall a fifth and rise a fourth or rise a fourth and fall a fifth is a D2 (⫺5/⫹4) sequence. Notice that this sequential two-chord pattern creates the deeper-level descent by second, as shown by the connecting beams in Example 17.4.

EXAMPLE 17.4 The D2 Sequence A. Major

–5

C:

STR EA MING AUDIO

B. Minor

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+4

I

I D2 (– 5/+4)

c:

i

i D2 (– 5/+4)

Another important function of sequences is that the second chord of the model (and of each of its copies) breaks up the potential parallels that result from moving downward by step. If the above example had only the beamed chords in Example 17.4, it would result in parallel motion in all voices. These helping chords that appear in each sequence are called voice-leading chords. Note that the major-mode D2 (⫺5/⫹4) contains a melodic tritone in the bass near its beginning; in the minor mode, the tritone occurs near the end of the sequence (tritones are circled in Example 17.4). Given the need to keep the pitches from spiraling outside of the key, this bass tritone leap, though uncommon in traditional harmonic progressions, is both acceptable and necessary in this sequence. For example, in the key of C major, if the sequence were to move in strict perfect fifths, it would spin off into chromatic areas and require six copies of the model to return to the tonic (C–F–[B–E–A–D–G]–B–E–A–D–G–C). In your analysis, you may have noticed that the harmonization of 7 in major and 2 in minor creates root-position diminished triads (vii° and ii°), which so far have not been permitted. Within sequences, these sonorities are members of a larger contrapuntal/harmonic pattern and are not independent entities; they are allowed in order to participate in the overall repeating pattern. In Example 17.5, the stately D2 (⫺5/⫹4) sequence in G minor maintains its contrapuntal/harmonic pattern through the entire circle of fifths in that key,

414

THE COMPLETE MUSICIAN

EXAMPLE 17.5 Handel, Concerto in B  major for Harp, op. 4, no. 6, Larghetto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

model

copy

copy

copy 5

Tui

arriving back at the tonic. Therefore, we hear not only the strong tritone E–A in the bass (E–[D–C–B]–A) but also the ii° in root position.

The Descending-Second Sequence in Inversion Given the angular, disjunct bass that occurs in root-position D2 (⫺5/⫹4) sequences, composers often place one of the chords of the model—usually the second chord—in first inversion. This technique, as we know, creates a more melodic bass. Sequence labels don’t change with the use of inverted chords; instead add inversion symbols underneath the inverted chords. See Example 17.6. Compare the outer-voice counterpoint of Example 17.4 with Example 17.6. Notice that in the earlier example, an octave occurs on the second chord of the model and each copy. This is acceptable, but the bass is not smooth. The outer-voice counterpoint of Example 17.6 consists exclusively of imperfect consonances (10–6), which enhances the smooth, melodic sound.

EXAMPLE 17.6 D2 Sequence with 63 Chords STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

10

C:

6

I

10

6

6

10

6 D2 (– 5/+ 4)

6

ii 6

V 42

I6

The Descending-Third (D3) Sequence The D3 (⫺4/⫹2) sequence contrasts nicely with the D2 (⫺5/⫹4) sequence, because it incorporates entirely different root motions in each stage.

415

Chapter 17 Harmonic Sequences

The Pachelbel Canon (Example 17.7) is a well-known example of this sequence. The sequence is two measures long, and three of the piece’s many repetitions are included in the example. Both the model and its copies are bracketed in the first two measures, and important bass notes are circled. Notice that the sequence seems to serve a double function in the piece: It prolongs tonic (I is the first and last chord of the sequence), but it also leads to the PD (the tonic at the end of the sequence sounds less like an arrival than like a voice-leading chord to ii65). D3 (⫺4/⫹2) sequences often function in this dual capacity.

EXAMPLE 17.7 Pachelbel, Canon in D major STR EA MING AUDIO W W W.OUP.COM/US/LAITZ ( = ca. 63)

(espr.)

(espr.)

(espr.)

( = ca. 63)

I V vi iii IV I ii 65 V I vi IV ii 65

I I

I T

ii 65 V PD D

As in the D2 sequence, the second chord of the D3 sequence’s model (and each copy) is a voice-leading chord, because it avoids the potential parallels that result from falling directly by thirds. Listen to Example 17.8A and note the miniature deceptive motion (V–vi) and the stepwise descending soprano line; these are common characteristics of the D3 (⫺4/⫹2) sequence. Also observe the minor v chord in m. 1 of Example 17.8C, which is necessary to avoid the augmented second between A and B.

The Descending-Third Sequence in Inversion Composers often use first-inversion chords to smooth the basses of D3 sequences. In Example 17.9, notice the stepwise bass descent that moves in parallel tenths with the soprano. This sequence is often called the descending 5–6 sequence because one voice (often the tenor, as in the example) remains stationary against the falling bass, forming first a fifth

416

THE COMPLETE MUSICIAN

EXAMPLE 17.8A

The D3 Sequence STR EA MING AUDIO

A.

W W W.OUP.COM/US/LAITZ

model

a

copy

b –4

copy

c +2

EXAMPLE 17.8B/C

The D3 Sequence in Major and Minor

B.

C:

STR EA MING AUDIO

C.

I

IV

D3 (–4/+2)

V7

I

c: i

W W W.OUP.COM/US/LAITZ

D3(–4/+2)

iv

V7

i

EXAMPLE 17.9 D3 Sequence with 63 Chords

5

C:

6

I

6

6

D3 (–4/+2)

I 6 IV vii

6

I

and then a sixth. The D3 (⫺4/⫹2) sequence is more common in inversion than with only root-position chords.

The Ascending-Second (A2) Sequence The ascending-second sequence, with ascending fifths and descending fourths, is much less common than the D2 (⫺5/⫹4) sequence, because it is not nearly as goal directed. Look at Example 17.10. In the progression I to V, the dominant’s natural tendency is to return to the tonic to create a strong progression; but V ascending a fifth to ii creates

417

Chapter 17 Harmonic Sequences

a weak retrogression. Common-practice composers occasionally use the A2 (⫹5/⫺4) sequence for two reasons: 1. Given its overall ascent, it provides a sense of drive. 2. The second chord of the model (and each copy) again serves as a voice-leading harmony that prevents potential parallels that would otherwise occur in a progression moving up by step. The A2 (⫹5/⫺4) sequence—which typically occurs in root position only—results in a large-scale step ascent that usually moves to a PD on 4 (or, as shown in Example 17.10B, a leap to 6 as part of a Phrygian cadence). Note that ii° and VI chords are skipped in Example 17.10B (marked by an asterisk). This is typically done to avoid the tritone leap (2–6) in the bass.

EXAMPLE 17.10 A2 (⫹5/⫺4) Sequence A.

B.

*

C:

I

A2 (+5/–4)

iii

IV

V7

I

c:

i

A2 (+5/–4)

iv

iv 6 V

Another Ascending-Second Sequence Similar to the A2 (⫹5/⫺4) sequence, the A2 (⫺3/⫹4) sequence is characterized by rising seconds leading to the PD, as illustrated in Example 17.11. The propulsion for this sequence comes from a springboard motion—up a fourth—to begin the next copy of the model.

EXAMPLE 17.11 A2 (⫺3/⫹4) Sequence

C:

I

A2 (–3/+4)

iii

IV

8 – 7 – 5 4 – 3

V6

I

418

THE COMPLETE MUSICIAN

EXAMPLE 17.12 A2 Sequence with 63 Chords

ascending 5–6

5

C:

I

6

6

6

6

A2 (–3/+4)

IV

V

I

c:

i

6

6

A2 (–3/+4)

6

iv

V

i

Listen to and study Example 17.12. As with the other sequences that employ firstinversion triads, the addition of the six-three chords makes the A2 (⫺3/⫹4) much smoother. In fact, the bass is sustained as a common tone throughout the model (and in each copy). This is, perhaps, the oldest of all sequences and can be found in the music of early sixteenth-century composers such as Josquin Despres (d. 1521). Parallels that would occur in a stepwise progression are averted by the intervening six-three chord, creating a 5–6 contrapuntal motion (which usually occurs in the outer voices). This sequence is also known as the ascending 5–6 sequence.

EX ERCISE INTER LUDE

WORKBOOK 1 Assignments 17.1–17.4

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

17.1 Analysis of Descending Sequences Listen to and study the following sequences. Do not place a roman numeral beneath every chord: The chords within a sequence are members of a linear motion and do not carry individual harmonic weight. 1. Bracket the beginning and end of each sequence. 2. Determine whether root-position chords or alternating first inversions are used. Label each sequence completely. 3. Determine whether each copy maintains the model’s voice leading precisely. Label the interval between bass and soprano in the model and in one copy. 4. For D2 sequences, mark the location of the single tritone that occurs between IV and viio in major and VI and ii° in minor.

Chapter 17 Harmonic Sequences

SOLVED/APP 5

B.

Bach, Gavotte, French Suite no. 5 in G major, BWV 816

SOLVED/APP 5

C. C.

D.

Mozart, Sonata for Violin and Piano in B  major, K. 372

419

420

THE COMPLETE MUSICIAN

17.2 Analysis of Ascending Sequences Bracket and label each sequence in the following examples. STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A. Schubert, String Quintet in C major, D. 956, Adagio Adagio

espr.

pizz.

cresc.

cresc.

cresc.

cresc.

cresc.

421

Chapter 17 Harmonic Sequences

SOLVED/APP 5

Handel, Trio Sonata in G minor, op. 2, no. 5, HWV 390, Allegro

B. 53

6

6 4 2

5

6

5

6

6

Sequences with Diatonic Seventh Chords Composers commonly add sevenths to harmonies involved in sequences, resulting in a stream of seventh chords. We will limit our study of seventh-chord sequences to the D2 (⫺5/⫹4) sequence. Listen to Example 17.13. Part A contains a D2 (⫺5/⫹4) sequence composed entirely of triads. Part B reproduces the opening of a movement by François Couperin, illustrating a D2 sequence that contains diatonic seventh chords. Notice the increased harmonic interest and richness in Example B compared with Example A, due in large part to the four different types of seventh chords used (mm, MM, dm, and Mm). Diatonic sevenths may be added to every chord (see Example 17.13B) or to every other chord in the D2 (⫺5/⫹4) sequence. However, you must prepare and resolve each seventh. See Example 17.13B; notice that the circled sevenths of each chord have been prepared by

EXAMPLE 17.13 Triadic D2 Sequence Becomes Seventh-Chord D2 Sequence STR EA MING AUDIO

A.

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5 3

5 3

5 3

etc.

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EXAMPLE 17.13 (continued) François Couperin “Les Nations,” Premier Ordre: La Francoise, XIV, Chaconne

B.

7

7

7

etc.

common tone and resolved down by step (the soprano-voice seventh moves to its upper neighbor, actually the root of the chord, before resolving down). Listen to and contrast the two D2 (⫺5/⫹4) sequences in Example 17.14. Example 17.14A has alternating triads and seventh chords and so is called a D2 (⫺5/⫹4) with alternating sevenths. Note that each seventh is prepared by a common tone (dotted slur in the example) and is resolved down by step (arrow in the example). Also, once the series begins, the resolution pitch serves simultaneously as the next preparation pitch.

EXAMPLE 17.14 Sevenths: Alternating and Interlocking STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

Alternating

B.

Interlocking

preparation by step 7

10

7

10

7

resolution by step

7

7

7

10

7

10

7

10

7

10

7

10

10

7

10

7

10

7

10

7

C

I

C

I

C

I

C

I

10

Every harmony in Example 17.14B contains a seventh; we call this type of sequence a D2 (⫺5/⫹4) with interlocking sevenths. The soprano and alto have interlocking sevenths above the bass: As the soprano resolves its seventh, the alto prepares its seventh; as the alto resolves its seventh, the soprano prepares its seventh; and so on. Notice that every other chord in Example 17.14B is incomplete (doubled root/omitted fifth).

Sequences with Inversions of Seventh Chords Just as first-inversion triads are used in D2 (⫺5/⫹4) sequences, so too are first-inversion seventh chords. Listen to Example 17.15, in which Mozart writes two back-to-back D2 sequences with first-inversion chords. The first sequence contains only triads. But for the

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EXAMPLE 17.15 Mozart, Symphony in G major, K. 74, Allegro 49

6

g:

6

i

D2 (–5/+4) 7th

54

6

ii 6 59

(vii 7 /V)

V (HC)

7th

6 5

6 5

i

D2 (–5/+4) 7th

ii 6 5

8 – 7

V6 – 5 4 –

i

repetition of the entire sequence, Mozart intensifies the drama by adding a pair of oboes that soar above the strings to present the falling sixths, whose suspension figure includes the chordal seventh (circled and labeled in the score). Seventh chords in third inversion (42) are also common in D2 sequences. They resolve to first-inversion triads or seventh chords. Listen to Example 17.16. As always, the seventh— this time in the bass—is prepared, giving the impression of a bass suspension. In general, when determining a sequence type, locate the root of each chord. In Example 17.16, the sequence unfolds with the roots E–A, D–G, C–F, B–E, revealing the underlying D2 (⫺5/⫹4) motion; figures reveal the interlocking inverted seventh chords (42 65).

W R I T I N G S E QU E N C E S Writing sequences does not involve any new chords, or any new voice-leading rules. In fact, given that each chord within a sequence must follow the voice leading and doublings in the model, you will encounter double leading tones, dissonant leaps, and even diminished triads in root position. These are all to be avoided in usual voice-leading situations,

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EXAMPLE 17.16 Leclair, Trio Sonata in D major, op. 2, no. 8, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

(e) (A) 4 2

D:

I

6 5

(D)

(G)

(c )

(f )

(b)

(e)

4 2

6 5

4 2

6 5

4 2

6 5

(A) (D) 4 2

6 6

D2 (– 5/+4)

ii

V

I

V

EPM

T

D

but they are perfectly acceptable within sequences (because of the overall repetition of the model). However, rely on your musical instincts, for the listener will soon tire of nonstop sequences. By contrast, the sequence is a compositional procedure that can be used without becoming stale. (Witness the continued popularity of works such as Pachelbel’s Canon.) Note the following guidelines:

Guideline 1 The voice leading in the model and first copy must be correct. Because the copies merely restate the model (at a different pitch level), any faulty voice leading in the opening will blemish every copy. Guideline 2 Write outer voices first. Try to incorporate contrary step motion between them and include at least one imperfect consonance (3, 6, 10). Example 17.17 shows various intervallic patterns between the outer voices of the D2 (⫺5/⫹4) sequence. Although the soprano becomes more disjunct with the nonstop tenths in Example D, such a contrapuntal framework has occurred often in music, particularly in popular music of the twentieth century (including Bart Howard’s “Fly Me to the Moon” and Jerome Kern’s “All the Things You Are”). Guideline 3 Prepare and resolve each chordal seventh.* Guideline 4 When you write sequences involving inverted seventh chords, make sure each sonority is complete.

*For a step-by-step procedure to compose sequences within the phrase model, see Appendix 3.

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Chapter 17 Harmonic Sequences

EXAMPLE 17.17 Outer Voices and Imperfect Consonances A.

5 — 10

B.

5 — 10

5 — 10

5 — 10

C.

10 — 8

8 — 10

8 — 10

8 — 10

8 — 10

10 — 10

10 — 10

10 — 10

D.

10 — 8

10 — 8

10 — 8

10 — 10

The following example (17.18) illustrates diatonic sequences in four voices.

EXAMPLE 17.18 Summary of Diatonic Sequences A.

Descending Seconds D2 (– 5/+4) + 63

D2 (– 5/+4)

etc.

B.

etc.

Descending Thirds D3 (– 4/+2) + 63

D3 (– 4/+2)

etc.

etc.

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EXAMPLE 17.18 (continued) C.

Ascending Seconds

A2 (+5/– 4)

etc.

D.

Ascending Seconds A2 (– 3/+4) + 63

A2 (– 3/+4)

etc.

E.

etc.

Descending Seconds (with Sevenths)

D2 (–5/+4)+7 (alternating)

(interlocking)

etc.

7

etc.

7

7

D2 (– 5/+4) + 65

7

7

7

D2 (– 5/+ 4) + 42

etc.

etc.

4 2

6 5

4 2

6 5

4 2

6 5

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Chapter 17 Harmonic Sequences

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 17.5–17.7

17.3 Triadic Sequences Identify the key of each excerpt, then bracket and label each sequence.

A.

Mozart, String Quintet in C minor, K. 406, iii 17

20

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B.

Handel, Keyboard Suite no. 7 in G minor, Passacaille A single sequence type is repeated twice. Notice how Handel elaborates the underlying structure. What is the relationship between the two hands in mm. 9–12 and mm. 13–16?

5

10

15

C.

Mozart, Violin Sonata in G major, K. 379, Andantino cantabile

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Pergolesi, “Il nocchier nella Tempesta,” from Salustia, act 2, scene 9 Andante

8

pur

ta

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lo

ra

sal

vo al

li

do lo

por

17.4 Analysis of Sequences with Seventh Chords Analyze the following examples that contain D2 (–5/+4) sequences with seventh chords. Circle each chordal seventh and label its preparation and resolution.

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A. Schumann, Kreisleriana, op. 16, no. 7 While this is not strictly a compound melody, it is possible to create a five-voice structure.

B.

Haydn, String Quartet in C major, op. 20, no. 2, Hob III.32, Trio

Chapter 17 Harmonic Sequences

429

C. Mozart, Symphony in G major, K. 124, Allegro Dissonant suspensions in violin 2 are shown with parentheses.

Vni

Vle

Vc. Cb.

T ER MS A ND CONCEP TS • harmonic sequence • ascending sequences • A2 (⫹5/⫺4 or ⫺4/⫹5); ascending second (by ascending fifth and descending fourth or descending fourth and ascending fifth) • A2 (⫺3/⫹4); ascending second (by descending third and ascending fourth) and A2 (⫺3/⫹4) with 63s • descending sequences • D2 (⫺5/⫹4 or ⫹4/⫺5); descending second (by descending fifth and ascending fourth or ascending fourth and descending fifth) and D2 with 63s; also with alternating and interlocking sevenths • D3 (⫺4/⫹2); descending thirds (by descending fourth and ascending second) and D3 with 63s • melodic sequence • model and copy • voice-leading chords (helping chords)

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CH A PTER R EV IEW 1. List the two components of any sequence.

2. List the two broad categories of sequences, described in the first letter of their labels.

3. Complete the summary of sequence terminology: (a) D2

(b)

(c)

(⫺5/⫹4)

a. The first part is the interval between the root of the first chord of both the __________ and the ___________. b. The second part indicates the interval [within/between] the root of each model or copy. c. The third part indicates the interval [within/between] the root of the second chord of the model and the first chord of the copy.

4. Only the __________ and the __________ chords in a sequence receive roman numerals. Another word for the descending-second sequence is the _____________.

5. The second chord of each two-chord unit in a sequence helps avoid parallel fifths and octaves, and is therefore called a _______________________________________________.

6. Pachelbel’s Canon is an example of a ___________________________ sequence.

7. The D2, D3, and A2 (⫺3/⫹4) sequences each have a variation in which every other chord is in ______________________ inversion.

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8. A D2 sequence with alternating sevenths has a seventh chord on: a. every beat

b. every other beat

9. In contrast, a D2 sequence with interlocking sevenths has a seventh chord on: a. every beat

b. every other beat

10. In both the alternating and interlocking sequences, all chordal sevenths are prepared by ___________________ tone and resolved [down/up] by step, just like a suspension.

S U M M A R Y OF PA R T 4 Part 4 presented new chords and concepts, including the remaining diatonic harmonies: the submediant, mediant, and subtonic, all of which have specific functions and add remarkable color to the diatonic palette. Both vi and iii (VI and III in minor) are used to split the fifth into two thirds: vi bisects the falling fifth between T and PD and iii does the same with the upper fifth from T to D. Bisecting large musical spaces, like the fifth, was only one step: we saw thirds divided into steps by using the descending stepwise motion of the lament bass. In subsequent chapters, we will learn how these diatonic steps can be further divided, filled in by half-step motions. VII serves a single purpose: it is the dominant of III in minor, and was our first example of an applied chord. We also generalized strong root motions (down fifths and thirds and up seconds) which, together with our contrapuntal expansions of harmonic functions, allow us to compose longer spans of music and to understand how composers balance counterpoint and harmony. The best representative of this balance is the harmonic sequence, which employs all diatonic harmonies but is grounded in a strong contrapuntal setting. The phrase model was extended and combined with other phrases to form periods, and the wonderfully proportioned sentence created a powerful drive toward the cadence. A major component of these chapters was a focus on musical context. Making compositional and analytical choices based on listening and musical context and function are crucial, and include such concepts as the deceptive motion, the back-relating dominant, and how the submediant can either serve tonic and dominant or vice versa.

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PA R T 5

FUNCTIONA L CHROM ATICISM

W

e have studied two types of chromaticism. The first type involves unharmonized embellishing tones (such as chromatic passing tones), which animate the texture, provide color, and intensify motion to the following diatonic chord tone. The second type—harmonized chromaticism—creates a leading tone in the minor mode by raising 7 a half step to give V a dominant function. Nearly all leading tones we have seen so far resolve to tonic. Now, however, we will expand our understanding of leading-tone chromaticism by examining how it can be transferred to chords other than V in a key. In doing so, we will learn how this chromaticism is a useful voice-leading tool and how it can participate in musical events at deeper levels of the structure. Despite the power of leading-tone chromaticism we’ll see that it remains subordinate to the diatonic events in a piece.

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C H A P T E R 18

Applied Chords OV E RV I E W

To this point, we have dealt exclusively with diatonic harmony. This chapter introduces the world of chromaticism, of which there are two fundamental types. We will explore the first type, which allows chords other than the dominant to function as dominants. As such, they can resolve to different harmonies within a key, which act as temporary tonics. CHAPTER OUTLINE Applied Dominant Chords ...................................................................................... 437 More-Extensive Tonicizations of Nontonic Harmonies ................................... 438 Applied Chords in Inversion................................................................................ 438 Tonicized Half Cadences ...................................................................................... 439 Recognizing Applied Chords ............................................................................... 440 Voice Leading for Applied Chords ...................................................................... 440 Cross Relation ............................................................................................... 441 Applied Leading-Tone Chords ................................................................................ 443 Incorporating Applied Chords Within Phrases ................................................. 444 Analytical Shorthand ............................................................................................ 444 An Example Composition .................................................................................... 445 Phrase One.................................................................................................... 445 Phrase Two ................................................................................................... 446 Sequences with Applied Chords ............................................................................. 450 The D2 (⫺5/⫹4) Sequence ................................................................................. 450 The D3 (⫺4/⫹2) Sequence ................................................................................. 451 The A2 (⫺3/⫹4) Applied-Chord Sequence ...................................................... 453 Writing Applied-Chord Sequences ..................................................................... 455 (continued)

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Summary of Diatonic and Applied-Chord Sequences ..................................... 455 Terms and Concepts ................................................................................................... 459 Chapter Review ........................................................................................................... 459

C H RO M AT I C I S M C O LO R S D I ATO N I C I S M ; therefore, chromatic pitches are generally not integral to the underlying diatonic structure. Instead, chromatic pitches take the place of diatonic pitches in a process called chromatic alteration. Diatonic passing tones can be harmonized by diatonic chords. Similarly, chromatic passing tones can be harmonized by chromatic chords. Compare the two excerpts in Example 18.1. Example 18.1A presents a chromatic passing tone (C) between the tonic and ii chords, invigorating the melodic motion between 1 and 2. In Example 18.1B, the chromatic passing tone is harmonized by an intermediate harmony, an A-major chord. The chromatic passing tone is of little help in avoiding the parallel octaves and fifths in Example 18.1A, but when C is supported with its own chord (A major in Example 18.1B), all the parallels disappear and the harmonic motion to the ii chord is intensified.

EXAMPLE 18.1 Harmonic Chromatic Passing Tones: Stabilization and Voice-Leading Corrective A.

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B.

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1 CPT 2

P8

C:

P5

I

ii

V

I

I

ii

V

I

Because the A-major chord functions as a dominant, it evokes the momentary impression that we are in the key of D minor. This sensation of briefly experiencing a key (e.g., for a few beats or even a measure or two) other than the tonic is tonicization, which is accomplished through the use of these applied dominant chords (also called secondary dominant chords or applied chords). The essential feature of tonicization is to endow a scale degree other than the tonic with temporary tonic status by stabilizing the “new” tonic with a short progression (such as I–ii6–V–I). For example, the tonicization in the example expands the PD: The realm of ii lists two chords (A major and D minor) rather than just one, but it still participates in the underlying structural harmonic progression of T–PD–D–T.

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Chapter 18 Applied Chords

A PPL I E D D OM I N A N T C HOR D S For a chord to function as an applied dominant, it must behave like a dominant. It must be a major triad (V) or a dominant seventh chord (V 7) and it will usually move to its tonic. Because dominant chords resolve to tonic chords that are either major or minor, any major or minor diatonic harmony can be preceded by an applied dominant chord. Example: We are in C minor and would like to determine the applied dominant of V. V is a G-major chord, so the applied dominant of G major is D major. This is not in the original key, so we label the roman numeral as “applied dominant of V,” or “V of V”—or simply “V/V.” It is common for a key’s dominant and pre-dominant to be preceded by their dominants. Just as common is the use of an applied dominant to III in minor—we have already seen this “V of III” chord in Chapter 14. In Example 18.1B, the A-major triad is the applied dominant chord to ii in the key of C major. In this case, we label the A-major triad as the dominant of ii, or “V/ii.” To summarize, there are two different methods for creating applied dominant chords. One way is to take any major or minor triad in a key and precede it with its applied dominant. In Example 18.2 the diatonic progression I–vi–IV–V–I is expanded with chromatic chords: V 7/vi precedes vi, V 7/IV precedes IV, and V 7/V precedes V.

EXAMPLE 18.2 Diatonic Progression Expanded with Applied Chords A.

D:

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B.

I T

vi

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V

I

I V 7/vi vi V 7/IV IV V 7/V V

I

PD D

I

T

T

IV

PD

D

The second method is to alter diatonic chords chromatically, changing them into applied dominants and seeing where they point as dominant chords. In Example 18.3, note that IV (in major) cannot be altered to create V/vii°, because vii° is dissonant (a diminished harmony) and the root of IV lies an augmented fourth (rather than a perfect fourth) below the root of vii°. Similarly, VI (in minor) cannot be altered to create V/ii° because ii° is dissonant and the root of VI lies an augmented fourth below the root of ii°. Example 18.3 shows the diatonic triads in both C major and C minor, their transformation into applied dominants (in parentheses), and to what diatonic triad they would lead. Notice that some diatonic chords are already major triads and therefore can be used as applied dominant chords (see the bracketed arrows): In major keys, V/IV is diatonic; in minor keys, V/VI and V/III are diatonic. In order to clarify their applied function,

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EXAMPLE 18.3 Generating Applied Dominants * C:

I

V/IV

ii

V/V

iii

V/vi

IV V/vii

V

vi

V/ii

vii

V/iii

* c:

i

V/iv

ii

V/V

III V/VI

iv V/VII

V

VI V/ii

VII V/III

these chords typically appear as V 7 chords, adding the minor seventh above the root. For example, V/IV–IV in major will most likely be heard simply as tonic moving to IV rather than as IV’s applied dominant. Adding the seventh transforms the diatonic harmony into an applied chord. Asterisks in Example 18.3 indicate applied chords that require the added seventh. Because of their strong connection, applied dominant chords and their tonics occur under the same function in second-level analysis. For example: I T

V/ii ii V/V V I ____________ _______________ PD D T

MOR E -E X T E N S I V E T O N IC I Z AT IO N S OF N O N T O N IC H A R MO N I E S

Applied Chords in Inversion The bass line in Example 18.4 is rather angular, so we use inversions to make it more melodic. Compare Example 18.4A with Example 18.4B, and notice that the latter sounds more polished.

EXAMPLE 18.4 Root Position Versus Inverted Applied Chords A.

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B.

I V7/vi T

vi V7/IV IV V7/V PD

D

V

I

I

T

T

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6

V /vi vi V43 /IV IV V56 /V V PD

D

I T

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Chapter 18 Applied Chords

In the same way that inversions of V prolong I (e.g., V6 usually expands I as a lowerneighbor chord), any other major or minor harmony in a key can be prolonged by its applied dominant chord. Example 18.5A reviews how tonic may be prolonged by any inversion of V 7. In Example 18.5B the supertonic is prolonged by its V 7 chord in precisely the same way. The only difference is the chromaticism: D must be altered to D in order to function as the leading tone to the key of ii (E minor). However, no matter how extensive the expansion of a nontonic harmony, that harmony will ultimately figure into the tonal motion of the phrase model. For example, in Example 18.5C, ii is considerably expanded, but it still functions in the capacity of the phrase’s pre-dominant.

EXAMPLE 18.5 Expanding the Pre-dominant STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

B.

V7

D:

V 65

V 43

V 42

V7/ii

I expanded by V 7 and its inversions

V 65/ii

V43 /ii

V24 /ii

ii expanded by V 7 and its inversions

C.

D:

I

V 65 I V 6/ii

ii V/ii ii V 65/ii

ii V 43/ii ii 6 V 56/V

V64 –– 53

I

I

ii

V

I

T

PD

D

T

Tonicized Half Cadences Applied chords intensify the drive to cadences, especially to half cadences, which close the first phrase of an interrupted period. Such tonicized half cadences help to stabilize the arrival on the dominant. The last movement of Beethoven’s E major Piano Trio opens with a PIP whose first phrase closes with a HC that includes V65 of V, which helps to secure the arrival on V. The following phrase, which closes the period, contains another applied chord that initiates the drive to the authentic cadence by the falling-fifth motion: vi–ii–V–I (see Example 18.6).

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EXAMPLE 18.6 Beethoven, Piano Trio in E  major, op. 1, Finale STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Presto

staccato

ii 6

V 65 /V

tonicized half cadence 8

staccato

(N)

V 65 /vi vi

V (HC)

ii 6

V

I (AC)

Recognizing Applied Chords Recognizing applied chords is not difficult: Aurally they have a distinctive dominant sound, and visually they have a distinctive notation. A chromatically raised note is often the third of an applied dominant chord (which is the leading tone for its key), and a chromatically lowered note is often the seventh of the applied dominant chord. In Example 18.7, the first chromatic pitch is F, and as a raised pitch it signals its function as a temporary leading tone to G (and, of course, G is iv in D minor, which helps you analyze the chord as a V/iv). Similarly, the E (diatonic E’s lowered form; m. 1, beat 4) implies that it will function as the seventh of an F dominant seventh chord, as V 7/VI.

Voice Leading for Applied Chords Two chromatic alterations are common in applied chords, both of which are tendency tones. One is the third of the chord, which is often chromatically raised and acts as a temporary leading tone. The other is the seventh of the chord, which often needs to be

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Chapter 18 Applied Chords

EXAMPLE 18.7 Detecting Applied Chords STR EA MING AUDIO

7th

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leading tone

d:

i

V 7/iv iv

V7 /VI VI V43 /iv iv V 65/V

V8 —

7

i

chromatically lowered in applied dominant chords. The voice-leading rules for the V 7 chord pertain to applied dominant chords as well. • Do not double the third (the leading tone) or the seventh of the chord. • The leading tone must resolve upward when in an outer voice. • The seventh of the chord resolves downward in any voice. Example 18.8 shows the proper voice leading for applied dominant chords to vi and IV in C major. Note that root-position applied dominant chords may be complete (V 7/vi in Example 18.8A) or incomplete (V 7/IV in Example 18.8B).

EXAMPLE 18.8 Part Writing Applied Chords A.

B. temporary leading tone

temporary leading tone

temp. 7th

C:

V7/vi

temp. 7th

vi

V 7/IV

Cross Relation

IV

Look again at the soprano line of Example 18.8A. The leading tone (G) is a chromatic passing tone between G and A, which creates a smooth chromatic line: G–G–A. You prepare chromaticism by preceding a chromatic tone with its diatonic version in the same voice, in this case resulting in a chromatic half-step line, because it softens the jarring effect of the chromatic tone.

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When a chromatic tone is prepared by another voice (instead of the same voice), it results in a cross relation. In Example 18.9, the chromatic G is not prepared in the tenor; the diatonic G occurs in the soprano voice. This cross relation should be avoided since it produces a clashing sound due to the awkward leaps in the soprano and tenor.

EXAMPLE 18.9 Cross Relation (avoid, since G can easily follow G in the soprano)

C:

I

V 7/vi

vi

Despite the desirability of chromatic preparation, in many instances it is impossible for chromatic pitches to follow their diatonic forms in the same voice. Example 18.10A shows one such scenario. • In a progression from I to V6/vi in C major, the bass leaps down from C to G, which resolves as it should, to A. This leap of a diminished fourth in the bass is acceptable and quite expressive; in Baroque music with text, this leap often accompanies words of great sorrow or pain. Clearly, the alto G cannot move to G when the bass sounds that pitch (since G is a leading tone in the applied V6/vi chord). • A similar scenario occurs with a leap to the seventh of an applied dominant chord in the soprano (Example 18.10B). • If you must write a cross relation, avoid writing the notes between the aurally prominent bass and soprano; instead, place the cross relation between inner voices or between one outer voice and an inner voice.

EXAMPLE 18.10 Legal Cross Relations A.

C:

B.

cross relation

I

V 6 /vi

vi

V

V65 /IV

IV

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Chapter 18 Applied Chords

EX ERCISE INTER LUDE W R ITING 18.1

WORKBOOK 1 Assignments 18.1–18.3

A.

SOLVED/APP 5

Spelling Applied Dominant Chords Notate the following applied dominant triads and seventh chords in close position on the treble staff. Use key signatures. 1. In G major: V 7/IV V 7/vi V 7/V 7 6 2. In D minor: V /iv V5/III V 7/VI 7 3. In B minor: V /V V6/VI V43/iv 4. In E  major: V6/iii V 7/vi V65/ii

B.

Notate the following applied chords in four-part keyboard style. Use key signatures. Remember not to double temporary leading tones or chordal sevenths. 1. In F major: V 7/V V65/IV V6/ii V 7/iii 7 6 4 2. In G minor: V /VI V5/III V2/V V65/iv 6 4 7 3. In E minor: V /III V3/V V /VI V65/iv

A PPL I E D L E A DI N G -T O N E C HOR D S Dominant substitutes—vii°6, vii°7, and to a lesser degree viiø7—can participate in contrapuntal expansions of the tonic. Often, these harmonies are also used as applied dominant substitutes that lead to other scale degrees. We have been using only those diminshed seventh chords that are built on 7 of the minor mode. With the introduction of applied leadingtone chords, we now may use vii°7 and its inversions to tonicize major and minor triads. Listen to Example 18.11, in which the applied chords in mm. 1–2 help tonicize ii of C major. Because of the varied types and inversion of applied chords—vii°7/ii, vii°6/ii and

EXAMPLE 18.11 Applied vii° and vii°7 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

C:

I

vii

I

N

T

7

I

vii 7/ii

ii

vii 6/ii

I

CPT

ii

P

PD

ii 6 vii ii 6

4 3 /ii

N

ii 6 vii ii 6

7/V

CPT D

V 64 V

— 5 — 3

I I T

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THE COMPLETE MUSICIAN

vii°43/ii—the supertonic can be tonicized for some time (nearly half of the example’s four measures). Note that the larger function of ii as a pre-dominant remains unchanged. The tonicized area functions as a way station that helps to connect tonic and dominant.

I N C OR P OR AT I N G A PPL I E D C HOR D S W I T H I N PH R A S E S There are no new rules to learn when writing applied chords in phrases; however, you must consider metric and rhythmic placement in order to create a balanced and pleasing structure. Listen to Example 18.12, and determine its phrase structure and the metrical placement of the applied chords. Beethoven has created a parallel interrupted period, and every applied chord appears on a metrically weak beat. Weak metrical placement of applied chords is common because they contain leading tones that precipitate motion toward a metrically stressed goal. Beethoven uses three applied chords in the first phrase; the first, a vii°7 chord, is applied to vi; the second, V/V, appears twice, the first time to lead to V and the second time to tonicize the half cadence. In the second phrase only a single V/V appears, because the dominant is not the goal of motion as it was in m. 4 of the first phrase. Rather, the tonic occupies the entire last measure, using the dominant to intensify the PAC.

EXAMPLE 18.12 Beethoven, String Quartet no. 9 in C major, op. 59, no. 3, Menuetto: Grazioso STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

3

3

C:

I

V

7

vi ii 65

6 5

V

I

vi ii 65

V

T

PD

D

7

V 8–7 HC

I ⁄⁄

V7

7

vi ii 65

6 5

V7

I

I

vi ii 65

V

I

T

PD

D

T

V7 I PAC

Analytical Shorthand A new notational symbol appears in Example 18.12, the curved arrow (哭), which represents that the chord preceding the arrow is an applied dominant or dominant substitute that leads to the chord to which the arrow points. This shorthand label is often quite useful, as in this excerpt with such fast harmonic rhythm and so many chords in so few beats. However, sometimes applied dominants (like the actual V(7) chord) resolve deceptively to

445

Chapter 18 Applied Chords

what would be vi in the temporary key. In such cases, you must supply the complete roman numeral for the applied chord, because the arrow alone will not indicate a deceptive motion. Further, you may also use the following analytical shorthand for both applied dominants (and dominant sevenths) and applied diminished seventh chords: For dominants, use only their figured bass symbols (e.g., 63, 7, 43); for diminished sevenths, add the accompanying diminished sign (e.g., °7, °65). You can also use the complete roman numeral followed by the arrow (e.g., V 7哭).

An Example Composition

Let’s write a contrasting continuous period, in $$ meter and G minor, incorporating several applied chords. First, plan the big picture by mapping out the overall structure. Then construct a single large-scale harmonic progression by closing the first phrase with a deceptive motion, moving to a PD to begin the second phrase, and closing on tonic. The following diagram presents a possible harmonic rhythm of this plan: Phrase 1 (DC) mm: 1 2 3 4 G minor: i——————V—— V I T

Phrase 2 PAC 5 6 7 8 ° V—i iv—————ii— PD

D T

Measures 2 and 6 provide opportunities to insert embellishing harmonies. First, try to connect the i of m. 1 with the V of m. 3, using the bass arpeggiation i–VI–PD. But because the phrase closes on VI, an early appearance of VI might make m. 4 sound anticlimactic. Another option to link i and V is to use the following progression: mm:

Phrase 1 1 2 3 4 i——— III———PD—V—VI

Although this looks like a workable harmonic plan, it still might sound a bit bare and simplistic. At this point, adding some contrapuntal and applied chords will help to establish the tonic in m. 1 and to intensify the overall progression.

Phrase One From this point on, envision your harmonic choices with the help of a bass line. First, arrange it so that every chord in the progression is preceded by an applied chord. (Remember that you can precede any consonant [major and minor] harmony with an applied chord, so only ii° may not be expanded by an applied chord.) In placing your applied chords, aim for weak beats so that the chord can resolve to structural chords on stronger beats, as in Example 18.13A. Don’t rely exclusively on root-position applied dominant chords, nor should you restrict yourself solely to triads. For variety, our taste demands a mix of applied chords as well as a smooth bass contour, as in Example 18.13B. A neighboring diminished seventh chord helps to establish the tonic in m. 1. In addition, the bass of the chord contrasts with the following F, the root of a V 7/III chord. The III is prolonged with an applied dominant substitute that acts as a

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THE COMPLETE MUSICIAN

EXAMPLE 18.13 Generating a Bass Line A.

g:

V/III

III

V/iv

iv

V/ V

iv6

iv vii

V

VI

B.

g: i

vii

7

i

i

V

7

III vii

6

III

6

III

4

V2 iv

7

7

V

VI

V

VI

passing chord. Rather than moving directly to the PD at the end of m. 2, the bass skips up to F, creating a V42/iv chord. The subdominant is then expanded with a simple chordal leap, and vii°7/V nicely fills the space between iv and V with a chromatic passing tone (C) in the bass. Now we will add a soprano melody and inner voices (Example 18.14).

EXAMPLE 18.14 Harmonizing a Bass Line STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

g:

i

vii

7

i

V7

/III

III vii

T

6

/III III

6

V42

/iv

PD

iv 6

iv

vii D

7

/V V

7

VI "T"

Phrase Two We can insert a sequence into the second phrase, because there is at least one measure— perhaps even two—to work with. A D2 (⫺5/⫹4) sequence starting on iv would lead to ii° in four chords (Example 18.15). However, the sequence unfolds in an unremarkable and rather clunky manner, moving in heavy half notes, with ponderous leaps. We can enrich the harmonic color and smooth the linear motion of the sequence by using first-inversion chords, and by adding an applied dominant chord leading to V in m. 3 (Example 18.16). Finally, the seam between the two phrases—an entire motionless measure of VI—does not fit well in what is otherwise a robust harmonic progression. You can use an applied chord

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Chapter 18 Applied Chords

EXAMPLE 18.15 Generating a Bass Line (Phrase 2) STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

g:

iv

ii

6

V64

– 5 –

4 – 2 – 3

D2 (–5/+4)

EXAMPLE 18.16 Harmonizing a Bass Line (Phrase 2) STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

g:

iv

6 — 5

6

6 —5

6

6

V65

V64

5

4

2

3

D2 (–5/+4) ii° 6

iv PD

D

T

to integrate the two phrases: V43/iv begins the second phrase and glues the disparate sections to form a continuous period, or, as interpreted, a single large phrase (Example 18.17). Since the chord-to-chord analysis has already been shown in previous versions of this example, only the underlying diatonic harmonic progression is shown in Example 18.17.

EXAMPLE 18.17 Completed Composition STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

7

i i

7

III

6

6

4 2

iv EPM

6

7

V

8 — 7

VI

IV

6 4 3

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THE COMPLETE MUSICIAN

EXAMPLE 18.17 (continued) 5

6 6

6 5

6

6

6

ii

6 5

6

PD

6 4

5

4

V

i

D

T

2

3

EX ERCISE INTER LUDE

SOLVED/APP 5

18.2 Write any two of the following applied-chord progressions in four-voice keyboard style. Choose any meter, but remember that applied chords are embellishing and often appear in weak metrical contexts. A. F major: I–V 7/IV–IV–V 7/ii–ii–V B. E minor: i–V 43 /VI–VI–V 65 /iv–iv C. D major: V–V 65 /vi–vi–ii6 –V 65 /V–V D. C minor: i–V 65 /III–III–iv6 –V

SOLVED/APP 5

18.3 Recognizing Applied Chords Each of the following excerpts contains at least one applied chord. Based on the key listed for each example, analyze each of the chords using roman numerals.

WORKBOOK 1 Assignment 18.4

A. Haydn, String Quartet in A Major, op. 55, no. 1, Hob III.60, Allegro

STR EA MING AUDIO

3

W W W.OUP.COM/US/LAITZ

A:

Chapter 18 Applied Chords

B. Haydn, String Quartet in B  major, op. 64, no. 3, Hob III.67 26

B :

C.

Haydn, String Quartet in E  major, op. 20, no.1, Hob III.31, Allegro

E : SOLVED/APP 5

D. Haydn, String Quartet in E  major, op. 20, no.1, Hob III.31, Finale Presto.

E :

449

450

THE COMPLETE MUSICIAN

W R ITING 18.4 Spelling and Writing Applied Dominant Substitute Chords (vii°6 and vii°7) A. Spell the following applied dominant substitute chords (vii°6 and vii° 7) in close position on the treble staff. Use key signatures. 1. In D major: vii° 7/IV vii°6/vi vii° 43 /V 2. In E minor: vii° 7/iv vii°65/III vii°6/VI 3. In B minor: vii°65 /V vii° 7/VI vii°6/iv SOLVED/APP 5 4. In E  major: V 6/iii vii° 7/vi vii° 43 /ii B.

SOLVED/APP 5

Write the following applied dominant substitute chords in four-part chorale style. Use key signatures. Remember not to double temporary leading tones or chordal sevenths. Write the resolutions of the applied chords. 1. In B  major: (a) vii° 7/V 2. In G minor: (e) vii° 7/VI

(b) vii° 43 /IV (f) vii°65/III

(c) vii°6/ii (d) vii° 7/iii (g) vii° 7/V (h) vii°65/iv

18.5 Writing Applied Chords in Context Write the following progressions in four-voice keyboard style. Choose any meter, but remember that all applied chords are embellishing and often appear in weak metrical contexts. A. D major: I–I6 -vii° 7/IV–IV–vii° 7/ii–ii–V B. A minor: i–vii°65/III–III–iv6 –V—vii° 7/V–V SOLVED/APP 5

S E QU E N C E S W I T H A PPL I E D C HOR D S Listen to the sequence in Example 18.18. Analysis of the chord roots (C–F, D–G, E–A) reveals that it is an ascending sequence. But it is different from the rising sequences we have studied: It contains applied-chord chromaticism. Removing the chromaticism would leave a form of A2 sequence, here unfolding as (⫹4/⫺3). In the chromatic sequence, applied 65 chords alternate with diatonic triads. When applied chords are added to diatonic sequences, they create applied-chord sequences, which significantly intensify sequential motion.

The D2 (ⴚ5/ⴙ4) Sequence Review the diatonic form of the D2 (⫺5/⫹4) sequence in Example 18.19A, then note that a chromatic version of it appears when applied chords substitute for diatonic chords. The result is the sequence seen in Example 18.19B. It is particularly common to add sevenths to the triads of the D2 (⫺5/⫹4) appliedchord sequence, thereby enhancing the sequence’s goal-directed motion. These seventh chords may be alternating (Example 18.20A) or interlocking (Example 18.20B). Notice the presence of parallel tritones in the upper voices of 18.20B and in mm. 9–12 in the left hand of Beethoven’s “Moonlight” Sonata (Example 18.21).

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Chapter 18 Applied Chords

EXAMPLE 18.18 Leclair, Sonata in C major for Flute and Continuo, op. 1, no. 2, Corrente STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

93

3

C

F

D

G

6

5

6

5

98 3

E

A

F

6

5

6

6

5

EXAMPLE 18.19 Diatonic Versus Applied D2 Sequences A. Diatonic D2

B. Applied Chord D2

C:

C:

*

*

The D3 (ⴚ4/ⴙ2) Sequence In the diatonic D3 (⫺4/⫹2) sequence, the second chord of each pair lies a fourth below the first, creating a back-relating dominant (Example 18.22A). A dramatic forward motion occurs in the applied-chord form of this sequence, seen in Example 18.22B. Because each applied chord creates a temporary leading tone that leads to its own following tonic, the second chord of each copy functions as a dominant of the following—and not the

452

THE COMPLETE MUSICIAN

EXAMPLE 18.20 Applied V 7 in D2 Sequences STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A. D2 (– 5/+4) with Alternating Sevenths

I

*

*

B. D2 (– 5/+4) with Interlocking Sevenths

*

*

*

*

*

*

*

EXAMPLE 18.21 Beethoven, Piano Sonata in C  minor, “Moonlight,” op. 27, no. 2, Trio STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

D:

V 43

I

I6

V 42

V 43

I

T

V7

I

D

T

9

B V 65

6 5

E V 42

4 2

A

6 5

V 56

D V 42

4 2

G

6 3

IV63

V7

I

D

T

D2 (– 5/+ 4) T

PD

previous—chord. Consequently, the chords have different roots from their counterparts in the diatonic sequence. The diatonic D3 (⫺4/⫹2) is transformed into the D3 (⫹3/⫺5) applied-chord sequence. Applied chords in this sequence most often contain sevenths, as shown in Example 18.22B.

453

Chapter 18 Applied Chords

EXAMPLE 18.22 Diatonic Versus Applied D3 Sequences A.

D3 (diatonic)

I

V

vi

iii

IV

V

I

IV

V

I

IV

V

I

IV

V

I

D3 (–4/+2) I

B.

D3 (with applied chords) 7

I

V7

7

vi

V7

D3 (+3/–5) I

Inverted chords help to smooth out the angular leaps created by root-position harmonies. Example 18.23 displays voice-leading variations on the D3 (⫹3/⫺5) applied-chord sequence. The form of the sequence in Example 18.23A is the most common, because the four-three inversion consistently provides a stepwise descent in the bass (which moves in parallel tenths with the soprano). Note the bass’s hooking contour in Example 18.23B: The dissonant leap to the applied chord’s leading tone is balanced by stepwise resolution in the opposite direction. Example 18.23C demonstrates that an applied root-position diminished seventh chord may also be substituted for the applied dominant chords in Example 18.23B, creating a D3 (⫺4/⫹2) sequence.

The A2 (ⴚ3/ⴙ4) Applied-Chord Sequence Of the two common sequences that ascend, A2 (⫺3/⫹4) is much more likely to incorporate applied chords. The form of the sequence that includes first-inversion triads—the ascending 5–6 sequence (Example 18.24A)—may be converted into an applied-chord sequence simply by raising the bass a half step. This creates a powerful harmonized chromatic passing tone that functions as a 7, which leads to the upcoming root-position triad (Example 18.24B). Example 18.24C adds the seventh to the applied chords. This sequence also employs root-position applied chords. In this case, the chromatic passing motion appears in the soprano rather than in the bass (Example 18.25).

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THE COMPLETE MUSICIAN

EXAMPLE 18.23 Applied V 7 and vii°7 in D3 Sequences STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A. Applied 43 (PTs)

V 43

B. Applied 56 (“hook”)

V 43

V 65

D3 (+ 3/– 5) + applied I

IV

4 3s

V 65

I

I

7

vii

D3 (+ 3/– 5) + applied V

C. Applied

6 5s

IV

7

vii

(“hook”)

7

vii

D3 (–4/+2) + applied V

I

7

7

I

ii

V

I

EXAMPLE 18.24 Applied A2 Sequences: First Inversion B. Applied V6

A. Diatonic

I5

6

5

6

5

6

IV V

I

I5

A2 (– 3/+ 4)

6

5

6

5

6

IV V

IV V I

IV V I

I

EXAMPLE 18.25 Applied A2 Sequence: Root Position

5 3

C:

I

V7

I

A2 (– 3/+ 4) + applied 6s

I

V7

V7

A2 (– 3/+ 4) + applied V 7

IV

V

I

STR EA MING AUDIO

C. Applied V 65

5

6

5

6

5

W W W.OUP.COM/US/LAITZ

6

A2 (– 3/+ 4) + applied I

IV V

I

6 5s

IV V I

455

Chapter 18 Applied Chords

Writing Applied-Chord Sequences When writing applied-chord sequences, simply remember the following: 1. Construct the two-chord model carefully so that the voice leading between the two chords and the first chord of the copy is correct. 2. Copies must follow the voice leading of the model. 3. The root of each chord to which an applied chord leads must be diatonic to the key. 4. Write complete seventh chords, especially when they appear in inversion. The only exception occurs in D2 (⫺5/⫹4) sequences with interlocking sevenths (Example 18.20B).

S U M M A R Y OF DI AT O N IC A N D A PPL I E D - C HOR D S E QU E N C E S An example of each of the sequence types we have studied appears next. The examples are organized by the four generic types of sequences: descending by second and by third, and two forms of ascending by second. The modifications within each of the four types are organized as follows: Diatonic: triads (53, 63), seventh chords [root, inversion(s)] Applied: triads (53, 63), seventh chords [root, inversion(s)]

Descending 2 (ⴚ5/ⴙ4) Root Position

Inversion 6s 3

5s 3

Diatonic

etc.

etc.

6

7ths (alternating)

6

6s 5

etc.

7

7

etc.

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THE COMPLETE MUSICIAN

Descending 2 (ⴚ5/ⴙ4)

(continued)

Root Position

Inversion 4s 2

7ths (interlocking)

etc.

etc.

7

7

7

4 2

7

5 3s

Applied

etc.

V

V

7ths (alternating)

etc.

7

V7

7

V7

7ths (interlocking)

etc.

V7

V7

V7

V7

6 5

4 2

6 5

4 2

6 5

457

Chapter 18 Applied Chords

Descending 3 (ⴚ4/ⴙ2) Root Position

Inversion

5 3s

6 3s

Diatonic

etc.

etc.

5 3

6 3

5 3

6 3

5 3

Descending 3 (ⴙ3/ⴚ5) Root Position

Inversion 6s 5

5 3s

Applied

etc.

V

etc.

V 65

V

V 65

4s 3

etc.

5 3

V 43

5 3

V 43

5 3

458

THE COMPLETE MUSICIAN

Ascending 2 (ⴚ3/ⴙ4) Root Position

Inversion 6 3s

5 3s

etc.

etc.

Diatonic

5 3

6 3

5 3

6 3

5 3

6s 5

etc.

5 3

6 5

5 3

6 5

5 3

6 3s

5 3s

etc.

Applied

V

etc.

V

V 63

5 3

V 63

5 3

6s 5

7ths

etc.

V7

5 3

V7

5 3

etc.

V 65

5 3

V 65

5 3

459

Chapter 18 Applied Chords

Ascending 2 (ⴙ5/ⴚ4) 5 3

etc.

Diatonic

WORKBOOK 1 Assignments 18.5–18.7

T ER MS A ND CONCEP TS • applied-chord sequences • D2 (⫺5/⫹4); A2 (⫹5/⫺4); D3 (⫹3/⫺5); A2 (⫺3/⫹4) • applied dominant chord • chromatic alteration • cross relation • temporary tonic • tonicization • voice leading of applied chords

CH A PTER R EV IEW 1. The use of an applied dominant chord containing chromaticism (accidentals) to emphasize a key other than tonic is called _____________________________________________.

2. Give two names for a dominant chord that belongs to a key other than tonic.

3. Summarize the two methods for creating applied chords.

4. A cadence ending with a dominant function harmony and an applied chord to that harmony is called a _________________________________________________________________.

5. In the type of cadence in question 4, scale degree ______________ must be [raised/lowered].

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THE COMPLETE MUSICIAN

6. Summarize the guidelines in “Voice Leading for Applied Chords.”

7. When chromaticism is not prepared by a common tone in the same voice, a _________________________ results, which should be avoided, if possible.

8. True or False: Strong metrical placement of applied chords is common.

9. When secondary dominants are added to sequences, ______________________________ occur.

10. Summarize the guidelines for “Writing Applied-Chord Sequences.”

C H A P T E R 19

Tonicization and Modulation OV E RV I E W

This chapter enlarges the scope of tonicization by introducing techniques for multiple chords and entire phrases to be centered around a harmony other than the tonic. Such emphasis on nontonic chords enriches the harmonic palette, extends phrases, and results in a goal-directed motion back to the home tonic. As a key part of this chapter, we define modulations and show how to analyze and write them. CHAPTER OUTLINE Extended Tonicization ............................................................................................... 461 Modulation ................................................................................................................... 467 Closely Related Keys ............................................................................................. 468 Analyzing Modulations ........................................................................................ 469 Writing Modulations ............................................................................................ 470 Modulation in the Larger Musical Context....................................................... 471 The Sequence as a Tool in Modulation .............................................................. 473 Terms and Concepts ................................................................................................... 480 Chapter Review ........................................................................................................... 480

I N C H A P T E R 18 W E L E A R N E D about applied dominant chords that led toward

chords other than the tonic through tonicization. We will now explore extended tonicizations and modulations.

E X T E N DE D T O N IC I Z AT IO N A tonicization is extended when it involves multiple applied chords. For example, let’s say you want to avoid the clutter of roman numerals in Example 19.1A, which has several 461

462

THE COMPLETE MUSICIAN

chords in a row applied to D minor (ii). In order to show that there is an extended reference to another key—but the phrase remains in the original key overall, with a cadence in C major: • Bracket the beginning and ending points of the tonicization. • Beneath the bracket, label the temporary tonic in relation to the main tonic using a roman numeral. • Above the bracket, analyze the chords in the key of the temporary tonic. Thus, the chords in the fifth measure—iv/ii and V/ii—become the progression iv–V in the key of ii. You are not changing the applied nature of the chords, but rather are providing a more holistic view of the chords’ tonicizing function.

EXAMPLE 19.1 Contextual Analysis of Extended Tonicizations A.

STR EA MING AUDIO

Schumann, “Talismane,” Myrten, op. 25, no. 8

W W W.OUP.COM/US/LAITZ

Got tes ist der O ri ent! The O ri ent is God’s!

C: V 6

Got tes ist der Oc ci dent! The Oc ci dent is God’s!

V6

I

I

IV

V 64

– –

5 3

I

V6

5

Nord North

iv/ii

und ern

süd and

V/ii

li ches Ge south ern

län de la nds

ii

ruht im Frie den sei ner Hän de. Repose in the peace of His Hand.

6

V /ii

ii

ii

6

8

V6 4

– – –

7 5 3

I

I

I6

463

Chapter 19 Tonicization and Modulation

EXAMPLE 19.1 (continued) B.

Measures 5–8 of the Excerpt with Extended Tonicization

5

Nord

und

süd

iv

li

ches

Ge

län de

V

i

ruht im Frie

V

6

i

i

6

8

V6 4

ii

den sei

– – –

7 5 3

ner Hän de.

I

Let’s apply this method of analysis to the following examples from the literature, each of which demonstrates an extended tonicization. After a PAC closes a phrase in the first measure of Example 19.2, an unexpected and jarring C-major harmony appears in the second measure. When such an unusual event occurs, you should always look beyond individual harmonies to understand how it participates in the phrase. Given that the C-major chord becomes a dominant seventh in the third measure, it functions as an applied dominant chord leading to F minor. The tonicization of F minor (ii in the key of E major) continues until the applied V/V chord. Thus, we see here an extended tonicization of ii. The tonic in Example 19.3 is not established but merely stated before it moves to B major (III) and D minor (v), in a repeating pattern (vi–V7–I). This brief tonicization of

EXAMPLE 19.2 Beethoven, Piano Sonata in E  major, op. 27, no. 1, Andante STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

cresc. decresc.

E :

V7

I

V

PAC T

V 42 i 6 V 6 i

vii

6 6

i

V65 V 7

I

ii PD

D

T

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THE COMPLETE MUSICIAN

EXAMPLE 19.3 Robert Schumann, “Sängers Trost” (“Singer’s Consolation”), Fünf Lieder und Gesänge, op. 127, no. 1 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Ziemlich langsam

Weint auch einst kein Lieb chen. Even if no beloved

vi

g:

V

i

7

I

Thrä nen auf mein weeps tears on my

VI

V

Grab: Grave:

7

i

III

v phrase continues

T

G, B, and D results in a large-scale arpeggiation of the tonic G-minor chord. Notice that G minor is reinterpreted as vi/III and that III becomes VI/v. The excerpt by Clara Schumann in Example 19.4 presents an extended tonicization of ii that follows a back-relating dominant in m. 4. Consequently, we can now understand the function of the A-minor chord in m. 4: It is a iv chord in the temporary key of E minor and not some sort of minor v chord in the home key of D. The ii leads to the structural dominant, which completes the excerpt’s overall progression, I–ii–V.

EXAMPLE 19.4 Clara Schumann, “Andante espressivo,” Quatre pièces fugitives, op. 15, no. 3 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5

4

cresc.

D:

HC I T

iv(p) V 43 i

V (BRD)

V 64 ii

PD

V 65 i V 74 D

3

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Chapter 19 Tonicization and Modulation

The excerpt by Robert Schumann in Example 19.5 contains tonicizations of two harmonies, vi and ii. As the second-level analysis reveals, over the course of the entire excerpt the tonicizations of vi and ii repeatedly expand the simple underlying harmonic progression, I–V–vi–ii–V–I.

EXAMPLE 19.5 Robert Schumann, “Mit Myrthen und Rosen” (“With Myrtle and Roses”), Liederkreis, op. 24, no. 9 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

3

3

3

3

Mit With

3

3

3

D:

i

V6

I

5

V

6

i

V 43

i

6

vi

6

V5

ritard.

3

3

ii

/ ii

V 3

Myr then und Ro sen, lieb lich und hold, mit duft’ gen Zy pres sen und Flit myrtle and roses, lovely and p rey with fragrant cypresses

ter gold, möcht’ ich and gold tinsel, 3

3

i I

V

9

V

6

6

i

4

V3

i

6

6

V5

vi

i

V

ii

ritard.

3

3

zie ren dies Buch wie ’nen Tod I would decorate this

ten schrein, und sar book like

gen mei ne Lie der hin ein. a co ffin and bury my songs inside it.

3

V6

i ii

4

V2

i6

3

i V 65

I

V 43

I6

7

V

I

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THE COMPLETE MUSICIAN

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignment 19.1

19.1 The following excerpts contain tonicizations. Listen to each example, and bracket the expanded harmony/harmonies; then provide a two-level roman numeral analysis.

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

SOLVED/APP 5

A.

Clementi, Prelude in A minor, op. 19

B.

Chopin, Nocturne in G major, op. 37, no. 2 Andantino

dolce

legato 5

Chapter 19 Tonicization and Modulation

467

C. Mozart, Symphony in D major, “Prague,” K. 504, Presto Presto Violino I.

Violino II.

Viola

Violoncello e Basso.

9

MODU L AT ION Longer tonicizations, which can occupy entire sections of a piece, are called modulations. Although it is difficult to draw a firm line between tonicizations and modulations, it is generally true that: Tonicizations usually occur within phrases. They do not disrupt the feeling of the home key; they do not have strong cadences in new keys, and they are fleeting. Modulations include a strong cadence in the new key, and the new key continues after the cadence. They give the feeling that a new key has usurped the home key (at least for the moment). Listen to the two excerpts in Example 19.6. Each excerpt tonicizes one or more keys, but the methods and degree of tonicization are fundamentally different. The Beethoven example contains extended tonicizations that are reminiscent of those we have already encountered: The first strong cadence occurs at the end of the excerpt, with the PAC in mm. 15–16. The first phrase is in the tonic key; phrase 2 is an extended tonicization of

468

THE COMPLETE MUSICIAN

EXAMPLE 19.6 Tonicization Versus Modulation A.

STR EA MING AUDIO

Beethoven, Violin Sonata in A major, op. 12, no. 2, Allegro piacevole

W W W.OUP.COM/US/LAITZ

5 dolce

dolce

A:

I

V (BRD)

T

ii PD

10

15

cresc.

IV

V

I

D

T

ii, and IV is tonicized until the cadence at the end. There is one overall harmonic progression, I–ii–IV–V–I, and none of the fleeting tonicizations disrupts the sense that we are hearing an A-major piece. The tonicization of the Haydn excerpt (Example 19.6B) evokes a different effect. The piece begins in E minor, and the second phrase closes in mm. 7–8 with a PAC in G major (III). On reaching mm. 7–8, it seems for a moment that G has usurped the home key of E minor. The listener’s sense of a G tonic is further confirmed when the music continues in m. 9. This motion to a strong, new tonal area is an indication that the music has modulated. Notice, however, that the D2 sequence leads to V, so the underlying progression is i–III–V.

Closely Related Keys Diatonic modulations move from a home key to any of its closely related keys, which we define as those keys derived from consonant triads that occur on each scale degree of the home key. For example, the keys closely related to C major are: D minor (ii), E minor (iii), F major (IV), G major (V), and A minor (vi). The keys closely related to C minor—using the natural minor scale—are: E major (III), F minor (iv), G minor (v), A major (VI), and B major (VII).

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Chapter 19 Tonicization and Modulation

EXAMPLE 19.6 (continued) B.

Haydn, Piano Sonata in E minor, no. 53, Hob XVI.34, Vivace molto

e:

i

V

5

i

III (G)

9

III:

VI

ii

6

V i

Another way to determine closely related keys is to identify the major and minor keys whose key signatures differ by no more than one sharp or flat sign from the original key. For example, the keys closely related to C major (0 sharps/flats) are: A minor (0 sharps/flats), G major (1 sharp), E minor (1 sharp), F major (1 flat), and D minor (1 flat). The keys closely related to C minor (three flats) are: E major (three flats), F minor (four flats), A major (four flats), G minor (two flats), and B major (two flats). Although it is possible to modulate to any major or minor diatonic key, we will focus on the most common modulations, which are listed in order of importance: • Major keys tend to modulate to V, vi, and iii. • Minor keys tend to modulate to III, v, and VI.

Analyzing Modulations We interpret the new key in relation to the initial tonic (by roman numeral) and its function within the overall harmonic progression (e.g., as part of a large-scale harmonic arpeggiation). We also identify the point where the original key and the new key are momentarily fused, a point where a single chord, called a pivot chord, that is diatonic in both the

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THE COMPLETE MUSICIAN

existing key and the new key smooths the connection between the two keys. Example 19.7 illustrates the modulatory process using a pivot chord.

EXAMPLE 19.7 Mozart, Piano Sonata in D major, K. 284, Thema, Andante STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

D:

I

ii 6

vi

V7

ii 6

I

4

V 64

– 5 – 3

I6

vi 6 A: ii 6 (V)

V7

I

ii 6

V 64

– –

5 3

I

To analyze modulations: 1. Look for the pitches that differ between the old and the new keys. Consider Example 19.7, which modulates from D major to A major. The pitches that are exclusive here are G (in D major) and G  (in A major). The G s begin in m. 6, which means that A major is already in effect in that measure. 2. Identify the last chord that is diatonic in both keys. If this is not a second-inversion ( 64) triad, then it can be a pivot chord between the two keys. In Example 19.7, the final chord in m. 5 is the last possible chord that is diatonic in both the old and the new keys. It is vi6 in D major and ii6 in A major; therefore, it is a good candidate to be a pivot chord. The rare nature of vi6 — and its spelling as the common ii6 in the new key—is one indication that the key is already changing.

Writing Modulations You must test your modulations with performance, because often what looks like a successful pivot chord may, in actuality, not work at all. This is because in addition to the following voice-leading rules, you must establish two keys in a convincing manner. The following guidelines will help you to write modulations. 1. Figure out the potential pivot chords. Line up the diatonic chords for each key, and identify chords that fit well into both keys. The best pivot chords act as PD

471

Chapter 19 Tonicization and Modulation

in the new key. To avoid harsh-sounding modulations, do not use the dominant of the new key as a pivot chord. 2. When establishing the original key and the new key, make sure that the duration of the two tonal areas is balanced. Place the pivot chord about halfway into a phrase that modulates. 3. Do not rush into a perfect authentic cadence immediately after the pivot. Try inserting a contrapuntal cadence or EPM, and close with a structural cadence only after you have strongly implied the key. 4. Use a stepwise soprano line to move to the strongest possible cadence in the new key: a PAC using a cadential six-four chord. Let’s create a phrase that modulates from F major to D minor. We first identify the potential pivot chords. Where the chord qualities match between keys, you have a potential pivot chord.

F major: D minor: Best choices: Good choices: Poor choices:

I III

ii iv *

iii v

IV VI *

vi i

*

vii° ii° *

* *

Start your progression with the descending bass arpeggiation, I–IV6–I6, and move to the pivot chord and then a strong cadence in the new key. For comparison, try out five possibilities for a pivot chord (Example 19.8). Listen to and study each progression, and identify which pivot chords work well.

Modulation in the Larger Musical Context Very few compositions end in a different key from the one in which they begin. Accordingly, modulations will never displace the prevailing tonic, and modulations in tonal music participate in a single overall harmonic motion. For example, a piece in C minor might modulate

EXAMPLE 19.8 Pivot Chords in a Modulation from I → vi STR EA MING AUDIO

A.

F:

B.

vi (d): iv ii

C.

ii 7

ii 6

V

i

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vi (d): iv 7 V

IV i

vi (d): VI

V

i

472

THE COMPLETE MUSICIAN

EXAMPLE 19.8 (continued) D.

E.

vii

vi vi (d):

i

iv 6 V

i

vi (d): ii

6

6

V

i

to E major and F minor before leading to the dominant and returning to C minor to close the piece. This series of keys would constitute a large-scale progression in C minor: i–III–iv–V–i. When analyzing modulations, you should refer to the new key in terms of its relationship to the original tonic. For example, a modulation from C major to G major should be viewed as a modulation from I to V; a modulation from F minor to D major is a modulation from i to VI. Listen to Example 19.9 and note the cadences and keys. The first eight measures include a modulation from G major to D major. Starting at m. 9, we have a modulation to E minor, followed by a return to G major. Therefore, the overall harmonic motion is as follows:

m. 1 m. 8 m. 16 m. 21 m. 22 m. 25 G: I V vi V I ii56 V I––––––––––––––––––– vi V I ii56 V T–––––––––––––––––––––––––––––––––––––––––––––––––PD D

m. 26 I I T

EXAMPLE 19.9 Handel, Prelude in G major STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Allegro

5

473

Chapter 19 Tonicization and Modulation

EXAMPLE 19.9 (continued) 9

13

17

20

24

1

2

The keys participate in the overall harmonic motion. The modulation to V in m. 8 is subordinate to the larger I–vi–V–I that leads to m. 22; this progression is embedded within a larger I–ii65 –V–I that occurs over the entire example.

The Sequence as a Tool in Modulation The function of a pivot is not limited to a single chord. Often, several chords that function in two keys will work together to create a pivot area. For example, a pivot chord might be expanded or tonicized. Or a group of chords that share the same harmonic function (such as pre-dominants IV and ii) might be coupled through a voice exchange, creating a pre-dominant complex that works in both the starting and ending keys. Sequences, too, make terrific pivots. In fact, one of the two functions of a sequence is transitional: It frequently takes the music from one harmonic area to another. Many

474

THE COMPLETE MUSICIAN

strategies exist for using sequences to modulate, given that a sequence touches on many chords, sometimes every chord within a key. Therefore, by prematurely quitting a sequence and reinterpreting one of its chords as a pre-dominant that moves to a dominant, you can effectively move to a new key. Listen to Example 19.10. Vivaldi invokes a D2 sequence that stops on VI (c–f–B–E–A). The A chord functions as IV in the new key of E (III of C minor). Example 19.11 demonstrates how easy it is to modulate to a variety of keys from within a sequence. Example 19.11A presents a D2 (⫺5/⫹4) sequence in G minor; Example 19.11B presents an A2 (⫺3/⫹4) sequence in B major. Each sequence contains at least two repetitions of the model, marked by brackets. Beneath each sequence are progressions that modulate to several different keys, accomplished by incorporating some, but not all, of the given sequence. (Arrows indicate the point of departure from the sequence and continuation in the new key.) The G-minor example modulates to III (two examples), VI, and v (two examples). The B-major example modulates to vi, iii, and V.

EXAMPLE 19.10 Vivaldi, Trio Sonata in C minor, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Allegro Violino

Violoncello solo

Basso continuo

c:

i

V

i

D2 (–5/+4)

5

VI III (E ): IV

IV 6

V7

V 42

I6

V

V42

Chapter 19 Tonicization and Modulation

EXAMPLE 19.10 (continued) 9

I6

V7 I

V7 I

8

7

4

3

ii 65 V 6 5

I

EXAMPLE 19.11 Modulation via Sequence A.

D2 as Pivot Area

g:

To III: (B )

To VI: (E )

To v: (d)

4 2

475

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THE COMPLETE MUSICIAN

EXAMPLE 19.11 (continued) B.

A2 as Pivot Area

(B ): I

IV vi: VI

iii iii: i (d)

iii V: vi (F)

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 19.2–19.5

19.2 Given are examples that end in a different tonal area from the one in which they begin. Assume that they would continue in the new key. Provide a two-level harmonic analysis; remember to describe the pivot chord in both keys—draw a box around the roman numerals for the pivot chord. A.

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

SOLVED/APP 5

B.

C.

477

Chapter 19 Tonicization and Modulation SOLVED/APP 5

D.

E.

F. Scarlatti, Sonata in G minor, K. 64 GAVOTTA Allegro

SOLVED/APP 5

G. Mozart, Piano Concerto in G major, K. 453, Allegretto Violino I.

Violino II.

Viola

Violoncello e Basso.

6

478

THE COMPLETE MUSICIAN

SOLVED/APP 5

19.3 Analysis of a Modulating Sequence Bracket and label the following modulating sequence. Then determine, using pivot notation, how the last chord of the sequence functions in the new key.

Handel, Concerto Grosso in B  major, op. 3, no. 2, HWV 313, Largo Violino I piano per tutti

Violino II piano per tutti

Viola piano per tutti

Violoncello I

Violoncello II

Basso Continuo 7

Senza Cembalo

7

7

6

7

6

6

6 4

5 3

W R ITING

SOLVED/APP 5

19.4 Modulation Warmup: Pivot Choices The pivot chord is important because it hides any abrupt motion that might result from a modulation and instead glues the musical seams together to create one fluid gesture. Given are several harmonic scenarios in which phrases modulate from the tonic to a closely related key. Determine (and list on a separate sheet of paper) all the possible pivot chords that will work between the two keys, and then mark with an “X” the pivot that you feel might work best. A. D major: I to vi D. A major: I to V

B. C minor: i to v E. D minor: i to iv

C. G minor: i to III

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Chapter 19 Tonicization and Modulation

19.5 Writing Modulating Progressions Initial key and pivot chords are given. You will write short progressions (seven to nine chords) that modulate. 1. Determine what the new key is, based on the information provided by the pivot chord (e.g., given the key of D major, if the pivot is ii → iv, then you know you are to modulate to B minor, since, in D major, ii is an E-minor chord, and E minor is iv in the key of B minor. 2. Establish the first key (use a three- to four-chord contrapuntal progression or EPM), move to the pivot chord (one chord), and lead to a strong PAC in the new key (three to four chords). Example: Given: key of E minor; pivot; iv6 ii6 The pivot is an A-minor chord in first inversion (iv6). Since it will become ii6 in the new key, we know we are modulating to G major (because A minor is ii in G). We then establish E minor (three to four chords), lead to the pivot, and write a cadential progression in G major. A. In B  major: pivot is C. In C minor: pivot is

vi ii

B. In B minor: pivot is

VI IV

III VI

D. In F major: pivot is

ii iv

19.6 On Your Own: Writing Short Modulations In approximately seven to nine chords, write the following modulations on a separate sheet of manuscript paper. Analyze—remember to identify the pivot chord. A. C. E. G.

In G major, modulate from I to V. In A major, modulate from I to vi. In B minor, modulate from i to v. In B  major, modulate from I to ii.

B. In D minor, modulate from i to III. D. In F major, modulate from I to iii. F. In E minor, modulate from i to VI.

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THE COMPLETE MUSICIAN

T ER MS A ND CONCEP TS • closely related keys • modulating sequences • modulation • pivot • pivot area • pivot chord • tonicized area

CH A PTER R EV IEW 1. Summarize the differences between tonicization and modulation.

2. Give the roman numerals for closely related keys in a major mode.

3. Give the roman numerals for closely related keys in a minor mode, using the natural minor scale.

4. How do the key signatures for all these keys relate regarding their number of accidentals?

5. A chord that is diatonic in the old key and the new key is called a _______________________.

6. Complete the chart below listing all the possible pivot chords between C major and G major. Put an “X” if the chord does not exist in G major. C M AJOR: G M AJOR:

I

ii

iii

IV

V

vi

vii°

Chapter 19 Tonicization and Modulation

481

7. The best pivot chords are pre-dominant in function in the new key because they can begin a phrase model (PD–D–T) that confirms the new key. Therefore, if ii, IV, and vi are pre-dominant in function, which triads are effective pivot chords between C major and G major?

8. True or False: ii, IV, and vi in the dominant will always be effective pivot chords when modulating to the dominant in a major key.

9. Several chords in succession (such as a sequence) that function in two keys will work together to create a _________________________________________________________________.

CH A P T ER 20

Binary Form and Variations OV E RV I E W

This chapter presents the binary form, our first complete type of piece, and arguably the most common type of piece in the tonal repertoire. More importantly, it is the model composers use to write longer, more involved works. We will also study a direct outgrowth of binary form: theme and variations. CHAPTER OUTLINE Binary Form ................................................................................................................. 483 Simple Sectional Binary ....................................................................................... 483 Simple Continuous Binary .................................................................................. 484 Rounded Sectional Binary.................................................................................... 485 Rounded Continuous Binary............................................................................... 487 Balanced Binary Form .......................................................................................... 488 Summary of Binary Form Types ......................................................................... 489 Variation Form............................................................................................................. 493 Continuous Variations .......................................................................................... 494 Sectional Variations ............................................................................................... 499 Compositional Risks and Solutions.................................................................... 500 Terms and Concepts ................................................................................................... 501 Chapter Review ........................................................................................................... 501 Answers to Exercise Interlude 20.1 ........................................................................ 503 Summary of Part 5...................................................................................................... 504

482

483

Chapter 20 Binary Form and Variations

T H E S T U D Y O F M U S I C A L F O R M can be discussed in three stages. We have al-

ready encountered the first stage, which explored how the fundamental building blocks of music—the phrase and the subphrase—combine to form units of modest length: the period and sentence. Here, at the second stage, we will explore how composers combine periods, phrases, and sentences to create binary form. (The third stage, encompassing rondo, ternary, and sonata forms, is discussed in Part 7.)

B I N A R Y F OR M Binary form, a term describing a complete work that can be divided into two sections, can be traced back to well before 1700. The Baroque suite comprises numerous dance movements, ranging from slow sarabandes to lively gigues, each of which is cast in binary form. The minuet was maintained in many compositions of the Classical period, such as instrumental sonatas, string quartets, and symphonies. In the nineteenth century the scherzo appeared more and more frequently in works by Beethoven and later composers. It, too, is cast in binary form, as are the theme and subsequent subsections of many variation sets. Throughout the common-practice period, repeat signs almost always mark the two sections of pieces in binary form; for this reason, binary form is also known as two-reprise form.

Simple Sectional Binary Listen to Example 20.1 and identify the different sections of the work and what differentiates these sections musically. Analyze the overall tonal structure and identify any material that recurs. This piece is obviously in two parts; the double bars indicate two sections. When describing binary form, which is similar to describing a period label, we consider the melodic structure (or thematic design) and the harmonic structure. Notice that no thematic material recurs in Example 20.1. In cases like this, when the two sections of a binary form share no melodic material, labeled ab, the melodic design is called simple. As for the harmonic label, when the cadence at the end of the first section ends on the tonic, the harmonic structure is called sectional (since both sections of the binary form are tonally closed). Thus, we can say that Hummel’s Bagatelle is in simple sectional binary form.

EXAMPLE 20.1

Hummel, Bagatelle in C major, op. 107 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Allegretto

C:

(PAC)

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THE COMPLETE MUSICIAN

EXAMPLE 20.1

(continued)

5

cresc.

(PAC) 11

(HC)

(PAC)

Simple Continuous Binary Now listen to Example 20.2, which illustrates a different type of binary form. Identify how the Weber piece is similar to and different from the Hummel. Melodically, this binary form is simple. Harmonically, the tonicization of the dominant at the end of the first section clearly presents a significant difference from the previous example. The dominant continues after the double bar but is weakened by the addition of the seventh, which forces it back into the orbit of G major. In cases like this, when the first section closes away from the tonic, and the following section continues away from the tonic, the binary form’s harmonic structure is called continuous. Thus, Weber’s piece is in a simple continuous binary form.

EXAMPLE 20.2 von Weber, Six Ecossaises, no. 2, J. 30 STR EA MING AUDIO

a

G:

W W W.OUP.COM/US/LAITZ

(PAC in V)

485

Chapter 20 Binary Form and Variations

EXAMPLE 20.2 (continued) b

(PAC in I)

We have been using period terminology to describe the harmonic structure of binary forms. If both sections are tonally closed, binary forms (just like periods) are sectional. If the first section ends away from tonic, and the second section starts away from tonic, binary forms (just like periods) are continuous.

Rounded Sectional Binary Listen to Example 20.3. In what ways does it differ from Examples 20.1 and 20.2? The first section closes on tonic; therefore, the piece’s harmonic structure is sectional. However, the piece has a lopsided structure: The material after the first double bar occupies 16 measures, exactly twice as long as the preceding material, and there is a distinct HC in m. 16 that divides the second half. After the HC, there is a literal restatement of the material that began the piece.

EXAMPLE 20.3 Haydn, Sonatina no. 4 in F major, Hob XVI.9, Scherzo STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A:

F: 4

(PAC in I)

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THE COMPLETE MUSICIAN

EXAMPLE 20.3 (continued) (PAC in I)

Digression: 9

//(interruption)

13

A:

cresc.

V

(HC)

17

21

The second section of Haydn’s binary form is more complex than Example 20.1 or Example 20.2. It features a new compositional tactic: Begin the second section with fragmented and unstable material that leads to a HC. We call this a digression, since it wanders from the preceding material but then quickly leads back to a restatement of the original material. When all or part of the opening material of a binary form returns in the second section after the digression, the binary form’s thematic design is called rounded, indicating the cyclical effect created by the return of the opening material. The scherzo by Haydn is in a rounded sectional binary form. Look again at Example 20.3. The structure of the binary form resembles a parallel interrupted period. The music works to a structural HC (mm. 1–16), after which the music begins again in the tonic (mm. 17–24). We call the structural HC in m. 16 an interruption (marked with a double slash (//), since this is the point where the harmonic progression is interrupted and begins again in the tonic.

Chapter 20 Binary Form and Variations

487

Rounded Continuous Binary Listen to Example 20.4, the theme that opens the variation movement of Mozart’s Piano Sonata in D major, K. 284. Consider the nature of the theme (simple or rounded) and whether there is an interruption. Further, consider whether the harmony is sectional or continuous, and whether the sections are similar in proportion (like the Hummel excerpt) or lopsided (like the Haydn excerpt). Example 20.4 contains two nearly symmetrical sections (of eight and nine measures, respectively), each of which is articulated by repeats and by cadences. The harmonic

Mozart, Piano Sonata in D major, K. 284, Thema, Andante

EXAMPLE 20.4

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D: 4

9

13

structure is continuous, since the first section ends away from the tonic. Thematically, there is a digression in mm. 9–12 that leads to an interruption; this is followed by a repetition of part of the opening theme in the tonic. Therefore, Mozart’s piece is cast in rounded continuous binary form.

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An interesting formal conflict arises when one compares the melodic design with the tonal structure. Mozart’s piece has a three-part design that is based on the melodic structure and surface rhythm articulations: Initial tune ⫽ A (mm. 1–8) Sequential figuration ⫽ digression (mm. 9–12) Restatement of tune ⫽ A⬘ (mm. 14–17) However, it has a two-part tonal structure based on the large-scale interruption and restart on the tonic. The following model illustrates the most common two-reprise form: the rounded continuous binary form. The model shows the three-part thematic design and two-part harmonic structure in both major and minor keys.

Rounded Continuous Binary Form Thematic Design in 3 Sections: in major:

a digression a⬘ (main theme) (sequence, etc.) (main theme) ||: I———to V—–—PAC in V :||: (x)———V(7)⬙ I——–V–I :||

in minor: ||: i———to III——PAC in III :||: (x)———V(7)⬙ i——–V–i :|| Harmonic Structure in 2 Parts: (interruption) I/i—————————––––––––—————V(7)⬙ I/i——V–––I/i

Balanced Binary Form Binary forms––whether sectional or continuous, simple or rounded—can have an additional characteristic: They can be balanced if the closing material in the first section is restated as the closing material in the second section. “Balanced” does not always refer to an exact repetition, because in many binary forms the first section closes in a nontonic key. To provide convincing tonal closure at the end of the piece, the restatement of this material will naturally occur in the tonic. Look back at Handel’s keyboard piece (Example 19.9). The first section closes in V (D major) in m. 8, making the harmonic structure continuous. In the digression (mm. 9–21), Handel develops the piece’s opening gesture by reversing the order of scale and broken chord and placing them within two sequences. Handel is in a quandary: The extensive, 13-measure digression creates an imbalance with the first section, which occupies only eight measures, yet he must provide convincing melodic and harmonic closure. Looking at Mozart's theme in Example 20.4, we see that he used the same strategy: Instead of repeating the harmonic and melodic material of the A section—which would further imbalance the proportions of the piece—he instead draws material from the close of the A section, to create a (balanced) continuous binary form. Balanced is in parentheses to show that it is an additional element of the form that does not disrupt the other melodic aspects of the label. Note that the last two measures of Mozart’s theme (Example 20.4) closes with the same gesture that occurs at the end of the first section, but transposed to the tonic. This, too, is a balanced element making the piece a “balanced” rounded continuous binary form. There are instances of binary forms that are neither simple nor rounded, but can

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only be described as “balanced.” Such cases involve material that is transposed near the end of the opening section but is the only material heard earlier that returns at the end of the piece but transposed to the tonic.

Summary of Binary Form Types The feature common to all two-reprise binary forms is the presence of two sections, often marked by double bars. We look at cadences to determine the harmonic structure.

Two-Reprise Binary Forms sectional:

||:

ends on tonic: :||:

ends on tonic: :||

continuous:

||:

ends away from tonic: :||:

ends on tonic: :||

To determine the melodic structure we discern whether material from the first section recurs in the second section. Finally, look at the closing material of each section to see if the binary form features a “balanced” element. Binary forms do not always fall neatly into one of our established theoretical categories. Categorization is merely an attempt to deal with the many and varied stimuli with which we are confronted at every moment of our lives. As such, categories are more general than specific. Given that music is an art form capable of multiple interpretations, we must be flexible and open-minded in our attempts to come to grips with it. In your analysis of form, always be sensitive to the music.

Summary of Binary Forms simple:

||:

a

:||: b

rounded:

||:

a

:||: dig.

:||

balanced:

||:

:||:

:||

:|| HC

EX ERCISE INTER LUDE A NA LYSIS

WORKBOOK 1 20.1–20.3

20.1 The following binary pieces present a variety of formal and harmonic issues. Analytical questions will take you through the process of analyzing binary forms. Study the questions that follow each excerpt, and then listen to the piece. Answer as many of the questions as

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THE COMPLETE MUSICIAN

possible before listening a second time. Finally, compare your answers with the answers provided at the end of the chapter. STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

Haydn, Piano Sonata no. 50 in D major, Hob XVI.37, Presto ma non troppo innocentemente

9

15

1. What is the form? Be precise when labeling binary forms. Include harmonic and melodic labels. 2. What melodic embellishment occurs in mm. 2 and 4? 3. How many phrases make up mm. 1–8? Do they form a period? If so, label the type of period. 4. What key is briefly tonicized in mm. 9–10? 5. What applied chord appears in m. 17?

B.

Mozart, Piano Trio in G major, K. 496, Allegretto

Allegreo

Chapter 20 Binary Form and Variations

491

4

9

12

1. What is the form? 2. How many phrases occur in mm. 1–8? Do they form a period? If so, label the type of period. 3. How long is the tonic expanded in the first phrase? 4. What sequential progression occurs in mm. 9–11? And to what harmony does it lead? 5. Since this is a trio, one would expect an equal division of melodic interest between the instruments. Is this the case? Why or why not? C.

Haydn, Piano Sonata in A major, Hob XVI.12, Trio

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8 dim.

cresc.

15

23 cresc.

dim.

1. What is the form? 2. What melodic embellishment occurs throughout the piece? 3. How would you label the bass motion from i to V in mm. 1–6? 4. What type of sequence begins in m. 7? How long does it last? Is it transitional or prolongational? 5. What key is the goal of the first section? What key is tonicized in mm. 15–18? 6. What is the underlying tonal progression for the entire excerpt? D. Handel, Concerto Grosso in F major, op. 3, no. 4, HWV 315, Allegro Tutti

Violin I Oboe I Violin II Oboe II Viola

Basso Continuo 6

6

6

6

6

6

6

6

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Chapter 20 Binary Form and Variations 8

6

6 5

17

1

6 5

6 5

2

6

1. What is the form? 2. To what key does the first section modulate? What is the pivot chord? 3. Immediately after the double bar, there is a return to the tonic (F major), which seems premature, given the length of the second section. Is this a true return to the tonic, or is it part of a larger progression that leads to a new tonal destination? 4. The syncopated tune that appears in m. 9 looks new, yet one could argue that this syncopation is an explicit statement of rhythmic irregularity implied in the first tune. What are two other similarities between the opening four measures and mm. 9–13? 5. What sequence occurs in mm. 17–20? What is its function?

VA R I AT ION F OR M One of the most difficult and important tasks for a composer is to balance unity with variety. Fulfilling that task raises a central question in composition: How do you handle repeating melodic material? As master listeners, composers are keenly aware of the potential stasis that is created by literal restatement, on the one hand, and of the potential for aural chaos when a listener is constantly assailed with new material, on the other. An important genre for exploring and developing this relationship between unity and variety is the variation set.

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Variation sets usually begin with an initial idea, or theme, from which a series of variations unfolds. These variation sets may be independent pieces, or members of larger, multimovement works, such as suites and sonatas. Variation sets are found in just about all musical combinations, including works for solo instruments, chamber works, symphonies, and vocal pieces. The two common types of variation sets are continuous variations and sectional variations. The difference between the two is based on how strong the division is between variations, and how smooth the progression of events is from the opening to the close of the piece.

Continuous Variations In a continuous variation set, the theme is relatively short (usually a phrase), and it often gives the effect of being incomplete in order to permit each variation to flow seamlessly into the next. This is often accomplished by an overlapping process whereby the ending tonic of one variation simultaneously acts as the beginning of the next. Listen to Example 20.5, which is the beginning of a continuous variation set. Notice the repeating bass pattern (bracketed in the example) that forms the foundation for the variations (notice also the brackets above the staves showing how some repetitions of the pattern are overlapped as part of an authentic cadence). Continuous variations are most often constructed through the use of a repeated idea, called an ostinato, rather than a lyrical tune. Ostinati provide the backbone of the variations, over which changes in register, texture, and motivic design occur. Ostinati generally appear in the lower voices and can be

EXAMPLE 20.5

Monteverdi, “Lamento della ninfa” (“Lament of the Nymph”), Madrigali guerrieri et amorosi STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A

(Lento, in due)

mor

A

Di

ce

a

Di

ce

a

Di

ce

a

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Chapter 20 Binary Form and Variations

EXAMPLE 20.5

(continued)

mor

A mor

il ciel mi

ran do il

piè

fer

mò

il ciel mi

ran do il

piè

fer

mò

il ciel mi

ran do il

piè

fer

mò

A mor do

ve

as simple as a repeating bass pattern, called a ground bass, a repeating harmonic pattern, called a chaconne, or both a repeating bass and a repeating harmonic pattern, called a passacaglia, as in the case of Monteverdi’s Lamento. Often, all three terms are used interchangeably. The distinction between the repeating bass line of the ground bass and the repeating harmonic pattern of the passacaglia and chaconne is often artificial; composers use repeating harmonies to accompany a repeating bass, and vice versa. In Example 20.6, Purcell harmonizes his eight-measure ground bass (circled notes) with a harmonic pattern that is used in each repetition. Examples 20.7, 20.8, and 20.9 illustrate how composers merge the two types of ostinati. Bach’s famous Chaconne is based on a repeating series of harmonies (Example 20.7). That the ostinato begins in midmeasure helps to maintain continuity between repetitions.

EXAMPLE 20.6

Purcell, Ground in G, theme and two variations STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Andante ( = 88)

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EXAMPLE 20.6

(continued)

7

13

19

EXAMPLE 20.7 Bach, Partita no. 2 in D minor for Solo Violin, BWV 1004, Chaconne STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

i

ii ø 42 V65

i

VI

ii o 6 V 46

4

i

ii ø 42 V65

i

7

i

VI

ii ø 65 V

ii ø 42

i

V 65

i

ii ø 65

VI

12

V

i

ii ø 42

V 65

i

VI

ii ø 65 etc.

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Chapter 20 Binary Form and Variations

EXAMPLE 20.8 Beethoven, Thirty-two Variations on an Original Theme, in C minor, WoO 80, theme and two variations STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5

9

i VAR. I

iv

V

i

leggiermente

13

17

VAR. II

leggiermente

21

Furthermore, the variations overlap, with each ending dovetailed with the beginning of the next statement; only the theme is not overlapped. In Example 20.8, Beethoven’s eight-measure theme—a repeating harmonic ostinato— traverses an indirect step-descent bass to iv, followed by a two-measure cadential gesture. Although the theme is tonally closed and there is no dovetailing between repetitions, continuity is preserved by the continuous figurations. Brahms combines the idea of ground and chaconne in the last movement of his E-minor symphony (Example 20.9). The harmonic pattern (chaconne) of the opening continues

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EXAMPLE 20.9 Brahms, Symphony no. 4 in E minor, op. 98, Allegro energico e passionato STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

THEME

VAR. 1

10

dim.

VAR. 2 16

ma marc.

VAR. 3

23

cresc.

31

VAR. 4

ben marc.

38

cresc.

Chapter 20 Binary Form and Variations

499

in the first variations. But in the following several variations, it is the theme’s upper-voice ascent (ground) that holds each variation together. Chaconnes and passacaglias often employ sequences. For stepwise bass descents the (⫺5/⫹4) sequence works well. Recall that the underlying structural motion is by step, usually leading to the pre-dominant function on 4. Accordingly, this sequence preserves the common step descent. For example, in the key of G minor the progression i–iv– VII–III–VI–ii°–V–I creates a direct step descent to the dominant, as shown in bold: G–C–F–B–E–A–D–G. Example 20.10, from a Handel Passacaglia, demonstrates this use of sequence.

EXAMPLE 20.10 Handel, Suite no. 7 in G minor, Passacaglia STR EA MING AUDIO

5

W W W.OUP.COM/US/LAITZ

10

15

Indeed, Pachelbel’s Canon is a good example of a continuous variation set: Its nonstop (⫺4/⫹2) sequence leads to the subdominant IV and rises to the dominant, preparing for the next statement of the pattern (Example 20.11).

Sectional Variations Continuous variation sets flow seamlessly from one variation to the next. The overlap between variations is achieved largely through tonal means: Each ground bass tends toward V, whose resolution thus coincides with the next variation’s start on tonic. In a sectional variation set, the theme and variations are usually in binary form (often a rounded continuous binary form) that is tonally closed, and therefore they are separated from one another. Sectional variations often have more substantive changes among variations. In addition to changes in texture and figuration, there may be reharmonization, tonicization of diatonic and chromatic keys, and changes between major and minor modes.

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THE COMPLETE MUSICIAN

EXAMPLE 20.11

Pachelbel, Canon in D major STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

( = ca. 63)

(espr.)

(espr.)

(espr.)

( = ca. 63)

D:

I T

(–4/+2)

I ii 65 V

I

PD D T

In general, composers strive to balance musical unity with diversity in each variation by retaining one or more characteristic elements presented by the theme. For example, if a composer significantly alters the theme’s melody by adding embellishment or ornamentation, the harmonic underpinning will most likely not stray too far from its thematic presentation. If the harmony is dramatically altered, the melody will often remain unchanged. One musical element that tends not to be altered is the form of the theme, including its general proportions and length. When we analyze variations, it is precisely the degrees and types of changes in the variations that interest us. It is particularly rewarding to find the seeds for such alterations sown in the theme itself—seeds that lie dormant until a particular variation provides the environment for it to germinate and flourish.

Compositional Risks and Solutions By their very nature, variation sets clearly run the risk of being merely a string of connected ideas devoid of any larger, goal-oriented musical process or development. To avoid such problems, composers use two common strategies. In the first strategy, they create a sense of drive that leads to a musical climax, most commonly by using ever-smaller note values (sometimes referred to as a rhythmic crescendo) or increasingly elaborate textures and expanded registers and dynamics (in which there may be one or more arches of intensity). In the second strategy, composers group two or more variations to create another level of organization, resulting in a large-scale ebb and flow in the unfolding of the entire set. For example, in a set of 12 variations, a composer might create three larger groups of five, two, and five variations respectively, with each group distinguished from the other by mode

Chapter 20 Binary Form and Variations

501

change (e.g., the central group may be cast in the parallel minor if the work is in major) and with each group unfolding in one of the processes described in strategy 1.

T ER MS A ND CONCEP TS • binary form • chaconne • continuous variations • digression • ground bass • harmonic structure • sectional • continuous • interruption • minuet • ostinato • passacaglia • sectional variations • thematic design • simple • rounded • balanced • theme • two-reprise form • variation set

CHA PTER R EV IEW 1. Name two types of movements that often employ binary form in instrumental sonatas, string quartets, and symphonies.

2. Why is binary form also known as two-reprise form?

3. “Sectional” means both sections are tonally [closed/open].

4. Conversely, “continuous” means at least one section is tonally [closed/open].

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THE COMPLETE MUSICIAN

5. Complete the two charts below. Terms describing binary form harmony: (same as period labels) F I R S T S E C T ION . . . SECTIONA L:

S E C ON D S E C T ION . . .

ends on tonic

CONTINUOUS: (IF EITHER OF THESE OCCURS)

continues away from tonic and ends on tonic

Terms describing binary form melody: (different from period labels: parallel/contrasting) F I R S T S E C T ION . . .

S E C ON D S E C T ION . . .

a

digression // (HC) aⴕ

SIMPLE: ROUNDED:

6. If the concluding material from the first section returns at the end of the second section, any binary form can have an additional label as being __________________________________.

7. The difference between continuous and sectional variations is based on two factors:

8. Name three kinds of pieces based on an ostinato.

9. Sectional variations are often in which form? Be specific.

10. In a few words, describe two compositional strategies that composers often employ in sectional variations. There are more than two possible answers.

Chapter 20 Binary Form and Variations

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A N S W E R S T O E X E RC I S E I N T E R L U DE 2 0.1

Exercise 20.1A 1. The material from the opening of the piece returns in m. 13, making the thematic design rounded. That the initial tune is slightly embellished by thirds and sixths does not interfere with the immediate perception that the tune recurs and is thus rounded. The dominant (A major) is tonicized at the double bar, leaving the section open on the dominant; therefore, the harmonic structure is continuous. This, then, is a rounded continuous binary form. 2. The contrapuntal technique employed is the suspension: in m. 2, a 7–6 suspension, and in m. 4, a 4–3 suspension, both of which are prepared. 3. There are two phrases, and they combine to create a contrasting progressive period. 4. The key of E minor is briefly tonicized (it is ii in the original key, leading to V65 in m. 11). 5. V42/IV.

Exercise 20.1B 1. The first section (mm. 1–8) closes on the tonic; therefore, the harmonic structure is sectional. The opening material returns in m. 13; therefore, the melodic design is rounded. Thus, the form is a rounded sectional binary. 2. The two phrases comprise a parallel interrupted period (PIP). 3. The progression is contrapuntal, since the tonic is extended through neighboring six-five chords (mm. 1–2) and passing vii°6 (m. 3). The only harmonic motion in mm. 1–8 is the V 7 harmony that occurs in mm. 4 and 8. 4. This is a D2 (⫺5/⫹4) sequence with applied chords. Since the applied six-five chords resolve not to diatonic four-twos but to yet other applied chords, this is a D2 (⫺5/⫹4) applied 65 42 (i.e., V65 of E resolves to V42 of A, which moves to V65 of D, etc.). Notice the telltale parallel tritones between the piano’s left hand and the violin. This sequence leads to the pre-dominant, ii6, in m. 11. 5. The piano and violin share the spotlight with their florid lines and melodies. The cello reinforces the piano’s bass line, providing harmonic support.

Exercise 20.1C 1. Since opening material returns in the last system, albeit altered in order to close in the tonic, the thematic design is rounded. Furthermore, the modulation to the mediant, C major, at the first double bar makes the harmonic structure continuous. The form is rounded continuous binary. 2. The contrapuntal technique is suspension, most often 7–6s. The suspensions are prepared in m. 1 in the tenor with the 5–6 motion (E4 –F4) that ties over the bar line. The bass descends to G 3, creating the suspended interval of a seventh with the tenor, resolving on beat 3 to E4. 3. The bass line is an example of the step-descent bass. 4. The sequence is an A2 (⫺3/⫹4) type. Beginning on E minor, the harmonic motion consists of ascending triads in root position: E3 –F3 –G3 –A 3 –B3 –C4. The

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5–6 motion helps avoid the potential parallel fifths. This sequence is a transitional type, since it begins in the tonic key area and, through its ascent, helps to secure the mediant key. 5./6. The mediant (C major) is the added key area that gives way to iv (D minor) in mm. 18–19. Notice how D minor is strongly implied by its PD and dominant, beginning immediately after the double bar. In fact, in a clever allusion to the opening octave leaps, Haydn transfers the dissonant seventh, G, of the dominant of D (A–C –E–G) down an octave in m. 17, where it finally resolves to F (the third of D) in m. 18. D minor as large-scale pre-dominant moves to the dominant and the interruption. The tonal structure of the movement, then, is i–III–iv–V || i–V–i.

Exercise 20.1D

WORKBOOK 1 Assignments 20.4–20.5

1. The first section does not close on tonic, so the harmonic structure is continuous. There is no obvious repetition of melodic material from the first eight measures, so the thematic design is simple. The form is simple continuous binary. 2. The new tonal destination is V, and the pivot may be traced to m. 4, the downbeat, at which point tonic becomes IV in the context of the dominant. 3. F major lasts only four measures but is followed by what sounds like a sequential restatement of the F-major material, the goal of which is to tonicize D minor (vi). 4. The new melody beginning in m. 9 is a loose inversion of the opening tune. Furthermore, the clear melodic ascent F5 –G5 –A5, which occurs prominently at the downbeats of mm. 1–3, reappears in mm. 9–13 but now on the weak, second beats of each measure. This motivic restatement may help to explain why F major reappears after the double bar. 5. This is a D2 (⫺5/⫹4) sequence with applied dominants. D minor (m. 16) is converted to D major with an added seventh, creating a V65 of G minor, to which it leads, followed by V65 of F major, thus securing the return to tonic.

S U M M A R Y OF PA R T 5 In Chapter 18 we learned that applied chords function as dominants of nontonic harmonies, and as such they are powerful agents of tonicizations. A tonicization may contain just a single applied chord, or it may be an extended area consisting of numerous applied chords, all working under the influence of a single harmony. When a tonicized area is stabilized through one or more cadences, we call this larger expansion a modulation. Regardless of how extensive tonicizations and modulations are, however, the expanded harmonies always retain their function within the overall key and participate in the unfolding of the underlying harmonic progression. We also have studied complete pieces for the first time in Part 5. In addition to simple, rounded, and balanced melodic plans, we built on large-scale motions from the tonic to one or more other tonal areas, followed by a return to (and closure in) the tonic. In labeling the harmonic content of binary forms, we saw how the large-scale cadences function analogously to the models of sectional and continuous periods.

Chapter 20 Binary Form and Variations

505

Finally, we saw how extensive works can be constructed using building blocks composed of small binary-form movements. Sectional variations are one such type; we will study several others in the chapters to come. We also encountered continuous variations, in which constant cadential overlappings permitted a nonstop musical effect.

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PA R T 6

EX PR ESSI V E CHROM ATICISM

C

hromatic harmony in the form of the applied dominant chord has existed essentially from the beginning of tonality. Examples of V/V can be found in the output of early-sixteenth-century composers, such as Josquin. Yet as music moved into the late Classical and Romantic eras, composers began to focus on the potential of pre-dominant, rather than dominant, harmony. For example, the off-tonic beginning—which typically involves starting a piece on a ii or IV chord and only eventually revealing the home sonority—is a hallmark of Schumann, Brahms, Wolf, and Mahler. A natural outcome of this new interest in pre-dominant harmony was that composers began investing pre-dominants with their own forms of chromaticism. In the following chapters, we explore the roles of these chromatic pre-dominants. We will see how they function both as expressive devices in local contexts and as stepping-stones to remote tonicizations at deeper levels. In fact, at the same time that these new chromatic harmonies were surfacing, so too were new motivic techniques and new genres (including the solo song with piano accompaniment). We also explore two special sonorities of remarkable pre-dominant power: the Neapolitan sixth chord and the augmented sixth chord.

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C H A P T E R 21

Modal Mixture OV E RV I E W

This chapter presents a type of chromaticism in which scale degrees and harmonies that occur in one mode are borrowed from the parallel mode. The result brings remarkable color to the music and opens wide the harmonic possibilities. CHAPTER OUTLINE Altered Pre-Dominant Harmonies: ii° and iv ..................................................... 512 Application: Musical Effects of Melodic Mixture ............................................. 512 Altered Submediant Harmony: VI ........................................................................ 513 Altered Tonic Harmony: i ......................................................................................... 514 Altered Mediant Harmony: III............................................................................... 516 Voice Leading for Mixture Harmonies ................................................................. 517 Chromatic Stepwise Bass Descents ........................................................................ 520 In Minor ................................................................................................................. 520 In Major .................................................................................................................. 520 Plagal Motions............................................................................................................. 522 Brahms, Symphony no. 3 in F major, op. 90, Andante ................................... 522 Modal Mixture, Applied Chords, and Other Chromatic Mediants .............. 524 Grieg, “Morning” from Peer Gynt Suite, op. 46, no. 1.................................... 524 Summary of Third Relations ................................................................................... 526 Terms and Concepts ................................................................................................... 529 Chapter Review ........................................................................................................... 529

509

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THE COMPLETE MUSICIAN

M U C H M U S I C O F T H E late eighteenth and early nineteenth centuries commonly

employs a type of chromaticism that cannot be said to derive from applied functions and tonicization. In fact, the chromaticism often appears to be nonfunctional—a mere coloring of the melodic and harmonic surface of the music. Listen to the two phrases of Example 21.1. The first phrase (mm. 1–8) contains exclusively diatonic harmonies, but the second phrase (mm. 11–21) is full of chromaticism. This creates sonorities, such as the A-major chord in m. 15, which appear to be distant from the underlying F-major tonic. The chromatic harmonies in mm. 11–20 have been labeled with letter names that indicate the root and quality of the chord. These sonorities share an important feature: All but the cadential V–I are members of the parallel mode, F minor. Viewing this progression through the lens of F minor reveals a simple bass arpeggiation that briefly tonicizes III (A), then moves to PD and D, followed by a final resolution to major tonic in the major mode.

EXAMPLE 21.1

Mascagni, “A casa amici” (“Homeward, friends”), Cavalleria Rusticana, scene 9 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1

Or che Now that

le ti hap - pi

zia ness

-

ras se re na brigh - tens o - ur

F: 6

3

3

sen za in du gio cor

riam.

straight a-way let’s hurry home.

3

3

gli a ni mi, hearts,

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Chapter 21 Modal Mixture

EXAMPLE 21.1 (continued) 11

a tempo

A ca sa, Let’s go home!

a ca sa, Let’s go home,

a mi dear friends,

che,

E

A

a tempo

m.s.

f

D 63

f

16

o ve ci a spet Where our men

ta no

i no stri are wait-ing

spo for

si, an diam; us; hurry up;

g 43

The Mascagni excerpt is quite remarkable in its tonal plan. Although it begins and ends in F major, a significant portion of the music behaves as though written in F minor. This technique of borrowing harmonies from the parallel mode is called modal mixture (sometimes known simply as mixture). We have already encountered two instances of modal mixture. The first occurred as the “Picardy third,” the cadence seen in minor-mode works that raises 3 to end on a major chord. A second instance arose through the use of the fully diminished seventh chord in the major mode, which had 6 as its seventh. Although harmonies may be borrowed from either the parallel major or minor, it is much more common for elements of the minor mode to be imported into the major mode. A quick review of the possible pitch material in the major and minor modes reveals why: In the minor mode, 6 and 7 each have two forms, depending on whether the melodic line ascends or descends. Consequently, the importation of natural 6 into a minor piece results

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THE COMPLETE MUSICIAN

from good voice leading and is not surprising. By contrast, the major mode does not include the altered forms of 3, 6, and 7; thus, if a musical passage is forging ahead in a major key but then introduces 6, the effect can be quite shocking.

A LT E R E D PR E - D OM I N A N T H A R MO N I E S : i i° A N D i v The most common scale degree involved in modal mixture is 6. There are four reasons why this is so: 1. 6 is least likely to undermine the integrity of the home key and mode. 2. Lowering 6 permits a strong half-step motion to the dominant. 3. Modal mixture invoked on 6 colors all PD harmonies. 4. 6 is the only scale degree outside of the tonic triad that can be consonantly supported by a harmony with 1 in the bass. Therefore, it is a component of the contrapuntal 5–6 motion that figures prominently in music. Example 21.2 shows how 6 which is drawn from the parallel minor, alters the most common pre-dominants, ii, ii7, and IV; the supertonic harmony becomes a diminished triad (ii°), ii7 becomes a half-diminished seventh, and the subdominant becomes a minor triad (iv). This type of chromatic alteration—which changes the quality of a chord but does not alter its root—is called melodic mixture. The labeling of chords to reflect melodic mixture is easy: You label the chord as if it were in a minor key.

EXAMPLE 21.2 Mixture Applied to Pre-Dominant Harmonies

C:

ii

ii

7

iv

Application: Musical Effects of Melodic Mixture We now explore the musical contexts for mixture chords. Listen to Example 21.3, and focus on the downbeat of m. 3, where mixture appears as the PD seventh chord incorporates 6 to become iiø7. One way to view this melodic mixture is to interpret the A in the voice—a heartbreaking cry—as a surprising foreign tone to C major. When A enters the melody in m. 3, it has a highly poetic function. Schumann is able to underscore the speaker’s pain (“I bear no grudge, even if my heart breaks”) by introducing dissonance through modal mixture. The jarring entrance of the A shatters the major mode, just as the poet’s heart (“Herz”) is broken. Schumann leads the phrase to its high point on the word heart, extending the word for most of m. 3. The A continues to intensify the pain by forming an even more dissonant minor ninth when the A is sustained over the dominant (G).

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Chapter 21 Modal Mixture

EXAMPLE 21.3 Schumann, “Ich grolle nicht” (“I bear no grudge”), Dichterliebe, op. 48, no. 7 STR EA MING AUDIO

Nicht zu schnell

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Ich grol le nicht, I bear no grudge

und wenn das and when the

Herz heart

A

C:

IV 6

I

IV

auch bricht, breaks,

A

ii

7

G

V7

I

Finally, melodic mixture harmonies work very well in contrapuntal expansions of the tonic, especially as embedded phrase models (EPMs), shown in Example 21.4.

EXAMPLE 21.4 Mixture and EPMs

C:

I T

(ii

V 42 ) I 6 (EPM) 6 5

I T

(ii 24 V65 ) I (EPM)

I 6 (iv vii 65) I (EPM) T

A LT E R E D S U B M E DI A N T H A R MO N Y: V I In melodic mixture 6 appears as the third or the fifth of a mixture chord. A different situation occurs when 6 appears as the root of a mixture chord. In these cases, the root of the chord has been shifted down from its usual position. We describe this as harmonic mixture and write roman numerals to reflect the change in the root. In Example 21.5 the A-major chord, with 6 as the root, is analyzed as a VI chord. Take a moment to examine the nomenclature for harmonic mixture (Example 21.5). Notice that the lowered root of the chord is indicated by a flat sign placed before the roman numeral. If the root (6) were the only altered pitch in the submediant chord, however, the resulting sonority would be a dissonant augmented triad (e.g., in C major,

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EXAMPLE 21.5 Common Contexts for VI STR EA MING AUDIO

A.

C:

B.

I

VI

iv

Arpeggiation

V7

I

I

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C.

VI

ii

6

V7

I

Descending fifths

I

V7

VI

ii

6 5

V 64

5 3

I

Deceptive Descending fifths

A–C–E), an unstable chord that common-practice composers never used as an independent harmony. Therefore, mixture is also applied to 3 in order to produce a consonant major triad on VI (just as it is in minor). We use the generic “VI” to refer to all major triads built on the lowered form of 6 and when generally describing the chord, even if a natural, rather than a flat, is used to notate the chord (e.g., in A major, the VI chord is built on F, not F). Despite its new roman numeral and chromatic inflection, VI continues to function as a submediant chord. 1. It participates in descending arpeggiations (Example 21.5A). 2. It participates in descending-fifth motions (Example 21.5B). 3. It precedes the dominant as a PD chord. 4. It follows the dominant (and substitutes for the tonic chord) in deceptive motions (Example 21.5C). 5. Because VI lies a half step away from the dominant, composers often take advantage of this proximity by using VI motivically as a dramatic upper neighbor that extends V.

A LT E R E D T ON IC H A R MON Y: i In addition to being part of VI, 3 creates melodic mixture in altered tonic harmonies. Eighteenth-century composers were keenly aware of the ambiguity that can result from making a major tonic minor. Because this modal juxtaposition calls the mode of an entire piece into question, a minor tonic is more often only implied rather than literally stated. For example, in Example 21.6, the long chromatic line—which extends the dominant (before it returns to the tonic) and includes F—implies the parallel mode, D minor. Despite this destabilizing effect, some eighteenth-century composers—including not only Bach but also Classical composers such as Haydn and Mozart—invoked modal mixture on the tonic. By the nineteenth century, some composers (such as Schubert) began to saturate their major-mode pieces with elements of the minor to such a degree that the

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Chapter 21 Modal Mixture

EXAMPLE 21.6 Mozart, Menuett in D major, K. 94 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

3

3

3

9

D: 17

HC

HC

implies D major

implies D minor

V

3 (

) ( )

( (

( )

(

)

)

(

)

)

( )

back to D major

24 major and minor keys seem to have fused into 12 major–minor keys. For example, it would seem impossible to tell if a piece were in D major or D minor if it had equal numbers of Fs/Fs and Bs/Bs; you could only be sure it was in D. Listen to Example 21.7 and note how the key of F major is pervaded with elements of F minor, including a tonicization of III (A).

EXAMPLE 21.7 Schubert, “Schwanengesang” (“Swan Song”), op. 23, no. 3, D. 744 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Sehr langsam (Molto adagio)

Wie klag’ ich’s aus, How can I lament,

F:

i

I

i

das the

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THE COMPLETE MUSICIAN

EXAMPLE 21.7 (continued)

6

Ster be ge fühl, feeling of death

das that

auf lö send durch die Glie der rinnt? flows, dissolving through my limbs?

wie sing’ ich’s aus, How shall I express,

V 86

III

das

7 5 3

4

A LT E R E D M E DI A N T H A R MON Y: I I I Just as VI arose from harmonic mixture, so too does the III chord, which has 3 as its root. The III chord also borrows 7 to create a consonant major triad. As Example 21.8 shows, III continues to function as a mediant chord. 1. It divides the fifth between I and V into two smaller thirds (Example 21.8A). 2. It is a bridge between T and PD (Example 21.8B and D). 3. It participates in descending-fifths motion (Example 21.7C), although less often than the diatonic iii chord. 4. It is a PD chord (Example 21.8A and E).

EXAMPLE 21.8 Common Contexts for III A.

B.

I

III

V7

I

I

T

PD

D

T

T

III

ii

6

PD

V7

I

D

T

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Chapter 21 Modal Mixture

EXAMPLE 21.8 (continued) C.

D.

I

III

VI

ii

6 5

V

I

I

V 43

III

ii

6

V7

I

D

T

(substitute for I 6 ) T

PD

D

E.

T

T

PD

F.

I

III

V 43

I

I

T

PD

D

T

T

V/ III

III

ii 6

V

PD

D

5. It can be preceded by its dominant (in minor keys, V/III leads to III; in major keys, this progression becomes V/III to III) (Example 21.8F). 6. It also is a substitute for I6 (although not nearly as common as diatonic iii, given that 3 is lowered in III; see Example 21.8D).

VOIC E L E A DI N G F OR M I X T U R E H A R MO N I E S The following guidelines restate and develop the rules we used when writing applied chords. • Avoid doubling a chromatically altered tone unless it is the root of a chord (as in VI). • Since 6 will be either a neighbor tone (5–6–5) or a descending passing tone (6–6–5), prepare and resolve it by step motion. Keeping the chromatic line 6–6–5 in a single voice will help avoid cross relations. • Once you introduce VI, iv, or ii°, continue to use mixture chords until you reach the dominant function. This is because 6 possesses such a powerful drive to 5 that any intrusion of the diatonic 6 would not only create a jarring cross relation but also ruin the drive to the dominant (Example 21.9).

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EXAMPLE 21.9 Part Writing Mixture Chords A.

B. avoid

good

?

C:

I

VI

ii 6

V7

I

I

VI

ii

6

V7

I

EX ERCISE INTER LUDE W R ITING

SOLVED/APP 5

WORKBOOK 1 Assignments 21.1–21.2

21.1 Complete the following tasks on a separate sheet of manuscript paper. Use a key signature. A. In the major keys of D, F, and A, write the following chords in four voices. Do not connect them to one another. VI III iv V7/VI V43/III iiø65 B. Write the following progressions in four voices and in your choice of meter. 1. In C major: I– VI–iv–V–I. Begin with 3 in the soprano. 2. In F major: I–iiø65 –V6–5 4–3 –I  3. In E major: I–IV–iv–V8–7–I 4. In G and E major: I–I6 –iv–I– III–iiø65 –V–I 5. In C and A major: I– VI–iv–vii° 7/V–V64 –6–53 – VI–iv6 –V8–7–I A NA LYSIS

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A.

21.2 Determine the locations and types of mixture harmonies in the following excerpts. Remember that not all chromatically altered chords result from mixture; some are applied chords. Mixture harmonies are independent chords that participate in the harmonic progression and usually carry a pre-dominant function. Applied harmonies, by contrast, function as dominants and thus merely point to more important chords that are tonicized. Provide a two-level harmonic analysis.

Chapter 21 Modal Mixture

B.

SOLVED/APP 5

C. J. S. Bach, “Christus, der ist mein Leben”

SOLVED/APP 5

D.

E. Mizzou Waltz

6

12

519

520

F.

THE COMPLETE MUSICIAN

Schubert, “Du bist die Ruh,” op. 59, no. 3

        



 



Lust.                                 von dei - ner

   

 

Dies

Au

-

  

 



gen - zelt,

von

dei





                        

-



nen

     

 

Glanz

al

-

           



 

lein

er

  -



hellt,

                                    f    cresc.                     

    

C H ROM AT IC S T E P W I S E B A S S DE S C E N T S

In Minor In Chapter 13 we encountered two types of stepwise bass descents leading to the dominant. Because there are two diatonic forms of 6 and 7 in minor, it is possible for this descent to be completely chromaticized (e.g., 1–7–7–6–6–5) in a minor piece, as shown in Example 21.10A, where Geminiani writes a fully chromatic descending bass line by using an applied chord (V42 of IV) that leads to major IV6.

In Major With modal mixture, we can import this powerful progression into major-mode pieces. Examples 21.10B and C illustrate two common settings. Example 21.10B shows a direct descent to V, and Example 21.10C shows an indirect descent to PD on 4 followed by the dominant. Note that the use of a passing minor v6 in Example 21.10C leads to the predominant, which is expanded through a chromatic voice exchange (where the A/F in the IV6 chord are exchanged by the F/A in the iiø65 chord). Notice that chromatic voice exchanges necessarily involve strong cross relations. In such cases, intervening passing chords diminish any harshness that would have occurred in a direct succession of chromatic tones. It is best to avoid direct outer-voice cross relations; instead, keep the chromatic motion within a single voice (Example 21.10D).

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Chapter 21 Modal Mixture

EXAMPLE 21.10 The Chromaticized Step-Descent Bass A.

STR EA MING AUDIO

Geminiani, The Art of Playing the Violin, op. 9, no. 8

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Allegro

d:

6

4 2

6

T

6

4 3

6 4

PD

5

D

B.

C:

V42 /IV

V6

I

IV 6

T

iv 6

V

PD

D

C.

C:

V6 v6

I T

IV 6 iv 6 P 64

ii

6 5

PD

8 — 7 — 5 — 3

V 64

I

D

T

D. D1.

C:

D2.

IV

ii

4 3

8 – 7 6 – 5 – 3

V4

Avoid (cross relation)

I

IV

ii

6 5

V 64

8 – 7 – 5 – 3

Good

I

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PL AG A L MO T IO N S During the nineteenth century, the role of the dominant harmony gradually changed. For the most part, progressions still led to the tonic, but the dominant was often conspicuously absent from the cadence. This is due largely to nineteenth-century composers’ obsession with creating novel harmonic combinations, along with a general distaste for commonplace formulas such as V7–I. The growing acceptance of mixture harmonies partially accounts for this change, since their dramatic effects made them popular substitutes for the dominant. For example, iv leads convincingly to the dominant in both major and minor modes. However, because 6 strongly desires resolution by half step to 5, iv also can move directly to the tonic at a cadence (Example 21.11A). Plagal motion is not restricted to the subdominant. Both the supertonic and the submediant may move directly to tonic (Examples 21.11B and C). The cadence in Example 21.11B is commonly heard in popular music of the 1920s through the l950s and in films today, and therefore we can call it a Hollywood cadence. Notice that the Hollywood cadence is a chromatically embellished plagal cadence (IV–I); a contrapuntal 5–6 motion and mixture transform IV into iiø65 before the resolution to the tonic chord. We use the term plagal motion and the abbreviation “PL” at the second level to describe progressions in which harmonies other than the dominant lead to the tonic.

EXAMPLE 21.11 Common Plagal Motions A.

B.

IV

PL

iv

I

T

STR EA MING AUDIO

C.

IV

ii

IV 55

6 5

PL

6 5

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I

VI

I

T

PL

T

Brahms, Symphony no. 3 in F major, op. 90, Andante Notice both the absence of dominant harmony (even at the final cadence) and the prominence of mixture in Example 21.12. The passage begins with an expansion of tonic harmony through an upper-neighbor figure G–A–G in the alto. Although a repetition of this figure is expected in m. 3, VI instead participates in the upper-neighbor figure, now chromaticized (G–A–G). The mixture continues with VI and minor iv resolving to the tonic in a plagal cadence.

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Chapter 21 Modal Mixture

EXAMPLE 21.12 Brahms, Symphony no. 3 in F major, op. 90, Andante STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5

6

5

5

6

5

I

VI I

poco rit.

8va

più

C:

I IV I I

(EC)

IV

I

(EC)

VI

T

iv

I

PL

T

The prominence of the neighbor figure—in particular, the conflict between A and A—indicates that this gesture is motivic. In fact, this motive is not restricted to the slow movement of Brahms’s third symphony. The seeds are planted in the opening measures of the symphony’s first movement (Example 21.13). The A/A conflict is set into motion by the cross relation in mm. 1–2 and is intensified in mm. 3 by a voice exchange. This pitch-class conflict between A and A that takes place in the first and second movements

EXAMPLE 21.13 Brahms, Symphony no. 3 in F major, op. 90, Allegro con brio STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A

A

A

A

F

Allegro con brio

passionato

F 5

A

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seems especially important, given that the two movements are in different keys: A and A function as 3 and 3 in F major; in C major they are 6 and 6.

MODA L M I X T U R E , A PPL I E D C HOR D S , A N D O T H E R C H ROM AT IC M E DI A N T S Two tonal processes account for chromaticism in tonal music. 1. Tonicization is intimately associated with dominant function, as new chromatic tones act as temporary leading tones. 2. Modal mixture usually occurs within the pre-dominant function, as the new chromatic tones retain their scale degree function but in an altered form. Occasionally, composers use two other chromatic harmonies on 3 and 6 of a major key, but these harmonies are not products of tonicization or modal mixture. The first is a major mediant chord (III) whose root is diatonic 3. Like diatonic iii and mixture III, III most often is part of a rising bass arpeggiation (I–III–V), which may include a PD (I–III–IV–V).

Grieg, “Morning” from Peer Gynt Suite, op. 46, no. 1

Look at Example 21.14A. The piece is in E major. Note that the G-major triad is not an applied chord (V/vi), but rather a self-standing harmony. The second chromatic harmony that one occasionally encounters is a major submediant chord (VI) whose root is the diatonic 6 (Example 21.14B). And, like vi and VI, VI most often leads to IV. Note that had VI led to ii, it would be better interpreted as V/ii rather than VI (e.g., in C major, VI [A major] leading to ii [D minor] would sound more like an applied chord than an independent harmony). That VI is an independent harmony is made clear by the behavior of C (in the alto): Rather than ascending to D, as it would had it functioned as an applied chord, it instead descends to C. Indeed, it is important in your analysis that you discern between these chords and applied dominant chords. For a final example, if you encounter a D-major harmony in B

EXAMPLE 21.14 Examples of III and VI STR EA MING AUDIO

A.

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Grieg, “Morning” from Peer Gynt Suite, op. 46, no. 1

5

E:

I

III

525

Chapter 21 Modal Mixture

EXAMPLE 21.14 (continued)

10

III

15

(as IV of G )

V

7

V

B.

C:

I

VI

IV

V7

I

major, you must determine whether it is the applied V/vi or the chromatic III chord. In Example 21.15A, D major functions as a chromatic mediant chord (III), leading to the PD ii6 chord. In Example 21.15B, D major is V/vi, an applied dominant chord leading to G minor (vi).

EXAMPLE 21.15 III Versus V/vi A.

B :

*

I

III

B.

ii 6

V

I

I

*

V/vi

vi

ii 6

V

I

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S U M M A R Y OF T H I R D R E L AT IO N S The major tonic now has access to three sets of third relations: to the diatonic upper and lower thirds (iii, vi), to the raised chromatic thirds (III, VI), and to the lowered chromatic thirds resulting from modal mixture (III, VI). Notice that the minor tonic’s options for third relations are very limited: A minor tonic will usually move only to its diatonic III and VI. Example 21.16 shows how the submediant and mediant harmonies fit into the common-practice tonal scheme. Upper thirds lead to 5 through arpeggiation, and lower thirds lead to 4 through arpeggiation.

EXAMPLE 21.16 Diatonic and Chromatic Third Relations Above and Below the Tonic V

III

iii

I

VI

III

i

vi

VI

IV / iv

Modal mixture plays a central role in tonal music—one that is much more varied than merely coloring harmonies for musical contrast. When paired with their diatonic counterparts, mixture chords present the potential for powerful musical conflicts that are often dramatically worked out over the course of a work. The complex workings of chromatic pitches became a critical feature of nineteenthcentury compositions. Through modal mixture, a chromatic pitch may appear early and at the surface of a work. As the work progresses, the mixture accrues significance and evolves until it participates in the deepest levels of musical structure.

Chapter 21 Modal Mixture

527

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 21.3–21.4

21.3 Analyze the following examples, which illustrate plagal motions and other chromatic chords. A.

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SOLVED/APP 5

B.

C. “Heartfelt Greeting Card” What type of period is this?

5

9

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THE COMPLETE MUSICIAN

13

SOLVED/APP 5

D. Chopin, Nocturne in C minor, op. 48, no. 1 29

E. Beethoven, Piano Trio no. 5 in D major, “Ghost,” op. 70, no. 1, Presto Presto

5

cresc.

Presto

cresc.

cresc.

COMPOSITION

SOLVED/APP 5

21.4 Complete the following tasks in four-voice chorale style (choose a meter) on a separate sheet of manuscript paper. Analyze; then play your solutions on the keyboard. A. In D major, write a progression that expands tonic with a mixture chord, includes two suspensions, and incorporates VI. B. In A major, write a progression that contains two short phrases that create a PIP, includes iiø65 in the first phrase and iv in the second phrase, and includes an applied chord in each phrase. C. Given an F-major triad, use it correctly within progressions in the keys of B  major, D minor, D major, and A major. D. In E major, write a progression that includes a chromatic step-descent bass that leads to iv. Close with a PAC.

Chapter 21 Modal Mixture

T ER MS A ND CONCEP TS • chromatic voice exchange • Hollywood cadence • mixture • harmonic mixture • melodic mixture • modal mixture • plagal relations

CH A PTER R EV IEW 1. Modal mixture borrows harmonies from the: a. parallel mode

b. relative mode

2. Which scale degree is most often altered in modal mixture?

3. Melodic mixture changes the [quality/root] of a chord but does not alter its [quality/root].

4. In contrast, harmonic mixture alters the [quality/root] of a chord.

5. Summarize the guidelines for “Voice Leading for Mixture Harmonies.”

6. How does a chromatic voice exchange differ from a regular (diatonic) voice exchange?

7. The Hollywood cadence applies modal mixture to which familiar cadence?

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8. Tonicization adds temporary leading tones, and is therefore most often linked with which of the three harmonic functions? a. tonic

b. predominant

c. dominant

9. In contrast to tonicization, modal mixture is most often linked with which function?

10. In one sentence, describe the difference in function between a chromatic III chord and V/vi, based on the chord that comes after each one.

C H A P T E R 22

Expansion of Modal Mixture Harmonies: Chromatic Modulation and the German Lied

OV E RV I E W

You learned in Chapters 18 and 19 that tonicizations as small as two chords can be expanded and generate full-scale modulations that occupy dozens of measures. Mixture harmonies also are often tonicized to the degree that they can control extensive spans of the music, becoming structural elements in a piece. We will first examine how this occurred in nineteenth century instrumental music. We will then explore a genre of music, the German art song (Lied), which arose at the same time that modal mixture became a vehicle for communicating images of the poetic text. CHAPTER OUTLINE Chromatic Pivot-Chord Modulations................................................................... 532 Analytical Interlude: Schubert’s Waltz in F Major............................................ 534 Writing Chromatic Modulations ........................................................................ 536 Unprepared and Common-Tone Chromatic Modulations ............................. 537 Schubert, Sonata in B major, op. posth., D. 960, Molto moderato ............... 539 Analytical Challenges ................................................................................................ 542 (continued)

531

532

THE COMPLETE MUSICIAN

Modal Mixture and the German Lied ................................................................... 543 Schubert “Lachen und Weinen,” D. 777, and “Die liebe Farbe” and “Die böse Farbe” from Die schöne Müllerin .......................................... 543 Analytical Interlude: Schumann’s “Waldesgesprach” from Liederkreis, op. 39 ................................................................................... 547 Analytical Payoff: The Dramatic Role of VI .............................................552 Terms and Concepts ................................................................................................... 552 Chapter Review ........................................................................................................... 552

CHAPTER 21 INTRODUCED THE concept of mixture, and presented examples in which the mixture sonorities lasted only a moment or so and served to color a progression. Yet surely modal mixture can be extended for more than a single chord. Remember the Mascagni example (Example 21.1), in which F minor intruded for several measures. Think back also to the discussion of applied chords versus mixture, which showed that when an applied dominant precedes a mixture chord, the two together serve as a mini-tonicization of a chromatic harmony. In this chapter, we explore chromatic modulations. This is based on the assumption that VI and III are the most commonly tonicized chromatic harmonies in eighteenthand nineteenth-century music. Composers less often tonicize VI (e.g., C major to A major) and III (e.g., C major to E major), but we consider these relations as well. We explore first the means by which composers move smoothly from diatonic harmonies to expanded chromatic harmonies within progressions, then learn how chromatic modulations function within the harmonic progressions of entire works.

C H ROM AT IC PI VO T- C HOR D MODU L AT IO N S In order to move smoothly from one key area to another, composers usually employ a pivot harmony that is common to both keys. When searching for a suitable pivot for chromatic modulation, however, there are no triads common to both keys. For example, there are no chords in common between C major and A (VI; see Example 22.1). However, the knowledge that a major key often borrows from its parallel minor lets us reenvision our move from C major as one from C major/minor to A major (Example 22.2). Permitting modal mixture to enter into the equation causes four potential pivot chords to emerge in Example 22.2. We can formulate the following rule for chromatic pivotchord modulations: In a modulation to a chromatic key that results from modal mixture (such as III or VI), the pivot chord must be a mixture chord in the original key. This rule holds so consistently for music of the nineteenth century that the presence of modal mixture—particularly of the tonic—often signals an upcoming tonicization of a chromatic key. This is true because, owing to the modal shift, the tonic loses its anchoring power and instead begins to act as a pre-dominant to an upcoming VI or III. Listen to Example 22.3A and note how the modal shift from E major (I) to E minor (i) nicely

533

Chapter 22 Expansion of Modal Mixture Harmonies

Absence of Common Chords Between C and A 

EXAMPLE 22.1 triads in C major:

I

ii

iii

IV

V

vi

vii

V

vi

vii

I

ii

triads in A major:

iii

IV

EXAMPLE 22.2 Common Chords Between C Major/Minor and A  major: I

ii

iii

IV

V

vi

vii

i

ii

III

iv

v

VI

VII

iii

IV

V

vi

vii

I

ii

triads in C:

minor:

triads in A major:

EXAMPLE 22.3

Chromatic Third Modulation (E → C) Through Modal Mixture STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

E:

I

V 43

I

V 43

I

i

V 43

i VI: iii (C)

I

vi

ii 6

V7

I

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THE COMPLETE MUSICIAN

prepares the motion from E major to C major (VI). The E-minor chord functions as iii in C major and as a bridge that connects the two distantly related keys. Now listen to Example 22.3B to see how Beethoven artfully uses this very same harmonic progression in his E-major piano sonata, considerably expanding it.

EXAMPLE 22.3 (continued) B.

Beethoven, Piano Sonata no. 27 in E minor, op. 90, Nicht zu geschwind und sehr singbar vorzutragen (To be played not too fast and yet very songfully) 97

cresc.

cresc.

E: 102

cresc.

I

cresc. poco a poco

i

i

107

(cresc.)

VI: (C)

i iii

V7

PD

112

dim.

V7

3

I

3

3

V 43

3

I6

3

ii 6

3

3

vii

7

/V V 64

3

5 3

Analytical Interlude: Schubert’s Waltz in F Major Listen to Example 22.4 and determine the following: 1. Which chromatic harmony is the goal of the modulation: III or VI? 2. What is the pivot chord used to change to the chromatic key? 3. When does the original key return? 4. What is the function of the chromatic modulation in the overall harmonic plan of the work?

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Chapter 22 Expansion of Modal Mixture Harmonies

EXAMPLE 22.4

Schubert, Waltz in F major, 36 Original Dances, D. 365, no. 33 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

F:

I

7

i III: (A ) vi

14

20

F: V 7 26

I

After an alternation of I and V in F major, the major tonic is converted to minor in m. 13, where it functions as a pivot leading to A major (III). The original key returns with a V7 chord in m. 25. Given that chromatic modulation participates in the overall harmonic progression of a passage, the tonicized III is actually part of a large tonal arpeggiation: I–III–V7–I. A motive that appears early in a work and on the music’s surface may reappear later at a deeper level. Even the most common progressions or fleeting nonchord tones can provide

536

THE COMPLETE MUSICIAN

the means for later development. This is just the case in Schubert’s Waltz, which opens with a melody projecting the upper-neighbor motive C–D–C. The same upper-neighbor motive is restated in the parallel minor (C–D–C at mm. 13–14) to prepare the entrance of III. Notice also that the neighbor motion has been transferred to the harmonic domain at mm. 13–14 where the bass F falls to E.

Writing Chromatic Modulations There are no new part-writing rules, but keep the following in mind: 1. Add the necessary accidentals in the new key, or, rather than writing many accidentals for several measures, simply add a new key signature. 2. The pivot chord must always result from modal mixture. Often, it is effective to use minor i (as vi or iii in the new key). 3. Try to create a seamless musical process by expanding the PD in the new key, either through inversions or a brief tonicization. This postpones the cadence in the new key and therefore allows the listener to become acclimated to the new tonal environment. Study the following model analysis (Example 22.5). • C major is established with an EPM. Note that the mixture ii°42 chord with its A—prepares for the upcoming tonicization of VI. • The pivot chord is a mixture chord in the original key (iv6 in C major) and a diatonic chord in the new key (vi6 in A major). • In the new key, the submediant is elaborated (with a V43/vi chord) in order to postpone the cadence. • This is followed by the cadential dominant and tonic, with a PAC in A major.

EXAMPLE 22.5

C:

I T

ii

4 2

V 65

Composing a Modulation from C → A 

I

V42 /iv iv 6 PD A : vi 6 V 43/vi ( VI) (T)

vi

ii 6

V 64

PD

D

– 5 – 3

I T

537

Chapter 22 Expansion of Modal Mixture Harmonies

EX ERCISE INTER LUDE 22.1 Answer the following questions. WORKBOOK 1 Assignments 22.1–22.2

1. Given the following major-key modulations, what pivot chords are possible? (Use modal mixture in the first key.) a. D to F ( III) b. G to B  ( III) c. E  to C  ( VI) d. A to F ( VI) 2. Complete the following chart.

SOLVED/APP 5

In what key is the triad . . . triads

I

D major

D major

III B major

IV

V

VI

A major

G major

F major

C major E major B major F major A major

22.2 The following short progressions end with a chromatic pivot chord. To which chromatic keys could the chord lead? Choose one of your solutions for each example, and write a convincing bass voice that secures the new chromatic key. SOLVED/APP 5

Example: C major: I–I6 –iv Answer: iv in C major can be vi in A  major ( VI) or ii in E  major ( III). D major: I–V6 –I–V7– VI F major: I– VI–V43/iv–iv A major: I–V6/III– III

U N PR E PA R E D A N D C OM MON -T ON E C H ROM AT IC MODU L AT ION S Unlike tonicizations achieved smoothly by means of a harmony that simultaneously functions in multiple harmonic contexts, unprepared chromatic modulations (sometimes referred to as direct modulations) occur without the aid of a pivot chord. Listen for the unprepared chromatic modulation in Example 22.6. The opening 11 measures could be interpreted in two ways: as a single phrase that is divided into subphrases

538

THE COMPLETE MUSICIAN

(I–V7, V7–I), or as a two-phrase parallel continuous period. After a grand pause in m. 12, the opening theme abruptly enters in A (VI).

EXAMPLE 22.6

Haydn, String Quartet in C major, op. 54, no. 2, Hob III.58, Vivace STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

G.P. Violino I G.P. Violino II G.P. Viola G.P. Violoncello

C:

V7

I

7

G.P.

G.P.

G.P.

G.P.

V7

I

13

V7

I VI

I

539

Chapter 22 Expansion of Modal Mixture Harmonies

Most chromatic modulations are not as abrupt as that of Example 22.6. Often the composer will communicate by rhetorical means that a chromatic departure is approaching by providing the listener with a thread that connects the two keys. Listen to Example 22.7, in which Schubert juxtaposes D major (I) with B major (VI). Even though there is no hint of the upcoming motion to VI, the pitch D in the violins is common to both keys: It is heard in retrospect as 1 of D major and is reinterpreted as 3 in B major. This type of modulation, which usually links two nondiatonic keys lying a third above or below one another, is called a chromatic common-tone modulation.

EXAMPLE 22.7 Schubert, String Quartet no. 3 in B  major, D. 36, Menuetto-Trio STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Trio

Schubert, Sonata in B  major, op. posth., D. 960, Molto moderato Both chromatic common-tone modulations and motivic development are common in nineteenth-century music. Listen to Example 22.8, the opening of Schubert’s last piano sonata, written just weeks before his untimely death in 1828 at the age of 31. Identify the location and type of chromatic modulation. The opening tune repeats in the key of G major (VI) in m. 20, and it returns to the tonic in mm. 36–37. The chromatic common-tone

540

THE COMPLETE MUSICIAN

modulation in mm. 18–20 is surprising; a written-out trill (in the bass) is all that separates I and VI (except for C and A, which help to prepare G major). The written-out trill was in turn prepared by the preceding mysterious trill on 6 in m. 8. Thus, the G seed that Schubert planted in the trill germinates when the trill is written out in m. 19 and blossoms in the modulation in mm. 20–35. When Schubert boldly heads the tonicized G major back to B in mm. 36–37, the listener is transported back to the initial measures of the piece and the moment when the neighbor motive, 6–5, was born.

EXAMPLE 22.8

Schubert, Sonata in B  major, op. posth., D. 960, Molto moderato STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

legato

5

10

14

19

Chapter 22 Expansion of Modal Mixture Harmonies

EXAMPLE 22.8

(continued)

21

24

27

30

33

3

3

36 36

cresc.

augmented sixth chord augmented sixth chord

541

542

THE COMPLETE MUSICIAN

A N A LY T IC A L C H A L L E N G E S Some chromatic modulations pose interpretive challenges. Listen to Example 22.9. The trio begins in D major, with its first section closing strongly with a PAC in m. 58. A sudden shift to the parallel minor (m. 59) is followed by a section in A major. How should we interpret the modulation to A major (V)? Consider Schubert’s dilemma. He obviously felt that this piece in D major should modulate to VI, which is B major—with a painful nine-flat key signature. He might have considered tonicizing some other scale degree, but his artistic sensibilities and the piece’s unity demanded that the music move to VI. What to do? For over two centuries composers have employed a simple and elegant solution to this problem: write in the

EXAMPLE 22.9 Schubert Impromptu in A , from Four Impromptus, D. 935, Trio STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Trio 3

3

D : 51

3

3

3

3

3

3

3

3

3

3

I

3

3

3

3

3

3

55

3

3

3

3

decresc.

3

3

3

3

3

3

3

3

3

3

3

3

3

3

F will become E

59 3

i

3

3

3

3

3

3

3

3

3

3

3

543

Chapter 22 Expansion of Modal Mixture Harmonies

EXAMPLE 22.9 (continued) 8va

63

3

3

3

3

3

3

3

3

3

3

3

cresc.

3

i (D ) VI: iii (C ) (A) 67

8

3

vi

3

3

3

V

3

3

3

3

3

3

3

3

3

3

3

I

enharmonically equivalent key. So, instead of composing a section of music in B major, Schubert wrote it in A major—a much easier key to navigate. Therefore, we interpret the relationship between D major and A major as I going  to VI (and not V). This is confirmed when the diatonic dominant (A major) returns: A remains a structural pillar and is never altered. We have a chromatic pivot-chord modulation: The shift to D minor in m. 59 is a pivot that links D to its VI key.

MODA L M I X T U R E A N D T H E G E R M A N L I E D We now examine songs written by two of the most important composers of the nineteenth century, Franz Schubert and Robert Schumann, to see how modal mixture functions in larger contexts. We will also explore how composers control the interaction of music and poetry to project underlying poetic meaning in their vocal compositions.

Schubert “Lachen und Weinen” D. 777, and “Die liebe Farbe” and Die böse Farbe” from Die schöne Müllerin In nineteenth-century Germany and Austria, the genre of song (Lied, plural Lieder) became an important laboratory for experimentation. The idea was to develop musically expressive forces capable of meeting the needs of communicating the emotionally rich poetry of the time. Modal mixture was often at the heart of these innovations. For example, the juxtaposition of mixture tones and harmonies against diatonic ones was almost always a sign of emotional conflicts, tensions, or contradictions. Consider the role of 6 (in both raised and lowered forms) in Schubert’s song “Lachen und Weinen” (“Laughter and Tears”) (Example 22.10). Notice that each form of 6 is highlighted within its respective

544

THE COMPLETE MUSICIAN

mode, but also listen to how 6 occurs in the major tonic, where it is starkly juxtaposed with its diatonic counterpart. The shift to the parallel minor prepares the listener for the substitution of 6 for 6 at m. 25, where the new expressive tone underscores the melancholy text “and why I weep now.” The specific placement of the F–E sigh, where the upper note is a dissonant ninth over the bass, strongly highlights the word weep. The next development of F (at m. 27) transforms the pitch 6 into the chord VI. Example 22.10 shows where a VI chord captures the protagonist’s wonder at love’s ability to arouse conflicting feelings of pain at twilight and joy at daybreak by means of a strange and wondrous-sounding chromatic harmony. In summary, the diatonic and mixed forms of 6 represent these two sides of his emotions. Both forms of 6 are neighbors to 5; that they share a common genesis in 5 may be analogous to the fact that love is the source of both his pain and his joy. Schubert’s song cycle Die schöne Müllerin furnishes another example of the role that mixture plays in projecting a poetic text. The drama begins with a roaming youth’s discovery of a brook that leads him to a mill and ultimately to a young woman with whom he falls in love. As he begins to press his affections, he finds that she does not love him but rather someone else. What follows is the youth’s downward spiral, characterized by anger, jealousy, bitterness, and finally, when nothing can quench his pain, suicide. In the second

EXAMPLE 22.10 Schubert, “Lachen und Weinen” (“Laughter and Tears”), D. 777 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Etwas geschwind

9

La

chen und Wei

Laughter

and

nen zu

jeg

li cher Stun

tears

at

any

hour

de

ruht

bei der

lieb

rest

on

love

auf so

545

Chapter 22 Expansion of Modal Mixture Harmonies

EXAMPLE 22.10 (continued) 15

man in

cher lei Grun so

many

de.

Mor

ways

In

gens the

lacht’ ich vor

morning

Lust;

I laugh with joy

22

und wa rum and why I

weep

ich nun now

wei

ne In

the

bei evening

decresc.

des A glow,

ben des Schei-ne

dim.

VI 31

a tempo

ist mir selb’ nicht be wusst, ist mir selb’ nicht be wusst. I myself

do

not

know.

half of the cycle, the young miller points to the fact that his gifts of green objects, such as the sash from his guitar, delighted her, and her delight—and with it her love—was only intensified as nature, in all of its green beauty, resounded in him. But with the entrance of the hunter, who symbolizes authority and physical power, the miller’s idyllic world comes crashing down about him. The woman is immediately drawn to the hunter, who is dressed in traditional green. The color is now poisoned for the miller, and, as he roams through the forest nature’s green only mocks him, providing a thorny reminder that his beloved’s affections are directed toward someone else. In the songs “Die

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THE COMPLETE MUSICIAN

EXAMPLE 22.11

Schubert, “Die liebe Farbe” (“The Beloved Color”) and “Die böse Farbe” (“The Evil Color”), from Die schöne Müllerin

Ziemlich geschwind

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

4

Ich möch I'd like

te zieh’n in die Welt hin aus, to go out into the world,

hin aus in die wei te Welt, into the wide world,

Etwas langsam

4

In In

Grün green

will will

ich I

mich

547

Chapter 22 Expansion of Modal Mixture Harmonies

EXAMPLE 22.11

(continued)

7

klei dress

den,

in in

grü green

ne

Thrä weeping

nen

wei willows

den:

liebe Farbe” (“The Beloved Color”) and “Die böse Farbe” (“The Evil Color”), modal mixture plays crucial roles in projecting the powerful feelings aroused by the color green (Example 22.11). In fact, vacillations between the major and the minor modes through modal mixture become an important musical metaphor for Schubert in conveying the young miller’s abrupt changes of mood.

Analytical Interlude: Schumann’s “Waldesgesprach” from Liederkreis, op. 39 Robert Schumann also used modal mixture to project poetic drama. In his song “Waldesgesprach” (“Forest Conversation”), from Liederkreis, op. 39 (Example 22.12), what appears at first as a simple chromatic tonicization is revealed through analysis to be an important dramatic moment. As the song gathers momentum, the motion to VI reverberates throughout, foreshadowing and directing the surprising turn of events that follows. In familiarizing yourself with this work start by reading the text carefully, and then listen to the song with the following questions in mind: 1. What musical techniques does Schumann employ in setting the scene of the forest? 2. How does Schumann differentiate the two characters musically? 3. What is the form of the song? 4. What is the relation of the chromatic tonicization to the overall key, and how does the composer secure the new key (i.e., is it prepared or unprepared)? The story begins traditionally enough: A horseman comes across a beautiful woman deep in the forest, and, after informing her of the dangers of the woods and extolling her beauty, he offers to guide her home. The unsettling chromatic departure to C major to herald the woman’s entrance is curious. This abrupt juxtaposition of E major and C major, coupled with the man’s inability to complete the final word of his phrase, heim (“home”), in his key rather than in her foreign key, not only enhances the strangeness of this woman, cloaking her in tonal mystery, but also plants the seeds for his later demise. The woman informs the man that she has been hurt in love before and by a hunter. Apparently, from her past unsuccessful encounters, she has now gained some sort of strength (intimating an otherworldly power) and warns the man that he does not know with whom (or what) he is dealing. She gives him one—and only one—chance to flee. Foolishly, the man stays and continues his

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THE COMPLETE MUSICIAN

flattery. But just as there was an abrupt shift in the first section, so too is there one here. As he realizes she is the infamous Lorelei (a demon in the form of a beautiful woman who lures men to their death), placid E major is thrown over by its parallel minor, the stark modal shift enhancing this terror-filled moment. In the final verse, the woman informs the man that he is ensnared and will never again leave the forest. He is hers. The introduction to the song captures an out-of-doors feeling with its sprightly triple meter. The simple alternation of tonic and dominant in the bass lends a folklike quality

EXAMPLE 22.12

Schumann, “Waldesgesprach,” from Liederkreis, op. 39, no. 3 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Es ist schon It is late,

6

spät,

11

es ist schon kalt, it is cold,

3

Wald? forest?

Der Wald ist lang, The forest is huge,

was reit’st why do

you

du ride

ein alone

sam durch den through the

3

du bist you are

al lein, alone,

du schö ne Braut, ich führ’ dich beautiful bride, I will lead you

549

Chapter 22 Expansion of Modal Mixture Harmonies

EXAMPLE 22.12

(continued)

15

heim! home!

Gross Great

ist der Män is the deceit

ner and

Trug guile

und List, of man,

vor

21

Schmerz pain

mein

Herz

ge

has

bro

chen ist,

wohl

irrt

das Wald horn

broken

my

the

horn

sounds

heart,

aug. 6th

V

27

her

und hin,

o

here

and there,

Oh flee!

aug. 6th

flieh’,

o

flieh’.

You do

du weisst not

know

nicht, wer ich bin. who

I am.

6

V (as IV/E)

ii 5

V

33

So reich ge So richly

schmückt ist Ross covered are horse

und and

Weib, so woman,

wun so

der schön, so wun der schön beautiful her

der

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THE COMPLETE MUSICIAN

EXAMPLE 22.12

(continued)

ritard.

39

Im tempo

ritard.

Im tempo 3

jun

ge Leib;

jetzt kenn’ ich dich, Gott steh mir bei,

young

body;

Now

I

du bist die He xe Lo re

know who you are—God save me!

lei!

You are the witch, Lorelei!

45

Du kennst mich wohl, Indeed you know me—from

du kennst rock's height,

mich wohl,

von ho hem

51

Stein schaut still

mein Schloss tief in den Rhein;

my

silently gazes deep into the Rhine.

castle

es

ist

schon spät,

It is late,

aug. 6th

es

ist

it is cold,

“V”

(P)

aug. 6th

schon

551

Chapter 22 Expansion of Modal Mixture Harmonies

EXAMPLE 22.12

(continued) ritard.

58

kalt,

kennst nim mer mehr aus die sem Wald, nim mer mehr, nim mer mehr aus die sem you

will

never leave

this

forest.

“V” ritard.

64

Wald.

to the song, while the syncopated upper voice of the left hand—with the emphasis on beat 2—creates a fifth drone and rhythmically suggests the feel of folk dances such as the mazurka and the polonaise. The lilting right hand also supports the rustic character of the introduction. In fact, the two-voice intervallic progression in the right hand with stepwise motion in the soprano (E–F–G) and leaps in the alto (G–B–E) is used by Schumann because of its connection with the sound of hunting horns. This trick of invoking the idea of the hunt has a double meaning in the song: Not only do we think immediately of the dense forest, its fauna, and the hunter’s horn, but we are also reminded of another meaning of the hunt—that of seduction. By the end of the poem, however, we discover that our original expectations are shattered as the roles of hunter and prey are reversed. The form of the song is dependent on the interaction of its two characters: A (he speaks)––B (she speaks)––A⬘ (he speaks)––B⬘ (she speaks)––Coda A number of musical features reinforce hearing the piece in this way: First, the piano interludes separate the sections; second, there is highly contrasting melodic, accompanimental, and tonal material in the B section. The motion from E major to VI, C major, powerfully separates the A and A⬘ sections from the B section. This motion to VI is quite surprising, yet, in retrospect, the listener realizes that it is prepared, in that the deceptive motion from V of E to VI turns the flatted submediant into the tonic.

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Analytical Payoff: The Dramatic Role of VI

WORKBOOK 1 Assignments 22.3–22.5

By virtue of its surprising arrival at m. 15 and its otherworldly sound, VI obviously plays an important role in creating mystery and distance. Its appearance, like a rock thrown into a pond, creates musical ripples that extend to the outer reaches of the song. This strange new harmony seems to characterize the speech of the unknown woman in the piece’s B section. But now let us turn to the moment in which he realizes who she is. The hunter begins his A⬘ section pretty much as his A began, seemingly oblivious to the woman’s warnings. But at the moment of the modal shift to E minor, the man’s tune moves in a new direction. His melody is strongly reminiscent of the Lorelei’s tune, with her ascending line G–A–B–C recurring in his ascending motion. The effect is more than simple association. The witch’s seductive powers have begun to permeate his being, and the decomposition of his melodic independence represents his loosening of will. On the other side, the modal shift from E major to E minor, which places the Lorelei’s key of C major within easy reach, further suggests that he is slipping into her tonal power. E minor is part of her tonal domain. It is diatonic to her C major, making his eventual abduction almost certain. The final step in his demise occurs in the Lorelei’s closing strophe. Her musical texture returns unchanged, save for one crucial alteration: It is recast in his key, E major. His tonal foundation of E major, a metaphor for his physical being, has now been secured by the Lorelei. Indeed, even his opening words, “Es ist schon spät, es ist schon kalt” (“it is late and cold”), are now possessed and sung ironically by the victor. It is clear that the man is ensnared in her forest arms, never to return home. That the postlude reprises the introduction—lilting, happy, and naive—shows that the forest returns to its placid and amiable state, but the Lorelei—like a Venus flytrap—awaits her next victim.

T ER MS A N D CONCEP TS • chromatic third relations • common-tone modulation • Lied, Lieder • prepared chromatic tonicization • text-music relation • unprepared chromatic tonicization

CH A PTER R EV IEW 1. In a modulation to a chromatic key that results from modal mixture, the pivot chord must be a mixture chord in the [original/new] key.

2. Summarize the guidelines for “Writing Chromatic Modulations.”

Chapter 22 Expansion of Modal Mixture Harmonies

553

3. Unprepared chromatic modulations, sometimes called ________________________, occur without the aid of a _______________________________________________________________.

4. Common-tone chromatic modulations usually link keys related by what interval?

5. How do composers often rewrite key signatures for keys with too many flats?

C H A P T E R 23

The Neapolitan Chord ( II) OV E RV I E W

In this chapter, we take up a special sonority, the Neapolitan chord. Aurally marked by its unusual construction, it often brings to the music a palpable gloom, even the connotation of death. The chord can easily function in a number of contexts, which, like other chromatic sonorities, involve tonicization. CHAPTER OUTLINE Characteristics, Effects, and Behavior of the Neapolitan Chord ................... 554 Writing the Neapolitan Chord ................................................................................ 556 Expanding II ............................................................................................................... 559 The Neapolitan Chord in Sequences ..................................................................... 562 The Neapolitan Chord as a Pivot Chord .............................................................. 562 Terms and Concepts ................................................................................................... 567 Chapter Review ........................................................................................................... 567

C H A R AC T E R I S T IC S , E F F E C T S , A N D B E H AV IOR OF T H E N E A P OL I TA N C HOR D Listen to the excerpt from one of Schubert’s songs in Example 23.1. The music divides clearly into three phrases, which are marked by cadence type. As you follow along, try to keep a running tally of particularly striking chromatic harmonies. Where are they, and what contributes to their novel sound? A new chromatic harmony first appears in m. 8 (and again in m. 16 and m. 25). We have seen previously that there are two main types of chromaticism: (1) applied chords, which alter the function (and roman numeral) of diatonic chords in order to tonicize other keys; and (2) mixture, which alters the quality of a diatonic chord but does not change its roman numeral or function. What 554

Chapter 23 The Neapolitan Chord ( II)

555

EXAMPLE 23.1 Schubert, “Der Müller und der Bach” (“The Miller and the Brook”), Die schöne Müllerin, D. 795, no. 19 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Mässig

(Der Müller)

Wo

ein treu es Her

Where

a

true

ze

heart

in

Lie

wastes

be ver geht, away

da

in love,

7

wel There

ken die Li lien auf wilt the lilies

je in

dem Beet; every bed;

da muss in die Wolk en der Voll mond Then into the clouds must the full moon go,

(PAC) 14

gehn, So

da mit sei ne Trä nen die Men schen nicht seh’n; that her tears Men do not see;

da hal

(HC)

22

Au shut

gen sich zu their eyes

und schluch zen und sin gen die see and sob and sing

to

le zur Ruh.

rest the soul.

(PAC)

ten die Eng lein die Then angels

556

THE COMPLETE MUSICIAN

kind of chord do we have here? The chord in m. 8 is a major triad; its quality suggests that it may be an applied chord. However, as such it would be the dominant of D (V of G minor), and we certainly have not encountered “V”! Clearly this is a pre-dominant function chord, with the bass C (4) and the pitch E (6) both pulling toward D (5). The A (2) is a chromatic pitch that substitutes for the diatonic A. As a result, instead of a ii°6 chord (C–E–A), we have a major triad in first inversion, a II6 chord (C–E–A). This chord, commonly called the Neapolitan chord, occurs: • more often in minor-mode pieces than in major-mode pieces (Example 23.2A). • usually occurs in first inversion in order to have a smooth bass motion to 5 rather than an awkward tritone leap from 2 to 5 (Example 23.2B). • in the major mode, both the supertonic and the submediant are lowered (2 and 6, respectively), as in Example 23.2C.

EXAMPLE 23.2 Common Neapolitan Contexts A.

B.

c:

i

II 6 V7 i

i

C.

II

V7 i

C:

A2

I

II 6 V 7 I

W R I T I N G T H E N E A P OL I TA N C HOR D • II6–V progressions will have a 2–7 motion in one of the upper voices—usually the soprano (Example 23.2A). • Double the bass, 4. (See Example 23.2A.) If necessary, double 6. • In minor, any chord that would precede ii°6 can also precede II6. • In major, the common chords before II6 are tonic (I) and mixture chords (III, VI, iv). When writing in major, avoid the augmented second that occurs between 3 and 2 (Example 23.2C). • The ultimate goal of the Neapolitan chord is to move to V. However, there are two common ways to move from II6 to V, both of which harmonize a passing 1 (Example 23.3).

Chapter 23 The Neapolitan Chord ( II)

557

EXAMPLE 23.3 Filling the Space Between 2 and 7 using 1 as Dissonant Passing Tone A. cad. 64 (P) 2

c:

1

II 6 V46

i

C. vii°7/V and cad. 64

B. vii°7/V (P) 7

2

– 5 – 3

i

1

(P) 7

II6 vii 7 V V

i

i

i

2

1

7

II 6

vii 7 V

V 64

– 5 – 3

i

EX ERCISE INTER LUDE A NA LYSIS 23.1 Provide a two-level roman numeral analysis for each of the following examples. To facilitate your chordal analysis, circle all embellishing tones in the melody.

WORKBOOK 1 Assignments 21.1–21.2

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Sample: Beethoven, Piano Sonata no. 14 in C  minor, “Moonlight,” op. 27, no. 2, Adagio 49

3

3

c :

V 43

i

3

3

3

V 65

i

LN

i

3

3

II 6

3

3

3

3

V7

i

D

T

(P) (i) T

UN

PD

3

558

THE COMPLETE MUSICIAN

SOLVED/APP 5

A. Beethoven, Bagatelle, op. 119, no. 9. Make a formal diagram.

7

14

B.

Chopin, Mazurka in C  minor, op. 30, no. 4, BI 105. Include in your discussion the underlying harmonic progression in the excerpt. 3 5

3

Chapter 23 The Neapolitan Chord ( II)

559

SOLVED/APP 5

Mussorgsky, “Bydlo” from Pictures at an Exhibition

C.

Sempre moderato pesante.

? # # # # 42 Π#

œ

? # # # # 42 œ # œ œœ œœ - œ? #### #

œœ œœ-

{ {

? ####

œ œœ -

# ‹œ #œ œ œ #‹ œœ œœ œœ œœ

œ J ‰

œ-

œ œ-

œ-

œ œ œ œ- œ-

- œ- œœ- œ

œ-

œœ œœ œ œ

œœ œœ œœ œœ œ œ œ œ

œœ œœ œœ œœ n œœ œœœ œ œ n œœ œœœ œ œ œœ œœ n œ œœ œœ œ œ œ œ nœ

œœ œœ œ œ

œ- ‰ J

œ œ œ J ‰

œ

œ œ

œ ‰ J

œœ œœ ‹ œ œœ œ œ ‹ œœ œ

œ œœ n œ œœ œœ œ n œœ œ

œœ œœ œ œ

E X PA N DI N G I I The Neapolitan chord is like any other consonant chord. It can be prolonged with a chordal leap in the bass (Example 23.4A), by tonicization (Example 23.4B and C), and by extended tonicization (Example 23.4D). Sometimes composers tonicize II merely by restating material up a half step—from I  to II. This procedure is common in middle-period Beethoven pieces, such as his String Quartet in E minor (Example 23.5). The root-position Neapolitan of mm. 6–7 occurs when the opening tune of mm. 3–4 is literally restated a half step higher in m. 6. Melodically, this presents an important motive, B–C, which is highlighted within mm. 3–6. The analysis shows that the pre-dominant still moves to dominant function and on to tonic, creating a large-scale i–II–V–i motion. Notice that two forms of the dominant appear: vii°7 is followed by V. The only two pitch classes involved in this subtle shift are C (6) and B (5), which can be heard as a melodic summary of the immediately preceding motion

EXAMPLE 23.4 Expanding II A. Chordal Leap Expands II

a:

i

6

II

6

V 64

– –

B. Tonicization Expands II

5 3

i

i

V/ II

II

6

V 64

– –

5 3

i

560

THE COMPLETE MUSICIAN

EXAMPLE 23.4

(continued)

C. Tonicization Expands II (in major)

A:

I

V 7/ II

6

II

V 64

– –

5 3

I

D. Extended Tonicization Expands II

V7 a: i

V

6

i

vii

6

i

6

I

vii

6

I6

IV

ii 6

V 24

I6 V

II

i

EXAMPLE 23.5 Beethoven, String Quartet no. 8 in E minor, op. 59, no. 2, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5

Violino I

Violino II

Viola

Violoncello

e:

i

II

Chapter 23 The Neapolitan Chord ( II)

561

EXAMPLE 23.5 (continued) 9

15

vii

(V65)

7

vii

V7

4 2

i

from tonic to the Neapolitan. Beethoven has therefore returned the upper-neighbor C to B, its point of origin. Listen to Example 23.6. The Neapolitan in m. 24 is contrapuntally prepared in the previous measure by the 5–6 motion from I; over the bass D/C, A moves to A (the

EXAMPLE 23.6 Chopin, Nocturne in B  minor, op. 9, no. 1 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

poco rallentando

21

5

6

V 65

D :I a tempo

24

cresc.

I

5 3

6 4

II

5 3

vii

4 3

/V

V7

I

562

THE COMPLETE MUSICIAN

enharmonic spelling of 6, B), creating a V65/II. When the Neapolitan arrives at the downbeat of m. 24, Chopin spells it enharmonically as D major rather than as E major. Chopin’s ppp dynamic marking at this moment helps the performer interpret this special harmonic coloration. The Neapolitan’s bass motion up to V is accomplished by the vii°43/V chord in m. 25; this chord is pivotal, for it sounds like a mixture coloring of the right-hand B in m. 24, yet the vii°43/V also leads to V 7 (A) as an applied chord.

T H E N E A P OL I TA N C HOR D I N S E QU E N C E S Look again at Example 23.6 and notice that the chords in m. 23, leading to the Neapolitan chord in m. 24, are identical to the way A2 (⫺3/⫹4) applied-chord sequences begin. Example 23.7A extends Chopin’s ascent, continuing the sequence to V. The use of II in the A2 (⫺3/⫹4) sequence is much more common in minor-mode works. A further bonus of incorporating the Neapolitan in sequences is that it allows for root-position 2 in minor pieces (Example 23.7B). (Remember, diatonic ii is diminished and cannot participate in applied sequences.)

EXAMPLE 23.7 The Neapolitan in A2 Sequences A.

In Major

I

D :

V

6

II

V

6

iii

V

6

IV

V

6

V

A2 (– 3/+4)

B.

In Minor

5

c: i

6

V6

5

II

6

5

6

V6

III

V6

iv

T H E N E A P OL I TA N C HOR D A S A PI VO T C HOR D The Neapolitan is an effective pivot chord when modulating to diatonic as well as chromatic keys. Example 23.8, in C minor, contains two statements of a D sonority. The D chord in m. 9 functions typically as a II6, leading to V. But when it returns in m. 23, it functions as a pivot that precipitates the modulation to A.

Chapter 23 The Neapolitan Chord ( II)

563

EXAMPLE 23.8 Schubert, String Quartet in C minor, “Quartettsatz,” D. 703 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Allegro assai Violino I Violino II Viola Violoncello c:

i

5

cresc.

cresc.

cresc.

cresc.

 II 6 9 11

V

iiȤ6

i

V7

20

dolce

II

6

VI: IV 6

V7

I

564

THE COMPLETE MUSICIAN

EX ERCISE INTER LUDE A NA LYSIS 23.2 The following excerpts illustrate expanded II. Provide a two-level analysis for each excerpt and a short paragraph that summarizes your analysis.

WORKBOOK 1 Assignments 23.3–23.4

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Sample: Chopin, Nocturne in C minor, op. 48, no. 1, BI 142 Lento m.v.

c:

5

i

6

V 65

i

ii

VI

T

6 5

PD

T 4 streo

V7

i

D

T

i

V7

ii 65

vi

V 64

ii

III (ARP)

5

v (BRD)

8

i

V 42

I6

V 65 II

PD

I

3

i V 65

i

D

T

Chapter 23 The Neapolitan Chord ( II)

565

Sample paragraph: Chopin’s C-minor Nocturne illustrates an extensive tonicization not only of II, but also of several diatonic harmonies. The nocturne opens with a descending-bass arpeggiation (C–A–F) that returns to tonic, followed by a balancing ascending arpeggiation (C–E–G), each member of which is tonicized. The descent from G to G (mm. 8–9) begins the Neapolitan’s expansion (m. 9). The G is harmonized as V42 of II, and it becomes a chromatic passing tone that connects G and the following F (m. 9), which is harmonized as II6. Root-position II follows its V65 chord in m. 10, ending the tonicization of II. The dominant (G) is secured in precisely the same way that II was: through chromatic passing tones that lead to V65 (D–C–B). Notice that this bass motion 2 to 7 is what usually takes place in the soprano when II in first inversion moves to V.

A. Beethoven, Piano Sonata no. 23 in F minor, “Appassionata,” op. 57, Allegro assai

5

10

14

poco ritardando

a tempo

566

THE COMPLETE MUSICIAN

B. Rachmaninoff, Prelude in G  minor, op. 32, no. 12 Be aware of the D  in the bass and the chord of which it is a part in m. 7. Allegro

rit.

3

meno mosso

ten.

dim.

5

accel.

a tempo

rit.

dim.

7

meno mosso

accel.

Chapter 23 The Neapolitan Chord ( II)

567

T ER MS A N D CONCEP TS • II, the Neapolitan chord

CH A PTER R EV IEW 1. The Neapolitan chord has which harmonic function? a. tonic

b. pre-dominant

c. dominant

2. In which inversion is the Neapolitan chord often found? Why?

3. Summarize the five guidelines under “Writing the Neapolitan Chord.”

4. In Chopin’s Nocturne in B minor, op. 9, no. 1, what kind of chord is used before the Neapolitan? a. pivot chord

b. applied dominant

c. cadential 64

5. True or False: The Neapolitan (II) is an effective pivot chord when modulating to diatonic as well as chromatic keys.

CH A PTER 24

The Augmented Sixth Chord OV E RV I E W

The augmented sixth chord is arguably the most important chromatic sonority. As a pre-dominant, the chord is known for its power to drive a phrase to the dominant. In addition, it possesses the chameleon-like ability to be transformed from a pre-dominant to a dominant function. CHAPTER OUTLINE Characteristics, Effects, and Behavior of the Augmented Sixth Chord ....... 569 Derivation of the Augmented Sixth Chord ....................................................... 570 Types of Augmented Sixth Chords......................................................................... 571 Writing Augmented Sixth Chords .......................................................................... 572 Augmented Sixth Chords in Major..................................................................... 573 Elided Resolution of the Augmented Sixth Chord ........................................... 573 ()VI and the Ger65 Chord .......................................................................................... 575 Augmented Sixth Chords as Part of PD Expansions ........................................ 575 Chromaticized Bass Descents .............................................................................. 577 Voice Exchange ...................................................................................................... 577 The German Diminished Third Chord .............................................................. 578 The Augmented Sixth Chord and Modulation: Reinforcement .................... 581 The Augmented Sixth Chord as Pivot in Modulations..................................... 583 Terms and Concepts ................................................................................................... 589 Chapter Review ........................................................................................................... 589 Summary of Part 6...................................................................................................... 591

568

569

Chapter 24 The Augmented Sixth Chord

C H A R AC T E R I S T IC S , DE R I VAT ION, A N D B E H AV IOR OF T H E AUG M E N T E D S I X T H C HOR D The two excerpts in Example 24.1 are from different style periods, yet they share several features. In terms of form and harmony, both divide into two subphrases and close with strong half cadences. Further, the pre-dominant harmony in both examples is the same: an altered iv6 chord. Indeed, we hear not a Phrygian cadence (iv6–V), but rather some chromatic version, where the diatonic major sixth above the bass is raised a half step to create the strongly directed interval of the augmented sixth (⫹6). The new half-step ascent (4–5) mirrors the bass’s half-step descent (6–5). We refer to such chromatic pre-dominants as augmented sixth chords because of the characteristic interval between the bass 6 and the upper-voice 4. Listen to both excerpts in Example 24.1, noting the striking sound of the augmented sixth chords.

EXAMPLE 24.1 STR EA MING AUDIO

A.

W W W.OUP.COM/US/LAITZ

Schubert, Waltz in G minor, Die letzte Walzer, op. 127, no. 12, D. 146

4 — 5

g:

6 — 5

HC

B.

Handel, “Since by Man Came Death,” Messiah, HWV 56 Grave

Soprano

Since Alto

8

a:

man

came

death,

since

by

man

came

by

man

came

death,

since

by

man

came

by

man

came

death,

since

by

man

by

man

came

death,

since

by

man

death,

death,

sost.

Since Bass

by

sost.

Since Tenor

5

4

sost.

came

death,

sost.

Since

came

death,

6

5

HC

570

THE COMPLETE MUSICIAN

Derivation of the Augmented Sixth Chord Example 24.2 demonstrates the derivation of the augmented sixth chord from the Phrygian cadence. Example 24.2A represents a traditional Phrygian half cadence. In Example 24.2B, the chromatic F fills the space between F and G. This passing motion creates an interval of an augmented sixth. Finally, Example 24.2C shows the augmented sixth chord as a harmonic entity, with no consonant preparation. Given that the augmented sixth chord also occurs in major, one might ask if it is an example of an applied chord or a mixture chord? To answer this question, consider the

EXAMPLE 24.2 Phrygian Cadence Generates the Augmented Sixth Chord A.

B.

c:

C.

4

5

4

6

5

6

4

5

4

5

5

6

5

EXAMPLE 24.3 Mixture ⴙ Applied Function ⴝ Augmented Sixth Chord A.

Diatonic progression using IV6

D:

C.

I

V 65

I

IV 6

V8

– 7

B. Mixture occurs, transforming major IV6 to minor iv6

I

Mixture occurs, transforming major IV6 to minor iv6

D:

I

V 65

I

vii 6 V

V8

– 7

I

D.

I

I

V 56

I

iv 6

V8

– 7

I

Merging of mixture (B) and tonicization (G) Create the Augmented Sixth Chord

V 65

I

+6

V8

– 7

I

571

Chapter 24 The Augmented Sixth Chord

diatonic progression in Example 24.3A. Then study the progression in Example 24.3B. There is a mixture iv6 chord in Example 24.3B, which introduces 6, a bass note that is a half step above 5. Compare Example 24.3A with 24.3C; the difference this time is in the chord’s function, with iv6 changed into the applied vii°6/V through the use of the soprano 4. Accordingly, the mixture iv6 uses 6 in the bass, and the applied vii°6/V uses 4 in the soprano. So how do we describe the augmented sixth chord that has both pitches (Example 24.3D)? It is the ultimate chromatic chord, combining mixture (bass 6) and tonicization (4) to create the augmented sixth that pushes toward the dominant. The augmented sixth chord is typically preceded by a tonic chord, a subdominant chord, (  )VI, or (  )III; it is almost always followed by V or the cadential 64 chord.

T Y PE S OF AUG M E N T E D S I X T H C HOR D S All augmented sixth chords have three basic components. 1. The bass is a half step above 5. a. In minor keys, the bass is the diatonic 6 and does not need an accidental. b. In major keys, the bass, natural 6, must be lowered a half step so that its distance from 5 is a half step. 2. One of the upper voices—often the soprano—is a half step below 5, on 4. 3. Another upper voice has the tonic, 1. We distinguish three types of augmented sixth chords, based on the pitch in the final upper voice (Example 24.4). We label augmented sixth chords using their “regional” names followed by their figured bass (without chromatic alterations). • If the final upper voice doubles 1, it creates an Italian augmented sixth chord, It6 (Example 24.4A). • If the voice is 2, it creates a French augmented sixth chord, Fr43 (Example 24.4C).

EXAMPLE 24.4 Common Types of Augmented Sixth Chords A. Italian

B. German

double

1

add

add

3

6 3

6 5 3

harmonic analysis: It 6

Ger 65

figured bass:

C. French

6 — 5 4 —

2

6 4 3

Fr 43

572

THE COMPLETE MUSICIAN

EXAMPLE 24.4 (continued) D. In Major

G:

IV 6

I

Ger

6 5

V 46

add 2 (rare)

E. In Major

add 3 (common)

5 3

G:

IV 6

I

Ger

4 3

V 46

5 3

• The German augmented sixth chord, Ger65, includes 3 in minor keys (Examples 24.4B). In major keys, this added pitch is 3 (Example 24.4D). When a Ger65 occurs in the major mode and leads to a cadential 64 with a major sixth above the bass, composers often notate 3 using the enharmonic equivalent 2 (Example 24.4E).

W R I T I N G AUG M E N T E D S I X T H C HOR D S The voice leading after an augmented sixth chord is straightforward, due to the number of tendency tones in the chord. The bass moves down by half step to 5, the upper voice with 4 moves up by half step to 5, and the other voices move as smoothly as possible (usually by step). The most common chord after the augmented sixth is V; however, the progression Ger65–V involves parallel fifths and is often avoided (Example 24.5A). Instead, a Ger65 is followed first by the cadential 64, before resolving to the V; this results in no forbidden parallel motions (Example 24.5B).

EXAMPLE 24.5 Avoiding Parallel Fifths When Resolving the Ger6 A.

B.

b & b b c œœ

{

w w

œ œ

˙ ˙

ww

œ #œ œ œ

Ger56 V

i

i

œ œ

n˙ ˙

parallel 5ths

? b b c œœ # œ b œ c:

i

œ œ

œ nœ œ œ

5 - 6 - 5

˙ ˙

Ger56 V64 ____ ____

5 3

w w ww i

573

Chapter 24 The Augmented Sixth Chord

Augmented Sixth Chords in Major When a German 65 occurs in the major mode and leads to a cadential 64 with a major sixth, composers often notate this chromatic ascent (from 3 to raised 3) using the enharmonic equivalent 2, which visually leads more effectively up to 3. See again, Example 24.4E. Given that the fourth above the bass is doubly augmented, this unfortunate-looking chord is referred to as the doubly augmented sixth chord or sometimes as the Swiss augmented sixth chord.

Elided Resolution of the Augmented Sixth Chord When the augmented sixth chord moves directly to V7, an elided resolution often occurs, in which 4 does not resolve literally to 5 but moves directly to  4 (and on to 3) (Example 24.6).

EXAMPLE 24.6 Elided Resolution of ⴙ6 to V 7 A.

B. 4

4

3

4

5

4

3

V 8–7

i

from:

c:

+6

V7

c:

i

+6

EX ERCISE INTER LUDE A NA LYSIS 24.1 Identification Determine the key in which each of the augmented sixth chords would function; then identify the type of augmented sixth chord that is notated.

WORKBOOK 1 Assignments 24.1–24.3

SOLVED/APP 5

1.

2.

g:

Ger 65

3.

4.

5.

6.

7.

8.

574

THE COMPLETE MUSICIAN

A NA LYSIS

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

24.2 Listen to and then provide a harmonic analysis for the following examples, which contain augmented sixth chords.

SOLVED/APP 5

A. Mozart, “Wer ein Liebchen,” from Abduction from the Seraglio

Doch sie treu Do not waste

sich zu your time

er in

hal chit

ten, chat

schliess’ er for a

B. Verdi, “Se mami ancor,” from Il trovatore, no. 19

Lie wo

chen sorg man’s like

lich a

ein; cat,

575

Chapter 24 The Augmented Sixth Chord

C.

Verdi, “Si, la stanchezza m’opprime, o figlio,” from Il trovatore, no. 21

a mezza voce

D.

Paganini, Caprice for Solo Violin, op. 1, no. 11 Andante

5

( )V I A N D T H E G E R 65 C HOR D A special relationship exists between VI and Ger65 in a minor key (and between VI and Ger65 in a major key). The Ger65 contains all of the pitches in the ( )VI chord, plus 4. This relationship is particularly helpful when VI moves to the dominant, since it helps to avoid the parallel octaves that would occur between 6 and 5. (See the second and third chords of Example 24.7.) Example 24.8 illustrates a second instance of this process in which a tonicized VI (mm. 10–12) is converted to—and destabilized by—a Ger65 (m. 13), which can then move smoothly to V (m. 14).

AUG M E N T E D S I X T H C HOR D S A S PA R T OF PD E X PA N S IO N S Augmented sixth chords frequently combine with other pre-dominant harmonies to expand the pre-dominant function (Example 24.9). Given that two of its voices are so goal-directed toward 5, the augmented sixth chord is usually the last event before the

576

THE COMPLETE MUSICIAN

EXAMPLE 24.7 Transforming ( )VI into an Augmented Sixth Chord 1

3

6

c: i

VI

Ger 65 V 86

7 5

i

4

EXAMPLE 24.8 Schubert, Waltz in C major, Valses sentimentales, D. 779, no. 16 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

C: 6

VI 1 8

Ger 65

V 86 4

2 8

12

VI

V/ VI

7 5 3

577

Chapter 24 The Augmented Sixth Chord

dominant, following either iv(6) or VI. In Example 24.9 Beethoven drives home the arrival in B minor by moving from iv6 to a Ger65 in mm. 129–30 (the vii°65 appears as a neighbor). The Ger65–V motion is then reiterated seven times in the following nine measures and highlighted by the sf marking.

EXAMPLE 24.9 Beethoven, Piano Sonata no. 13 in E  major, op. 27, no. 1, Allegro vivace STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

124

b :

iv 6

vii (N)

6 5

Ger 65

130

V 86

7 5

Ger 65

i

V

Ger 65

i

V

4

135

i

Ger 65 V

i

Ger 65 V

i

Ger 65 V

i

Ger 65 V

i

Chromaticized Bass Descents Augmented sixth chords often appear in chromaticized bass descents as the final step before the dominant (Example 24.10).

Voice Exchange One of the most important techniques for expanding the PD is to move from iv through a passing 64 chord to iv6, as in Example 24.11A. It is also common for iv to move to a different PD harmony, such as the iiø 65 in Example 24.11B. In both cases, the expansion of the PD involves a prominent voice exchange between the bass and one of the upper voices.

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THE COMPLETE MUSICIAN

EXAMPLE 24.10 Chromaticized Bass Descent Expands PD STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

g:

V 6 V 42

i

IV 6 It 6

/IV

T

PD

V

D

EXAMPLE 24.11 PD Expanded by Diatonic Voice Exchange A.

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B.

c:

i T

vii

7

i

iv PD

P 64 iv 6

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V

i

D

T

vii

7

i

iv 6 P 64 ii PD

6 5

V D

When chromatic augmented sixth chords occur with other diatonic pre-dominants (such as iv and ii6), the resulting voice exchange is not exact. This can be seen in m. 1 of Example 24.12A, in which the C and E of the iv chord swap to become the E and C of the It6 chord. This special swapping of cross relations is called a chromatic voice exchange. Example 24.12B illustrates both a diatonic voice exchange (m. 108 to downbeat of m. 109) and a chromatic voice exchange (m. 109).

The German Diminished Third Chord In rarer cases where the PD expansion involves only an augmented sixth chord, the resulting voice exchange is literal, as in Example 24.13. The chord on the downbeat of m. 1 in Example 24.13 is a Ger65. The chord on beat 3 of that measure sounds like—and contains the same pitches as—a Ger65, although the pitches have been reordered such that 4 appears in the bass and 6 in an upper voice. The resulting chord is therefore an inversion of the augmented sixth and is called a German diminished third chord. Since the figure for this chord would be “7,” we label the German diminished third chord as Ger7.

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Chapter 24 The Augmented Sixth Chord

EXAMPLE 24.12 Chromatic Voice Exchange Incorporates Augmented Sixth Chord STR EA MING AUDIO

A.

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g:

i

iv

T

PD

P64

It 6

V D

C. P. E. Bach, Flute Sonata no. 6 in G, Wq 134 H548, Allegro

B.

diatonic voice exchange chromatic voice exchange 107

g:

v6

i

iv 6

T

V 65/IV

iv

P 64

PD

c:

6 5

i

Ger 65

T

PD

i

6 4

7

P64 Ger 7

V D

EXAMPLE 24.13 Prolonging the Augmented Sixth Chord

i

It 6

V D

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THE COMPLETE MUSICIAN

EXAMPLE 24.14 Part Writing the Ger7 Chord 4

c:

( 6)

Ger 65

5

( 6)

5

5

4

5

5 V 64 — — 3

Ger 7

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5 V 64 — — 3

The individual voices of this chord behave identically to those in any augmented sixth chord—6 descends to 5 and 4 ascends to 5. But given that the pitches are switched from the traditional Ger65 arrangement, the voices contract on resolution rather than expand (Example 24.14). In the second scene of Tchaikovsky’s ballet Sleeping Beauty (Example 24.15), an extended PD involves IV, ii6, and Ger7, which Tchaikovsky marks ff in m. 72. The Ger7 chord returns in m. 76, elaborating the V64 as its neighbor (see the reduction in Example 24.15B).

EXAMPLE 24.15 Tchaikovsky, Sleeping Beauty, scene 2 A. 62

A:

V43/ii

IV

V43/ii

ii 70

67

ii

6

6 4

5 3

(ii) 6

Ger 7 (as CPT)

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Chapter 24 The Augmented Sixth Chord

EXAMPLE 24.15 (continued) 73

3

3

3

3

3

3

3

3

Ger 7 (as neigh.)

V

3

3

3

3

3

3

3

V

B. Tchaikovsky, Sleeping Beauty (reduction) meas:

A:

71

ii6

72

73

Ger 7 V 46 (PT)

76

Ger 7 (N)

77

78

6 4

5 3

T H E AUG M E N T E D S I X T H C HOR D A N D MODU L AT IO N : R E I N F ORC E M E N T Because of its half-step tendencies to 5, the augmented sixth chord contains more linear drive toward the dominant than any other PD harmony. Therefore, its appearance after a pivot chord is particularly helpful in securing a new key. Listen to Example 24.16. As the analysis of Example 24.16 shows, the excerpt’s two phrases form a contrasting progressive period. The first phrase moves from the opening tonic to the dominant on the downbeat of m. 4. After a brief connective passage (over a passing V42), the second phrase restarts on the tonic and modulates to V. At first glance, it seems there are two possible pivot chords in the excerpt: the tonic that begins the second phrase (m. 5) and the chord that follows in m. 6. Because the chord in m. 6 functions in only one way—as a Ger65 in the key of E (V)—the tonic is best regarded as the pivot chord. Now we can understand why Haydn began the second phrase with the tonic in first inversion. As a pivot, it becomes IV6 in the key of V, which smoothly moves by step to the Ger65 in m. 6. In most modulating passages, composers take special care to make the harmonic motion to the new key as smooth as possible. In situations where composers desire a more

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EXAMPLE 24.16 Haydn, String Quartet in A major, op. 55, no. 1, Menuetto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

PAC in V

HC

A:

I

V 43

I 6 ii 6 V 65

V

I

(P)

I 6 ii 6

V

PD

D

T

4 2

I

6

V: IV 6

T

Ger 65

V 64

PD

D

5 3

I

T

EXAMPLE 24.17 Schubert, Sonatina in D major for Piano and Violin, op. posth. 137, no. 1, D. 384, Allegro molto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

29

Ger Fr It

D: V:

III VI

+6

V

7

Chapter 24 The Augmented Sixth Chord

583

striking effect, they often juxtapose radically different chromatic harmonies but then confirm the second tonal area by using the augmented sixth chord. In Example 24.17, Schubert boldly moves from the tonic D major to F (III) in m. 33. At this point, he reinterprets F major as VI and converts it into an augmented sixth chord that resolves to V of A (V). (Note that all three types of the augmented sixth chord appear in m. 35 as the alto voice moves by step from C to G.)

T H E AUG M E N T E D S I X T H C HOR D A S PI VO T I N MODU L AT IO N S You may have already discovered that the It63 is enharmonically equivalent to an incomplete V7 chord, and the Ger65, shown in Example 24.18, sounds like a complete V7 chord.

EXAMPLE 24.18 Sonic Equivalence of Ger56 and V 7

+6

Ger 65 in C

m7

V 7 in D

Despite the aural similarity between the augmented sixth chords and their V7 respellings, their distinct functions are based on their resolutions and voice leading. • An augmented sixth chord is a PD chord and leads to dominant. The bass descends by half step to 5, and another voice ascends by half step to 5. • A V 7 chord is a dominant chord that leads to tonic. The seventh of the chord descends by step as the bass leaps. But voice leading aside, the two chords are sonically interchangeable, and their identities differ only by one enharmonic pitch. Look again at Example 24.18. See how the only difference between the Ger65 chord in C and the V7 in D is the shift of F to G? To take advantage of this enharmonic relationship, composers treat this sonority as a pivot chord. Such enharmonic reinterpretation permits certain chromatic modulations, as shown in Example 24.19. Example 24.19B illustrates how Beethoven’s enharmonic reinterpretation allows him to tonicize II effortlessly: A quick modal shift from G major to G minor prepares the Ger65 (mm. 163–165). In m. 167, D appears (rather than the previously notated C). As the chordal seventh of the E chord, the D resolves by step descent and leads to the restatement of the theme in A (II).

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EXAMPLE 24.19 Enharmonic Pivot: Ger56 → V7 STR EA MING AUDIO

A.

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Ger

F

= G

6 5

=

V7

c minor

B.

D major

Beethoven, “Rage Over a Lost Penny,” op. 129

154

V 65

G:

I

160

cresc.

V 43

I6

V 65

vii 56/V

i

Ger 65

166

dim.

V Ger 65 II (A ): V 7

I

etc.

Composers do not always notate the Ger65 and the V7/II successively in their two forms, as in Example 24.19. Rather, they notate one form, which functions as a pivot chord between the two harmonic areas. Example 24.20 shows how to label such a dual-functioning sonority.

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Chapter 24 The Augmented Sixth Chord

EXAMPLE 24.20 Ger65 as Pivot

c:

Ger 65

i

II: V 7

I

Just as the Ger65 and V7 are enharmonically equivalent, so too are the Ger7 and V42 chords. Example 24.21 illustrates how these chords can be used interchangeably. In m. 1 of Example 24.21A, the Ger7 chord (labeled x) functions as part of a PD expansion that leads to V. In m. 2 the Ger7 chord (labeled y) expands the dominant through chromatic neighbor motion. Its final appearance in m. 2 (labeled z) is sonically identical to its previous statement, but G appears in the bass, transforming the chord into a V42 of D (II). This enharmonic pivot is boxed to show how it secures the tonicization of II.

EXAMPLE 24.21 Ger7 as Pivot STR EA MING AUDIO

A.

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x

i

Ger 56 P 64 Ger 7 V PD

y

z

Ger 7

Ger 7

D

II:

V 42

8

I6

IV V 46

7 5 3

I

B. Tchaikovsky, Sleeping Beauty, Pas de Six, “Violente” Allegro molto vivace

cresc.

d:

V

Ger 7

V

V

Ger 7

V

V

V 42

II

586

THE COMPLETE MUSICIAN

Example 24.21B, from Tchaikovsky’s Sleeping Beauty, contains many examples of modulations using enharmonically respelled Ger7 chords. The opening of the “Pas de Six” begins on V of D minor, which is expanded by the Ger7 chord in mm. 2 and 4. In m. 6, the chord is respelled as a V42 of E (II), to which it resolves. The reverse of this enharmonic reinterpretation in which V7 is reinterpreted as a Ger6 is shown in Example 24.22. This procedure is not nearly as common as the move to II, because the new tonic is 7, a scale degree that is rarely tonicized in tonal music.

EXAMPLE 24.22 Enharmonic Pivot: V 7 → Ger56 F

c:

i

V7 b: Ger 65

STR EA MING AUDIO

E

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V 86

— — 4 —

7 5

i

In Chapter 18, you will remember that it is possible to precede any consonant triad in a key with its own V7. With enharmonic reinterpretation, you can now change any of these V7s into augmented sixth chords. This transformation provides composers with easy access to both closely and distantly related keys.

EXAMPLE 24.23 Chopin, Mazurka in B major, op. 56, no. 1, BI 153 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

39

D =E

B:

V 7/IV E : (III ) Ger 65

587

Chapter 24 The Augmented Sixth Chord

EXAMPLE 24.23 (continued) Poco più mosso 45

leggiero

V8

7

I

Listen to Example 24.23. Notice how B major (I) closes the phrase in m. 44. Immediately, a seventh is added to the tonic, creating the aural expectation that it will function as V7 in the key of E (IV). Remarkably, this chord is resolved differently: It acts as a Ger65 moving to the dominant of the new key D major (III, enharmonically spelled as E). The roman numeral analysis below Example 24.23 shows how the pivot functions. Enharmonic reinterpretation functions just like a pun. Based on traditional syntax, the listener has clear expectations. But a good pun leads the story in an entirely unexpected direction. Consider the following: “I couldn’t understand why the ball was getting bigger and bigger. Then it hit me.”

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 24.4–24.7

24.3 Analytical Snapshots from the Literature Listen to and then provide roman numerals for the following excerpts, which contain examples of the following techniques: • converting VI into an augmented sixth chord • pre-dominant expansions using augmented sixth or diminished third chords • enharmonic conversion using augmented sixth and dominant seventh chords

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

Mozart, Adagio in C major, K. 356

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THE COMPLETE MUSICIAN

B. Gluck, Chorus, “Bettet den Vater,” from Alceste, act 1

C. Mendelssohn, “Weh mir!” Ariette, from Elijah, no. 18 Andantino

D.

Beethoven, Andante in F major, WoO 57

13

cresc.

decresc.

19

cresc.

589

Chapter 24 The Augmented Sixth Chord

E.

Schubert, “Die Liebe hat gelogen” Langsam

&

bbb c

b & b bc œ œœ

{

p

? bb c œ b

b ™ ™ & b b œJ œR œJ

œœœ œœœ b œ˙˙™ fp

œ œ b œ˙˙™ ˙ œ œ R

&

{

? bb

œœœ

b œ

œ œ ˙ # œœ œœ n ˙˙ œ œ

˙

Œ

‰ œj

œ™ œ œ™ J R J

Die

Lie - be hat

œJ n œœœ # œœœ œœœ n ˙˙˙ œ J

n œœœ

be - tro - gen, ach,

œ œ R

œœ œœ # ˙˙ œ œ n˙

œ œ

œ œ œ œ

œ œ J J

ge - lo - gen, die

œœœ œœœ

˙˙˙

œ

œ œ

˙

œ ™ œ nœ nœ ˙ J R J J

j j nœ œ

be - tro - gen hat

n œœ œ

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œœœ

pp

œœ œœ ˙˙

j j nœ ™ œ œ ™ œ œ J R J

Sor - ge la - stet schwer,

bbb

Ó

∑

al - les mich um - her!

?n

fp

n˙ n˙

n œœœ b œ n œœœ œœ ˙œ ™ œ n˙

b œj

fp

œ œ

œ œ œ œ œ œ

œ

T ER MS A ND CONCEP TS • augmented sixth chord • chromatic voice exchange • doubly augmented sixth chord • enharmonic reinterpretation • French augmented sixth chord (Fr43) • German augmented sixth chord (Ger65) • German diminished third chord (Ger7) • Italian augmented sixth chord (It6)

CH A PTER R EV IEW 1. In an augmented sixth chord, the lowered 6 (pre-dominant in function) and raised 4 (dominant in function) combine which two types of chromaticism?

590

THE COMPLETE MUSICIAN

2. Summarize the three subcategories of augmented sixth chords. ITA LIA N (IT 6 ) . . .

. . . doubles scale degree ______________

FR ENCH (FR 43) . . .

. . . adds scale degree ______________

GER M A N (GER 65) . . .

. . . adds scale degree ______________

3. Summarize the voice-leading guidelines for resolving augmented sixth chords. THE BASS (6) MOV ES TO . . . THE UPPER VOICE ( 4) MOV ES TO . . . THE R EM AINING VOICES MOV E . . .

4. Give two names for a German augmented sixth chord in major that resolves to a cadential six-four chord.

5. In an elided resolution of an augmented sixth chord, 4 resolves directly to scale degree ___________________________________________________________________.

6. The German diminished third chord is the same as the German augmented sixth chord, but with scale degree ____________ in the bass and scale degree _________ in an upper voice.

7. Through the process of enharmonic reinterpretation, a German or Italian augmented sixth can act as the dominant of roman numeral ___________________________________. What is another name for this triad when it acts as a pre-dominant?

8. The Ger7, or German diminished third chord, is enharmonically equal to what inversion of V7?

Chapter 24 The Augmented Sixth Chord

591

S U M M A R Y OF PA R T 6 With the examination of modal mixture, the Neapolitan chord, and augmented sixth chords, we have completed our study of common-practice harmony. We have seen that mixture is a procedure through which pitches belonging to the parallel mode can be incorporated and—in the cases of III and VI—tonicized. Such stabilization is one of the hallmarks of nineteenth-century music. These chromatic third tonicizations, so called because the tonicized keys lie a third away from the tonic, function identically to their diatonic counterparts. Furthermore, these new chromatic harmonies are often connected to an underlying musical narrative, or drama, whether or not a text is present. We learned that these chords can function in vocal music as musical analogues that highlight, clarify, or even expand on a text. Finally, we have seen yet again how counterpoint is a central force behind not only mixture sonorities but also both the Neapolitan and augmented sixth chords.

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PA R T 7

L A RGE FOR MS: TER NA RY, RONDO, SONATA

N

ow that we have completed our study of common-practice harmony, we begin a journey through three important large forms: ternary, rondo, and sonata. Taken together, these forms fittingly describe the structure of vast numbers of instrumental and vocal works composed throughout the eighteenth and nineteenth centuries. Learning to recognize these forms and their local and large-scale harmonic procedures is a major step toward comprehending the design of classical works. In addition to exploring formal strategies in large works, we also look at musical processes that unfold throughout a piece and that provide musical narratives for both listener and performer. Generally these processes are motivic, and they range from simple repetitions that are slightly obscured by the musical surface to significant transformations in which the motive is expanded at the very deepest level of structure.

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C H A P T E R 25

Ternary Form OV E RV I E W

In this chapter, we will explore ternary form, the first of three large, important, and widely used musical structures. Found in numerous musical styles and genres, ternary structure is different than binary structure in that ternary consists of three independent sections, each closed harmonically, with the middle section being highly contrasting to the outer sections. Such a structure is very different than the threepart design of a rounded binary form, in which each section is interrelated, and connected by key, mood, and texture. CHAPTER OUTLINE Characteristics ............................................................................................................. 595 Transitions and Retransitions ................................................................................. 597 Illustration .............................................................................................................. 597 Da Capo Form: Compound Ternary Form .......................................................... 600 Da Capo Aria ............................................................................................................... 602 Minuet-Trio Form....................................................................................................... 602 Ternary Form in the Nineteenth Century ............................................................ 605 Terms and Concepts ................................................................................................... 614 Chapter Review ........................................................................................................... 614

C H A R AC T E R I S T IC S Ternary and rondo forms (to which we’ll turn in Chapter 26) are composite forms constructed of multiple sections that are self-contained. The independent sections feature strong melodic contrast and tonal closure; the various sections usually begin and end 595

596

THE COMPLETE MUSICIAN

conclusively in the same key. Binary form is not a composite form, since its sections are tonally dependent on one another and are more organic in construction. Ternary form has a three-part melodic design (ABA or ABA⬘) and a three-part tonal structure (original key–contrasting key–original key) (Example 25.1A). Contrast the design of ternary form with the rounded binary form of Example 25.1B, which has a threepart melodic design (a–dig.–a⬘) but a two-part tonal structure.

EXAMPLE 25.1 Comparison of Ternary and Binary Forms STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A. Ternary Form A

B

A or (A)

original melodic material

contrasting melodic material

literal repetition of A (or altered restatement, labeled A)

original key

contrasting key: (major mode: IV, vi, iv, VI, i) (minor mode: III, iv, VI, I)

original key

B.

Rounded Binary Form

: a in one key I

: :

digression

a

V 

I

:

V

I

Listen to Grieg’s “Hjemve” (see the Anthology no. 57), which is in ternary form. Its three distinct and autonomous parts may be labeled ABA⬘. The fast, folklike B part in the parallel major key highly contrasts with the brooding A and A⬘ parts. The piece is in ternary form because each of the three sections is harmonically and thematically closed, and the B section is self-standing. If each of the three sections of a ternary form closes in its respective tonic, as in the Grieg example, we call the form a full sectional ternary form (A||B||A||). When either the A section (A||BA––not common) or the B section (AB||A––common) closes away from its tonic chord and this closure is integral to the tonal motion of the section, then we refer to the form as a sectional ternary form. When both A and B close away from their respective tonic chords, we call the form a continuous ternary form (ABA⬘).

Chapter 25 Ternary Form

597

Sometimes it is not easy to distinguish a continuous ternary form from a rounded binary form. To decide whether a form is rounded binary or continuous ternary, consider how much the B part is dependent on the A part. If there is little connection, a ternary form is indicated. By contrast, if there is a thematic or motivic connection and little or no change of key, the form is better termed a binary form. Like much of your musical analysis, you must interpret such works according to how you hear them and then support your answer.

T R A N S I T IO N S A N D R E T R A N S I T IO N S Composers sometimes write bridging sections in order to create a sense of continuity in a ternary form. Material that bridges between tonic and a new key (from A to B in ternary form) is called a transition. Bridging material that leads from a contrasting key back to tonic is a returning transition, or retransition. Note that a ternary form may have a transition and a retransition, a transition without a retransition, a retransition without a transition, or no bridging material at all. Retransitions occur much more frequently than transitions. Transitions and retransitions make for some of the most exciting music in a piece, because their material is unpredictable. They may be as simple as presenting the dominant of the upcoming key, or they may be considerably more involved, delicately foreshadowing motives and harmonies of the upcoming section. It may be hard to determine whether a piece is in continuous ternary form or in sectional ternary form with a transition or retransition. If there is a conclusive end to a section followed by a modulation with melodic fragmentation, this is most likely a transitional area. By contrast, if a section closes in another key but the closure is integral to the tonal motion of a section, then there is most likely no transitional area.

Illustration Consider the relationship between the A and B sections in Example 25.2, a work by Brahms. The outer sections of Brahms’s Romanze are in F major, and the contrasting B section (beginning in m. 17) is in the remote key of D major (VI). The B part is further distinguished from A by a faster tempo and a meter change.

EXAMPLE 25.2 Brahms, Romanze in F, Six Piano Pieces, op. 118, no. 5 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Andante

espressivo

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THE COMPLETE MUSICIAN

EXAMPLE 25.2 (continued) rit.

4

8

più espress.

11

dolce

rit.

14

dim.

so 17

molto

e dolce sempre

If we view the transition only as the final measure of the A section (m. 16), then it is present but quite short. Here, a bass arpeggiation of D minor prepares the upcoming D major section: All that is required is a modal shift to the parallel major. But Brahms has

599

Chapter 25 Ternary Form

done much more than tack on a measure of D minor; examine the A section to see the musical process. The A section contains four four-measure phrases with the relationship a-a⬘-a-a⬘. The first a (mm. 1–4) closes with a HC, and the first a⬘ (mm. 5–8) moves to vi and closes with a HC in D minor. It is only the quick shift to A minor that prepares the return to F major in m. 9. The second a (mm. 9–12) is almost identical to mm. 1–4, but the second a⬘ (mm. 13–16) closes on V of D, which leads nicely to the next section. Thus, the large A section closes in a different key from the one in which it began. A retransition prepares for the return of A after the B section (Example 25.3). The retransition begins by shifting to the lullaby-like $^ meter of the A section and by reprising the A section’s two-note slurred chords in parallel sixths (m. 45). Yet elements of the B part are retained in the retransition, the most obvious of which are the key of D major and the trills

EXAMPLE 25.3 Brahms, Romanze in F STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

37

41

10

44

( = )

dim. 10

Tempo I 48

espressivo

600

THE COMPLETE MUSICIAN

that close the retransition. In m. 46, D major moves to D minor, which functions as diatonic vi in F major. This is followed by a cadential six-four chord in F major that resolves directly to the tonic (mm. 47–48). Therefore, Brahms’s work is a sectional ternary form.

DA C A P O F OR M : C OM P OU N D T E R N A R Y F OR M Ternary forms can be found in several genres and style periods, such as a Classical sonata, a da capo aria from the Baroque period, a minuet and trio from the Classical period, and a character piece from the nineteenth century. Ternary forms are found in many more genres and styles than we can explore here. For example, although da capo form is the primary form of the Baroque aria, it can be found in almost all genres, style periods, and instrumental combinations of the common-practice era. The Presto by Haydn in Example 25.4 is in da capo form. The ABA structure of da capo works is realized by following the marking at the end of the score, Da Capo (al ), which in literal translation means “from the head to the fermata sign,” telling the performer to return

EXAMPLE 25.4 Haydn, Divertimento in G major, Hob XVI.11, Presto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

9

17

25

601

Chapter 25 Ternary Form

EXAMPLE 25.4 (continued) 33

Da Capo (al

41

)

to the beginning of the piece and play to the fermata sign. It is the return that creates the final balancing A section; the da capo instruction merely saves space and ink. Haydn’s Divertimento is much like Grieg’s work in the Anthology no. 57: Both are full sectional ternary forms, and both include smaller binary forms within the larger ternary form. These are compound ternary forms, because larger parts contain smaller nested forms (Example 25.5).

EXAMPLE 25.5 Form Diagrams A.

Grieg

measures: large parts: small parts:

1–8 A a

9–18

19–27

dig.

a

(rounded binary)

B.

28–35 36–43 44–51 52–59 60–67 68–75 76–85 86–94 B A dig. a b dig. b dig. b a b (rounded binary x 2) (rounded binary)

Haydn

measures: large parts: small parts:

1–8 9–16 17–24 A a dig. a (rounded binary)

25–32 33–40 41–48 B b dig. b (rounded binary)

1–8 9–16 17–24 A a dig. a (rounded binary)

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DA C A P O A R I A Instrumental works are by no means the only type of da capo structures. In fact, the da capo aria is possibly the most important ternary structure in the Baroque period. One or more instrumental interludes, called ritornellos, usually punctuate formal parts and sections of text. Attempt the following tasks before you listen to Bach’s “Ich will Dir mein Herze schenken” (see the Anthology no. 6). 1. Locate and mark the division between the A and B sections; remember that the third section is a repeat of the A, from the beginning up to the fine. What underlying keys control each section? Are the sections divided into subsections? If so, mark them and indicate the prevailing keys in each with roman numerals. 2. What sequential progression unfolds in the opening instrumental passage (called a ritornello)? Discuss relationships between the ritornello tune and the soprano’s opening melody. 3. What musical events help to distinguish the B section of this aria from the flanking outer parts? The form in Bach’s aria unfolds as shown in Example 25.6. The A part, which remains in the tonic key, markedly contrasts with the B part, which begins after the instrumental ritornello. The B part is more transitory and sequential, similar to the digression of a binary form. The B part closes in B minor, the minor dominant of E minor (or the mediant of the returning G major). Therefore, this is a sectional ternary form.

EXAMPLE 25.6 Bach, “Ich will . . . ,” Form Diagram

section: measures: subsection: keys:

A 1–6 ritornello G: I (HC)

7–24 voice V–I

25–30 ritornello I

B 31–37 voice vi (e)

38–41 42–48 ritornello voice V–i PAC in v of vi (b)

A (da capo) 1–30 I

M I N U E T-T R IO F OR M The Baroque minuet is a type of dance that remained popular in the following Classical period, when it became a standard inner movement in symphonies and chamber pieces such as serenades, divertimentos, and sonatas. In the hands of first Haydn and then Beethoven, the minuet was often transformed into a more spirited piece called the scherzo (or “joke”). The Classical minuet is followed without pause by a companion piece of lighter texture, called a trio, after which a da capo marking indicates that the minuet is to be repeated. The

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result is a large ternary form called minuet-trio form. As with many composite forms, the minuet-trio form is often a compound ternary, with nested binary forms. Before listening to Example 25.7—a minuet-trio movement from one of Beethoven’s early piano sonatas—review the following points and questions. 1. The minuet and trio are clearly delineated by Beethoven’s use of titles. Yet even if no clues were provided, you would still be able to differentiate the A and B sections. Identify at least three features of the trio that distinguish it from the minuet. 2. Identify three features of the trio that are shared with the minuet. 3. What nested forms occur within the minuet and trio? 4. What is the underlying harmonic progression in the minuet? This movement is a full sectional ternary form, and both the minuet and trio are rounded continuous binary forms (Example 25.8). The minuet, in F minor, moves from i to III in the first a section. The digression is characteristically more transitory, tonicizing

EXAMPLE 25.7 Beethoven, Piano Sonata no. 1 in F minor, op. 2, no. 1, Menuetto-Trio: Allegretto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Menueo

11

22

31

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EXAMPLE 25.7 (continued) Trio

41

49

57

(

)

66

D.C.

EXAMPLE 25.8

section: measures: keys:

Beethoven, Menuetto-Trio, Form Diagram

A (minuet) 1–14 15–28 a digression i–III iv–V 

29–40 a i–V–i

B (trio) 41–50 b I–V

51–65 digression –V 7 

66–73 b I–V–I

A (minuet) 1–40 i

iv briefly in mm. 19–25 before the V and interruption in m. 28. The underlying tonal progression of the minuet is i–III–iv–V // i–V–i. To achieve variety in the rounded binary forms, material from the a section is often presented so that what was in the upper voice is now in the lower voice (and vice versa) in the a⬘section. The procedure in which contrapuntal lines are swapped is called invertible

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counterpoint (see Appendix 1 for a detailed presentation of invertible counterpoint). Beethoven uses this contrapuntal technique in both the minuet and the trio; a common procedure thus ties the two together. In the minuet, the reprise of the a⬘ section in m. 29 places the initial tune in the left hand rather than in the right. The right hand again takes over the melody in m. 31. Similar registral shifting takes place in the trio, where Beethoven intensifies the effect by introducing it immediately in back-to-back phrases (mm. 41–44 and 45–48). Invertible counterpoint and registral change become ever more explicit in the digression of the trio, which is shown in Example 25.9: The chromatic line C4–B3–B3–A3 begins on C2 in m. 51 and repeats one and two octaves higher than the tune (m. 55 and m. 65). One can find the seeds of registral shifting and invertible counterpoint planted in the opening of the minuet: The tenor-voice entrance at the end of m. 2 restates the soprano-voice entrance down an octave.

EXAMPLE 25.9 Beethoven, Piano Sonata no. 1, Trio 41

45

51

55

65

T E R N A R Y F OR M I N T H E N I N E T E E N T H C E N T U R Y Some of the species of ternary forms from the eighteenth century, such as the minuet-trio, continued to serve composers throughout the nineteenth century. Others, such as the da capo, fell out of favor and were replaced with new—or at least hybrid—forms whose very titles suggest the intense Romanticism that gave rise to them. One new addition, the character piece, was a short, expressive work often written for solo piano. Some important nineteenth-century character pieces include the bagatelles of Beethoven and the impromptus and Moments musicaux of Schubert; and the ballades, nocturnes, polonaises, and mazurkas of Chopin. In addition, composers who were influenced by the literature of the time wrote entire cycles of piano pieces with highly descriptive titles, such as Robert Schumann’s Papillons and Carnival. Character pieces continued to be composed throughout the nineteenth century by Liszt, Brahms, Scriabin, and Grieg, whose “Hjemve” (“Homesickness”) we encountered earlier. In the following examples from the cusp of the nineteenth century and onward, we explore how composers used motives to link independent sections of ternary works—in particular, how apparently new musical material actually concealed repetition or a transformation of earlier material. (See Appendix 2 for an extended presentation of motivic structure.) Although it reaches its apogee in the music of Liszt and Wagner, motivic

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transformation is not new to the nineteenth century. One often encounters instances of transformation in the music of late-Classical composers such as Mozart and Haydn, some of whose string quartets are unified through the recurrence of the same one or two motives in multiple movements. Consider the minuet-trio pair from a Haydn string quartet shown in Example 25.10. At first glance, the minuet and trio seem to be highly contrasting. Not only are there dynamic and key changes (from C major to A minor), but the trio is more sparse in texture than the minuet, with the first violin given the lion’s share of melodic material and the lower instruments merely punctuating the tune with an occasional chord. However, even a slightly more detailed look reveals important connections between the minuet and trio. The minuet opens in C major with the angular violin falling by ever-increasing large intervals: a sixth, a seventh, and finally a ninth. The other instruments imitate the first violin’s jaunty contour, but the cello line (C, F, B, C) is particularly exposed. The opening

EXAMPLE 25.10 Haydn, String Quartet in C major, “Emperor,” op. 76, no. 3, Hob III.77 STR EA MING AUDIO

Menuetto: Allegro

A.

C:

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F

B. Trio C Trio

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C 60

B

C

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of the trio reveals a barely hidden repetition of the earlier cello figure in the first violin, even though the trio is cast in the relative minor (see Example 25.10). This important association between the minuet and trio is one that performers should consider, since recognizing such motivic recurrences can render their performances more organic and insightful. Consider two of Chopin’s mazurkas. Example 25.11 shows the opening A section of a mazurka in A minor, a section that contains a nested small ternary form (aba). After an ambiguous four-measure introduction, a wandering melody enters at m. 5. The opening notes of the right hand (B4–C5–D5) help to explain the function of the introduction, where the middle voice moves with this same three-note figure, almost as if it were lying in gestation before flowering into an expressive melody at m. 5. The next seven measures are filled with chromaticism, including the descending line E4–D4–D4–C4 in mm. 8–13 (Example 25.11). Again, the mood remains somber, such that

EXAMPLE 25.11 Chopin, Mazurka in A minor, op. 17, no. 4 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Lento, ma non troppo ( = 152)

espressivo 3

so o voce ten.

6

15

11

3

16

3

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delicatiss.

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EXAMPLE 25.11 (continued) ten.

21 3

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36

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poco riten.

a tempo

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Chapter 25 Ternary Form

EXAMPLE 25.11 (continued)

15

51

3

56

3

3

ten.

ten.

6

we crave relief. It arrives in mm. 37–42, as a more sprightly tune unfolds over a dominant pedal—this is the b part of the nested aba form. Despite the contrast, one discovers a compressed repetition of the chromatic line from mm. 8–13 in mm. 37–42 (Example 25.12; for the full score, see the Score Anthology #51). In his late F-minor mazurka, also cast in ternary form, Chopin juxtaposes the very distant keys of F minor and A major in the two halves of the A section, yet he subtly links these disparate keys with a neighbor motive that he presents at various structural levels in the opening moments of the piece (Example 25.13). Following the initial statement of the neighbor C5–D5–C5 (5–6–5) in m. 1, a chromatic descent from C5 to G4 (in m. 6) is compensated by an upward leap that recaptures the upper neighbor figure, D5–C5, in mm. 6–7.

EXAMPLE 25.12 Chopin, Mazurka in A minor, op. 17, no. 4 Lento, ma non troppo ( = 152)

espressivo 3

sotto voce

6

ten.

D

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EXAMPLE 25.12 (continued)

11

15

B

3

3

delicatiss.

3

36

3

D–B

3

3

The contrasting melody (starting in m. 15) begins with a stepwise ascending line that balances the more angular, predominantly descending line that characterized the opening. It is not surprising that C is the most prominent pitch in this section, since it functions as a hugely expanded statement of its enharmonic twin, D. In fact, given that C occupies the B section and returns to C in the restatement of the A material, Chopin’s choice of A major for the contrasting melody is actually quite logical, given that it nicely harmonizes the expanded neighbor D as C.

EXAMPLE 25.13 Chopin, Mazurka in F minor, op. 68, no. 4 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

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N

sotto voce

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legatissimo

N

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Chapter 25 Ternary Form

EXAMPLE 25.13 (continued) 10

sempre legatissimo

B N (C = D ) 14

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 25.1–25.3

25.1 Draw a formal diagram for the following pieces. If a piece is a compound form, include the nested, smaller forms. Then answer the accompanying questions on a separate sheet of paper. A.

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Haydn, Piano Sonata in C major, Hob XVI.10, Menuet and Trio 1. What type of period opens the minuet? 2. What is somewhat unusual about the harmony in the digression? 3. What harmonic and melodic technique occurs in the bass line that opens the trio? 4. Discuss the pre-dominant that occurs in the first phrase of the trio. 5. What key(s) is/are tonicized after the first double bar of the trio? 6. Why could one support the assertion that the melodic structure of the trio is simple, or rounded, or balanced?

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3

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molto legato

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sempre molto legato

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Menuet da capo

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B.

Paganini, Caprice no. 20, from 24 Caprices, op. 1 Allegretto

dolce 9

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Fine. 8

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D.C. al Fine.

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T ER MS A ND CONCEP TS • character piece • composite form • compound form • da capo aria • da capo form • minuet • minuet-trio form • retransition • ritornello • scherzo • ternary form • continuous • full sectional • sectional • transition • trio

CH A PTER R EV IEW 1. Why are ternary and rondo called composite forms?

2. Using capital letters, diagram the two possible forms for the melody of ternary form.

3. Whereas binary form is a [two-part/three-part] harmonic structure, ternary form is a [twopart/three-part] harmonic structure.

4. Fill in the last blank in the table below. FULL SECTIONAL TERNARY FORM

All sections are closed.

SECTIONAL TERNARY FORM

Either A or B is open.

CONTINUOUS TERNARY FORM

Both A and B are __________.

Chapter 25 Ternary Form

615

5. If the A and B sections are melodically and harmonically related, the form may be _______________ rather than ternary.

6. A retransition leads from the [contrasting/tonic] key to the [contrasting/tonic] key.

7. A da capo aria is often punctuated by instrumental interludes called __________________.

8. A minuet is usually followed by a __________________________ with a da capo sign, resulting in a large ternary form: ABA.

9. Beethoven and Haydn often replaced the minuet with a ______________________________, meaning “joke.”

10. The procedure in which contrapuntal lines are swapped between voices is called _______________________________________________________________.

CH A P TER 26

Rondo OV E RV I E W

In this chapter, we will discuss the concept of rondo, an ancient form based on the simple notion of alternating a recurring initial section A with added new sections. This form would be represented as ABACAD, and so on. Although highly sectional, with diversity mixed with repetition, composers have found ways to connect sections in ways that create a highly interwoven work of art. CHAPTER OUTLINE Context .......................................................................................................................... 616 The Classical Rondo ................................................................................................... 617 Five-Part Rondo..................................................................................................... 619 Coda, Transitions, and Retransitions ................................................................. 619 Compound Rondo Form ...................................................................................... 620 Seven-Part Rondo .................................................................................................. 623 Distinguishing Seven-Part Rondo Form from Ternary Form ................... 623 Missing Double Bars and Repeats ...................................................................... 623 Terms and Concepts ................................................................................................... 629 Chapter Review ........................................................................................................... 629

CON T E X T “Variety is the spice of life” and “There’s no place like home” are two popular sayings that convey very different meanings. Although most of us desire new experiences to keep life interesting, we also need frequent returns to the familiar so that our lives don’t feel like they’re becoming too chaotic. This balance of variety and return—so fundamental to human nature—is reflected not only in ternary form but also in rondo form. 616

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Chapter 26 Rondo

Ternary form and rondo form are composite forms, constructed of multiple selfcontained sections. The sections of a ternary form introduce variety (in the B section) and return (in the final A section). Rondo form continues the balance of variety and return as it incorporates more and more sections. We can think of rondo form as an extension of ternary form, or we can consider ternary as a small three-part rondo: Ternary form (three-part):

A

Rondo form (five-part): Rondo form (seven-part):

A1 A1

B B B1

A2 A2

C C

A⬘ A3 A3

B2

A4

Rondo form alternates sections of recurring material (A1, A2, A3, etc.), called refrains, with sections of contrasting material (B, C, etc.), called episodes. The rondo is a common form in eighteenth-century French Baroque instrumental music, where it is called rondeau. Works by Louis Couperin (ca. 1626–1661), his nephew François Couperin (1668–1733), and Jean-Philippe Rameau (1683–1764) often consist of very short refrains and a variable number of episodes in the form ABACADA, and so on. These early works became the model for later eighteenth- and nineteenth-century compositions, and it is here where we will begin our study of rondo. Listen to Example 26.1, which contains a rondeau by François Couperin. The refrain is the first thing heard and most often occurs in the home key—this is common in most rondos. The refrain occurs three times: measures: section: key:

1–8 A1 i

17–24 A2 i

33–40 A3 i

There are two episodes: The first, at mm. 9–16, is in B major (III). This episode begins off-tonic: The C-minor chord of m. 9 is ii in B. The second episode begins at the upbeat to m. 25 and moves toward D minor (v) in m. 28. If we order our findings, we see that Couperin’s piece follows a five-part structure that is very common in the later Classical period: measures: section: key:

1–8 A1 i

9–16 B III

17–24 A2 i

25–32 C v

33–40 A3 i

T H E C L A S S IC A L RO N D O Rondos in the late eighteenth century often occur at the end of larger multimovement works, such as sonatas, chamber pieces, and symphonies. With themes that are often taken from folk or popular sources—or at least imitate those sources—they provide a light finish and a welcome contrast to the usually more complex first movements and serious slow movements. Moreover, rondos provide an opportunity to demonstrate the player’s ability to change style quickly between contrasting sections. We next explore the two most important types of Classical rondos: the five-part rondo and the seven-part rondo.

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François Couperin, Les Goûts-réunis, Concert no. 8, “Air tendre”

EXAMPLE 26.1

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EXAMPLE 26.1

(continued)

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Five-Part Rondo Before you listen to the final movement of a Clementi piano sonatina (Score Anthology no. 26), glance at the score to familiarize yourself with the key and the melodic shape of the refrain’s opening. Now observe how Clementi articulates the beginnings of new sections with double bars. Do you see any significant changes in melodic contour, key, mood, and texture at these locations? Next, listen to the work in its entirety at least twice. On a separate sheet of paper, start your own form diagram of the piece, indicating refrains with A1, A2, and A3; indicate episodes with the letters B and C. For each section, capture its location and duration in measure numbers and its key with the proper roman numeral. Your form diagram should look something like this: measures: section: key:

1–24 A1 I

25–46 B V

47–70 A2 I

71–104 C i

105–119 A3 I

120–end Coda I

Coda, Transitions, and Retransitions In listening to Score Anthology no. 26, you probably heard one final section that did not sound like a refrain but merely served to confirm the home key and provide a satisfactory

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ending. Technically, the final return of a refrain is the structural end of a rondo; however, when extra musical material occurs beyond the point at which a piece could have ended, it is called a coda. The foregoing form diagram represents at the large scale how Clementi’s five-part rondo is put together (ABACA–Coda), but it misses a lot of detail. First of all, rondo forms can have connecting sections that move from refrain to episode (transition) or return from an episode back to the refrain (retransition). Look at the end of section A1: There is no modulation, there is no new theme or thematic development, and the cadence in m. 24 serves as a strong close for the section; therefore, there is no transition section. Contrast this with the end of section B: There is a PAC at m. 40, and the remaining material is fragmented and leads back to the original key. Measures 40–46 form a retransition. A similar retransition occurs at the end of section C, beginning at m. 90, so the form now looks like this: measures: 1–24 section: A1 key: I

25–40 B V

40–46 Retrans. →

47–70 A2 I

71–90 C i

90–104 Retrans. V→

105–119 120–end A3 Coda I I

Compound Rondo Form The second important detail missing from the form diagram involves nested forms. As with ternary form, rondo form can be a compound form with nested forms. Note that A1, B, A2, and C are in rounded binary form. measures: section: subsection: key:

1–24 A1 a-dig.-a⬘ I

25–40 40–46 B Retrans. b-dig.-b⬘ V →

47–70 A2 a-dig.-a⬘ I

71–90 C c-dig.-c⬘ i

90–104 Retrans.

105–119 120–end A3 Coda

V→

I

I

The rondo in Example 26.2 is composed entirely of nested forms. Use the criteria of repetition and contrast of thematic and tonal materials to help group smaller sections into larger formal units that represent the refrain and contrasting episodes. Be especially alert to where 16-measure units may be interpreted as small binary forms, and be on the lookout for transitions and retransitions. (For another example of compound rondo form, see the Anthology no. 37, Beethoven’s String Quartet in C minor, op. 18, no. 4, Allegro.)

EXAMPLE 26.2 Mozart, Viennese Sonatina in C, Five Divertimenti for Two Clarinets and Bassoon, K. Anh. 229, Allegro STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

grazioso

Chapter 26 Rondo

EXAMPLE 26.2 (continued) 9

18

27

36

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EXAMPLE 26.2 (continued) 71

80

89

cresc.

98

The Form and Harmonic Structure of Mozart’s Rondo This diagram summarizes both the form and the harmonic structure of Mozart’s rondo. Note that each part contains two eight-measure units that together comprise a binary form. The refrain is a simple sectional binary form, and the episodes are (balanced) continuous simple binary forms. measures: section: subsection: key:

1–16 A1 a a⬘ I

17–32 B b b⬘ i→I

33–48 A2 a a⬘ I

49–64 C c c⬘ IV

65–80 A3 a a⬘ I

81–end Coda I

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Chapter 26 Rondo

Seven-Part Rondo The seven-part rondo adds another episode and refrain to the five-part rondo. These two added parts create a symmetrical form, which some liken to a musical arch. The following diagram shows the symmetrical form and the typical keys for the seven-part rondo: A1 B1 A2 C A3 B2 A4 in major keys: I V, i, or IV I i, IV, or vi I I or i I in minor keys: i III or iv i iv, IV, III, VI, or I i I i As in the five-part rondo, the sections of the seven-part rondo are often cast in rounded binary forms.

Distinguishing Seven-Part Rondo Form from Ternary Form Because of its symmetrical construction and because section C may be longer and distinct from the flanking ABA sections, the seven-part rondo can sound like a large ternary form: Seven-part rondo: Ternary:

A1 B1 A2

C

A3 B2 A4

A

B

A⬘

It is possible to confuse a large ternary form with a seven-part rondo, especially if a ternary form contains its own nested binary form in the A section. Generally, the context will help you distinguish between the two. • Rondos were favored in the eighteenth century and ternary forms in the nineteenth century. • One is less likely to encounter a slow rondo than a spirited one. • Seven-part rondos usually contain repeated, nested smaller forms, adding yet another level of structure that is sometimes absent from ternary forms. • Seven-part rondos are often more sectional than ternary forms. This gives a feeling of refrain when A returns (A1 | B1 | A2 | C etc.), rather than the three-part A sections achieved with ternary’s larger harmonic trajectories (a dig. a⬘ | B etc.).

Missing Double Bars and Repeats Keep some additional points in mind as you continue to analyze rondos. First, because double bars demarcating large formal sections or subsections do not always appear in rondos, you may need to appeal to other musical signals (changes in key, motive, or texture) in supporting your formal choices. Remember that transitions and retransitions may or may not be present in rondo form. Also, many rondos end with a coda that restates earlier material. Usually, codas are cadential and emphasize the tonic, but they may sometimes emphasize IV before returning to V and I. Finally, after the statement of A1 and B1, composers often omit the repeats or write out ornamented repeats. An example of the latter may be seen in a comparison of A1 (mm. 1–16) and A2 (mm. 33–64) in the rondo from a Haydn string quartet in Example 26.3. Notice that A2 occupies exactly twice as many measures as A1. This is because each of the two eight-measure repeated phrases of A1 have been written out and ornamented in A2.

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EXAMPLE 26.3 Haydn, String Quartet in D major, op. 33, no. 6, Hob III.42, Finale A.

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Allegretto

stacc.

stacc.

stacc.

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Chapter 26 Rondo

EXAMPLE 26.3 (continued) 40

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EXAMPLE 26.3 (continued) 60

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 26.1–26.3

26.1 For the following piece, study the score then answer the questions on a separate sheet of paper. Haydn, Piano Sonata in C major, Hob XVI.35, Finale: Allegro 1. What is the form? Make a formal diagram that includes section labels and key structure. Make sure to show transitions and retransitions, and include measure numbers. 2. What is the period and formal structure of the opening refrain? Are there any changes in subsequent repetitions of this refrain? 3. Make a reduction of mm. 1–8 of the refrain that shows the contrapuntal relationship between the outer voices. In your analysis, distinguish between contrapuntal expansions and harmonic progressions. 4. Are there any motivic relationships between the refrain and episodes? Focus on contour. 5. If transitions or retransitions exist, describe their content (e.g., sequential) and function (e.g., modulatory, leading back to the refrain).

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T ER MS A ND CONCEP TS • coda • episode • five-part versus seven-part rondos • refrain • retransition • rondo (rondeau form) • rondo aria • section • subsection • transition

CH A PTER R EV IEW 1. The recurring sections of a rondo are called _____________________________, and the sections of contrasting material are called _____________________________.

2. Extramusical material that occurs after a piece could have ended is called a _______________. (Note: This section can also be structurally important.)

3. Like ternary form, a rondo often uses bridging material that leads away from and back to tonic. These sections are called _______________ and _______________, respectively.

4. A rondo form that contains sections with smaller nested forms is called a _______________ rondo.

C H A P T E R 27

Sonata Form

OV E RV I E W

This is the third and final chapter that explores large tonal forms. Sonata form, arguably the most important of the three forms, is derived from the lowly binary form, which provides all of the necessary—and crucial— ingredients to generate movements whose durations can occupy 15 minutes or more. Guided by the delicate balance between the underlying tonal structure and a complex surface structure, the form arose in the mid-eighteenth century, dominated large works through the nineteenth century, and continues to this day in widely varied incarnations. CHAPTER OUTLINE Historical Context and Tonal Background.......................................................... 631 The Binary Model for Sonata Form ....................................................................... 632 Beethoven, Piano Sonata No. 19 in G Minor, op. 49, no. 1, Andante .......... 633 Transition...................................................................................................... 636 Closing Section.............................................................................................. 636 Development and Retransition .....................................................................637 Recapitulation and Coda ..............................................................................637 Additional Characteristics and Elements of Sonata Form............................... 638 Monothematic Sonata Form ................................................................................ 638 The Slow Introduction.......................................................................................... 638 Harmonic Anomalies ............................................................................................ 640 Other Tonal Strategies ............................................................................................... 642 Three-Key Exposition ........................................................................................... 642 Extended Third-Related STAs ............................................................................. 642 (continued)

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631

Sonata-Rondo Form ................................................................................................... 645 Analytical Synthesis: Sonatas of Haydn and Mozart ........................................ 648 Haydn: Piano Sonata no. 48 in C major, Hob XVI.35, Allegro con brio ...... 648 Exposition...................................................................................................... 648 Development ..................................................................................................650 Recapitulation................................................................................................651 Mozart, Piano Sonata in B major, K. 333, Allegro .......................................... 652 Exposition.......................................................................................................652 Development ..................................................................................................653 Terms and Concepts ................................................................................................... 658 Chapter Review ........................................................................................................... 658 Summary of Part 7...................................................................................................... 660

H I S T OR IC A L C ON T E X T A N D T ON A L B AC KG ROU N D Sonata form is a structure on which many of the greatest compositions from the later eighteenth and nineteenth centuries are based. We explore its history, trace the evolution of its form, and analyze examples from the literature. Originally, in the sixteenth century, the term sonata was used as a signal that a given musical work was to be performed instrumentally and not sung. To a large degree, this meaning has held constant for centuries. The term applies to multimovement works for solo instrument or a small ensemble of instruments (there are almost no sonatas for voice). Over the years, musicians also have extended the word sonata beyond its original meaning and have applied it to discussion of movements with a very particular form. This form is as important (and just as common) as the other forms we have learned: variation, binary, ternary, and rondo. Since the 1780s all of the important genres of art music, including symphonies, concertos, operas, and instrumental sonatas, have featured movements cast in sonata form. The two terms often used as synonyms for sonata form—sonata-allegro form and firstmovement form—are misnomers, because movements cast in sonata form may be in any tempo and occur in any movement of larger works. Furthermore, the first movements of these works may not even be cast in sonata form. At a deeper level, even the term sonata form itself is problematic, given that it implies a rigid formal mold governed by a series of compositional rules that composers are required to follow. This most certainly is not the case. We consider sonata form as a way of composing, one that is the outgrowth of a large-scale musical process that is dependent on a powerful yet simple tonal strategy: 1. State the opening material in the tonic. 2. State additional material in a contrasting key. 3. Restate all of the material in tonic. This very general model is an outgrowth of binary form.

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T H E B I N A R Y MODE L F OR S ON ATA F OR M Sonata form may be seen as arising from a combination of balanced and rounded continuous binary forms (Example 27.1). The first large section of a sonata is called the exposition, and can be viewed as analogous to the material in a binary form up to the first double bar. There are several sections within the exposition. In the first tonal area (FTA)––the initial part of the exposition––material is presented in the tonic key. In the second tonal area (STA), material is presented in the exposition in a contrasting key (usually V in major mode and III in minor mode). • On the level of the form as a whole, the FTA is dependent on the rounded-binary characteristics, returning with the original material (recapitulation) after a digression (development) and a HC with an interruption. • By contrast, the STA is dependent on balanced-binary characteristics: Material (STA, usually with a new theme) presented at the end of the first section (exposition) returns at the end of the piece (recapitulation) in the tonic key. This is the sonata principle.

EXAMPLE 27.1 Comparison of Binary Form with Sonata Form A. Balanced Rounded Continuous Binary Form (major mode) balanced:

same material || :

thematic design:

I

harmonic design:

B.

: || :

A

digression

: ||

A

HC  I

V

Sonata Form (major mode)

sonata principle:

material originally not in tonic returns in tonic || :

thematic design: harmonic design:

Exposition FTA

STA

I

V

: || :

Development

Recapitulation FTA

: ||

STA

HC  I

The FTA and STA may contain similar or contrasting thematic material; they may also contain multiple themes. To avoid confusion and ambiguity, each theme will be labeled with its tonal area and a subscript number to indicate the order. For example, given three themes in the FTA and two in the STA, the labels would be FTA1, FTA2, FTA3, STA1, and STA2.

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Beethoven, Piano Sonata No. 19 in G Minor, op. 49, no. 1, Andante Listen to a small sonata movement by Beethoven in Example 27.2 and see if you can label the thematic sections (exposition, development, recapitulation) and harmonic sections (FTA and STA). Be aware that you will encounter passages that seem not to belong to any of these five sections. For now, we’ll ignore the additional passages. Keep the following

EXAMPLE 27.2 Beethoven, Piano Sonata no. 19 in G minor, op. 49, no. 1, Andante STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

8

15

(dolce)

21

27

32

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EXAMPLE 27.2 (continued) 39

44

49

54

59

65

73

(

)

(

)

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Chapter 27 Sonata Form

EXAMPLE 27.2 (continued)

78

dolce

83

89

95

102

questions in mind as you proceed. What is the large-scale tonal progression? Does it conform to our model of binary form? If not, what are the differences? Beethoven’s movement does indeed blend and expand aspects of rounded- and balanced-binary forms, but only the exposition repeats. The following diagram reveals why only the exposition is repeated: The development and recapitulation together are over twice as long as the exposition, and Beethoven achieves a proportional balance by

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repeating only the exposition. The letter “X” designates a new melody in the development, not based on FTA1 or STA1. measure: thematic design: harmonic design:

1 16 ||: Exposition FTA STA i III

34 :|| Development STA x STA VI V//

64 80 Recapitulation || FTA STA i

Transition Now that we have determined the large-scale tonal and formal sections in Beethoven’s movement, let’s return to those passages that seem not to belong to the sections in the preceding diagram. Between the FTA and the STA (mm. 9–15) is a passage that begins identically to the opening of the piece. Given that this passage follows a half cadence, we might expect this to be a consequent phrase that makes a period in the FTA. Instead, there is an alteration in m. 13, and the passage modulates to B major (III), ending on a half cadence and preparing for the entrance of the STA. This seven-measure passage that leads to the STA is called a transition (Tr). There are two types of transitions: 1. A dependent transition (DTr) begins with a restatement of the initial theme from the FTA. 2. An independent transition (ITr) uses new thematic material. Both types of transition modulate to the STA and end either on the new tonic or the new dominant (in which case the actual statement of the tonic is reserved for the opening of the STA). The pause that very often occurs between the end of the transition and the beginning of the STA and that marks the approximate midpoint of the exposition, is called the medial caesura. In the recapitulation, the FTA and STA remain in the tonic. There is no need for a transition, but transitions often reappear in the recapitulation. Since the ending key for the “transition” is now the original key, this passage is often altered (harmonically and/or melodically) to create a sense of motion. In Beethoven’s example, the transition returns at m. 72. This time, there is more activity (in the right hand) and a quicker movement toward III that is deflected; instead, tonic is retained as the phrase closes on a HC in G minor (at m. 79).

Closing Section The contrasting tune of the STA ends with a PAC (in III) in m. 29 of Example 27.2. The following cadential section, still part of the STA, which closes the exposition, is called the closing section (CL). The closing section follows the appearance of contrasting thematic material in the STA and a conclusive cadence of that material. Because the closing section’s purpose is to reinforce the new key, it usually contains multiple cadential figures that are cast in two or more subsections that may even contain new thematic material. As such, the closing section is often longer than the STA, which may occupy eight or even fewer measures. A double bar (or repeat sign) usually marks

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the end of the exposition, just as it marks the close of the A section in a binary form. Accordingly, the exposition for Beethoven’s sonata has the following form: measure: thematic design: harmonic design:

1 FTA i

9 DTr i

16 STA III

29 CL III

Development and Retransition The development is usually the freest section in sonata form and is analogous to the digression in binary form. Material presented in the exposition is transformed, although composers are free to introduce one or more new themes, explore new and often remote harmonic areas, and develop thematic and motivic material through transformations that include thematic fragmentation and sequence. Given the improvisatory character of the development, there is often a complete absence of regular phrasing and periodicity. Thus, developments are often the most complex and dramatic sections of the movement. Underneath the chaotic surface, however, lies a logical unfolding of tonal and melodic events that imbue the form with a sense of coherence. Beethoven begins his development with a variation of STA, followed by a new melody in E major (VI) that enters in m. 38. The melody from the closing section enters in m. 46, ushering in a tonally unstable section that drives to the dominant and the interruption in m. 54. The retransition (RTr) is the final area of the development, where the dominant prepares the return of the tonic in the recapitulation. In major-mode sonata forms, the dominant would be secured much earlier (in the STA), and from that point is implicitly prolonged through the development. In this case, the retransition explicitly restates and expands the dominant at the end of the development and moves to the interruption that precedes the recapitulation.

Recapitulation and Coda Almost always the recapitulation repeats many events of the exposition, but it contains crucial changes, the most important of which is that not only the FTA’s material but also that of the STA and CL return in the tonic key. We have also seen how transitions are altered so they lead back to the tonic. In addition, composers often alter the recapitulation by compressing thematic material from the FTA, introducing brief tonicizations using modal mixture, or even reversing the order of themes from the exposition’s FTA and STA. Although the movement could have ended in m. 97, Beethoven instead concludes it with cadential material from the STA in a coda. Codas occur after the recapitulation. They also can occur at the end of the exposition, where they are called codettas, since they are typically shorter and end away from the tonic key. Codas are optional, as their name implies (in English, “tail” or “appendage”). They serve to confirm the closing key and often incorporate material from the FTA or STA. Material is often stated over a pedal point, which creates a strong cadential feeling. Finally, codas often emphasize the subdominant, which provides a large plagal motion that extends the prevailing key. The following diagram provides a complete summary of the prototypical events that occur in a sonata form written in either major or minor mode.

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Sonata Form Thematic Design: ||: Exposition :||: Development Harmonic Design: FTA Tr STA CL (Codetta) RTr Keys (major mode): I V // → V V V Keys (minor mode): i → III III III V //

Recapitulation Coda :|| FTA “Tr” STA CL I → I I I i

→ (or

i I

i I

i I)

A DDI T IO N A L C H A R AC T E R I S T IC S A N D E L E M E N T S OF S O N ATA F OR M

Monothematic Sonata Form Example 27.3 illustrates one of Haydn’s string quartets, in which the opening of the FTA theme reappears in the STA. Haydn frequently used the same theme (although often varied) in both the FTA and the STA, to create a form called a monothematic sonata form. The lack of differentiation between sections plays havoc with attempts to define a first theme and a second theme, but, as you will see, it poses no problem for our analytical labeling system.

The Slow Introduction Some movements cast in sonata form contain slow introductions that touch on foreign harmonic territory and chromatic key areas and incorporate modal mixture. This is particularly common in large works, such as symphonies. Slow introductions usually begin on the tonic (although I is not well established) and eventually move to and close on a half

EXAMPLE 27.3 Haydn, String Quartet in A major, op. 55, no. 1, Allegro A.

STR EA MING AUDIO

FTA

W W W.OUP.COM/US/LAITZ

Allegro Violino I

Violino II

Viola

Violoncello

in I (A):

3

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Chapter 27 Sonata Form

EXAMPLE 27.3 (continued) B.

STA (using FTA theme)

30

in V (E):

cadence. Because the slow introduction wanders harmonically before moving to V, and because V is often extended, hovering with its added seventh, in anticipation of leading to the tonic, the introduction can be heard to function as a hugely extended upbeat that resolves to the tonic “downbeat” at the FTA. Example 27.4 shows the 12-measure introduction to Beethoven’s Symphony no. 1 in C. A brief look at the opening four measures reveals Beethoven’s game plan. Although the first sonority is a root-position C chord, it contains a seventh; as V 7/IV, it moves to F, conferring on this sonority apparent tonic status. Tonal clarification is not given in the following measure since the V 7 that appears (G7) moves deceptively to vi. The following crescendo sets up the expectation of tonal stability, but, yet again, Beethoven thwarts our expectations by falling in fifths, as vi moves to V 7/V to V, where a seventh is added. Subsequent attempts to resolve V 7 are thwarted, and the closing cadential gestures in mm. 9–12 reinforce the dominant. At last, in m. 13, V 7 resolves to tonic, which signals the beginning of the exposition.

EXAMPLE 27.4 Beethoven, Symphony no. 1 in C major, op. 21, Adagio molto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ 8

cresc.

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EXAMPLE 27.4 (continued) ten.

ten.

6

cresc.

ten. 10

Allegro con brio

ten.

Harmonic Anomalies Two harmonic anomalies frequently appear near or at the point of recapitulation. The first is the false recapitulation, in which the theme from the FTA appears in the “wrong” key; the real recapitulation, in the tonic, usually follows soon thereafter. Thus, false recapitulations are actually part of the development. The first movement of Haydn’s op. 33, no. 1 quartet contains a false recapitulation (Example 27.5). The movement is in B minor (although tonal ambiguity is present from the movement’s beginning, since D major is strongly implied). The apparent retransition strongly suggests a dominant. But rather than its being the V of B minor, it is instead V

EXAMPLE 27.5

Haydn, String Quartet in B minor, op. 33, no. 1 STR EA MING AUDIO

44

Retransition?

V/f (not V/b)

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Chapter 27 Sonata Form

EXAMPLE 27.5 (continued) 47

V/f

FTA?

50

A! (not b) 54

Retransition? Yes, finally! cresc.

cresc.

cresc.

cresc.

b: V

of F minor. And the joke doesn’t stop there. Haydn doubly fools the listener: Rather than the expected (albeit false) recapitulation beginning on F minor, A major boldly enters, stating the original theme. Only the twists and turns leading through an augmented sixth chord and arrival on V of B minor in mm. 56–57 redirect the tonal trajectory to the true recapitulation in m. 59 (not shown). The second harmonic anomaly is the subdominant return, in which the recapitulation begins not on I but on IV (Example 27.6). This procedure arose to create harmonic interest in the recapitulation since so much of it is traditionally cast only in the tonic. Given

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the exposition’s tonal model of root motion up a fifth from I to V and given that the STA in the recapitulation must appear in the tonic to prepare for closure of the movement, composers begin the recapitulation down a fifth from the eventual tonic. Mozart’s Piano Sonata in C major, K. 545, is an example of one such work with a subdominant return.

The Subdominant Return

EXAMPLE 27.6

Exposition FTA

Recapitulation STA

FTA

STA I

V I

IV (up a fifth)

(up a fifth)

O T H E R T ON A L S T R AT E G I E S

Three-Key Exposition Sonata form remained an important formal structure in the nineteenth century. However, the opening years of the 1800s brought with them tonal innovations of many types, including supplanting the traditional tonic and dominant polarity with other tonal progressions. One of these, the three-key exposition, is found in major-mode works in which the STA moves to a diatonic third–related key, which bisects the traditional fifth motion from I to V. The motivation for such procedures may have been the century-old minor-mode binary and sonata forms whose overarching i–III–V|| create an arguably more dramatic progression than the I–V———|| characteristic of major-mode works. For example, Bruckner’s sixth symphony in A major moves from I–iii–V in the exposition and I–vi–IV in the recapitulation before returning to tonic. However, notice that the traditional dominant is secured by the end of the exposition.

Extended Third-Related STAs An even more dramatic tonal strategy is to postpone the structural dominant until the retransition and to remain in the mediant for the entire STA. For example, beginning in 1800, Beethoven explored such motion in his so-called “middle period” works, including his Piano Sonata in G major, op. 31, no. 1 (Example 27.7). The piece begins with a jaunty G-major gesture leading to the dependent transition, which we would assume would nicely place the STA in the traditional key of V (D major). Instead, the surprising arrival on F, with its dominant flavor (m. 64), leads us to the chromatic third–related key of B major (III). However, Beethoven quickly downgrades the novelty of this tonal

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EXAMPLE 27.7 Beethoven, Piano Sonata in G major, op. 31, no. 1, Allegro vivace STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

43

G:

G:

I

50

iii: vi i

iv 6

V

It 6

V

57

iv

V

iv 6

It 6

iv 6

V

It 6

V iv

It 6

64

III ! (not iii) V 69

74

finally iii

etc.

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progression by converting the B major to B minor (iii), the diatonic key in which the rest of the exposition unfolds. Two years later, in his “Waldstein” sonata (Example 27.8), Beethoven again invokes the tonal tactic of moving from I to chromatic III. But this time, after the opening in C major, he remains in E major (III) throughout the exposition (m. 35ff ). The development focuses on various forms of IV, and V is really only secured at the retransition.

EXAMPLE 27.8 Beethoven, Piano Sonata in C major, “Waldstein,” op. 53, Allegro con brio STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

14

C:

V

I

17

20

cresc.

iii: vi 6 iv 6

It 6

23

V 26

cresc.

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Chapter 27 Sonata Form

EXAMPLE 27.8 (continued) 29

decresc.

33

dolce e molto ligato

cresc.

III !

S O N ATA- RO N D O F OR M Recall that rondo is a sectional (“composite”) form that composers use for closing multimovement works, including symphonies, concertos, and sonatas. These often-playful movements provide a good-natured close to what are usually large and serious works. The seven-part rondo is characterized by the refrain (labeled A1, with subsequent statements incrementing the number as follows, A1, A2, A3, etc.) that alternates with episodes to produce the following sectional structure: A1 B1 A2 C A3 B2 A4. This model is often modified by the addition of transitions and retransitions, as shown, along with the common tonal framework in which tonic and dominant are used in the first three sections (ABA⬘), a contrasting (usually plagally related) key used in the C section, followed by the return to and continuation in the tonic for the final A3 B2 A4, creating a large three-part form overall: ABA || C || ABA.

Seven-Part Rondo A1 I

Tr

B1 V

RTr A2 I

C RTr A3 IV, i, I vi, etc.

Tr

B2 I

A4 I (coda)

By the later Classical period (1780–1800), composers imbued the rondo with dramatic significance in three ways: 1. increasing its length by extending and developing specific episodes, particularly the C section; 2. varying the refrain (with melodic embellishments, the insertion of sequential material, or modal mixture); and 3. incorporating new themes and keys.

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Clearly, first-movement sonata form was a model for such changes. Classical composers were aware of the underlying similarities between the sonata and rondo forms including the tonal structure. For example, the basic sonata design reveals a large three-part form: exposition, development, and recapitulation.

Basic Sonata Form |-----------Exposition-------------------------|Development------------|-----Recapitulation------------| FTA I

STA Tr

CL

RTr

V

IV, i, vi, etc.,

FTA I

Tr

STA

CL

I

I

The similarities run even deeper: Sonata form’s tonal structure is predicated on a motion from the tonic to the dominant in the exposition, a tonal contrast and loose-knit structure in the development, and a return to the tonic in the recapitulation. This is nearly the same large-scale plan as the rondo, where the appearance of B1 is usually in the dominant—the difference being that its return (B2) is transposed to the tonic. Indeed, a rondo modified by (1) a second B transposed to the tonic and (2) a C section that functions as a development is clearly a hybrid form, effectively combining attributes of both rondo and sonata into what is called sonata-rondo form. Two additional modifications occur in sonata-rondo form that make the connections even stronger. First, transitions and retransitions create a more fluid structure, and, second, the C section unfolds in a more digressive, developmental fashion and may include thematic material from the A and B sections. The diagram that follows shows how the various elements of rondo and sonata form combine to create the sonata-rondo form. The top level of the diagram shows the three large sections (exposition, development, and recapitulation), and beneath these the smaller formal sections of the rondo are illustrated, supported by the underlying tonal structure.

Sonata-Rondo Form |-------------Exposition -------------------| Development-------------- |-------Recapitulation------------| A1 = FTA I

Tr

B1 = STA

A2 = ?

C (expanded) RTr A3 = FTA Tr B2 = STA A4 = Coda

V

I!

IV, i, vi, etc. V 7

I

I

I

Notice the moment in the diagram (marked with a question mark and an exclamation point) that reveals a noncongruency between sonata and rondo: The second statement of the refrain (A2), which leads to the exposition’s close, brings back the initial theme, but does so in the tonic. As we know, in sonata form, this would be the closing section and would necessarily remain in the dominant. Composers often solve this formal tonal problem by modifying A2, either shortening it, or destabilizing the return to the tonic through modal mixture or elision, effecting a transition to the developmental C section. Such blurring of the form may lead the listener

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to think that the return of the refrain is actually the beginning of the development, and that the composer is restating the initial theme in preparation for its development. On the other hand, the composer may simply repeat the refrain literally, closing it strongly in the tonic. In such a case the listener is led down the wrong path, assuming the movement is in sonata form, and this is the repeated exposition, back in the tonic. But when C immediately follows the A section, the listener realizes they are party to an aural bait-and-switch tactic in which the composer has duped the listener. Mozart’s Piano Sonata in D major, K. 311 (Score Anthology no. 29) is a clear example of sonata-rondo form. Listen to and mark the large sections of the movement, keeping in mind the major sections just discussed. The movement is cast in a seven-part rondo as follows: A1 B1 A2 C A3 B2 A4 (1–26) (41–56) (86–102? 119?) (102? 119? to 157? 168?) (173–189) (206–220) (249–266) I----------V---------- I-------? vi----iv---ii-----I----------------------------------------Notice the transposition of B2 to the tonic is also a feature of the sonata-rondo. The question marks in the diagram indicate more than one possibility for determining the beginnings and endings of sections (specifically A2 and C). Such blurring of sectional boundaries in a rondo form also indicates sonata-rondo form. The formal elision within the A2 section—where the refrain recurs in tonic—is a monkey wrench thrown into sonata form: the STA and closing should remain firmly in the new key and cannot return to the tonic until the recapitulation. However, Mozart has changed the A2 refrain by tonally destabilizing its tonic at m. 104 and even developing the cadential material in mm. 112–119 by constantly transposing it, weakening the A2 to the degree that the listener cannot be sure where it ends and the C section begins. There are many measures not accounted for in this formal summary. These transitions and retransitions create a more fluid, dramatic effect. A more complete formal diagram follows, detailing the transitional material as well as the refrain and its repetitions. Notice that Mozart has added a cadenza that highlights the crucial retransition that leads from the end of C (development) to A3 (recapitulation). Mozart, Piano Sonata in D major, K. 311, Rondeau Exposition----------------------------------------------------------------Tr B1/STA CL RTr A2 A1 (FTA) 1–26 27–40 41–56 56–79 79–86 86–102 (or 119?) 1–16 (refrain) 16–26 (suffix) I--------------V--------------------I--------------????

Development ------------------------C RTr cadenza 102 (or 119?) to 157 (or 168?) 173

vi-----IV---ii------V---------------------

Recapitulation ----------------------------------------------------------------------------------------------------------------Tr B2 (STA) CL RTr A4 cadential tag A3 (FTA) 173–189 190–205 206–220 221–244 244–248 248–266 266–269 173–189 (refrain suffix appears 256–266! only, no suffix) I----------------------------------------------------------------------------------------------------------------------------------

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A NA LY T IC A L S Y N T H E SIS: SONATA S OF H AY DN A N D MOZ A RT To provide analytical models for your own analysis, we will continue with an analysis of two sonata movements, the first by Haydn and the second by Mozart. In addition to exploring the form of these movements, we will see how each composer fleshes out the structure. In the Haydn sonata, we will focus on tonal issues to see how surface events penetrate into deeper musical structures and influence the form. In Mozart’s piece, we will discover how an analysis of motivic expansion helps to clarify the meaning behind what appears to be tonal chaos in the development.

Haydn: Piano Sonata no. 48 in C major, Hob XVI.35, Allegro con brio Haydn’s well-known Piano Sonata in C major (Score Anthology no. 23) provides a good introduction to analysis of sonata form, although it does not always adhere strictly to traditional procedures. Remember that sonata form is really not a “form” at all, but a dynamic process in which certain conventions of form can often be counted on to appear. In beginning your study, listen to the piece, marking the following events (some may not be present) and providing roman numerals for keys: Introduction Exposition: FTA, DTr or ITr, STA, Cl, Codetta Development: RTr Recapitulation: FTA, DTr or ITr, STA, Cl Coda

Exposition The piece begins without an introduction. At m. 1, the exposition commences with the FTA in the tonic. The opening eight-measure theme begins with simple arpeggiations (mm. 1–4) followed by a mostly stepwise descent with incomplete neighbors (mm. 5–8). A bit of melodic reduction reveals a stepwise motion from the repeated G that descends a fifth to C in m. 8 (Example 27.9). Notice that the final D5 and C5 do not really participate in the stepwise descent in m. 6 but wait until the final cadential motion in mm. 7–8; the contrapuntal motion and voice exchange in m. 6 simply prolongs the E5 in m. 5.

EXAMPLE 27.9 Haydn, Sonata in C, mm. 1–8 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Allegro con brio

C:

I

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EXAMPLE 27.9 (continued) 4

3

V

6

I

ii 6

V

I

Measures 9–16 are an almost literal repeat of mm. 1–8 except for the triplet accompanimental figure and the more varied harmonic setting in mm. 13–15. Therefore, we are not finished with the FTA until at least m. 16 and the second PAC. A new theme appears in m. 20 (Example 27.10). When F5 (m. 23) instigates a move to G major (V), we know that we have entered the modulatory transition. So, the proper label for this section is ITr. In general, the use of accidentals in a major-key sonata marks

EXAMPLE 27.10 Haydn, Sonata in C, mm. 20–30 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

20

cresc. 3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

24 3 3

3

3 3

3

3

3

3

3

3

3

3

27 3 3 3

3

3

3

3

3

3

3 3

3

3

3

3

3

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the transition section, and the dominant of the key of the STA marks the end of the transition section (i.e., V/V in m. 35). In minor-mode pieces it is the opposite: The opening minor tonic requires an accidental (raising 7 to create a leading tone), but the move to the relative major reinstates the lowered form of 7 since it now functions as 5 in the new key. Motivically, the beginning of the transition contains a stepwise ascent, C5–D5–E5, 5 E –F5–G5 (Example 27.10); this is reminiscent of the opening arpeggiation (now filled in with passing tones), as well as an inversion of the linear descent from G5 to C5. Another correspondence follows when, after G5 rises a fifth to D6 (mm. 24–26), D6 descends a fifth to G5 (mm. 26–28 and 28–30) in exact imitation of the opening stepwise-fifth descent from G5 to C5.

EXAMPLE 27.11 Haydn, Sonata in C, mm. 36–41 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

36

3

3

3

3

3

3

3

3

3

3

3

3

39

cresc. 3

3 3

3

3

3

3

3

3

3

The STA begins in m. 36 with a new theme. However, even a cursory examination reveals that the ascending fifth recurs (Example 27.11). A strong cadence in mm. 44–45 closes the STA. The CL, which occupies mm. 46–62, begins with yet another manifestation of the descending fifth (filled-in arpeggiation figure), which releases the tension of the exposition (Example 27.12). A codetta (mm. 62–67) restates the opening theme in V. The following chart presents the exposition’s formal and harmonic events.

measures: thematic design: harmonic design:

1–19 FTA I

20–35 ITr

36–45 STA V

46–62 CL V

62–67 Codetta V

Development The development begins with an apparent return to the tonic, C major. The linear descent of a fifth in the soprano ends in an unexpected half cadence in A minor (vi) in m. 71.

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Chapter 27 Sonata Form

EXAMPLE 27.12 Haydn, Sonata in C, mm. 44–48 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

44 3

3

3

Haydn—a composer with a penchant for surprise—does not continue in A minor, but instead sets the opening theme in F major. Only after the theme is completely stated (mm. 71–79) and an A2 (–3/⫹4) sequence accrues dramatic tension (mm. 80–83) does A minor return, in m. 83. Haydn next retraces his harmonic steps, using a D2 (–5/⫹4) sequence to return to F major (mm. 86–90). However, the F harmony continues to descend to E, the same chord that was abandoned in m. 71. A pedal point on 5 usually indicates the retransition, but the pedal here is on E (V/vi) rather than on G (V). A strong circle of fifths moves to the dominant (E–A–D–G in mm. 94–103), so the pedal on E in m. 94 may be regarded as the beginning of the retransition.

Recapitulation The recapitulation begins in m. 104 with a restatement of the FTA theme, one octave lower than its original presentation. A dramatic change occurs in m. 111 when, just as the listener anticipates a literal restatement of the theme, the initial tonic chord appears in the parallel minor. It is followed by many changes, including modal mixture, all of which suggest that Haydn is redeveloping material (i.e., that the movement has not really left the development and begun the recapitulation). However, in m. 118 he returns to the established model by repeating the FTA material first heard in m. 13. Suddenly, Haydn skips ahead to the dramatic arpeggiations and half cadence that characterized the end of the transition section, compressing the second part of the FTA and the transition into a 15-measure phrase, nearly half the length it occupied in the exposition. The STA is stated in the tonic (mm. 126–135), followed by the CL (mm. 136–151), at which point a dramatic diminished seventh chord (m. 141) heralds an extended coda that closes the piece. This diagram presents a complete formal and harmonic diagram of the movement:

measure: 1 20 36 46 thematic design: Exposition harmonic design: FTA ITr STA CL I V V

62

68 94 Development Codetta RTr V I–vi–IV–vi–V//

104 111 126 136 Recapitulation FTA “ITr” STA CL I I I

152 Coda I

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This movement generally conforms to our model of sonata form. However, departures from the norm, such as the pedal point at the end of the FTA, the very short STA, the curtailed FTA in the recapitulation, and the dovetailing of the missing material in the transition of the recapitulation, demonstrate how composers might mold the sonata form to accommodate their creative impulses.

Mozart, Piano Sonata in B  major, K. 333, Allegro

The first movement of Mozart’s Piano Sonata in B major, K. 333, appears to be a random series of harmonies in the development section. Our goal is to seek an underlying compositional logic for these curious excursions. Listen to and study Score Anthology no. 28, locating the important formal sections and their controlling key areas. The formal structure is clear in this movement. The exposition, demarcated by the double bar and repeat signs, occupies mm. 1–63. The FTA closes at m. 10, the dependent transition begins at m. 11 and closes on the arpeggiating dominant of the new key, and the STA in F major (V) occupies mm. 23–38. The closing section divides into two smaller sections (mm. 38–50 and mm. 50–59), and a codetta closes the exposition (mm. 59–63). The recapitulation and coda (mm. 94–165) unfold in the same manner as the exposition. The following chart shows the main formal sections of the movement. Notice that the harmonic progression in the development (mm. 64–93) remains to be interpreted.

measure: 1 11 23 39 59 64 87 thematic design: Exposition Development harmonic design: FTA DTr STA CL Codetta RTr I V V V ??? V//

94 104 119 135 161 Recapitulation Coda FTA “DTr” STA CL I I I I

Exposition We will now explore the thematic and motivic materials in Mozart’s sonata. Let’s make a contrapuntal reduction of the outer voices of the FTA theme in order to understand the underlying voice-leading framework from which motivic figures might emerge (see Example 27.13). A clear I–ii–V7 progression opens the piece and is followed by a contrapuntal elaboration of the tonic (mm. 5–6). This movement does not initially appear to contain any clear-cut motives based on surface contours, except for the descending scalar sixth (comprising a fifth, preceded by an upper-neighbor grace note that should be played as a sixteenth note) that begins the piece. Although the B4 in the upper voice of m. 1 is clearly an arrival point, the E5 (m. 2) that eventually moves to D5 (m. 4) seems to be more important, given those pitches’ durational, metrical, and registral prominence. Might the initial scalar descent be emerging and expanded over many measures? This is the interpretation given in Example 27.13. Note that the overall descent of a fifth (the same fifth that opened the movement) is bisected into thirds by range: F5–E5–D5 and D6–C6–B5. The F5 in the upbeat to m. 1 is prolonged through the downbeat of m. 2 before it descends to E5 (m. 2) and D5 (m. 4). The continuing C4–B4 in mm. 5–6 is not a strong arrival on tonic, because the tonic chord is in inversion and is not preceded by a PD–D motion; the chords in mm. 5–6 act

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Chapter 27 Sonata Form

as part of a voice exchange that prolongs tonic, which further indicates the subordinate nature of the B in m. 6. The strong structural arrival of C6–B5 in mm. 9–10 completes the fifth descent.

EXAMPLE 27.13 Mozart, Sonata, Essential Counterpoint (mm. 1–10) 1

mm:

6

9

N 6

5

4

3

6

I

(3)

2

5 3

ii 6

1

V

I

The initial theme in the STA literally repeats the same fifth-plus-neighbor descent from the FTA, in the key of F major (V). However, this time Mozart develops the upper neighbor to 5 by harmonizing 6 with B major (IV) in m. 24, therefore stabilizing the soprano D5 (Example 27.14). Notice that just like the FTA’s fifth-plus-neighbor descent, the STA’s descent is interrupted by a pause on 3 (in F major, m. 26). The complete descent does not occur until m. 38.

EXAMPLE 27.14 Motivic Correspondence Between FTA and STA

23

∧ 5

∧ ∧ ∧ 6 5 4

∧ 3

∧ 2

∧ 1

∧ 6

∧ 5

etc.

F:

Development The development contains unusual modal shifts and curious tonicizations that make it difficult to determine any underlying harmonic progression. It begins with a simple righthand restatement of the initial tune in F major (V), with the upper neighbor, D5. A bass ascent begins with F3 in m. 64 and moves through G3, A3, B3, and C4; the line continues with the D4 (m. 69) and resolves to C4 (m. 70). This results in another setting of the familiar motive of a stepwise fifth-plus-neighbor, this time in exact retrograde of the opening gesture of the STA and expanded over seven measures. Notice that the chord in m. 69

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sounds out of place, as if Mozart has marked it for our consciousness. Could he be preparing us for other hidden statements of the motive? (See Example 27.15.)

EXAMPLE 27.15 Bass Line of Development Restates Opening Motive in Retrograde 64

F:

∧ 3

∧ 2

∧ 1

∧ 5

∧ 4

∧ 6

∧ 5

etc.

The unexpected cadence on F minor (rather than major) in m. 71 and motion to a G7 harmony in m. 73 imply a tonicization of C minor. However, the “arrival” on C minor is greatly weakened when the bass is left unresolved on G, resulting in a six-four harmony (m. 75). G3 descends to an F7 harmony (mm. 76–78), implying the beginning of the retransition. However, once again the listener’s expectations are thwarted when F3 rises to F3 and then resolves to G minor in m. 80. There is no strong cadence in G minor; instead, V43 of V suddenly appears in m. 87 and moves to V in mm. 88–89. The recapitulation begins in m. 93. We now step back and interpret these events. We know that F major (V) controls the opening of the development and that C minor (ii) and G minor (vi) follow. Accordingly, a series of ascending fifths (F–C–G, and D, as V of G) underlies the development until the motion to F at m. 87. But many questions remain unanswered. For example, why are the tonal areas so weakly tonicized? And how can we explain the odd shift from the unusually long and unresolved D-major harmony that moves to the weak V43/V chord in m. 87. Let’s look to the eight-measure motivic expansion of the fifth-plus-neighbor motive for clues.

EXAMPLE 27.16 Development as Enlarged Statement of Opening Motivic Gesture mm:

64

73

77

80

5

6

81

87

94

3

2

1

N 5

6

5

4

The bass F3 ascends to G3 in m. 73; the sustained G3 was followed by the chromatic passing tone G3, which returned to F3 (mm. 76–77). Again, the bass rose to G3 through F3, followed this time by a rapid descent to D3, which was sustained from mm. 81–86. Through registral transfer, D3 then fell to C4 (V43 chord in m. 87), leapt to F3 (m. 88), and finally returned to B3 at the opening of the recapitulation. Example 27.16 presents a notated summary of this progression.

Chapter 27 Sonata Form

655

From this bass-line summary, we see that Mozart is projecting the small opening gesture (G–F–E–D–C–B) over the entire development. Remember that the very first expanded statement of the descent (mm. 1–10) stopped on D for five measures. We now can understand why Mozart extended D major for so long (mm. 81–87) and didn’t resolve it to its tonic. We also know why Mozart did not resolve the G3 to C in m. 75, for to have done so would have obscured the remarkable linear parallelism. Finally, in light of the controlling nature of the motive, we understand why Mozart used the V43 chord in m. 87 rather than the expected and much stronger root position: because the inversion (with C in the bass) preserves the motive’s stepwise descent. The goals of the preceding analyses were to understand the mechanics of sonata form, to show how sonata form is an outgrowth and expansion of binary form, and to demonstrate how sonata form is a flexible and fascinating process that composers employ to express uniquely personal musical statements. Discovering and interpreting hidden and transformed manifestations of motives are some of the rewards of analysis.

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 27.1–27.2

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

27.1 Platti, Sonata in C Major, Six Sonatas for Harpsichord, op. 4, no. 4 Listen to and study the following movement. On a separate sheet of paper, answer the following series of questions. 1. Make a formal diagram that includes names of sections and their respective measure numbers as well as the tonal plan (use roman numerals). 2. The phrase lengths in the exposition vary from four to eleven measures. Mark the phrases in the exposition. And when you encounter long ones, explain how they are extended. Consider the possibility that Platti has repeated small subphrases or inserted sequences. For example, the first phrase occupies six measures, but mm. 5–6 are a repetition of mm. 3–4, which help to reinforce the first cadence. 3. Bracket and label all sequences in the piece. 4. What contrapuntal technique is used in mm. 22–24? 5. The transition in the exposition prepares not only the new key but also the motivic and thematic material in the STA. Discuss at least two examples of how Platti achieves this preparation. 6. The development begins much the same way the exposition does. However, an important change occurs that sets into motion the fragmentation and tonal adventures that are characteristic of development sections. Discuss the relationship of the opening of the development to the opening of the exposition, and then focus on the changes that follow. Include in your discussion the motives used and the harmonic areas explored. 7. There appears to be no retransition that would prepare the recapitulation. However, a slight ritard into the recapitulation just might allow one to hear an implied dominant that leads to the recapitulation. Develop this idea in a few sentences.

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8. Given that the tonic key is maintained throughout the recapitulation, you might assume that transitions are not necessary. In fact, they might be viewed as hindrances, for they must give the impression of motion, only to lead eventually back to the tonic, in which the tune from the STA is cast. However, Platti has written a transition that is much more interesting than the usual fare. List at least three differences between this transition and the transition in the exposition. Allegro

3

3

7

3

3

3

3

3

3

3

3

13

19

25 25 3

3

3

3

3

30 30 3

36

3

3

3

3

3

3

3

3

3

3

3

657

Chapter 27 Sonata Form 42 3

3

48

3

3

54 3

60

66

72

78 3

3

3 3

3

3 3

3

3

3

3

3

3

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T ER MS A ND CONCEP TS • closing section (CL) • false recapitulation • first tonal area (FTA) • monothematic sonata form • second tonal area (STA) • slow introduction • sonata form • exposition • codetta • development • recapitulation • coda • subdominant return • three-key exposition • transition (Tr) • dependent transition (DTr) • independent transition (ITr)

CH A PTER R EV IEW 1. In contrast to the first tonal area (FTA) in the tonic key, the second tonal area (STA) is in a contrasting key, usually _____________________________ in major, and _____________________________ in minor. Note: The FTA and STA only define tonal areas. Each section may have more than one theme.

2. List the three large sections of a sonata.

3. Describe how both types of transitions (Tr) differ thematically. 1. Dependent transition (DTr): 2. Independent transition (ITr):

4. Both types of transitions modulate to the STA, and end either on the _____________________________ or the _____________________________.

Chapter 27 Sonata Form

659

5. The pause that very often occurs between the end of the transition and beginning of the STA is called the _____________________________.

6. The development of a sonata form is analogous to the ___________________ in binary form.

7. The area at the end of the development where the dominant prepares the return of the tonic in the recapitulation is called the _____________________________.

8. Whereas a coda closes the entire movement (end of the recapitulation), a codetta closes the _____________________________.

9. A sonata in which the opening of the FTA theme reappears in the STA is called a _____________________________. Note: The FTA and STA only define tonal areas. Each section may have more than one theme.

10. A slow introduction often opens on tonic, wanders harmonically, and closes with which kind of cadence? (IAC, PAC, or HC)

11. List two kinds of harmonic anomalies in sonata form, and describe each in one sentence.

12. In a _____________________________, the STA is not in V, but instead in a diatonic thirdrelated key.

13. Sonata-rondo form is a rondo that is modified in two ways: 1. B2, initially in the dominant, is transposed to the _____________________________. 2. C functions as a _____________________________.

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S U M M A R Y OF PA R T 7 We have seen that even though binary form lies at the heart of ternary, rondo, and sonata forms, there is a crucial distinction between sonata and the other two forms: Ternary and rondo are additive, composite forms, whereas sonata is an organic form. That is, ternary and rondo forms—while often demonstrating important motivic and harmonic connections between their various sections—contain tonally closed units, and thus the omission of one or more of these sections would not seriously jeopardize the structural integrity of the piece. Sonata form, by contrast, is a more continuous structure, each part of which depends on every other part, resulting in a single integrated whole. We also learned that the basic root motions of tonal music, which we first encountered in the chord-to-chord progressions beginning in Chapter 5 and later learned may be expanded by tonicization, also were part of these large forms. Finally, motivic connections between the various strata of a piece create carefully woven webs that make each piece a unique artwork.

PA R T 8

INTRODUCTION TO NINETEENTH- CENTURY H A R MON Y: THE SHIFT FROM ASY MMETRY TO SY MMETRY

F

ar too often, people rely on general proclamations to characterize the new developments of nineteenth-century music. There is some truth both in effusive and subjective statements such as “It is a period evincing a lush hodgepodge of thick, wandering harmonies” and in technical and clinically objective statements, such as “the chromatic tonal system replaces the diatonic system.” The music of nineteenth-century composers is indeed lush, and it features thick, rapidly changing harmonies built from novel combinations of four and five voices. And later nineteenth-century music is more chromatic than eighteenth- and early-nineteenthcentury music. But neither proclamation provides us with examples of these new attributes or with tangible explanations of how early-nineteenth-century harmonic practice influences the music of the late nineteenth and early twentieth centuries. Part 8 explores some of the innovations of tonal composition that occurred from 1820 to 1900. These developments were naturally suited to the artistic sensibilities of the nineteenth century, an era in which sharp social, philosophical, political, and artistic changes took place. We start by tracing the seeds for these new harmonic tendencies in the music of composers such as Mozart, Beethoven, Schubert, and Chopin. From there, we witness the flowering of these harmonic techniques in the music of composers such as Wagner, Liszt, Brahms, Tchaikovsky, Wolf, and Grieg. 661

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CH A PTER 28

New Harmonic Tendencies OV E RV I E W

This is the first of two chapters that introduces tonal processes and devices used in nineteenth-century music. In this chapter, we will see how the rise of tonal ambiguity is generated from modal mixture, which ultimately overtakes the standard dominant-tonic axis. Further, purely half-step motion has major repercussions for the traditional diatonic framework. CHAPTER OUTLINE Tonal Ambiguity: The Plagal Relation and Reciprocal Process ..................... 664 Tonal Ambiguity: Semitonal Voice Leading ........................................................ 667 Semitonal Voice Leading and Remote Keys ...................................................... 667 Tonal Clarity Postponed: Off-Tonic Beginning ................................................. 670 Double Tonality .......................................................................................................... 670 Symmetry: The Diminished Seventh Chord and Enharmonic Modulations ........................................................................... 674 Analysis ................................................................................................................... 676 Analytical Interlude............................................................................................... 677 A Paradox: “Balanced” Music Based on Asymmetry ........................................ 680 Symmetry and Tonal Ambiguity............................................................................. 682 The Augmented Triad ................................................................................................ 683 Altered Dominant Seventh Chords ........................................................................ 687 The Common-Tone Diminished Seventh Chord ............................................... 689 Common-Tone Augmented Sixth Chords ........................................................... 690 Terms and Concepts ................................................................................................... 692 Chapter Review ........................................................................................................... 692

663

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T ON A L A M B IG U I T Y: T H E PL AG A L R E L AT ION A N D R E C I PRO C A L PRO C E S S Modal mixture (Chapter 21) and tonicization (Chapter 19) allow chromaticism to permeate deeper levels of music. The free interchange of major and minor modes results in a compression from 24 major and minor keys to 12 “major-minor” keys. Such compression allows composers easy access to chromatically related keys such as III and VI. In the nineteenth century, this weakened the dominant function. As a result, the final structural cadence of pieces incorporated harmonies such as iv and iiø65—chords that substitute for the dominant—and moved directly to the tonic in a technique called the plagal relation. Paradoxically, this caused the dominant to become much more important as it retained its ability to signal where the tonic should be. The rise of the plagal relation contributed to tonal ambiguity, an important aesthetic in the music of the nineteenth century. An example of this deliberate obscuring of the location of the tonic may be heard at the end of Chopin’s Etude in C minor (Example 28.1). Note how the final section of the piece sounds like a coda, because the major tonic functions as an applied chord of F minor (iv). Because this coda-like section treats the tonic as an applied chord of iv, you might have heard the piece close not on a tonic harmony but rather on the dominant of iv. If, after careful listening, you can discern both functions of

EXAMPLE 28.1

Chopin, Etude in C minor, “Revolutionary,” op. 10, no. 12 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

77

poco rallentando

soo voce

(a tempo) 81

ed appassionato

c:

I

V7/iv

or f:

V

7

IV — iv

I4 –3

I —

V4 – 3

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Chapter 28 New Harmonic Tendencies

the progression, then you are being sensitive to an important type of nineteenth-century tonal ambiguity called the reciprocal process. The reciprocal process occurs when the listener loses tonal grounding because of conflicting tonal implications that confuse the three harmonic functions (T, PD, and D). Composers such as Robert Schumann and Johannes Brahms were fond of incorporating the reciprocal process in their compositions. Study the close of Schumann’s song “Auf einer Burg,” which begins in E minor (Example 28.2); then listen carefully to the excerpt. Although the song looks like it ends in E major, does it sound like it ends in that key?

EXAMPLE 28.2 Schumann, “Auf einer Burg” (“In a Castle”), Liederkreis, op. 39, no. 7 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

22

Drau ßen ist Outside it

es still is quiet

und fried lich, al le sind ins Thal ge zo gen, Wal des vö and peaceful: all have gone to the valley; wood birds

gel

27

ein sing

sam sin alone

gen

in in the

fährt da un passing by

ten below

auf on

den lee ren empty arching

Fen ster bo windows.

gen.

Ei ne Hoch zeit A wedding

31

dem Rhein im Son the Rhine, in the

nen schei sunlight:

ne,

Mu si kan musicians

ten

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EXAMPLE 28.2 (continued) ritard.

35

spie len mun ter, play gaily

ii 7

i

und die schö ne and the fair

6

Braut, bride

Ger 65

PD

die she

wei weeps.

a: V

4

(or e: I

4

net.

?)

The closing five measures use augmented sixth and cadential six-four chords to tonicize a minor (iv), effectively transforming the E major into the V of A minor. Consistent with this transformation, the E-major triad that closes “Auf einer Burg” functions as a dominant preparation leading to the start of the next song of the cycle, “In der Fremde” (Example 28.3). Notice that the songs are linked not only by their large-scale dominant– tonic motions but also by the melodic motive that permeates both songs (marked by brackets in Examples 28.2 and 28.3).

EXAMPLE 28.3 “In der Fremde” (“In a Foreign Land”), Liederkreis, op. 39, no. 8 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Zart, heimlich

Ich hör’ I hear

a:

(V)

i

die Bäch lein the brook lets

rau rush

schen ing

im Wal here and

de her there in

und the

hin, wood,

667

Chapter 28 New Harmonic Tendencies

T ON A L A M B IG U I T Y: S E M I T ON A L VOIC E L E A DI N G Nineteenth-century composers often connected distantly related chords or tonal areas with a technique that transforms one chord chromatically into the next. Semitonal voice leading moves two or more voices by a half step while usually keeping one common tone in another voice. A good introduction to semitonal voice leading can be seen in the slow introduction of Mozart’s “Dissonance” Quartet, shown in Example 28.4. Here, the sinuous motion of all the voices clouds the tonic of the piece, C major. The repeated C3s in the cello that open the piece imply the key of C. But the entrance of the viola’s A calls into question the possibility of C major, especially given that the first complete sonority is an A-major triad in first inversion on the downbeat of m. 2. On the next beat, however, violin I boldly enters with A5. The resulting pungent cross relation with A3 thwarts our expectations that A major might be the key. Only at the downbeat of m. 4, when a G-major triad (in first inversion) occurs, is there any evidence to support our initial expectation that C major is the key. In retrospect, we can understand that both the A and the A displace G, postponing its arrival.

EXAMPLE 28.4 Mozart, String Quartet in C major, “Dissonance,” K. 465, Adagio STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Violin I cresc.

Violin II cresc.

Viola cresc.

Cello cresc.

Semitonal Voice Leading and Remote Keys Example 28.5A illustrates a harmonic succession that involves chords whose roots lie a major third away from one another: C major–A minor–E major–C major (note the presence of intense enharmonicism, shown by slurs that indicate retention of common tones). The chord-to-chord connections sound relatively smooth, given their consistent step motion, yet tonal stability evaporates; there is no sense of tonic, pre-dominant, or dominant. In fact, one might say that tonal function is suspended so that the harmonic motion is more a chordal succession than a functional progression. This sense is corroborated by the lack of

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EXAMPLE 28.5 Semitonal Voice Leading and Distant Harmonic Relations A.

STR EA MING AUDIO

B. M 3rds

C

a

6

E 64 C

T.T.

C

F

T.T.

4 3

A

6 5

D42

W W W.OUP.COM/US/LAITZ

m 3rds

B7

g

6

B

7

D 64 B B :

4 2

E

6 3

IV

B 46 V

I

cadence. See how the return to C major is not satisfying as an arrival, even though the opening voicing returns. Example 28.5B illustrates the same principle as Example 28.5A but works by transforming major-minor seventh chords. Note the recurring two-chord pattern of the succession, in which each pair of chords juxtaposes the most distantly related root possible—a tritone. A series of minor-third root relations follows. The chord succession in mm. 3–5 is based on contrary motion that resolves to the new key, B major. Overall, B is secured by a stepwise chromatic descent from C (m. 1) to the new dominant (m. 4). Although the modulation could have been accomplished much more simply, its present form creates tonal ambiguity and demonstrates how its arrival on VII of C is but one of any number of potential tonal destinations. A good place to look for moments that exhibit the power and potential ambiguity of semitonal voice leading are pieces that employ enharmonic transformations of the augmented sixth chord and dominant seventh chord. Example 28.6 illustrates this common

EXAMPLE 28.6 Brahms, “Parole” (“Password”), op. 7, no. 2 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Andante con moto

Sie

e:

VI

Ger 65

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Chapter 28 New Harmonic Tendencies

EXAMPLE 28.6 (continued) 6

stand wohl am She stood at her

Fen ster arched window

bo

gen

und flocht sich trau And sadly braided her

rig

das

V 9

cresc.

Haar, hair,

der Jä The hunter

ger war fort had gone off,

ge

zo

gen,

der

cresc.

V 7/ II 12

rit.

Jä ger ihr Lieb ster war. The hunter who was her lover.

Ger 65 (in e)

procedure. Because Brahms’s song begins on a C-major sonority, the first-time listener will most likely assume C major to be the tonic. However, the addition of A3 in m. 3 destabilizes the C-major triad. The attentive listener will probably hear the chromaticism as the lowered seventh (B), rather than the augmented sixth (A), and thus assume that C has become V 7/IV. The semitonal movement to the cadential six-four chord in m. 6 requires the listener immediately to revise this expectation. At m. 6 we head to E minor rather than C major; the following PAC in m. 9 confirms this key.

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THE COMPLETE MUSICIAN

WORKBOOK 1 Assignment 28.1

The listener, in an attempt not to be misled by the C major-minor seventh chord when it returns at m. 9, is likely to interpret it this time as an augmented sixth chord. Brahms, however, fools the listener again by making the chord a V 7, which moves to an F-major sonority and a dominant pedal in II rather than to the expected dominant of E minor. Only in m. 14 does the augmented sixth return. The ambiguity of the dominant seventh and augmented sixth chords, paired with semitonal voice leading, allows Brahms to fool the listener again and again.

T ON A L C L A R I T Y P O S T P ON E D : OF F -T ON IC B E G I N N I N G Nineteenth-century composers often postpone tonal stability to create a sense of ambiguity and heightened expectation. Rather than beginning a piece (or an important subsection) with the tonic and its prolongation, composers may begin on a harmony other than the tonic. We have already seen examples of such an off-tonic beginning. For example, Brahms’s song “Parole” in Example 28.6 began on an extended PD that occupied the entire introduction. In the Classical period, off-tonic beginnings were approximated in the slow introductions of works in which a weakly stated initial tonic was quickly displaced by chromatic harmonies that veered into distant regions. The tonal goal of the slow introduction was almost always the dominant, and the strong arrival on the tonic was postponed until the following allegro section. Off-tonic beginnings were often a mainstay of popular music in the twentieth century. The G-major refrain of “Sweet Georgia Brown” (Example 28.7) begins far away from the tonic; a series of applied dominants (E7–A7–D7) finally leads to G in m. 33.

D OU B L E T O N A L I T Y Sometimes you may encounter pieces in which two keys vie for supremacy simultaneously. Often the ambiguity is acute, and the analyst has little choice but to interpret the piece in the key in which it ends. Some analysts conclude that highly ambiguous pieces are being controlled not by a single key but by the two keys juxtaposed throughout the piece. Such

EXAMPLE 28.7 Pinkard, “Sweet Georgia Brown” STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

21

No gal

G:

V7/ii

made

has got a

shade

On Sweet

Geor gia

Brown.

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Chapter 28 New Harmonic Tendencies

EXAMPLE 28.7 (continued) 25

Two left

feet

but

oh so

neat

has Sweet

Geor gia

Brown,

V 7/V 29

They all

sigh

and wan na

die

For Sweet

Geor gia

Brown, I’ll tell you just

V7

why,

I

pieces display double tonality. For example, some of the songs by Schubert, scenes and acts of operas by Wagner, and orchestral works of late nineteenth-century composers, including Liszt, Mahler, and Strauss, fall into the double-tonal category. Most of the time, double-tonal pieces are better interpreted as being in a single key: the key in which the piece closes. One might consider Brahms’s song “Es hing der Reif ” (see Example 28.8) to be a double-tonal example, given that C major and A minor are set in conflict throughout. Although the interior cadences and tonicizations are all in C major, the closing key of the piece suggests that the song might best be interpreted in A minor.

EXAMPLE 28.8 Brahms, “Es hing der Reif” (“Hoarfrost was hanging”), op. 106, no. 3

Es hing Hoar-frost

molto

e dolce

der was

Reif hanging

im

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THE COMPLETE MUSICIAN

EXAMPLE 28.8 (continued) 7

Lin den in the lime

baum, tree.

wo durch Through which

das light

Licht streamed

wie like

Sil silver

ber

Traum in a

ein dream

bli tzend a sparkling

floß

Ich I

Fe

en

13

sah saw

dein your

schloß fairy

ein castle

Haus, house,

wie as

hell brightly

im as

19

bli

tzend

Fe

en

schloß

65

daß

Frost

that

it

und was

actually

Win

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Chapter 28 New Harmonic Tendencies

EXAMPLE 28.8 (continued) 71

ter

war.

winter.

EX ERCISE INTER LUDE A NA LYSIS STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

28.1 Study the following excerpts, which contain ambiguities resulting from mixture, semitonal voice leading, the reciprocal process, and enharmonic puns. Bracket the area or areas in which ambiguity plays an important role. Then describe in prose the type of ambiguity involved.

A. Brahms, “Dämmrung senkte sich von oben” (“Twilight sank from high above”), op. 59, no. 1 While tonal ambiguity in this excerpt is minimal, a harmonized melodic motive appears in the introduction that somewhat obscures the surface harmony. What is this motive? Consider also the metric placement of the motive (i.e., where do the embellishing tones occur in relation to the chord tones? Is Brahms consistent in their metric placement?). Langsam

Dämm rung senk te sich von o

mezza voce

ben, schon ist al

le

Nä

he fern

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THE COMPLETE MUSICIAN

Dvořák, Symphony no. 9, “New World,” Largo

B.

Sm. con sord.

dim.

Timp.

S Y M M E T R Y: T H E DI M I N I S H E D S E V E N T H C HOR D A N D E N H A R MON IC MODU L AT ION Beginning in the eighteenth century, composers used the diminished seventh chord both as a powerful goal-oriented applied chord and as a dramatic signpost. For example, a strategically placed diminished seventh chord could underscore a particularly emotional image from the text of a song. A vivid and painful example is heard in the last moment of Schubert’s “Erlking.” Immediately before we learn of the fate of the sick child (“and in [the father’s] arms, the child . . .”), the previous 145 measures of frantic, wildly galloping music come to a halt. The fermata that marks this moment, and which seems to last forever, is accompanied by a single sustained diminished seventh, underscoring this crucial moment (Example 28.9). We learn immediately thereafter that in spite of his valiant attempts to rush his sick son home by horseback, the father was too late: The child was dead. Even before the time of Bach, composers also used the diminished seventh chord to create tonal ambiguity. Ambiguity is possible because the chord in any of its inversions

EXAMPLE 28.9 Schubert, “Erlkönig,” D. 328 Recit.

144

Hof

mit Müh und Noth;

in sei nen Ar men das Kind

war todt.

Andante

g:

I6

vii 43 II

vii 7/V

V7

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Chapter 28 New Harmonic Tendencies

partitions the octave into four minor thirds and its three inversions produce no new intervals (Example 28.10A). Chords that possess this special ability to partition the octave into identical intervals are known as symmetrically constructed harmonies. This is not the case for other sonorities such as the major triad, which contains six intervals through its inversions (m3, M3, P4, P5, m6, M6). See Example 28.10B.

EXAMPLE 28.10 A.

Intervallic Characteristics of Symmetrical Harmonies B.

all m3s/A2s

M3, m3, P5

m3, P4, m6

P4, M3, M6

Composers exploit the potential of symmetrically constructed harmonies by using them to access both close and distant key areas. Example 28.11A contains a diminished seventh chord that implies C minor or C major. When we spell the same chord a bit differently (Example 28.11B), it leans toward a different tonic: A major.

EXAMPLE 28.11 A.

vii°7: Symmetry and Enharmonicism B.

root

7th

7th

root

c:

vii 7 i

A: vii

6 I6 5

Consider the ramifications of what we’ve just seen: Within a given chord, the inaudible enharmonic alteration of a single note (here, A becomes G ) allows the chord to function in two remotely related keys. C minor and A major (six accidentals apart) both become instantly accessible by virtue of this single respelled pitch. In fact, through enharmonic reinterpretation, the vii°7 becomes a vehicle that can modulate to many other key areas. This technique is similar to the reinterpretation of the German augmented sixth chord (respelled as a V 7 in Chapter 24); given that the German sixth is not symmetrical, its access to remote keys is limited. Example 28.12 shows four different spellings of our diminished seventh chord, along with its resolutions. The diminished seventh is a remarkable pivot chord that can access distant tonal areas, even keys that lie a minor third or a tritone away from each other. A good way to determine the four accessible keys is to interpret each of the four pitches in the diminished seventh chord as a leading tone, as shown in Example 28.12.

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THE COMPLETE MUSICIAN

Enharmonic Reinterpretation of vii°7

EXAMPLE 28.12 A.

B.

C.

STR EA MING AUDIO

D.

W W W.OUP.COM/US/LAITZ

7

7

7

7

7

C:

vii 7

A:

I

vii

6 5

i6

f : vii

6 4 3

i6

E :

vii

6 4 2

V 64

5 3

I

The clock face reveals the special properties of the diminished seventh chord. Moving the diminished seventh chord up by one half step (i.e., starting the next “square” on C) does not, of course, alter its symmetrical structure. Transposition by three semitones (i.e., starting the chord on E) results in a restatement of the same pitch classes, therefore revealing how there are only three distinct transpositions (Example 28.13).

EXAMPLE 28.13 Properties of vii°7: Only Three Distinct Transpositions

B

C

C

B

B

E E

G G

F

C

B

D

A

C

D

A

E E

G G

F

B

F

F

C

C

B

B D

A

E E

G G

F

F

C

C

B

D

A

E E

G G

F

F

Analysis When analyzing tonicizations that result from the enharmonic reinterpretation of a diminished seventh chord, use the same pivot-chord technique that we employed in Chapters 19 and 22. It is important to show how the chord functions in both the original key and the new key. Example 28.14 begins in G major and ends with a tonicization of B major (III). Note that the first appearance of the diminished seventh chord functions as a passing chord (m. 1). Arrows reveal the resolution of the root (F) and seventh (E). The enharmonically transformed diminished seventh chord in m. 3 is initially still heard as vii°65; but because of where it progresses, it actually functions and is notated as a root-position vii°7 in the new tonal area.

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Chapter 28 New Harmonic Tendencies

EXAMPLE 28.14

Analyzing Enharmonic Modulations Using vii°7 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

G:

6

I

vii

6 5

6

I

V

4 2

I6 III:

I

P

I

V

vii

6 5

vii

7

I

I

ii 65

V7

I

I

PD

V

I

6

I

Be aware that composers are not consistent in the way they notate enharmonic modulations using diminished seventh chords. They may notate the chord either as it functions in the new key or as it functions in the old key (in which case it would appear to have an unusual resolution).

Analytical Interlude Example 28.15 illustrates two distant modulations from the literature that rely on the enharmonic potential of the diminished seventh chord. Example 28.15A, from the first movement of Beethoven’s “Pathetique” sonata, is the passage that leads from the exposition to the development. The excerpt begins in G minor, yet it moves with little effort quickly into the remote key of E minor. Notice how m. 134 begins identically to the previous measure; but as the voice exchange unfolds, C5 leads not to E5 but to D5. This inaudible change has powerful ramifications, for the resulting enharmonic spelling sets the stage for E minor to enter. What was vii°43 in G minor has become vii°42 in E minor.

EXAMPLE 28.15 A.

Sample Analyses STR EA MING AUDIO

Beethoven, Sonata in C minor, op. 13, I

W W W.OUP.COM/US/LAITZ

E becomes D 132

Grave

g:

i

vii

7

/V V

vii

4 2

vii

4 3

i6

vii

4 2

vii

e: vii

4 3 4 2

8

V 64

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THE COMPLETE MUSICIAN

EXAMPLE 28.15 (continued) Allegro molto e con brio

135

cresc.

decresc.

7 5

B.

i

Schubert, String Quartet in A minor, D. 804, I B not rewritten as C

G not rewritten as A (until after pivot)

a: vii

7

vii E : “ vii

7 4 ” 3

V42

I

6

Example 28.15B contains a particularly bold modulation using vii°7 enharmonically in A minor that allows a tonicization of the tritone-related key, E major. This example is particularly intriguing, given that not only is the enharmonic conversion inaudible, it is also not visible to the players! The excerpt begins with vii°7 that apparently continues in the next measure. However, the motion to V42 of E major in m. 3 indicates that we have already made it to E. We not only didn’t hear the modulation, but we didn’t see it. The pivot, then, must be in m. 2. To be sure, Schubert has transformed the vii°7 of A minor into vii°43 in E major, only implying the correct spelling of the vii°43 chord.

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 28.2–28.4

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

28.2 Following are excerpts that either modulate using enharmonically reinterpreted diminished seventh chords or begin off-tonic. Analyze each. Mark the pivot in enharmonic modulations.

679

Chapter 28 New Harmonic Tendencies

A.

Schumann, Symphony no. 2, op. 61, Allegro Vivace Be aware of the possibility of enharmonically reinterpreted Ger65 chords. Allegro vivace

4

cresc.

9

B.

1

Tchaikovsky, Sleeping Beauty, act 1: La Fée des Lilas Tempo di valse

6

C.

Lamm, “Saturday in the Park”

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THE COMPLETE MUSICIAN

A PA R A D OX : “B A L A N C E D ” M U S IC B A S E D ON A S Y M M E T R Y Balance characterizes tonal music—especially Classical music, where the idea of symmetry pervades most aspects of composition. Melodically, the music moves in predictably proportioned patterns. Formally, we usually think of Classical musical units at all levels as structures featuring regularly recurring measure lengths, such as four-measure phrases and eight-measure periods. Metrical and formal symmetries allow a deeper level of periodicity to arise, in a phenomenon called hypermeter. At the level of whole works, the idea of perfect symmetry is replaced by tonal balance, as can be seen in both binary and sonata forms, which can be heard as harmonic arches progressing from tonic to dominant and back again. It is consequently curious that the “well-balanced” tonal system itself is predicated on asymmetrical structures that contain unequal and asymmetrical intervallic divisions. Major and minor triads and dominant seventh chords are asymmetrical structures that consist of a mix of major and minor thirds. Even harmonic progressions in tonal music are asymmetrical. Root motions divide the octave unequally—V to I (ascending perfect fourth) answers I to V (ascending perfect fifth)—and common descending and ascending arpeggiations move in a mix of major and minor thirds. Most significantly, diatonic sequences are also highly asymmetrical. For example, the common D2 (⫺5/⫹4) sequence does not move exclusively by perfect fifths; a tritone occurs within the sequence in order to maintain the scale degrees of the key. Indeed, it is precisely the breaking of the perfect-fifth pattern by the diminished fifth that makes the progression so goal-oriented, for without the tritone, the symmetrical sequence would wander over the entire 12 chromatic steps before returning to its beginning point. Just as asymmetrical structures such as major and minor triads help to create tonality, the use of symmetrically constructed harmonies and harmonic progressions results in tonal ambiguity, an important feature of nineteenth-century music. But how does symmetry fit into our asymmetrical harmonic models? Actually, the tonal system contains the seeds for symmetry: Harmonic motions up to the dominant and down to the subdominant symmetrically flank the tonic by perfect fifths. However, common-practice music will not usually permit the subdominant to lead directly back to the tonic, but rather to the dominant (Example 28.16). The model in Example 28.17 represents eighteenth-century diatonic motion, with the symmetrical perfect fifths asymmetrically divided by major and minor thirds.

EXAMPLE 28.16 Dominant and Subdominant Flank Tonic Dominant

Tonic

start here

Subdominant

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Chapter 28 New Harmonic Tendencies

EXAMPLE 28.17 Eighteenth-Century Tonal Paths Dominant

Mediant

G (V) E (III)

e (iii) rises to

Tonic

c (i)

C (I)

start here falls to

Submediant

Subdominant

A (VI)

a (vi)

f (iv)

F (IV)

We have learned that chromatic third relations can emerge from the combination of parallel modes through mixture. The model in Example 28.18 represents the rise of chromatic third relations from the end of the eighteenth century to the first half of the nineteenth century. Notice that the combinations of major and minor thirds continue to form asymmetrical tonal progressions. Notice also that the subdominant need not progress to the dominant; rather, it may move directly to the tonic (through the plagal relation).

EXAMPLE 28.18 Late Eighteenth- and Nineteenth-Century Tonal Paths: Mixture Incorporated G

Dominant

Mediant

Eb

e

E rises to

Tonic

c

start here

C

falls to Submediant

Subdominant

Ab

a

F(f)

A

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THE COMPLETE MUSICIAN

S Y M M E T R Y A N D T ON A L A M B IG U I T Y The model in Example 28.19 is fundamentally different from the preceding models. The long diagonal lines represent symmetrical paths that circumvent both the dominant and the subdominant. Notice that root progressions move by a single repeating interval of either a major third or a minor third (or their enharmonic equivalents) until these intervallic cycles reach a perfect octave.

EXAMPLE 28.19 Late Nineteenth-Century Tonal Paths: Symmetrical Third Relations Replace Asymmetrical Fifth Relations c or C

c or C A

ascending minor thirds

G

G E

E c

C

A descending major thirds

ascending major thirds

A

F

F

descending minor thirds E

c or C

c or C

We can understand that the basis of tonality’s gravitational field, which pulls scale degrees and harmonies toward tonic, is predicated on asymmetry—specifically the asymmetry associated with major and minor scales. Imagine what would happen to tonality if scales were composed solely of whole steps or half steps or of consistently alternating half and whole steps. If you try singing the scales in Example 28.20, you will soon discover that a sense of goal-directed motion and tonal grounding disappears because every scale step is as stable (or as unstable) as every other step.

EXAMPLE 28.20 Symmetrical Scales chromatic = all half steps 1

1?

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Chapter 28 New Harmonic Tendencies

EXAMPLE 28.20 (continued) whole tone = all whole steps 1?

1

octatonic = alternating half and whole steps 1?

1

T H E AUG M E N T E D T R I A D So far, we have considered only one symmetrical triad—the diminished triad. It has a symmetrical construction because its two component intervals are both minor thirds (Example 28.21). It does not, however, equally partition the octave (since it spans a tritone, it only partitions half of the octave evenly).

EXAMPLE 28.21 Diminished Triad Clock

B

C

C

B

D

A

E

A

E G

F

F

Like the diminished triad, the highly dissonant augmented triad (shown in Example 28.22) is symmetrical, consisting of two major thirds and spanning an augmented fifth. Moreover, like the diminished seventh chord, the augmented triad also partitions the octave equally. Unlike every other triadic structure, the augmented triad retains its major third and augmented fifth intervals (or their enharmonic equivalents) under inversion. Compare the inversions of the minor triad to the inversions of the augmented triad. A minor triad in root position contains a minor third (e.g., C–E) and a major third (E–G), which together span a perfect fifth (C–G). Its first inversion yields a major third (E–G) and a perfect fourth (G–C), which together span a major sixth. Its second inversion yields

684

THE COMPLETE MUSICIAN

EXAMPLE 28.22 Augmented Triad Clock: Only Four Distinct Transpositions

C

B

C

B

B

E

G

F

E G

C

B D

A

E E

G G

F

F

C

B

E

G

F

B D

A

E

G

C

B

D

A

C

F

F

C

C

B

B D

A

E E

G G

F

F

C

C

B

D

A

E E

G G

F

F

a perfect fourth (G–C) and a minor third (C–E), which together span a minor sixth. But when we invert an augmented triad (such as C–E–G), no matter how many times we cycle the three pitches, only major thirds (or diminished fourths) and minor sixths (or augmented fifths) result. Consequently, there is no way aurally to distinguish inversions of the augmented triad. Its symmetrical construction is harmonically ambiguous and well suited to the experimental works of the late nineteenth century. The augmented triad originally was a by-product of melodic motion before becoming an independent sonority. Listen to Example 28.23. It is likely that you heard an augmented triad (G–B–D) on the upbeat to m. 1. It is metrically weak, with the Ds arising from passing motion; therefore, it is not an independent harmonic entity.

EXAMPLE 28.23 Beethoven, Theme and Variations in G major, WoO 77, Thema: Andante, quasi Allegretto STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5– 5

G:

I I T

ii 6

V7 I EPM

I

V

I

V 65 I

V

CL

I

N I

V HC

Now listen to Example 28.24, and note the function of the augmented triads. Again, the augmented triad in m. 2 is not an independent triad, because F is functioning simply as an appoggiatura to the chord tone G. Often, augmented triads participate in sequential progressions, filling in the whole steps with chromatic semitones. Beethoven’s Bagatelle (Example 28.25) plays on the augmented

685

Chapter 28 New Harmonic Tendencies

EXAMPLE 28.24 Schubert, “Der Atlas,” from Schwanengesang, D. 957, no. 8 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

g:

i6

i

APP

i

APP

i

triad’s harmonic ambiguity: The chromatic passing tone G creates an augmented triad. At the same time, the tonic is extended to its first inversion on beat 3. An interesting effect results from the parallel-tenth motion between the bass and the soprano voices, where the G4 begins to sound a bit like a leading tone to A. This “applied dominant” to A minor is intensified by the fact that E is in the bass. Although it is customary to label this sonority as a C–E–G chord (C-major triad with a raised fifth), there is no reason it cannot be called an E-major chord with a raised fifth (E–G–B, with B as an enharmonic respelling of C).

EXAMPLE 28.25 Beethoven, Bagatelle in C major, op. 119 STR EA MING AUDIO

Moderato cantabile

molto ligato

10

5 — 6– 5 —

C:

I I

W W W.OUP.COM/US/LAITZ

10

10

V6

V

10

10

5 — 6 —

I

6

IV ii PD

D

V 65

V7

I T

Some late-nineteenth-century composers exploited the harmonic ambiguity of the augmented triad. Listen to the opening of “Illusion” in Example 28.26 and determine the key, the location where the key is explicitly stated, and how Grieg earlier implies the key. What musical devices make the opening tonally ambiguous?

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THE COMPLETE MUSICIAN

EXAMPLE 28.26 Grieg, “Illusion,” Lyric Pieces VI, op. 57 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Allegretto serioso

a:

V7 i T

VI

V7

vi VI

V7

V 7/IV iv PD

ii 6

Ger 7

V

Ger 7

V D

The excerpt closes on V of A minor, the tonic of the piece. The opening’s unharmonized and ambiguous C5 could imply the key of C major or the dominant of F or any number of other keys. However, C5 turns out to be a dissonance that is first heard as the minor sixth above the dominant of A minor. (Note that the first sonority, E–G–C, is identical to the chord in the previous example, which we hypothesized could work just as well in A minor.) The V 7 resolves deceptively to VI; this pattern begins again in m. 2, transposed down a third. Only in m. 3 does a goal-directed progression begin, leading to a half cadence in A minor. It is difficult to miss the explicit connection between the meaning of the song’s title and Grieg’s musical setting. Finally, the augmented triad can become an independent sonority. Listen to the opening of Liszt’s “Nuages gris” (Example 28.27), in which all of the chords but the first take the form of augmented triads. As Liszt obscures all sense of tonality with chromatically descending augmented chords (m. 11), he brings to life the image of visible yet amorphous gray clouds.

EXAMPLE 28.27 Liszt, “Nuages gris” (“Gray Clouds”), S199, LW 305 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

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Chapter 28 New Harmonic Tendencies

EXAMPLE 28.27 (continued) 6

11

dim.

+5 3

+5 3

+5 3

16

+5 3

+5 3

A LT E R E D D OM I N A N T S E V E N T H C HOR D S The fifth of the V 7 chord, 2 is a weak tendency tone when compared to the leading tone (7) and the chordal seventh (4). But when 2 is raised—creating an altered dominant seventh chord—it forms an augmented sixth interval with 4, and, as a strong tendency tone, it must rise to 3 (Example 28.28). Because of the proper resolution of the chordal seventh, the following tonic chord has a doubled third.

EXAMPLE 28.28 V57

+6

7 5

C:

V7

5

I

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THE COMPLETE MUSICIAN

It is also possible to alter V 7 by lowering 2 a half step; this chord often plays a crucial role in late-nineteenth-century music (Example 28.29A). When 2 is lowered it forms an augmented sixth with the leading tone; composers place the chord in second inversion so that 2 is in the bass. This inversion, shown in Example 28.29B, produces a chord that is identical to a French augmented sixth chord. Therefore, the altered dominant seventh chord functions in a reciprocal process: The chord sounds like it participates in a half cadence (Fr43→V), but it actually functions as part of an authentic cadence (altered V43→I). For now, we will label this type of altered dominant as Fr V43 which shows its function as a dominant and its intervallic properties that are similar to the regular Fr43.

EXAMPLE 28.29 V57 and Fr V43 A.

B.

+6

7 5

C:

V7

5

C:

I

I

6

V 34

Fr V 43

I

F:

Fr 43

V

I

Listen to the opening of the last movement of Brahms’s Symphony no. 4 (Example 28.30). What is ambiguous about the cadence? Perhaps you were once again struck by a disparity between what you saw and what you heard at the cadence in m. 8. There are two reasons why a weak authentic cadence—in which V43 (F replaces F) resolves to I— ambiguously sounds like a half cadence. First, the altered V43 chord (m. 7), with F prominently placed in the bass (F–A–B–D) is identical to a Fr43 chord in the key of A minor, not the key of E minor. Second, the Picardy third (G) in the final chord sounds like

EXAMPLE 28.30 Brahms, Symphony no. 4 in E minor, op. 98, Allegro energico e passionato STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

e:

iv 6

ii 6 plagal motion

i

iv 6

V 7/V

i6

Fr V43

I

authentic cadence

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Chapter 28 New Harmonic Tendencies

Fr43–V rather than an authentic cadence (V43–I). This altered dominant seventh therefore functions in a reciprocal process.

T H E C OM MO N -T O N E DI M I N I S H E D S E V E N T H C HOR D We have encountered a number of ways to extend an underlying harmony contrapuntally. In addition to embedded phrase models (EPMs), we have learned about passing and neighboring chords, such as vii°6, P64, Ped64, vii°65, and IV6, which usually occur in first or second inversion so as to allow them smoothly to connect structural harmonies in root position. Two additional harmonies can prolong I and V through neighboring and passing motions. These new chords contain chromaticism and maintain the root of the harmony they extend. Example 28.31 shows the first type of harmony: The lower neighbors on beat 3 of m. 1—together with the 5–6 motion (A–B) in the left hand—create a diminished seventh chord. Notice that the root of the tonic chord (D) is sustained as a common tone. Contrapuntal diminished seventh chords such as this one are called common-tone diminished seventh chords, labeled “c.t.°7.”

EXAMPLE 28.31 Schubert, Waltz in D major, 34 Valses Sentimentales, op. 50, no. 12, D. 779 STR EA MING AUDIO

1

D: I

UN

LN

5 5 3

6 4 2

c.t.

W W W.OUP.COM/US/LAITZ

5

5 5 3 7

I

V7

I

We now have two functions for diminished seventh chords: They can be tonicizing (as a vii°7 or an applied vii°7) or contrapuntal (as a c.t.o7 or an applied c.t.°7) (Example 28.32). The following guiding principles may be useful when attempting to determine the function of a fully diminished sonority. • Common-tone diminished seventh chords share a common tone with the following chord of resolution (Example 28.32A). • vii°7 and applied vii°7 chords have no common tones with the following chord of resolution (Example 28.32B). 7 • Beware of the progression vii°7/V to cadential 6–5 4–3. The vii° /V chord shares common tones with the cadential 64 chord. The common tones, however, are misleading, for they are not chord tones but suspensions that fall to the 53 chord, which shares no pitches with the applied vii°7 chord (Example 28.32C).

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EXAMPLE 28.32 vii°7: Common Tone Versus Applied Forms A.

B.

C.

common tone

A:

I c.t.

7/V

V

no common tones

no common tone

A:

I

vii 7/ii

ii

C:

I 6 vii 7/V

V64

5 3

I

It can be difficult to distinguish between the different types of diminished seventh chords. The chromatic bass line in Example 28.33 suggests that the diminished seventh chord will function as a vii°7/ii. However, B is not the root of the chord on the downbeat of m. 2; it is a V43 chord. Further evidence against viewing the diminished seventh chord as vii°7/ii may be seen in the octave E, which is a common tone of both the diminished seventh chord and the following V43 chord. As you know, there are no common tones between an applied vii°7 chord and its resolution, so this diminished seventh cannot be applied. Rather, it is a contrapuntal chord (c.t.o7 of V) that connects I and V43 by means of a chromatic passing tone in the bass.

EXAMPLE 28.33 Brahms, “Heimweh III” (“Homesickness III”), op. 64, no. 9 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

vii 7/ii ? (no) c.t. 7/V ? (yes)

C OM MON -T ON E AUG M E N T E D S I X T H C HOR D S Example 28.34 contains another chromatic common-tone harmony over a tonic pedal that arises from contrapuntal motion, but it is not a diminished seventh chord. Look at the figure for the first chord. Does the presence of both flat and sharp accidentals remind you of any other chords we have learned? The sonority sounds and looks like a Ger65 chord, since it contains an augmented sixth (A–F). It is a bit peculiar, however, not to have

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Chapter 28 New Harmonic Tendencies

EXAMPLE 28.34 Schubert, “Am Meer” (“By the Sea”), Schwanengesang, D. 957, no. 12 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Sehr langsam

Das Meer erg länz te

weit hin aus im letz ten A

bend schei

ne,

molto ligato

C:

6 4 2

5 5 3

c.t.+6 I

the 6–5 motion in the bass, for we expect an augmented sixth chord moving to its resolution. Instead, the bass voice sustains a common-tone C. The result of this voice leading is a chord that extends the tonic rather than leading strongly to the dominant. Such a chord is referred to as a common-tone augmented sixth chord (c.t.⫹6). The bass in c.t.⫹6 chords may skip down a major third to what would be the usual bass of an augmented sixth chord (Example 28.35). The fact that the augmented sixth chord returns to the tonic, however, demonstrates its common-tone function. Nineteenthcentury music contains a variety of chromatic third–related vacillations.

EXAMPLE 28.35 Common-Tone Augmented Sixth

C:

I T

WORKBOOK 1 Assignments 28.5–28.10

c.t.+6

I

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T ER MS A ND CONCEP TS • altered dominant seventh chords • augmented triad • chromatic common-tone harmonies • common-tone augmented sixth chords • common-tone diminished seventh chords • enharmonic modulation • enharmonic reinterpretation • vii°7 • V 7/Ger65 • off-tonic beginning • double tonality • plagal relation • reciprocal process • semitonal voice leading • symmetrical versus asymmetrical relationship • symmetrically constructed harmonies • tonal ambiguity

CH A PTER R EV IEW 1. Final structural cadences which incorporate harmonies such as iv and iiø65 as dominant substitutes exploit the _______________________________________________________________.

2. Tonal ambiguity can obscure the functions of T, PD, and D by employing the ____________________________________________________________________________________.

3. Motion that moves two or more voices by a half step while keeping one common tone in another voice is called _______________________________________________________________.

4. When a piece or section of a piece starts in a harmonically ambiguous way, it employs an _________________________________________________________________________________.

5. Some pieces seem to project two key centers, therefore exhibiting _______________________.

Chapter 28 New Harmonic Tendencies

693

6. Chords that possess the special ability to partition the octave into identical intervals are known as ___________________________________________________________________________.

7. The vii°7 chord and other symmetrically harmonies can function in multiple keys through __________________________________________________________________________________.

8. Give an example of a symmetrically constructed harmony built from two major thirds.

9. V 7 with 5, V 7 with 5, and the Fr43 are all examples of __________________________________.

10. Common-tone diminished seventh chords (c.t.o7) and common-tone augmented sixth chords (c.t.+6) maintain the ____________________ of the harmony they extend (i.e., the harmony that follows).

C H A P T E R 29

Melodic and Harmonic Symmetry Combine: Chromatic Sequences OV E RV I E W

This chapter explores chromatic chord progressions—particularly sequences—that further weaken, and destroy, tonal focus. From such chromatic motions we will see how composers replace traditional diatonic melodies with small melodic cells, which become the generating force in a piece, often at the deepest harmonic levels. CHAPTER OUTLINE Distinctions Between Diatonic and Chromatic Sequences............................. 695 Details of Chromatic Sequences ............................................................................. 696 Chromatic Sequence Types ...................................................................................... 697 The D2 (⫺P4/⫹m3) Sequence ........................................................................... 697 The Chromatic Forms of the D2 (⫺5/⫹4) Sequence ...................................... 698 The Chromatic Forms of the A2 (⫺3/⫹4) Sequence....................................... 701 Other Chromatic Step-Descent Basses ................................................................. 703 Six-Three Chords ................................................................................................... 704 Diminished Seventh Chords ................................................................................ 705 Augmented Sixth Chords ..................................................................................... 705 Writing Chromatic Sequences ................................................................................. 707 Chromatic Contrary Motion ................................................................................... 708 The Omnibus ......................................................................................................... 710 A Final Equal Division of the Octave.................................................................... 711 (continued)

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Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

Sequential Progressions ............................................................................................ 713 Nonsequential Progressions and Equal Divisions of the Octave ................... 716 The Intervallic Cell ..................................................................................................... 718 Analytical Interlude: Chopin, Prelude, op. 28, no. 2 ....................................... 720 Terms and Concepts ................................................................................................... 724 Chapter Review ........................................................................................................... 724

DI S T I N C T ION S B E T W E E N DI AT ON IC A N D C H ROM AT IC S E QU E N C E S Sequences are paradoxical musical processes. At the surface level they provide rapid harmonic rhythm, yet at a deeper level they function to suspend tonal motion and prolong an underlying harmony. Tonal sequences move up and down the diatonic scale using scale degrees as stepping-stones. In this chapter, we will explore the consequences of transferring the sequential motions you learned in Chapter 17 from the asymmetry of the diatonic scale to the symmetrical tonal patterns of the nineteenth century. You will likely notice many similarities of behavior between these new chromatic sequences and the old diatonic ones, but there are differences as well. For instance, the stepping-stones for chromatic sequences are no longer the major and minor scales. Furthermore, the chord qualities of each individual harmony inside a chromatic sequence tend to exhibit more homogeneity. Whereas in the past you may have expected major, minor, and diminished chords to alternate inside a diatonic sequence, in the chromatic realm it is not uncommon for all the chords in a sequence to manifest the same chord quality. Consider Example 29.1A, which contains the D3 (⫺4/⫹2)—or “descending 5–6”—sequence. The sequence is strongly goal directed (progressing to ii) and diatonic (its harmonies are diatonic to G major). Chord qualities and distances are not consistent, since they conform to the asymmetry of G major. For example, see how the first chord of the model, G major, repeats down a minor third on E minor, while the next repetition begins down a major third on C major.

EXAMPLE 29.1

A.

Comparison of Diatonic and Chromatic Forms of the D3 (“Pachelbel”) Sequence STR EA MING AUDIO

Diatonic

G:

G I

T

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e

C

D3 (–4/+2)

a ii

V7

I

PD

D

T

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THE COMPLETE MUSICIAN

EXAMPLE 29.1 B.

(continued)

Chromatic

G:

G I

T

E

F

D2 (–P4/+m3)

iv

V

I

PD

D

T

Example 29.1B illustrates a new chromatic sequence, and its sense of harmonic ambiguity and lack of direction might unsettle you as you hear it, because its harmonies do not fit into one key, and it is not goal directed (it ends on B major, whose function as III becomes clear only after the final strong cadence in G major). The two-chord model is identical to that of Example 29.1A, but the copies contain numerous chromatic alterations that result in harmonies foreign to G major. The model and its repetitions contain all major triads and each repetition occurs down a major second. It is as if the copying mechanism has been perfected so that every repetition reproduces exactly the harmonic pattern of the model.

DE TA I L S OF C H ROM AT IC S E QU E N C E S The sequence in Example 29.1B is a type of chromatic sequence. Chromatic sequences are distinguished from diatonic sequences by the fact that their main chords—those chords we use to reckon the first portion of a sequence label such as D2 or D3—contain altered scale degrees. (Note: The designation chromatic has nothing to do with the mere presence of accidentals; many of the applied-chord sequences seen in Chapter 18 contain accidentals, yet they are still diatonic sequences because their main chords are diatonic.) Furthermore, chromatic sequences maintain strictly both chord quality and intervallic distance between repetitions, whereas diatonic sequences conform to the whole-step and half-step characteristics of the diatonic key. Because these chromatic sequences divide the octave into the same-sized intervals (such as the major seconds in Example 29.1B), they avoid the shifting whole steps and half steps that precipitate the goal-directed motion of traditional, diatonic sequences. The basic contrapuntal motion remains the same but the overall root movements are altered. For example, the diatonic sequence in Example 29.1A is labeled D3 (⫺4/⫹2) since the root movements change to conform to the diatonic key. The chromatic sequence in Example 29.1B differs in that the root motion always contains a P4 and a m3 in a repetition; this creates a M2 descent between repetitions, which is reflected in the label D2 (⫺P4/⫹m3). We distinguish chromatic sequences from diatonic sequences by including the specific interval motions within the parenthetical portion of the label.

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Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

C H ROM AT IC S E QU E N C E T Y PE S

The D2 (ⴚP4/ⴙm3) Sequence Both the diatonic D3 (⫺4/⫹2) sequences and the chromatic D2 (⫺P4/⫹m3) sequences are related by the underlying 5–6 motion. Example 29.2 contains the chromatic D2 (⫺P4/⫹m3) sequence in its alternating 63 form. The “?” that appears under the tonic indicates that it does not sound like an arrival because it carves out an intervallic path consisting exclusively of whole tones (or their enharmonic equivalent) and divides the octave symmetrically into six major seconds (G–F–E–D–C–A–G). Note especially how the whole-tone path of this sequence skips over the dominant D as the line moves from the E to D in mm. 3–4. As it stands, the sequence is barely tonal. To reintroduce tonal focus, one must break off the sequence after the repetition of the pattern on VI. From here it will lead to the pre-dominant function. (Example 29.3 shows two ways of doing this.)

EXAMPLE 29.2 Chromatic D2 (ⴚP4/ⴙm3) Sequence STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

V6

G:

V6

V6

V6

V6

V6

EXAMPLE 29.3 Chromatic D2 Sequence Returns to Diatonic Context A.

sequence ends

G:

I T

III 6 D2 (–P4/+m3)

chromatic

iv

V

I

PD

D

T

diatonic

I ?

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THE COMPLETE MUSICIAN

EXAMPLE 29.3 (continued) B.

sequence ends

G:

I T

D2 (–P4/+m3)

VI

Ger 65

V

5 3

I

D

PD

chromatic

6 4

T

diatonic STR EA MING AUDIO

C.

Schubert, String Quartet in G major, D. 887, Allegro molto moderato

G:

I

D2 (–P4/+m3)

VI PD

6 4

IV

V

6 4

IV

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V

I

D

T

In general, chromatic sequences occur more often in the major mode than in the minor. Example 29.4 demonstrates the minor-mode form of the chromatic D2 (⫺P4/⫹m3) sequence. Example 29.4C, from a particularly evocative passage from a Franz Liszt piano piece, contains a phrase and its repetition down one octave using the chromatic D2 sequence. Each phrase begins and ends on I6 (with B in the bass), but between these stable points, the chromatic falling pattern etches out a whole-tone pattern filled in by passing tones (B–B–A–F–E–D–C–B). Notice that the second half of each phrase is diatonic, but Liszt is able to maintain the whole-tone motion in spite of the prevailing harmonic asymmetry.

The Chromatic Forms of the D2 (ⴚ5/ⴙ4) Sequence Recall that the D2 (⫺5/⫹4) (falling-fifth) sequence is asymmetrical because it contains perfect fifths and a single tritone. To become symmetrical, the chromatic D2 (⫺P5/⫹P4) sequence contains exclusively perfect fifths. A secondary difference between the two forms of the sequence concerns length of time required to cycle back to tonic: A complete

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Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

EXAMPLE 29.4 Chromatic D2 in Minor A.

STR EA MING AUDIO

Root position

g:

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g i

D2 (–P4/+m3)

T

B.

iv

V

i

PD

D

T

iv

V

i

PD

D

T

Alternating Six-Three Chords

g:

i

D2 (–P4/+m3)

T

C.

e

f

Liszt, “Aux cypres de la Villa d’Este I: Threnodie” (“To the cypresses of the Villa d’Este”), from Anneés de Pèlerinage (Years of Pilgrimage); Third Year chromatic

diatonic

senza agitazione e molto legato

G:

I 6 G 63 b

F 63

a

E 63

f

V43/V V

vii 43 I 6

G 63

ten.

poco più marcato (ma poco)

b

F 63

a

E 63

f

V43/V

vii 43

ten. 6

I

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THE COMPLETE MUSICIAN

statement of the diatonic D2 (⫺5/⫹4) sequence requires seven diatonic steps, while a complete statement of the chromatic form requires 12 chromatic steps. This provides a compositional problem of sorts for the D2 (⫺P5/⫹P4) sequences, given that a complete statement of the sequence requires so many repetitions. Composers use two techniques to avoid sequential stasis: (1) partial statements of the series (only one or two repetitions) and (2) three or more fifth-related chords within the model (rather than two) in order to reduce the number of repetitions. For example, a three-chord model would require only three repetitions to make it all the way through this chromatic sequence’s 12 chordal members (Example 29.5).

EXAMPLE 29.5 Chromatic D2 (Falling-Fifth) Sequence (three-chord model) STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

G:

G

C

F

B

E

A

D

G

C /B

E

A

D

G

Now, let’s compare this falling-fifth sequence to the other chromatic D2 sequence we have just studied. Both the D2 (⫺P4/⫹m3) and the D2 (⫺P5/⫹P4) fall by major second, but the latter is more goal-directed because it moves more naturally by descending perfect fifths. The D2 (⫺P4/⫹m3) sequence contains back-relating dominants, and the sequence itself never lands on the dominant V chord. To feel this distinction, try playing Examples 29.2 and 29.6 while noting the direction of the arrows.

EXAMPLE 29.6 Chromatic D2 (Falling-Fifth) Sequence (two-chord model) STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

G:

V

V

etc.

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Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

It is also possible to have a chromatic sequence descending by minor seconds, D2 (⫺P5/⫹A4). This is accomplished by following the perfect-fifth descent by a tritone ascent. For example, the perfect-fifth bass pattern of a whole-tone D2 (⫺P5/⫹P4): C

F

B

E

A

D

G

C/B

E

A

D

G

B

E

B

E

A

D

A

D

G

C

C

would become: C

F

Example 29.7 contains such a pattern, beginning on B. Members of the stepwise chromatic descent are circled; the tritone leaps between them are bracketed.

EXAMPLE 29.7 Chopin, Mazurka in A minor, op. 59, no. 1, BI 157 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

ten.

B V7

B E

V7 E 3

A

V

7

D

The Chromatic Forms of the A2 (ⴚ3/ⴙ4) Sequence Like the diatonic A2 (⫺3/⫹4) sequence, the chromatic forms derive from the contrapuntal 5–6 motion. Let’s examine how the diatonic form evolved into the chromatic, symmetrical form. Example 29.8 reviews two forms of the diatonic A2 sequence: the simple

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THE COMPLETE MUSICIAN

EXAMPLE 29.8 Diatonic and Applied A2 Sequences STR EA MING AUDIO

A.

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I

IV

G

a

b

V

I

V

I

C

Diatonic scale degrees

B.

I

IV

G

a

b

C

Applied chord A2 (still diatonic)

diatonic form and a variation that uses alternating applied chords to tonicize briefly each diatonic scale degree. These sequences are diatonic because the structural chord of each two-chord repetition falls on a diatonic scale degree that is diatonically harmonized. Two chromatic variants of this sequence are shown in Example 29.9.

EXAMPLE 29.9 Chromatic A2 Sequences STR EA MING AUDIO

Variant 1:

G I T

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6 5

A

6 5

A2 (– 3/+4)

B

6 5

C IV

V

I

PD

D

T

Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

703

EXAMPLE 29.9 (continued) Variant 2:

G

6 5

A

6 5

A

I

6 5

B

6 5

B

6 5

A2 (–M 3/+P4)

T

C IV

V

I

PD D

T

Variant 1 lies somewhere between diatonic sequences and chromatic sequences: The root of every chord is diatonic (asymmetrical), but the structural chord of each repetition is chromatically altered; each is major. Variant 2 is fully chromatic, A2 (⫺M3/⫹P4): The structural first chord of every repetition is major, and the sequence ascends by half step. Although the bass is sustained through the two-chord repetition, every second chord is transformed into an applied 65 chord. This is reflected in the enharmonic respelling of the bass in mm. 2 and 4, showing the leading-tone function of the bass. Example 29.10 demonstrates how the applied chords may appear in root position, a technique often used in popular music and at baseball games.

EXAMPLE 29.10 Chromatic A2 in Root Position STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

G

V7

A

V7

A

V7

B

O T H E R C H ROM AT IC S T E P - DE S C E N T B A S S E S In addition to the usual two-chord sequential models that become chromatically descending sequences, it is possible to descend chromatically using a one-chord pattern, although such descents are not true sequences (as we learned in Chapter 17). Three common sonorities are used in such chromatic descents: six-three chords, diminished seventh chords, and augmented sixth chords.

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Six-Three Chords The diatonic descending six-three chord pattern (Example 29.11A), with 7–6 suspensions (Example 29.11B), can be transformed into a chromatic motion (Example 29.11C). The dissonant seventh usually occurs over a chromatic bass note and resolves over a diatonic bass note. This alignment of dissonance with chromaticism (and consonance with diatonicism) is common. Furthermore, the metrically emphasized beats on which the suspensions occur are harmonized by various types of seventh chords, making this pattern particularly expressive and useful in slower tempo pieces with emotional

EXAMPLE 29.11 Chromatic Step-Descent Bass Sequences A.

5

g:

B.

6

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6

6

6

6

vii

7

6

i

ii

T

PD

V V D

Diatonic Descent with 7–6 Suspensions

5

g:

C.

STR EA MING AUDIO

Diatonic Descent

6

7

6

7

6

7

6

7

6

vii

6

i

ii

T

PD

7

V4

6–5

V D

Chromatic Descent with 7–6 Suspensions

5

g:

6

7

6

7

6

7

6

7

6

V6

7

V4

6

i

ii

T

PD

D

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Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

EXAMPLE 29.11 (continued) D1. Chopin, Impromptu in A

A :

6

I

6

6

6

6

6

6

6

6

6

6

(rit.)

V 64

ii

5 3

D2. Reduction of Chopin UN

3

A :

I

5 3

6

6

6

6

6

6

3

2

ii

V 64 V

5 3

PD

D

6

T

texts. In Chopin’s Impromptu, a chromatic six-three motion extends tonic before leading to the pre-dominant (Example 29.11D).

Diminished Seventh Chords The diminished seventh chord may be used in descending chromatic sequences, such as the DM2 (⫹P4/⫺P5) sequence in Example 29.12. The notation in this example reflects careful voice-leading practice, but it is not possible aurally to differentiate root-position and inverted diminished seventh chords (due to the symmetry of the chord). Rather, the sequence sounds like a stream of root-position diminished seventh chords.

Augmented Sixth Chords Example 29.13A illustrates the potential ambiguity between the German sixth and the dominant seventh chords. Without seeing the score, the listener will probably assume that

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EXAMPLE 29.12 Parallel Diminished Seventh Chords STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5

6

7

7

4 3

7

4 3

ii 7

4 3

6

V46

vii 7

5

6 5

EXAMPLE 29.13 Descending Augmented Sixth and Dominant Seventh Chords STR EA MING AUDIO

A.

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in C:

V

7

in B: Ger 6 Fr 4 5

3

V

7

in B : Ger 6 5

Fr 4 3

V

7

in A: Ger 6 5

Fr 4 3

V

7

in A : Ger 6 5

7

Fr 4

V

in G:

Ger 6

3

Fr 4 3

5

G: I

V7 V

B. Chopin, Prelude in A major, op. 28 E as V 7 16

A :

V7

I

VI: (E)

V 7/IV

IV

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Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

EXAMPLE 29.13 (continued) E as +6 21

V7 /vi

V7

vi

I

6 5

4 3

6 5

V7 25

6 5

6 5

V

7

V

6 5

V

I

7

these are streams of dominant seventh chords with an anticipation in the soprano voice. Yet one might also hear a descending PD–D progression, resulting in a descending series of keys related by half step. The analysis below Example 29.13A shows how V7/IV (C) becomes a German sixth, a technique that we already know effectively lowers the temporary tonal center a half step. Notice that this PD–D progression is clarified at the end of each measure by the transformation of the ambiguous German sixth to the harmonically clearer French sixth. The French sixth’s lowered fifth also avoids parallel fifths, in that it anticipates the perfect fifth of the following dominant seventh. Through all of this sequencing, the real underlying motion is from tonic to dominant in G major. Chopin uses this pattern in Example 29.13B.

W R I T I N G C H ROM AT IC S E QU E N C E S Although there are no new guidelines for writing chromatic sequences, the following issues arise. 1. Use enharmonic notation instead of writing double flats or double sharps. 2. Like diatonic sequences, chromatic sequences usually break off at the predominant, whether the sequences rise or fall. 3. Chromatic sequences require that copies maintain the model exactly—both the chord quality and voicing.

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EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 29.1–29.3

29.1 Analyze the following sequences. Your choices are: 1. descents by seconds, thirds, and streams of six-threes, diminished sevenths, and augmented sixths 2. ascents by seconds

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

You may also encounter examples of diatonic asymmetrical sequences. Bracket each sequence and label it. Then circle the notes of the outer-voice model and each repetition, ignoring any embellishing tones.

A.

B.

C H ROM AT IC C O N T R A R Y MO T IO N We have learned many ways to extend an underlying harmony using contrary motion. We began with the chordal leap, which results in a voice exchange with no intervening chords (Example 29.14A). Next we added passing chords, such as vii°6, V43, and vii°65 (Example 29.14B). We can extend not only consonant triads but also dissonant harmonies—most often a dominant seventh chord—by contrary motion. The dissonant prolongation spans a third in Example 29.15A and a tritone in Example 29.15B. Notice how little the inner voices move. In these preliminary examples, it is easy to see what harmony is prolonged because the outer-voice counterpoint is diatonic. Contrary-motion expansions containing chromaticism, in contrast, manifest a larger degree of tonal ambiguity. Example 29.16, demonstrates

Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

709

EXAMPLE 29.14 Diatonic Voice Exchange A.

B. chordal leaps

passing motion

6

I

I

vii

6

I6 6

I

EXAMPLE 29.15 Voice Exchange Using Diatonic Passing Chords STR EA MING AUDIO

A. Third/Sixth Exchange B. Tritone Exchange

7

F:

V

6 5

7

6 5

V

P 53

6 4

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P 63

V42

7

EXAMPLE 29.16 Voice Exchange Using Chromatic Passing Chords STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

“

F:

V

7

3”

P 64

“Ger 65 ”

6 5

the prolongation of a dominant seventh chord with outer voices moving by half step. The beams show the underlying diatonic stepwise motion; the nonfunctional Ger7 and Ger65 act as passing chords filling the space between the diatonic chords. This densely chromatic progression works well because the inner voices are able to remain stationary.

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Examples 29.15 and 29.16 showed expansions of a dominant seventh chord—from 65 to and from 7 to 65 respectively. Example 29.17 expands the previous models by demonstrating how a 65 to 42 tritone can be expanded chromatically in a seven-chord progression. 4 2

EXAMPLE 29.17 Tritone Voice Exchange Using Chromatic Passing Chords

F:

B

E

E

B

V 65

V42

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Notice that when we use these sequences, it is possible to begin and end the contrary motion at any point in order to prolong different diatonic entities. Example 29.18 shows how we can prolong tonic or a °3/⫹6 complex by using different spans of the sequence; depending on which portion is used, the chromatic contrary motion can prolong tonic, pre-dominant, or dominant.

EXAMPLE 29.18 Expanding Tonic, Pre-Dominant, and Dominant Functions

expands PD expands tonic

F:

expands dominant

The Omnibus In a final expansion, the same chromatic contrary motion that prolongs dominant (V7 to V65) can be stretched so that it traverses an entire octave (ascending or descending). In Example 29.19, the bass ascent partitions the octave into minor thirds: Different rootposition dominant seventh chords appear on every third sonority (the dominant seventh chords are sometimes spelled enharmonically as Ger65 chords).

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At each dominant seventh chord, a remarkable enharmonicism is invoked, allowing the contrary chromatic motion to begin anew: • The soprano and bass start a major tenth apart and work in contrary motion. • At the next dominant seventh chord, the tenor and bass start with the M10 and work in contrary motion. • At chord 7, the alto and bass are on a M10 and start a voice exchange; the bass and soprano return to a M10 at chord 10. The bass arrives on C3 at chord 13 to complete its one-octave ascent. In total, this prolongation is called the omnibus. The omnibus, first described by Viennese music theorists around 1800, was used by composers throughout the nineteenth century (such as Beethoven, Schubert, Chopin, and Liszt). In practice, composers generally used only part of the omnibus.

EXAMPLE 29.19 The Omnibus Expands V 7 1

2

3

soprano/bass

F:

C V7

5

6

tenor/bass

10th

7

4

6 4

7

E

8

9

6 4

7

11

12

13/1

10th

3

6 4

G

7

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soprano/bass

10th

3

10

alto/bass

10th

3

7

10th

3

6 4

A

7

C

A F I N A L E QUA L DI V I S IO N OF T H E O C TAV E We have seen that chromatic parallel-motion sequences and contrary-motion progressions partition the octave into equal-sized intervals:

Descending minor seconds: Descending major seconds: Ascending minor seconds: Ascending and descending minor thirds:

D2 (⫺P5/⫹A4) D2 (⫺P4/⫹m3) and DM2 (⫺P5/⫹P4) A2 (⫺M3/⫹P4) Omnibus

We consider one more interval that can symmetrically divide the octave: the major third. Example 29.20 presents a slight variation of the diatonic D3 (⫺4/⫹2) sequence that partitions the octave into major thirds, D3 (⫺P4/⫹m2). The voice-leading irregularities result from maintaining the sequential progression exactly. The overall progression,

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EXAMPLE 29.20 Major-Third Division of the Octave STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

BRD C

BRD A

BRD E

C

which prolongs C major, contains descending major thirds (C–A–E–C) in the bass and a whole-step descent in the soprano. Chromatic sequences all create the temporary effect of tonal ambiguity. It was but a short and natural step for composers to begin to use autonomous symmetrical progressions independent of sequential motion. Such progressions, which we take up in Chapter 30, extend ambiguity to deep structural levels of the music.

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 29.4–29.6

A.

B.

29.2 Contrary-Motion Progressions Given are progressions that employ contrary-motion chromaticism. Determine the harmonic function that the chromaticism extends; then bracket and label that function (tonic, dominant, or pre-dominant). Circle the pairs of pitches involved in the contrarymotion chromaticism; for more extended examples, the pairs will change between voices. Is there a deeper harmonic pattern that emerges?

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Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

C.

7

S E QU E N T I A L PRO G R E S S IO N S The increased use of mixture resulted in the increased use of chromatic third relations in the late eighteenth century. Motion to the fifth above and below the tonic was often divided by chromatic thirds (I–III–V and I–VI–IV, for example). Although these progressions were goal-directed, they were asymmetrical because they contained root motions that were a mixture of major and minor thirds. It is possible to incorporate two or more identical intervals into progressions that segment the octave into equal intervals, called equal divisions of the octave. See Example 29.21, which shows how intervals of one, two, three, four, or six half steps can equally divide the octave.

EXAMPLE 29.21 Equal Divisions of the Octave by six half steps (tritone) by four half steps (M3) by three half steps (m3) by two half steps (M2) by one half step (m2) half steps

C C C C C 0

F E C 1

D D 2

E 3

E E E 4

F 5

F F F 6

G

G 7

G G 8

A A 9

B B 10

B 11

C C C C C 0

Example 29.22 contains two important symmetrical progressions. Example 29.22A moves by descending major thirds from C major to A major (VI), to E major (III or IV), and back to C major. The two-chord model is exactly copied by two-chord repetitions

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EXAMPLE 29.22 Division of the Octave by Thirds A.

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By Major Thirds

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VI A

I

VI E

I

VI C

I

D3 T

B.

T

By Minor Thirds

C

VI E

IV

VI F

VI

IV A

VI

IV C

IV

A3 T

T

that preserve the motion of each voice. Notice how each major-third-related key is secured when the pivot (VI) becomes I in the new key. Example 29.22B ascends by minor thirds: C major (I)–E major (III)–F major (IV)– A major (VI)–C major (I). Given the progression’s consistent transposition and sequential behavior, we call it a sequential progression. The sequential progression is symmetrical because it ascends by minor thirds. Roman numerals are not helpful in Example 29.22, because labels such as “IV” and “IV” reveal nothing about the interdependence within the progression. Each part of the progression is like a spoke on a wheel, supporting the final shape yet nearly meaningless when examined separately. John Coltrane’s piece “Giant Steps,” from the legendary 1960 album by the same title, is a model for major-third divisions of the octave (Example 29.22C). In fact, asymmetrical

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Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

EXAMPLE 29.22 (continued) By Major Thirds at Two Levels of Structure (Coltrane, “Giant Steps”)

whole tones

e

e

3rds

p

e

r

V 43

G

m

a

j

V43

B

o

r

E

V

G

↵

V

E t

V

G h

i

B

V

d

E E

B r

↵

G

↵

B

E

↵

m a j o r

V

↵

E

↵

whole tones

↵

s u r f a c e d

V 43

G

↵

V 43

B

↵

C.

s

and symmetrical divisions of the octave occur simultaneously at different levels. The first half of the tune (mm. 1–7) is characterized by falling motion: major and minor thirds outline major seventh chords, first on G and then on E. The supporting chord changes on each downbeat also fall, but symmetrically by major thirds, traversing the octave with the following cycle in mm 1–3: B–G–E. After a transitional ii–V motion (m. 4) the pattern is repeated down a major third (mm. 5–8): G–E–B. The second half of the tune (mm. 8–15) rises by major thirds, balancing the previous falling-major-third gestures: the ii–V–I motions lead from E (m. 9) to G (m. 11) and B (m. 13), returning to E. Finally, each applied V7 chord in mm. 1–7 appears in second inversion. As we know, such four-three chords create a stepwise line, but in this case the steps are all major seconds. By using this specific progression and inversional pattern, Coltrane has created yet another level and type of intervallic symmetry to “Giant Steps,” a title that one can now see is particularly appropriate. When you encounter these kinds of progressions, do not focus solely on the roman numeral analysis but look instead for a larger pattern: bracket sequential progressions, label the interval of transposition, and try to determine whether the chords prolong an underlying harmony or whether they progress to a new harmony.

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N ON S E QU E N T I A L PRO G R E S S ION S A N D E QUA L DI V I S IO N S OF T H E O C TAV E Example 29.23 demonstrates that equal divisions of the octave also occur in progressions that are not sequential. Notice that each tonicized area contains a different harmonic progression. Such progressions often occur over large spans of music, with intervening tonicizations of independent musical sections. Again, when analyzing such passages, you will need to interpret the tonal structure both within each section and between sections in order to see the deeper-level progression.

EXAMPLE 29.23 Nonsequential Progression That Divides the Octave in Major Thirds

F:

I

V7

VI

VI:

I

IV 6 V 65

I

F

V

VI

III:

I

IV 6 I 6

IV

D

V 64 –– 53

VI

I:

I

I6

8 – 7

V6 – 5

4 – 3

I

A F

A series of falling major thirds divides the octave into three segments. The brief tonicization of each segment disrupts our sense of tonal orientation. D major is easily accessed through mixture when VI functions as the tonic in m. 1. Similarly, both the tonicization of A major and the return to F major are secured when VI of the preceding key functions as the tonic.

EX ERCISE INTER LUDE A NA LYSIS WORKBOOK 1 Assignments 29.6–29.7

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29.3 Sequential Progressions That Symmetrically Divide the Octave Analyze the following sequential progressions, which divide the octave symmetrically into major and minor thirds, by bracketing the transpositions of material and labeling the tonicized area with key names (e.g., A major). Then label the interval of transposition between each statement of material.

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Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

A.

B.

C.

D.

Brahms, “Immer leiser wird mein Schlummer” (“Ever More Peaceful Grows My Slumber”), op. 105, no. 2 You will encounter several six-four chords. Some are cadential; others are consonant.

43

Wald:

Willst If

du you

mich

noch

want

to

see

me

ein

mal

yet

again

poco cresc.

46

sehn,

komm, come,

o oh

kom come

me

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49

bald,

komm,

o

kom

me

soon,

come,

oh

come

soon!

bald!

T H E I N T E RVA L L IC C E L L Mixture and the structuring of passages based on symmetry are two of the three processes that create ambiguity and that underlie much late-nineteenth- and early-twentieth-century music. The third process involves a subtle yet unmistakable shift from easily singable, periodic melodies to more-abstract collections of pitches that are defined by their intervallic structure and contour rather than by their melodic design. These malleable and motivic structures are called intervallic cells, or just cells. Cells can easily be developed in both the melodic and the harmonic domains, and there is a close relationship between musical events that unfold in time (melodies, which occupy the horizontal domain) and events that unfold in space (harmonies, which occupy the vertical domain). Such an emphasis on the intervallic aspect of music was a central focus of composers writing music between 1900 and 1920, to which we will turn in Chapters 30–31. As the nineteenth century unfolded, melodic cells became more common because of their capacity for diverse harmonizations and because of their potential ambiguity. Like motives, cells appear early in a composition and are developed and transformed at various levels of the musical structure.* Such transformations include transposition, inversion (reversing the contour of each interval of the cell), interpolation (adding pitch elements between some or all of the members of the cell), rhythmic diminution (shortening the rhythmic value of members of the cell), and rhythmic augmentation (lengthening the rhythmic value of members of the cell). Listen to Example 29.24. It initially appears that much of Brahms’s piece is composed of a descending three-note cell (C6–B5–A5). This cell is transposed down in thirds in mm. 2–3 (A5–G5–F5) and mm. 4–5 (F5–E5–D5). After the double bar (m. 10), the cell reverses direction and ascends chromatically (G5–G5–A5). This contour inversion is enhanced by the descending broken-chord figure in the bass, which balances the opening ascending figure. Note that the cell appears to be longer after the double bar: The chromatic

*See Appendix 2, which explores motive and motivic processes.

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Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

EXAMPLE 29.24 Brahms, Intermezzo in A minor, op. 118, no. 1 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A

A

B a

4

a

b

espress.

A (inverted) 8

dim. e rit.

A 12

fragment is followed by a leap to C6. The added length is confirmed in mm. 14–16, in which a chromatic fragment is followed by a leap (C5–C5–D5–F5). At the beginning of the piece, as the right hand takes over the broken-chord figure in m. 2, the left hand attacks octave Es on the downbeat. The decrescendo that occurs on the

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downbeat of m. 1 allows this octave to be heard above the broken-chord figure. Played this way, the left-hand E4 is heard as a continuation of the right-hand cell C6–B5–A5, making the opening cell a four-note figure, rather than a three-note figure that is lengthened to four notes in the second half of the piece. Example 29.25 shows these figures.

EXAMPLE 29.25 mm: 1

A

3

11

A⬘

A (inv.)

15

A⬘ (inv.)

Analytical Interlude: Chopin, Prelude, op. 28, no. 2 Let’s now analyze a short prelude by Chopin that incorporates intervallic cells. Listen to Example 29.26 with the following issues in mind. 1. Is this piece in a key? If so, which one or ones? 2. Is there an underlying harmonic progression? If so, what is it? 3. Is there a tune? If so, compare it to tunes we have encountered before. 4. Discuss the structure of the accompanimental figure that underlies the entire piece. The prelude begins ominously in E minor but ends clearly in A minor. We may immediately wonder if this piece is double tonal (in both E minor and A minor) or progressive (moving from E minor to A minor). Or is it merely an off-tonic piece that begins on minor v and moves to the tonic, A minor? We must seek answers through analysis. The first phrase (mm. 1–6) moves from E minor to G major (i to III in E minor). But could E minor simply function as vi in G major? Because E minor is not strongly established as a tonal area and because the progression works well in G major (vi–V–I), the prelude might begin off-tonic. The restatement of the opening tune abruptly begins in B minor. Given its relation to the opening, the listener accordingly anticipates that B minor will yield to D major, just as E minor led to G major. However, only the melody confirms our expectations. The left hand continues to repeat the bass note A2 (mm. 9–12), which is sustained through a half-diminished seventh chord that is transformed into a fully diminished seventh chord (D–F–A–C) until it falls to an F2 in m. 13. In m. 14, when F2 yields to F2, the Fr43 chord (F–A–B–D) foreshadows the eventual resolution to A minor. We must base our overall structural interpretation on how we view the first phrase and its modified repetition up a perfect fifth. In Example 29.27, path 1 illustrates the goal-oriented tonal progression G major–D major–A minor, in which the cadence of each phrase is considered to be more important than the opening harmony. This interpretation suggests that two large-scale fifth motions propel the music toward the tonal goal, A minor. Path 2 illustrates the progression E minor–B minor–A minor, in which the opening

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EXAMPLE 29.26 Chopin, Prelude, op. 28, no. 2 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

5

9

13

dim.

18

sostenuto sieniando

harmonies take precedence over the cadential harmonies. In this case, we might decide that the piece contains a large-scale modal shift from the minor to the major dominant. Neither interpretation is particularly revealing. All we know is that the large-scale progression is atypical, but we understand little about what motivates this progression.

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EXAMPLE 29.27 Harmonic Analysis of Chopin’s Prelude Path 1:

vi–V–I G major

Path 2:

vi–V–(I) D major A minor: i–V/III B minor

i–V/III E minor

vii° 43—65 of V (III)

Fr 43

V

i

Let’s look to the melodic domain for more answers. The opening right-hand melody is curiously disjunct, built of a three-note segment (E4–B3–D4) in mm. 3–4, which is followed by a modified repetition (D4–A3–B3) (mm. 5–6). Because this melodic figure consists of only three notes, is repeated (with slight changes) down a major second, and appears consistently throughout the remainder of the piece, it can be said to function as a melodic cell. While melodic contours are defined hierarchically with terms like neighbor and passing that render certain tones subordinate to others, ambiguous cells are often defined by their intervallic content. For example, the opening two-measure cell of Chopin’s prelude comprises a falling fourth and rising third, with the result that the first and third pitches are a major second apart. (Therefore, the perfect fourth contains a second within it.) Given that the intervals of the repetition recur, we can establish a close connection between the cell’s model and its copies. Note, as in Example 29.28, that a copy need not be exact for it to be considered a melodic cell. If we compare E–B–D to D–A–B, we see that the position of the second has changed within. The overall intervallic content, however—a fourth, a third, and a second—remains constant. We can easily relate the two statements by simply saying that a small skip or step follows a larger leap. If we look at the pitches that are strongly articulated at phrase beginnings and endings, we see that E4 falls to D4, which in turn falls to B3. This expanded statement of the initial cell now occupies almost half of the prelude. Example 29.28 illustrates how the two statements of the cell in mm. 3–6 combine to make one super cell at a deeper level. For further influence of the melodic cell, let’s examine the left-hand ostinato that begins the piece. It comprises two voices. The lowest voice, which leaps a tenth (E2–G3), is

EXAMPLE 29.28 Melodic Contours in Measures 3–6 of Chopin’s Prelude E

E

D

B

D

B

Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

723

counterpointed against a moving voice (B2–A2–B2–G2). It seems that Chopin is investing the moving voice with the generative potential of the intervallic cell, because it is composed of a small step (B2–A2) and a larger interval (B2–G2). Yet another manifestation of the cell, this time harmonic, appears in the bass in mm. 1–6: E2–D2–G2 spans a perfect fourth (D2–G2) and contains a second (D2–E2) within the fourth. In fact, recognition of the existence of the cell helps to explain the deep-level parallel octaves (E–D) that occur between the outer voices, which are especially strange given that Chopin’s counterpoint is impeccable and that such obvious voice-leading errors would never escape his perceptive ears and eyes. Let’s continue this method of hearing the cell at ever-deeper levels of the musical structure. The melodic pattern is restated up an octave, on B (B4–F4–A4) in mm. 8–9; the same expansion of those pitches also occurs over mm. 8–11. The anticipated arrival on D is derailed at the F4, and the progression moves instead toward A minor. Thus far, the structural melodic units are the opening E4 and the highly marked F4: E4–D4–B3, B3–A3–F4. The next four statements of the melodic cell are accompanied by a traditional harmonic progression in which Fr43 moves to V and then resolves to i. The beginning and ending points of these statements both occur on A: A4 in m. 14 and A3 in m. 23. The overall beginning and ending points (E–F and A) combine to create a final statement of the cell, one that lies at the deepest structural level of melody. In addition to the connection we have drawn between different functions of the cell across Chopin’s prelude, we also may consider extramusical factors in our analysis. For example, the inner line of the left-hand ostinato clearly invokes the opening portion of the well-known religious chant “Dies irae” (Example 29.29). The hymn, which appears in Berlioz’s Symphonie fantastique, written around the same time as Chopin’s prelude, is part of the Mass for the Dead, and its use here is particularly poignant, given that at the time of composing these preludes Chopin was sick with tuberculosis, a disease that eventually killed him. Let’s ask two more questions before leaving this piece. Why is there harmonic ambiguity between relative minor and major modes, and why is the second phrase transposed

EXAMPLE 29.29 Comparison of the Inner Line Ostinato of Chopin’s Prelude with “Dies irae” A.

Di Day

B.

es of

i rae, wrath,

Di day

es of

il la doom

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WORKBOOK 1 Assignments 29.7–29.9

up a perfect fifth? If we extend our analysis to consider that this is but one of a set of 24 preludes, the large-scale tonal plan reveals that each of the 12 major and minor pieces is connected by a pattern. The preludes are paired: A major-key piece is followed by one in the relative minor. The pattern continues by ascending a fifth through each of the keys (e.g., C/a, G/e, D/b). Notice that this pattern corresponds to both of our harmonic interpretations of the A-minor prelude, the second of the set. The opening is harmonically ambiguous because of the juxtaposition of the relative minor and major modes (e/G), which are repeated up a fifth (b/D). Might Chopin be giving the listener a glimpse of the harmonic model that will unfold over the next 22 pieces? This analysis enables us to see that a short, three-note cell influences both surface and deeper-level melodic and harmonic events in this piece. Most important, exploring the generative role of the intervallic cell provides us with insight into a compositional process that transcends roman numeral analysis.

T ER MS A ND CONCEP TS • chromatic versus diatonic sequences • chromatic A2 (⫺M3/⫹P4) sequence • chromatic D2 (⫺P4/⫹m3) sequence • chromatic D2 (⫺P5/⫹P4) sequence • contrary-motion chromaticism • dissonant prolongation • equal divisions of the octave • intervallic cell • omnibus • sequential progression • whole-tone path

CH A PTER R EV IEW 1. Complete the table, contrasting chromatic sequences with diatonic sequences. DI AT ON IC S E QU E NC E S INTERVA L BET W EEN “COPIES” . . .

follows whole/half step pattern of diatonic scale, changing quality (M, m, dim.)

CHORD QUA LITIES . . .

are varied (M, m, dim.)

FIRST CHORD OF EACH “COPY” . . .

has a diatonic root (no accidentals)

A NA LY TICA L L A BEL . . .

only shows generic intervals— D2 (ⴚ4/ⴙ3)

C H ROM AT IC S E QU E NC E S

Chapter 29 Melodic and Harmonic Symmetry Combine: Chromatic Sequences

725

2. Name three common sonorities used in chromatic step-descent basses.

3. Dissonant prolongation extends a harmony most often through which kind of motion in the outer voices? a. parallel

b. oblique

c. similar

d. contrary

4. A complex type of dominant seventh prolongation where all voices move chromatically, with enharmonic dominant sevenths occurring every third chord, is called the _______________________________________________________________.

5. Complete the table describing equal divisions of the octave.

I N T E RVA L

N U M B E R OF H A L F S T E P S

N U M B E R OF DI V I S ION S OF T H E O C TAV E

tritone M3 m3 M2 m2

6. John Coltrane’s “Giant Steps” is an example of a ______________________________, which can be likened to a chromatic sequence where the “model” consists of an entire passage of music.

7. Name five processes that can be applied to intervallic cells.

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PA R T 9

T W ENTIETH- A ND T W ENT Y- FIRST- CENTURY MUSIC

U

p to this point, the music that we have studied has all fallen into a single category called “tonal.” Whether this music was written by Corelli in 1672, Haydn in 1772, Brahms in 1872, or by the group Chicago in 1972, most of this repertoire uses a consistent pitch structure, from the individual sonorities, to the chordto-chord connections and voice leading, to the play between dissonance and consonance and chord successions, and even to the deepest harmonic levels that underlie an entire piece. Indeed, the number of specific sonorities used in tonal music is small: a total of ten fundamental three- and four-note chords (four triad types and six seventh-chord types). And yet the immense number of musical styles, textures, and other characteristics that can be created using this basic material allows the listener to relish the differences between Couperin and Chopin, Mozart and Mendelssohn, and Bach and Beethoven. In the world of twentieth- and twenty-first-century “classical” music (i.e., not popular, jazz, commercial, or other examples that rely on the traditional tonal language), the situation is very different. Thus, Chapters 30-32 focus on music written after 1900. While commercial and popular music continues to be composed in the tonal tradition, for which you possess more than adequate tools to deal with, we will explore music that leaves behind the well-circumscribed world of tonality, a world based on the tenets of a single tonal focus, the tonic, and the harmonic hierarchies that support and point to the tonic. The goal of these three final chapters is to provide you with the context, concepts, and compositional and analytical methodologies necessary for you to appreciate and comprehend important musical processes at work in this fascinating and wildly disparate music. 727

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After exploring new sonorities and pitch collections in the music of diverse composers, we will learn how composers manipulate and relate small pitch units. After a glance at new rhythmic and metric techniques our study of non-tonal music will end with the ways composers use ordered sets of pitches that include all twelve pitch classes. Our study of repertoire will be wide ranging, beginning with works that appeared in 1900 and ending with compositions written after 2000 by such notable composers as Samuel Adler, Joan Tower, Tan Dun, David Rakowski, John Corigliano, and Augusta Read Thomas.

CH A P TER 30

Vestiges of Common Practice and the Rise of a New Sound World OV E RV I E W

Chapter 30 is the first of three chapters that explore twentieth-century music. In this chapter, we will see the shift from the tonal system and all that it means—including its hierarchies, asymmetrical tonal structure, and constraints based on dissonance treatments and counterpoint—to a new aesthetic, one based on extending and transforming common-practice tonal features in novel ways. This new approach worked with both smaller and larger pitch collections than our well-known major and minor scales. These collections contain as few as five notes and as many as eight notes. They are remarkably malleable, allowing the composer to meld them into a variety of styles, none of which rightfully can be called “tonal.” We’ll learn how composers use sonorities that are not generated by thirds, but rather by seconds, fourths, and fifths. We will explore specific works by a variety of composers including: Messiaen, Debussy, Stravinsky, Schoenberg, Berg, Bartók, Ravel, and Webern. CHAPTER OUTLINE Centricity ...................................................................................................................... 737 Form and Process ........................................................................................................ 741 Always the Same, But Never in the Same Way: Melodies, Motives, Harmony, and Line ............................................................................................... 744 Triadic Extensions ...................................................................................................... 752 Split-Third Ninths ................................................................................................. 755 (continued)

729

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THE COMPLETE MUSICIAN

Another Way to Stack Intervals ........................................................................... 756

Pitch Classes (PCs) and Collections ...................................................................... 762 Seven-Note Collections: Diatonic Modes .......................................................... 763 Five-Note Collections: Pentatonic ...................................................................... 768 More Symmetry: Six-Note Collections .............................................................. 771 Pitch-Class Collections with Six Members #1: Whole-Tone Collection ..... 771 Combining Collections: The Intersection of Quartal and Whole-Tone Worlds .......................................................................................... 776 Pitch-Class Collections with Six Members #2: Hexatonic Collection ......... 776 Major and Minor Triads Within the Hexatonic Scale ..................................... 777 Eight-Note Collections: Octatonic ........................................................................ 778 Subsets..................................................................................................................... 781 Seventh-Chord Subsets ......................................................................................... 782 Form ............................................................................................................................... 784 Terms and Concepts ................................................................................................... 787 Chapter Review ........................................................................................................... 787

L I S T E N TO R E C O R D I N G S of the brief excerpts below, all of which were completed within 36 months of one another. The differences could not be more stark. Consider harmonies, chord progressions, and whether there is even a sense of tonic (see Examples 30.1A–H).

EXAMPLE 30.1

Diversity of Styles in Contemporary Music

A. Bartók, Allegro Barbaro: 1911   

 



        



 

                                                    



  

    

    

    

    

                



 

    

              

                          

           

       

                

731

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.1 (continued) 

       

      



 

       

   



  

             

B. Schoenberg, “Nacht” from Pierrot Lunaire: 1912 

 




 

   

  



 





 













 







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732

THE COMPLETE MUSICIAN

EXAMPLE 30.1 (continued) 



        

  
    



    

   

 







       

 

    


  

    

   



                 

 

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733

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.1 (continued) D. Berg, “Über die Grenzen” from Five Orchestral Songs: 1912
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734

THE COMPLETE MUSICIAN

EXAMPLE 30.1 (continued) E.

Stravinsky, “In Petrushka’s Room” from Petrushka: 1911




    






            









             



 

  



 

 



    
    



  




 

 

 

           



      

 






  



     



     

 

    

      
    












       

          
        





 

      

   

    



     

   


   

  

         













   

 







  
   

           

     


      

           







 


 


    

 

  



    

  



 








                                         




                                         

735

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.1 (continued) F. Scriabin, Prelude for Piano, op. 74, no. 2: 1912 Très lent, contemplatif

4 &8

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736

THE COMPLETE MUSICIAN

EXAMPLE 30.1

(continued)

Webern, Five Movements for String Quartet, op. 5: 1909

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737

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.1 (continued) 







  









 

 











 

   

 













































    


 

























   
























 









   










  




Most likely you were struck by the remarkable diversity of styles, pitch worlds, timbres, textures, and character of these examples. Few of them give much sense of pitch priority, no clear tonic undergirding the other harmonies and few triads; instead, sonorities arise from other intervals, particularly dissonant ones. And if there are triads, they did not behave in any ways we have encountered before. Further, some of these pieces do highlight individual pitches, but not in the ways done in tonal music. And what about the single most important event in tonal music, the cadence? Are there alternate techniques used to create closure? Most excerpts left us in a sea of ambiguity; however, there must be a musical logic driving this repertory. Clearly this musical potpourri, written by a wide variety of composers, is not tonal. The three-century-old tonal system and all that it means has been largely overturned by many new and divergent aesthetics based on broadening conceptions of music which questioned conventional values and techniques. We identify this music as post-tonal, and distinguish two types: The post-tonal music that gravitates toward a certain pitch or sonority is called centric, and that which doesn’t is called atonal.

C E N T R IC I T Y Centric music, such as the examples by Ravel and Debussy that we just encountered, does project a sonority that is more important than surrounding sonorities. It also provides closure to musical units, even if the closure is not secured by traditional cadential gestures. However, the material within the phrase does not operate according to the phrase model. It’s a modified sort of tonality, a post-tonal emphasis on pitches that are important enough to make the piece gravitate toward them, but without the baggage of dissonance treatment. A good way to think about the meaning of centric is that all tonal music is, to some extent, centric (projecting a true “tonic”), but not all centric music is tonal. Indeed,

738

THE COMPLETE MUSICIAN

EXAMPLE 30.2 A.

Bartók, “Ostinato” from Mikrokosmos, Book 6, no. 146 Vivacissimo q = 176 - 168

?2 4

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739

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.2 (continued) & ?

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7 ° 4 &4 Ostinato 1:

Ostinato 2:

Ostinato 3:

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740

THE COMPLETE MUSICIAN

EXAMPLE 30.2 (continued) D.

Prokofiev, Sarcasms, op. 17, no. 3 Allegro precipitato

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741

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.2 (continued) F.

Ravel, “Passacaille” from Piano Trio in A minor Très large q = 40

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the third movement of the Webern piece mentioned projects C as an important pitch—it begins and ends the piece, and provides an ostinato—but by no means is this piece tonal. In fact, the ostinato is one of the most important twentieth-century techniques for emphasizing a pitch, in light of the fact that there is no tonal hierarchy, or clear distinction between dissonance and consonance: just pure repetition, either of harmony or a set of harmonies, a melody, or a combination of the two (see Examples 30.2A–E). The passacaglia, a repeating bass line or series of sonorities, was particularly popular in the twentieth century (see Example 30.2F).

F OR M A N D PRO C E S S Composers like Ravel wrote numerous pieces in readily identifiable forms; for example, his Menuet Antique and Sonatine. Schoenberg, a powerful force in directing music into uncharted waters, wrote pieces in traditional forms. One of his most forward-looking pieces, entitled “Suite for Piano,” contains movements with titles like “Waltz,” “Musette” (Anthology no. 64), and “Gavotte” (see Example 30.3). Points of repose or closure are important. We can still refer to them as cadences, albeit few of which aurally relate to the half, plagal, and authentic cadences that we worked with previously. In twentieth-century music there are many ways to create closure, where units

742

THE COMPLETE MUSICIAN

EXAMPLE 30.3 Schoenberg, “Gavotte” from Suite for Piano, op. 25

2 &2

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of music are marked off, including the mere cessation of movement, arrival in a new register, and contrary motion to a single pitch (some examples are shown in Example 30.4). Variation form can be viewed as varied ostinatos. The idea of using a repeating figure that is transformed is a hallmark of twentieth-century music. This includes continually recasting an opening element in various lights, such as changes in density, register, dynamics, articulation, and placement in the measure. Debussy’s extraordinary “Footsteps in the Snow” (“Des pas sur la neige,” Example 30.5) is but one of many works that uses a single accompaniment pattern, which provides undergirding in the left hand over which subtle upper-voice changes occur.

743

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

Cadences in Twentieth-Century Music

EXAMPLE 30.4

A. Prokofiev, Visions Fugitives, op. 22, no. 16 Meno mosso

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B. Schoenberg, Drei Klavierstück, op. 11, no. 1 5

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A simple rising figure from a pedal D, first to E, and then E–F recurs throughout much of the piece, but in various contexts. For example, in mm. 2–4 it harmonizes a sorrowful tune while in mm. 5–7 it becomes a fulcrum around which contrary-motion outer voices move to a cadence on D in the left hand. That D is projected in two different ways: first as

744

THE COMPLETE MUSICIAN

EXAMPLE 30.5

Debussy, “Footprints in the Snow” (“Des pas sur la neige”) from Préludes, Book 1

Triste et lent (q = 44)

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∑

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?

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pp

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,

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Œ

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3

m.d.

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p expressif et douloureux

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4 & b4 ˙œ œ œ œ -

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˙-

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˙œ œ œ œ œ- Œ Œ j œ œ œ œ ˙ n ˙˙

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bœ

œ

3

œ œ œ œ .

œj œœ ‰ Œ œœ ‰ J

j œ˙ œ œ œ ˙ ˙˙

œ œ œ b ˙˙ œ œ œ œ bb ˙˙ œ

˙œ œ œ -

œ.

Ó

n n œ œ œ œ n œœ bb œ˙˙ œ œ œ ˙ Œ

bœ œ b˙

expressif

&b ˙™ ˙˙ ™™ ? b bœ

{

the generator of the rising-third figure, and then the arrival point in m. 7, which illustrates the idea of centricity. Also notice that the right hand has a D in its rising line, but comes to rest on E, pairing with the left hand D to recall the opening D–E motive (melodically and harmonically). The right hand does eventually get to D, but only in m. 8.

A LWA Y S T H E S A M E , BU T N E V E R I N T H E S A M E WA Y: M E L ODI E S , MO T I V E S , H A R MO N Y, A N D L I N E We have explored various types of motives. In Chapter 28 we saw how they took on a purely intervallic character rather than a more-typical melodic shape, and called them “intervallic cells.” They became the driving force in much twentieth-century music. Ravel’s three-movement Sonatine (Example 30.6) is a more traditional work. It conforms to numerous structural procedures we have studied in earlier chapters, most notably its

745

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.6 Ravel, “Modere” from Sonatine doux et expressif

Modéré

# #2 

Piano

œj œ œ œ œ œ œ œ ® œ œ ® œ œ œ ® œ œ œ ® œ œ œ œ œ œ ® œ œ œ œ œ

‰

{

p

# #2 

r œ œJ

‰

≈

≈

œœ

œ

≈

≈

œœ

≈ œ

œœ

≈

œœ

≈ œ

œœ

pp subito

mf

> ### œ œ œ œ œ ≈ œ œj œ ™ œ œ œ œ œ œ & ® œ œ ® œ œ ≈ œ ® œ œ ™ ® œ œ œ ® œ œ œ œ® œ œ œ œ œ œ œ ® œ œ œ œ œ ® œ œ œ ® œ œ œ

3

{

3

## ≈ œ ≈ œ ≈ œr ≈ & # œœ œ≈ œ œ J

™™ œ ≈ œ ≈ œ ≈ œ ≈ œ œ œ œ

≈ ≈ œ ≈ œœ ≈ œœ œ œœ œ

œ œ œ ### œ œ œ œ œ œ œ œ œ œœ œn œ œ œ œ œ œ œ œ œœ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œœ œn œ œ œœ œ œ œ œ œ & ® ® ® ® ® ® ® ®œ œ®

6

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œ

. œ #œœ

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. œ

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. ### œ & #œœ

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nœ # œœ Rall.

nœœ nœ a Tempo

. n œ # œœ

. œ

œ # œœ

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œ

> œœ œ œ > œ œœ œœ œ œ œ œœ

∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏

œœ œ œœ ### œœ œ œœ œœ œ œ œœ œœ ® œœ ® œ œœ œ œ œ œ œ ® ® ® œ œ & œ œ œ œ œ

9

œ

œ

œ œœ

∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏

{

##œ & # #˙œ

?

œœ œ

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{

∏∏∏∏∏

œ r r en dehors ### ≈ œœ œœœ œ ≈ œ œ œ œ ™™ œ œ ™™ œ œ œ nœ œ œ œ œ œ œ & œ œ œ œœ œœ ‰ œ #œ ‰ œ #œ ‰ œ #œ nœ ‰ #œ nœ œ p > œœ œ œ œ œ œ œ ### œ œ ‰ œœ ‰ œ œœ nœ ‰ œ œœ nœ ‰ œ œœ & œœ œ ? œ J J >

12

&

746

THE COMPLETE MUSICIAN

EXAMPLE 30.6

(continued) Un peu retenu

œ œ œ œ œ œ œ œ œ ‰ œ J ‰ œ œ ppp J œ #œ œ œ œ œ ‰ œ œj œ œ

## œ & # œ‰ œ #œœ œ nœ œ œ #œœ œ nœœ œœ ‰

{

? ### ‰

œœ œ J œ

œœ

‰

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22

{

Rall.

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m.g.

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a Tempo

long

œœ

n œœ œ

œ J Uj œœ

j œ œ pp

‰ -œ œ nœœ ™™ &

.r >j œ œ œ œ œ œœ œ œœ œ ? ### œœœ œœœ œ œœ œœ R ≈ &® œ œ œ ™™

27

{

32

## & # œœ #œœ-

pp subito

{

œœ-

# # œ œ œj œ &# œ œ œ œ œ

j œ œ

œœœ ™™™

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? ### œ œ œ œ œ. ≈ œr R &œ œ œ œ œ J

très expressif

Rit.

17

≈ ™ ™

j œ œ

œœœ ™™™ ‰ -œ œ nœœ ™™ &

?œ

œJ

œ œ œ œ œ ‰ œ J œ #œ œ œ œ œ

1.

> œœœ œœ .

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?œ œ

p

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p

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> œœ œ œœ œ œ œ œ œ œ œ nœ œ œ œ œ œ œ œœ nœ œ œ œœ œ œœ œ

j œœ #œœ-

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mf très espressif

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“” > œ œœ œœ œ œ œœ œ œ œ œ nœ œ œ # # nœ œ & # œ œ œ œ œ œ œ œ œ œ œnœ œ œ œ œ œ œ œ œ œ œ nœ œ œ nœ œœ œ œ œ œ œ œ œ œ œ

36

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## & # nœ

f

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nœ

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747

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.6 (continued)

:“; ### œ

Poco rit.

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39

{

## &#

{

r œ œ n œœ

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œ ? ### ‰ œ œ œœ

le

49

# # nœœ ™™ & # b œ™

{

-

-

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cre

a Tempo

43

ran

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do

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j œœ œœ ‰

œ œ œ œ nœœ nn œœ œ ‰ œœ œ œ ‰ œ

œ œ œ œ œœ œ œ œœ œ n œœœ nœ œ œ

‰ œœ œ œ

-

scen

‰ œœ

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j œœ ‰

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j ™ œ œœœ ‰ nœœœ ™™ œœœ mf œ œœ ™ œœ œ œ ‰ ™ œœ œ

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59

{

3

mp très expressif

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r œœ ≈ œ ≈ œœ ≈ œœ ≈ ≈ J œ

mf

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62

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## ≈ ≈ &# œ ≈ œ œ ≈ œ œ œ œ œ

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748

THE COMPLETE MUSICIAN

EXAMPLE 30.6

65

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(continued)

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œn œ œ œ œ œ œ œ œ œ œ œ œ ® œ œœ œ ® œ œ œ ® ® ® ® ® ® œ

. ### œ & #œœ

. œ

#nœœœ

#œ˙œ

nœœ nœ

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71

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{

. œ

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f

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œ œœ œ ### ® œ œ œ œœœ & œ ® œ œ œ ® œ œ

68

. ### nœ & # œœ

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#### # #

œ #œ

#### # #

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a Tempo

# # # en dehors r r œ œ ™™ œ œ & # ## œ ™™ œ œ œ #œ œ œ œ œ œ œ ‰ ‹œ œ ‰ œ ‹œ œ ‰ œ ‹œ #œ ‰ #œ nœ œ

{

#œ ‰œ œ ‹ œœ œ # œ œ

p

? #### # ‰ œœ œ #œœ œ #

‰ œœ œœ #œœ

‰ œœ œœ J

j œ

‰ œ œ

‰ œœ œœ J

Un peu retenu très expressif

œ œ œœ œ # ## # œ œ & # # œ œ œ œ œ? J& ‰ ‰ #œ nœ œ ‰ ppp œ j j ? #### # ‰ œ ‰ œ # œ œ œ œ œ

76

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82

a Tempo

## # & # ##

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Rall. Uj œ œœ œ œœ œj ‰ œ œ œJ n œœ œ œ m.g. U pp œ #œ œ œ œ œ ?œœ œ œ œ œ & œœ œJ u

œ œœ ‰ œ œ œJ œ #œ œ œ œ œ

-

tan

-

> n #n œœœ J

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&

749

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

clearly defined key of F minor. Much of its material is generated from the perfect fourth, F down to C, in much the same way that tonal music develops motivically. In the first movement, the fourth is embellished by a lower neighbor and followed by various ascents. However, its pitch material is treated to inversion, reharmonization, and transposition, while its rhythms are derived from the opening gesture and are augmented and diminished. Even the accompaniment is comprised of “double” statements of the initial gesture as it builds toward the climax. The movement closes with the theme cast in the parallel major. The second movement, “Mouvement de Menuet,” is in D major (the dominant of the first movement, written as D for reading ease; see Example 30.7). It inverts the falling

EXAMPLE 30.7 Ravel, “Mouvement de Menuet” from Sonatine

œœ .

™ œœ œ œœœ œœ . . .

b 3 & b bbb8 œœ .

œœ .

œœ .

œœ.

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p

{

b & b bbb

nœ œ

{

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bœ œ

?

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j œœœ œœœ Œ œJ -.

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nœ œ œ œ J œnœ œbœ

‰

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j nœ nœ œ

‰

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> œ œ

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6

13

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750

THE COMPLETE MUSICIAN

EXAMPLE 30.7 (continued)

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{

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f

œœ œ œ ™ œ œ ‰ & œ™ œ œ ‰ œ p

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33

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26

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39

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le Mouvt

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55

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j œœ œ œ œ œ ™ œœ ™œ œœ ™™ œj œ Œ œJ

> œœ œ œœ œ j œ œ œ œ œœ œœ . . j œœœ œœœ œœ œœ ? Œ œJ œ. œ. -.

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751

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.7 (continued) Un peu plus lent qu'au début 62

b ‰ & b bbb œœ œ œ œœ œ œ œ œ œ œJ œ J j œœ œ ? bb b œ œœ œœ œJ bb œ ‰ œ. œ & .

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69

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fourth to a rising fifth, D–A, yet the rhythm of the theme is retained in mm. 1–2, linking it explicitly to the first movement. The following D2 sequence (with sevenths and ninths) is logically chosen, given that it rises and falls by the very intervals of the central motive: fifths and fourths. In the following pp section, the motive is transposed and used as the basis for a transition. The theme is restated in the B section in E minor in m. 23. The retransition is a tour de force that combines the motive used in its original form from the first movement but in an augmentation canon: the soprano falls a fourth followed by the faster rising gesture, and the top voice of the left hand imitates an eighth note later playing the identical theme half as fast. The relentless C–G, harkening back to the first movement, is reinterpreted as D–A in m. 53 to bring back the minuet’s initial motive and theme. Note that the keys of the first and second movements—F and D—are the first two tones of the piece: F and C. The melody of the final movement opens with the first movement’s gesture, but with the pitches reversed: C up to F. Even the faster-note sixteenths, accented in mm. 8–10,

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THE COMPLETE MUSICIAN

EXAMPLE 30.8 Ravel, “Animé” from Sonatine Animé

# #3 

Piano

4

{

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#œ œ œ œ œ œ œœ œ

#œ œ œ œ œ œ œœ œ

f

œ #œ >

> >˙ ≈ œR

œ >

œ #œ >

très marqué

## &# ‰

{

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‰

> ≈ >œ ˙˙ R

œ >

‰

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‰

> >˙ ≈ œR

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>˙ 8 ### œ >œ >œ &

{

follow the rhythms of the first movement (see Example 30.8). The material in %4 beginning in m. 37 is identical to the opening movement’s, transposed to E (V/A). Cascading through the first movement’s motive, the rest of the movement relentlessly restates the opening theme in various characters, ending with nearly two-dozen statements of the motivic germ, the falling fourth (see Example 30.9).

T R I A DIC E X T E N S ION S As you listened to these examples, you certainly encountered triads and seventh chords. Many twentieth-century composers continued to work with these sonorities to great effect. However, they often viewed the seventh chord less as a by-product of passing motion than as a third stacked above a triad. By continuing the process of stacking thirds, these composers added another third above the seventh, creating a ninth chord (e.g., C–E–G– B–D); by adding another third above that ninth they created an eleventh chord (C–E–G– B–D–F). A final member, the thirteenth, may appear as well, using every pitch in the key (in F, a V13 chord would be spelled C–E–G–B–D–F–A). These chordal extensions became commonplace in French music at the turn of the century, particularly in the music

753

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.9 Ravel, “Animé” from Sonatine Même Mouvt Tranquille

Rit.

j œ œ œ œ œ œ œ ### 5 œnœœ œ œœœ œ œ œ œn œ œ#œœ œ œ œnœœ œ œœœ œ œ œ œn œ œ#œœ œ œ œnœœ œ œœœ ≈œn œ œ #œ œ œ# œ œ & 4 œ

37

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très doux et expressif

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of Debussy and Ravel. Influenced by these composers, jazz musicians adopted them in the 1940s and continue to use extensions to this day. Listen to the opening of Rachmaninoff ’s Moment Musical, op. 16, no. 3 (Example 30.10A) and Ravel’s “Rigaudon,” from his Le Tombeau d’ Couperin (Example 30.10B).

EXAMPLE 30.10 Triadic Extensions A. Rachmaninoff, Moment Musical, op. 16, no. 3 Andante cantabile (q = 56)

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754

THE COMPLETE MUSICIAN

EXAMPLE 30.10 (continued)

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STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

Ravel’s piece (Example 30.10B) contains extended triads, but not merely stacked mechanically as thirds. Rather, the voicing projects various combinations of chordal members, in exactly the same way common-practice composers voiced triads and seventh chords. In fact, we often encountered incomplete triads and sevenths in our study of common-practice music. When twentieth-century composers employ sonorities with five, six, and even seven tones stacked in thirds, the chords may or may not be complete: Context clarifies the chord. For example, ninth chords are often voiced with the root and ninth next to one another with the fifth omitted. In this voicing, the minor ninth chord is particularly pleasing. Again, the fifth may be omitted, or a complete chord can be used. Finally, by omitting more than one chordal member one can interpret these sonorities in multiple ways. For example, the chord C–E–G–B–D–F–A might be reduced to the following sonority: C–E–G–A, creating what could be viewed as a C major chord with added sixth (the thirteenth) or as a minor seventh chord in first inversion. Using jazz notation it would be labeled “Am7/C”; that is, A–E–G over C, or C–E–G–A, respectively (in the bass; see Example 30.11). This chord is often used as a tonic, in spite of the added fourth pitch.

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Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

Two Possible Interpretations of the Sonority C–E–G–A

EXAMPLE 30.11

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Mahler, Song of the Earth

EXAMPLE 30.12

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Split-Third Ninths A final type of ninth chord is particularly interesting, given that it can be considered an outgrowth of composers’ attempts to “bend” a pitch to create a blue note: a note slightly flatter in pitch than the major third above a chord, often giving the impression of major and minor at once. Unfortunately, there is no way to create this effect on the piano, so composers use the “split third”—a chord with both a major and minor third, a reasonable

756

THE COMPLETE MUSICIAN

attempt to create the sound of a blue note. For example, the dissonant “sharp ninth chord” (C–E–G–B–D)—hugely popular in jazz music of the past 60 years—can be voiced in numerous ways, but one is particularly popular. For the sharp ninth chord, the ninth, D , is often juxtaposed with E in the “outer” fingers of the right hand (E in the thumb and D  in the pinky) with the seventh usually occurring in the “middle” of the right hand (see Example 30.13).

EXAMPLE 30.13 Possible Voicing of the Sharp Ninth Chord

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The essential elements of the chord are root, third, seventh, and ninth: C–E–B–D/  E . The chord is popular with guitarists; Jimi Hendrix famously used it, often built on E, giving rise to the nickname the “Hendrix chord.” If you stop to think about it, the chord minus its seventh gives us a major-minor triad, considering D to be enharmonically equivalent with E. This sonority, built on G (G, B, B, D), ends Bartók’s “Boating” (see Example 30.14).

EXAMPLE 30.14 Bartók, “Boating” from Mikrokosmos, Book 5, no. 125

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Another Way to Stack Intervals

Given an eleventh chord stacked in thirds from D we get: D–F–A–C–E–G. However, by rearranging these pitches into non-third structures, we obtain a variety of sounds. We have already seen how the ninth is often set against the root or the third of the chord, creating a dissonant second. For example, we could skip every other third, the result of which would be a stack of fifths: F–C–G | D–A–E. Chords built of stacked fifths are called quintal chords. We could do the same by falling by fifths from E; the result would be ascending fourths: E–A–D | G–C–F. Chords built of stacked fourths are called quartal chords. These non-tertian sonorities provide a distinct contrast to the third-based chords of tonal music, and can be voiced in a variety of ways. The first two perfect fourths could be heard as a major second and perfect fourth (built upward from the first pitch class): F– G–C. Recall that this was the same intervallic cell Chopin used in his A minor Prelude.

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Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

We will see that such sonorities, and many other combinations of intervals, become the sound world of the twentieth century. Once again, Bartók’s “Boating” illustrates chords built on the perfect fourth/fifth. The three-pitch sonority G–C–F is followed by A–D–E, a perfect fourth and second. Bartók expands the sonority at the end of the measure, so that the three-note chord takes a rising quartal form (E–A–D) or falling quintal form E–A–D, thus maintaining the same pitches but providing a very different color. Because the first sonority unfolds as rising fourths (G–C–F), we can “glue” the last three pitches (E–A–D) similarly; the result is a six-note perfect-fourth sonority: E–A–D–G–C–F. The right hand enters in m. 3 with the risingfourth motive. Placing B on the bottom yields B–E–A–D. Combined, this series forms rising fourths through ten of the twelve tones of the chromatic scale except for B and F, which are reserved and appear a few measures later (Example 30.15A). Bartók opens his monumental Concerto for Orchestra (Example 30.15B) using the perfect fourth pattern (C–F–B) followed by the perfect-fourth plus major second sonority (B–A–E and E–F–C).

EXAMPLE 30.15 A. BartÓk, “Boating” from Mikrokosmos, Book 5, no. 125, mm 1–10 E–A–D– G– C–F–B –E –A –D – G –B (E) Allegretto q = 116

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EX ERCISE INTER LUDE 30.1 Pitch Centricity and Ostinati In one or two sentences, discuss how the ostinato in each of these passages contributes to the pitch centricity (or centricities) of the passage.

758

THE COMPLETE MUSICIAN

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759

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

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cant.

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THE COMPLETE MUSICIAN

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761

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

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30.2 Triadic Extensions Provide a two-level analysis of Exercise 30.2A. Remember that triadic extensions can occur melodically as well as harmonically. For Exercise 30.2B, identify the types of triadic extensions used, and comment on how they affect pitch centricity in the passage. A. Franck, Violin Sonata, movement 1 Allegretto ben moderato

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762

THE COMPLETE MUSICIAN

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PI T C H C L A S S E S ( P C s) A N D C OL L E C T IO N S Triads and seventh chords have traditionally been defined as sonorities made up of three or four tones stacked as thirds. We want to broaden our analytical terminology to include sonorities and intervals, so we’ll leave “chord” behind. Instead, we’ll generalize the idea as pitch classes (PCs), or, more informally, a collection, which we define as a repository of PCs from which a composer draws musical material. One way we can assess the relationships between pitch classes is to view collections by PC name in alphabetical order, as a scale. Then, if a particular PC is highlighted (e.g., begins or ends sections or is a PC toward which other PCs are directed), then this would be the pitch (or pitch class) center, akin to the tonic in a tonal piece. The seven-note quartal/quintal collection that we studied in Bartók’s “Boating” could be ordered in one of seven ways, given that all seven letter names appear. Beginning on C,

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

763

a natural minor scale emerges (C–D–E–F–G–A–B); or beginning on E would produce an E-major scale (E–F–G–A–B–C–D); and so on. The pitch center depends on which pitch is the center of gravity, the resting tone. What we’ve done is merely rotated scalar order (which equals alphabetical order) as long as we think of the first seven letters of the alphabet wrapping around (e.g., C–D–E–F–G– A–B–C // D–E–F–G–A–B–C–D // E–F…). All major and minor scales are collections. Because these two types of scales both have seven PCs, each uses a letter name once and only once, and includes five whole steps and two half steps, they belong to a larger collection called the diatonic collection. We know this already as the major and natural minor scales. The largest collection commonly used in Western art music is the 12-PC chromatic collection, often called the total chromatic, the aggregate, or the universal set. We now explore other types of diatonic collections, in addition to the major and minor forms we’re used to. We’ll also explore three collections with fewer members than seven (one that contains five PCs and two that contain six PCs) and one collection with eight PCs.

Seven-Note Collections: Diatonic Modes There is an extensive world of music we haven’t studied: Western “modal” music, at least 1,200 years of music composed in Europe before the late seventeenth century. The ancient Greek seven-PC modes include our modern major and natural minor scales (called since ancient times Ionian and Aeolian, respectively) but also include five other modes that use the same diatonic collection, simply beginning on a different PC in the collection. Originally, the seven modes occurred on specific pitches. For example, the Phrygian mode begins on E and includes the pitches that cover the octave E to E using the white keys on the piano only (i.e., E–F–G–A–B–C–D–E). Modes were used consistently until about the middle of the seventeenth century. (Of course there was no fixed pitch in the early Medieval period, so in practice, transposition was a given.) By 1670, two favored modes were retained: the two we use today, major and minor. The Medieval/ Renaissance modes were revived by post-tonal composers and used in new ways. These diatonic collections can be viewed most easily by constructing seven-note scales beginning on each of the white keys of the piano (Example 30.16).

EXAMPLE 30.16

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Phrygian

Lydian

Mixolydian

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764

THE COMPLETE MUSICIAN

You should be able to recognize all seven modes both analytically and aurally. As we know, the Ionian mode is identical to the major scale, and the Aeolian mode is identical to the natural form of the minor scale. The remaining modes share characteristics with the Ionian and Aeolian modes: notably the type of third, either major (Ionian) or minor (Aeolian). For example, the mode on G, Mixolydian, has the same intervallic configuration as the Ionian, except that its seventh scale degree lies a whole step below 8. Similarly, the mode on F, Lydian, is the same as the Ionian mode except for the whole step between 3 and 4, creating a tritone between the F and the fourth degree B. These three modes, the Ionian, Mixolydian, and Lydian, fall into the category of “major” modes, given the major third between the tonic and 3. “Minor”-type modes include the Aeolian and the Dorian, which is built on D. It is the same as the Aeolian except for the whole step between 5 and 6. The Phrygian mode also falls into the minor type, but is special: although it is similar to Aeolian, its lowered 2 gives it a unique sound. Finally, the Locrian, built from B, is rarely used for several reasons, not the least of which is that it does not have a perfect fifth above its tonic. The grouping of modes by major and minor grows out of the work of music theorists and composers during the early sixteenth century, which was documented by Zarlino in the mid-sixteenth century. Example 30.17 gives a summary of the contents of the seven modes. Note that each is created merely by rotating the pattern such that the first note of one mode becomes seventh of the next mode. Twentieth-century composers transpose the modes. When you encounter either a key signature that does not accord with the usual tonic (such as one flat in G minor), and/or

EXAMPLE 30.17 The Diatonic Modes 1

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765

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

missing or added accidentals that do not conform to the major or minor mode, consider the possibility that the piece is cast in one of the other modes. Follow this procedure to determine the mode: • Find the tonic (usually highlighted by duration, metrical placement, a point of departure and/or arrival, etc.). • Arrange the pitches into a scale, with the tonic as the lowest note. The intervallic pattern that emerges will tell you which mode is used. To transpose a mode so that it begins on a different pitch, derive the key signature as follows: • Every flat added to a key signature reveals a transposition up a perfect fourth. For example, transposing Dorian (on D) up a fourth to G requires one flat; to C, two flats; etc. • Every sharp added transposes a mode down a fourth. Dorian with two sharps means the mode has been transposed to begin on E (i.e., Dorian on D has zero sharps, fall a fourth to A and it will have one sharp, fall another fourth to E, and the key signature will have two sharps). Example 30.18A contains one flat such that the collection is: G–A–B–C–D–E–F–G, which is Dorian on G. What modes are Examples 30.18B and C in?

EXAMPLE 30.18 Examples of the Use of Different Modes A.

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766

THE COMPLETE MUSICIAN

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Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.18 (continued)

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j & œ ‰ ‰ Œ™ &

{

n œœ œ

? n œœ œ

œœ ™™ œ™ ‰

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who

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‰

œ œ œ

œ œ œ

∑

œ œ #œ ™ #œ œ but my

œ œ œ #œ J

œœ n œ J œœ

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‰ œ

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‰

œ ‰ œœ

dy

-

‰ # œœ œ ™™

‰ œœ

pp

la

œ œ œj # œ # œ ™ #œ œ J

∑

œ œ œj # œ # œœ # œ ™ œ œ œ J ‰ # œœ ™™ œ™

Ϫ

œ œ

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Green

œœœ œœ #œ J œ ‰ œœ

#œ œ œ

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sleeves.

-

# œœ œ

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˙™ ˙™ ˙™

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C. Bartók, “Tale” from Mikrokosmos, Book 3, no. 95 Moderato q = 96

b2 & b b4

{

b2 & b b4

∑

∑

f molto espr.

œ œ œ œ

œ œ 42 œ ™

b &b b

Œ

{

3 4 nœ n˙

b2 œ œ œ & b b4 œ

{

œ ? b 42 œ bb meno f

Œ

Ϫ

œ

œ J

nœ œ #œ œ

j œ

2 4 bœ bœ b˙

, œ™ Œ?

n œœ

∑

2 œ œ 4 œ™

œ œ œ nœ œ J

œ œ œ œ 43 œ œ œ nœ ™

2 4

∑

j 3 4œ œ œ œ œ œ œ œ

Ϫ

b œ 3 & b b œ œ nœ 4 œ œ œ ∑

3 4

∑

œ˙

#œ

molto espr.

œ œ 2 œ™ 4

œ 3 nœ nœ #œ #œ nœ nœ œ 42 n œ J 4

∑

j œ

œ nœ œ Œ

œ J

bn œœ

œ J

œ˙ n œ

3œ œ œ œ œ œ 2 4 4 ˙

3 œ˙ ™ 4

∑

?

œ ™ bœ J

Ϫ mf

2 4 œ 3 J 4

œ œ nœ œ 3 4

768

THE COMPLETE MUSICIAN

EXAMPLE 30.18 (continued)

j ? b b 43 ˙œ œ n œ œ b œœ ‰ & 42 J ‰ b œ™

{

3 j b œJ 4 ˙ œ œ œ œ b œœ J più f j Œ b œ 42 ˙ œ œ œ œ 43 b œœ ‰ Œœ J J ‰ ™

? b b 43 b œ ‰ œ ™ b J più f

b œ œ &b b œ nœ

{

? bb #œ ™ b

j œ œ œ nœ œ

‰ 42 œ ™ ‰

∑

f dim.

2 ∑ œJ 4 œ œ b œ b œ

Ϫ

œ J

p

∑ œJ ‰ Œ

œ nœ œ œ

poco allarg.

œ œ œ

œ #œ nœ nœ #œ J

œ

œ cresc.

œ b œ nœ

3 4˙

nœ 3 4Œ

œ

œ

nœ

#˙ ™

n˙

˙f ˙˙-

œœœ-

∑ ∑

Five-Note Collections: Pentatonic Arguably the most ancient of all pitch collections, the five-PC pentatonic, distributes its pitches nearly evenly through the octave (as does the diatonic collection). We will focus on the most common type of the pentatonic collection: the form that does not contain any half steps. This collection is used widely in Pacific Rim countries (indeed, viewed as the oldest of all collections, it can be found throughout the world) and is comprised of major seconds and minor thirds. Not only are there no half steps, but also no tritones, thus the collection has little dissonance to Western ears (recall that there is one tritone in the diatonic collection). To create a pentatonic scale, remove the two notes that create a tritone from the diatonic collection. For example, the Ionian (major) collection C–D–E–F–G–A–B (C) will become a pentatonic collection by removing the two pitches F and B. The result is: C–D–E–G–A. As with the diatonic collection, we can rotate the pitches of the pentatonic collection, which will create new intervallic patterns above the “tonic.” Because there are five tones in the collection, five rotations are possible, each presenting a different intervallic pattern. For example, using the C–D–E–G–A collection beginning on A would yield A–C–D– E–G. Given the minor third between A and C, this particular pentatonic collection has a minor sound, and therefore is called the “minor pentatonic,” in contrast to the “major pentatonic” that begins on C, which has a major third between C and E. You may already be aware that the intervallic pattern of the pentatonic scale can be expressed by using all of the black keys on the piano, and only these. Naturally, this leaves the white keys comprising the diatonic collection. Combining these two collections produces the aggregate. When two collections are combined with no pitch class overlap to form an aggregate, we say that one collection is the literal complement of the other. For example, the literal complement of the chromatic perfect fourth C–C–D–E–E–F is F–G–A–A–B–B because together they form the aggregate. So, if you form a pentatonic scale on any pitch class, the complement will be a diatonic collection.

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Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

Some other properties of the pentatonic collection are as follows: • If we lay out the pentatonic collection by fifths starting on C, we see how quintal/ quartal sonorities arise: C–G–D–A–E. • The subsets within the pentatonic scale include triads (C–E–G and A–C–E) and seventh chords (A–C–E–G). • One other important subset that is not a triad, seventh chord, or quintal/quartal sonority is Debussy’s favorite: a combination of a major second and minor third, which span a perfect fourth (e.g., D–E–G or D–F–G) or perfect fifth (D–A–E or D–G–A). Example 30.19 shows various pentatonic subsets.

EXAMPLE 30.19 Debussy, “Reflets dans l’eau” from Images, Book 1 Andantino molto

b 4 & b bbb 8 ≈

Piano

{

œœœ

œœ œ

œœœ

? bb b 4 Œ b b 8 ˙˙

≈ œ

œœœ

œœ œ

œœœ

œœœ

œœ œ

œœœ

œ

œœ œ

œœœ œ ‰™

œœ œ

œœœ

œ œ R

EX ERCISE INTER LUDE 30.3 Modal Identification Identify the mode of each of the following examples. Each example is notated in ascending stepwise order from the tonic.

D. w w w b w B. w C. b w b w w w w w w w #w w w #w w b w b w b w n w w w & bw w w w bw w w bw A.

E. F. G. bw w # w ? b w nw b w b w nw b w b w b w w w w bw w w w # w w w w w #w H. bw ? bw bw w w bw bw w

I.

&

w #w #w #w w #w #w

# w J. # w # w w # w # w w w w

30.4 Analysis Study each of the following excerpts to determine its mode. Write out each collection in ascending stepwise order beginning with the centric pitch.

770

THE COMPLETE MUSICIAN

A.

Tempo guisto

# 4 & # 4 œj œ œ œ # œ œ œ œ # & # œ œ œ œ œ œ œ

B.

j œ œ™

œ

œ œ œ œ œ œ œ

œ œ œ œ œ œ œ œ

j œ œ™

œ

Ϫ

œ œ™ J

Œ Œ

Allegretto

#2 & 4 Ϫ

œ J

mp

œ œ œ œ

œ œ œ œ

# & œ œ nœ nœ

œ

œ

Ϫ

Œ

œ

# & œ

œ nœ

œ

œ

œ

Ϫ

œ J

œ

œ œ œ œ

˙

Moderato

2 &4 œ

œ œ

& Ϫ

œ J

mf

œ œ

œ œ

œ œ œ œ

œ œ œ œ

mf

C.

œ J

œ œ œ #œ œ œ œ

œ J

œ œ œ œ

œ œ œ œ

œ œ

œ

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œ œ œ œ

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œ #œ œ œ

œ

mp

œ œ œ œ

œ œ œ œ

f

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˙

œ œ œ nœ

Ϫ

œ œ œ nœ

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Ϫ

œ J

œ

œ

p

œ

‰

Ϫ

œ

Œ

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p

‰

œ œ™ œ œ™ œ œ™ œ œ

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‰ œœ ‰ œ œ. œœ. œ œ

œ

œ

Ϫ

‰

D. Kabalevsky, Toccatina Allegretto

2 &4 ‰

{

p

?2 œ 4J

œ. œ. & ‰ œœ œœ

{

?

mf

Ϫ

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‰ œœ ‰ œ œ. œœ. œ œ

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. . ‰ œœœ œœœ

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œ J

Ϫ

œ J

‰ œœ œœ œ. œ. œ™

‰ œœœ œœœ œœœ . . . œ œ™ J

‰ œœœ œœœ œœœ . . . œ œ™ J

‰ œœ ‰ œœœ œ. . œ œ

‰ œœœ ‰ œœœ . . dim. œ œ

‰ œœ ‰ œœœ œ. . cresc. œ œ

‰ œœ ‰ œœœ œ. . œ œ

‰ œ œ œœ œœ . . p œ™

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

771

E. Poulenc, Waltz Assez vif œ œ œ #œ œ œ 3 &8 œ

{

3 &8 ™ œ‰ j œ &

{

&

œ

# œ œ œ œ œ œ # œ-

œ J

mf

œœ œœ œ œ

# œj

™ ‰œ œ- œ œ

f

f

œ œ œ‰ ™ œ œ

œ œ œ‰ ™ œ œ

œœ œœ

œœ

œ œ œ‰ ™ œ œ

œ œ œ œ œ œ œ œ œ

œ œ œ œ

œ œ‰ ™ œ

™ œœ œœ ‰œ

™ ‰œ

œœ

œœ

œ œ œ‰ ™ œ œ

More Symmetry: Six-Note Collections The seven-PC diatonic world and the five-PC pentatonic world cannot be divided evenly into 12 (there is always a remainder). Thus, there is no way to spread out the members of these collections evenly within a single octave using the same interval between each member. This is because the diatonic and pentatonic scales contain different-sized intervals and an unequal number of each (e.g., five whole steps and two half steps in the diatonic world). Because of this asymmetrical distribution of intervals (discussed in Chapter 28), tonal gravity exists, one that can easily project a tonic, which is why these collections have been so widely used for so long. Because the diatonic collection is not symmetrical, it may begin on each of the 12 pitch classes without all its members being equivalent to a diatonic collection beginning on another pitch class (i.e., there are 12 different major scales, one for each of the notes in the chromatic scale). Those diatonic collections that share a great number of pitch-class content, such as C major and D major, both of which contain E, G, A, and B, are closely related, but the fact remains that one must transpose the major mode collection 12 times in order to return to that version of the collection where all of the same pitch classes return. The six- and eight-note collections we will now study have remarkable symmetrical properties, and because of this, composers have often used them in their compositions.

PI T C H- C L A S S C OL L E C T ION S W I T H S I X M E M B E R S #1: W HOL E -T ON E C OL L E C T ION Alban Berg’s “Nacht” (Example 30.20) opens with the first three notes of an E-major scale followed by B, to which is added B and D, which, with F, forms an augmented triad. Arranging these PCs in an ascending scale we have: E–F–G–B–B–D, a string of whole steps. If we continued the pattern of whole steps, D would lead back to E, the starting point. Distributing a six-PC scale evenly among 12 half steps results in the whole-tone scale. This collection has important properties, including: It partitions the

772

THE COMPLETE MUSICIAN

octave symmetrically, and its complement is itself a whole-tone collection. The six missing pitches will complete the chromatic aggregate. As we’ve done before, we can rotate the scale by placing the first pitch last and work through the entire cycle of six whole-tone scales, each of which begins above the previous

EXAMPLE 30.20

Berg, “Nacht” from Seven Early Songs

Sehr langsam (q = ca. 48)

&

Voice

### c

p

nœ ™

∑

Däm

< >

&

Piano

{

### c

j ‰ b#n œœœ # œ ## œœ

Œ œ pp

? ### c Œ œ

œœ œœ œœ

œœœ œœ

ü - ber

œœ œœ œœ

œœœ œœ

œœœ œœ

œœ œœ œœ

P

˙

nœ ™

und

Tal,

Ne

Œ œ pp

#œ

‰ ## œœ

j b#n œœœ

‰ ## œœ

#œ

j nœ

œ

#œ

-

-

bel

schwe

-

ben,

nœ n### œœœœ ### œœœ # œ # œœ

œœœ œœ

œœ œ œœœ

œœœ œœ

œœ œ œœœ

œœœ œœ

< > j b#n œœœ

œœ œ œœœ

pp

∑

&

P

P

###

j j j # œ # œ œ n œj

mp

j œ

Œ

˙

Was - ser rau -schen sacht.

“” # # nœ #œ & # ## œœ #n œœ &

Wol - ken

j nœ

∑

j #œ

###

? ### Œ œ

{

mern

j #œ

pp

< >

&

j # œ b œJ

P

Nacht

{

#œ nœ n# # œœœ ### œœœ # œ # œœ

< > j ‰ b#n œœœ # œ ## œœ

## & # Ϫ

&

-

#œ J

###

## œœ n## œœœ P

Nun

œœ #n# œœœ #nnn œ˙˙˙ n œ # œ # œ n œ œ nœ nœ œ œœ n œœœ #n œœ # œ P

nœ #nn œœœ

œœ œ

œœ œœ

poco a poco cresc.

nœ J

nœ ™

ent - schlei

œ nn ˙˙ # œ œ œ œ n œ # œœ œ # œœj n œœJ # œœ p j nn# œœœœ P

? # œœœ n œ

poco a poco cresc.

œ J -

# œœœœ

-

ert

œ # œœœ J

œ #œ #œ œ œ œ œ œ

P

773

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

EXAMPLE 30.20

&

(continued) Rit.

###

j œ

nœ J

sich's

j œ

œ J

mit

œ

œ J

ei - nem - mal:

j #œ

nœ ™

gib

acht!

O

nœ J

Gib

˙ acht!

œ # # œ˙ # œ œ œ œ #œ # ˙ nn œœ & # n ˙ n œ œ œ œ œœ œœ œœ ˙ n œ n# œœœ n nœœ ## œœœ œœ ## œœœ nn œœœ n# œœœ ## œœœ œœœ œœœ œœœ œœœ œœœ œœœ # œœœ ##n œœœ poco f -j #œ œ n œ n œ n œ œ œ œ œ œ #œ œœ ? # # # n# œœœ œœ œœ ‰ #œ nœ # œ œ J J w marc.

{

P

f

P

Wei

-

œ

-

-

-

3

œ

˙ ˙

auf

nœ nœ

tes

Wun

œ

œ

œ

œ

3

œ

œ

#œ J -

### bœ & b œ nœ bœ

{

nœ J

3

3

œ

#œ J

nn œœ

œœ

œ

-

## & # bœ ™

? ###

#œ #œ

œ œ

A tempo

## & # œœ

{

#œ #œ

P

# # #œ ™ & #

? ###

œœœ œœœ œœœ n œœœ # œœœ #b œœœ nœ

-

œ

-

-

-

œ

n œ nœ # œ

nœ bœ bœ œ œ

ge

der

-

land

-

ist

n œœ

œ nœ

nbb ˙˙˙

j nœ

j œ

b œ nœ

bœ

bœ

œ

b œ nœ

bœ

n˙ tan.

-

œ #œ

œ #œ nœ

j nœ

œ œ

œ

# œœ œ

œ œ

œ #œ

œ

œ

œ

œ

œ

œ #œ

scale. Such a transposition by any even number (2, 4, 6, 8, 10) retains all of the pitch classes, or “holds them invariant.” Let’s show the level of transposition by the number of half steps distant from the set that begins on C. We label the transpositional operation “T” followed by the number of half steps distant from the first set.

774

THE COMPLETE MUSICIAN

T0:

C–D–E–F–G –A /B  T2: D–E–F–G –A /B –C T4: E–F–G –A /B –C–D T6: F–G –A /B –C–D–E T8: G –A /B –C–D–E–F T10: A /B –C–D–E–F–G  T12 ⫽ T0: C–D–E... (i.e., transposition by 12 steps) retains all of the PCs

Berg develops the whole-tone collection, restating the pitches heard in m. 1. The piano part contains whole-tone sonorities that vacillate by a whole tone, thus staying within a single whole-tone collection. The voice enters in m. 2 and falls first by an augmented triad (E–B–G) then, from B, another augmented triad (B–F–D). The augmented triad, as an important subset of the whole-tone scale, partitions the octave evenly into three major thirds. Transposition by a whole tone gives us a different augmented triad (C–E–G at T2 ⫽ D–F–A, which, combined with the first triad, forms a whole-tone scale (C–D–E–F–G–A). Like the seven-pitch-class diatonic collection, all PCs of a whole-tone scale are invariant in all rotations, but different than the diatonic scales, all whole-tone rotations contain the same intervallic content because only a single interval is used: the major second. As noted, given the repeating intervallic pattern, there are far fewer than twelve unique transpositions of the scale: There is only one (the scale built on C and the one transposition to the one built on C). After this, the one on D contains the identical PCs as the one on C, etc. Notice that intervals absent from the whole-tone scale are those comprised of an odd number of semitones. This would include the perfect fifth and perfect fourth (seven and five half steps, respectively), the minor second and minor third and their inversions (major seventh and major sixth). Because the pattern is comprised solely of whole steps, there are no “tonal markers” such as one or more half steps, which create a sense of arrival, as there is in the diatonic collection. The whole-tone collection, then, is a tonally ambiguous collection. Returning to “Nacht,” (Example 30.20) a new phrase begins in m. 4, this time using entirely different PCs than the ones Berg used in m. 1. Once again, we arrange the PC content alphabetically: C–D–F–G–A–B, which, as we saw in m. 2, also vacillates down a whole step. This time, then, Berg has used the whole-tone collection on C. A glance at the melody in the first half of m. 5 presents the opening pitch classes, F,  G , and D, which belong to the whole-tone collection on C that began the song (the harmonies below provide the remaining pitch classes of that whole-tone set). However, the leap of a perfect fifth from D to A—an interval not in the whole-tone scale—indicates that Berg has moved to a new collection, and sure enough, on the word sacht the C whole-tone collection is presented. Berg is accelerating the harmonic rhythm, with three measures on the whole-tone collection on C, one measure on C, and in m. 5, just half a measure for each whole-tone collection. What follows in mm. 6–7 is a surprise: The half-diminished seventh chord (F–A–C–E) is not a member of a whole tone scale because it contains minor thirds as well as a major third. In fact, the half-diminished seventh chord is a common tonal sonority, usually carrying a pre-dominant function. It leads in the second half of the measure to a B seventh sonority, the combination sounding like iiø43 to V, in E, which is the very sonority to which

775

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

the B chord leads in m. 8. As a V dominant, E leads to the huge arrival in m. 9 on A major. Taken together, the roots of the chords from mm. 7 to 9 are as follows: F–B–E–A, a series of fifths, the most tonal progression possible. A look at the three-sharp key signature confirms that Berg has cast this piece in A major, but also that key signatures do continue to flourish in music of the twentieth century. This off-tonic beginning—found in countless common-practice works—is a powerful way to start a piece; the amorphous opening wends its way to the tonic, which appears only after eight measures. This transition, from tonal ambiguity in mm. 1–5 using wholetone collections to clarity through a descending fifth progression in mm. 6–9 and arrival on A major, is intimately tied to the opening text that appears below: mm. 2–3: m. 4: m. 5: mm. 6–9

Over night and valley the clouds grow dark, Mists are hovering, water rushes by Now the covering veil is lifted: Come look! Look! Distant…

It appears that the text dictates the musical setting: “night,” “clouds,” “dark,” “mists,” and “hover” paint a picture of gloom and fear, a sense of being lost, with no literal or

EXAMPLE 30.21 Schoenberg, Chamber Symphony no. 1

f sf

? #### C Ó

n Ów Ó

n˙

Sehr rasch h = ca. 104

## & ## Œ

{

f

? # # # # n>œ

8

&

{

^ nbn ˙˙˙ n˙ n˙

r.H.

b>œ

5

4 4

n>œ n >œ

4 n>œ 4

#^ nn ˙˙˙

& b>œ ™

œ ? #### œ ‰ œ n œ nœ J ‰ Œ œJ “‘ 3

ff

“” # ^˙˙ ˙ sf

?

Ó

Œ

U ‰

n œ-

^ b˙ ™

sf

&

j n œœ ‰ Œ nœ pp

>œ

?

n˙ #œ bn n œœœ nnn ˙˙˙

n# œœœJ ‰ ##n œœœ ‰ J . pp stacc. . n œ ≈ œ ## œœ ‰ # œ ≈ n œ nœ J #œ

j œœ œ œ œ n œœ # œ œ œœ J ‰ #œ p > 3 >œ 3> n >œ œJ nœ nœ ‰ Œ >œ n >œ > ff f

œœœ œ # œ ™ œ œœœ ™™ œœ œ # œ ™ # œ n# œœ J

# # # # # n# ˙˙˙˙˙

œ

# œœ œ

Π^ bn ww bw

?

# œœ ™™ # œ œœ ‰ # œ ™ # œ # œJ f . œ nœ œJ ‰ # œ ≈ #œ

∏∏∏∏

b ^˙

“”n œ- ™ nn œ ™ & n œœ ™™

∏∏∏∏

{

bw Ó

^ nb ww nw

∏∏∏∏∏

&

^ b˙ ™

Πb ww

∏∏∏∏

Langsam h = 52

#### C

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n œœ œ

n >œœ

>œ >œ œ

3

j œœ œ

mf

776

THE COMPLETE MUSICIAN

musical compass. It is in these measures that Berg infuses the elusive, tonally confusing whole-tone scales. And it is no coincidence that in the measure where the text proclaims “Now the covering veil is lifted,” tonal clarity, in the form of powerful fifth-progression motions, drives to the structural A-major tonic.

Combining Collections: The Intersection of Quartal and Whole-Tone Worlds Schoenberg opens his Chamber Symphony no. 1 (Example 30.21) with a combination of collections that emerge slowly and place the listener in a musical limbo until an arrival on the tonic nearly a dozen measures later. The piece begins with a lone A, to which is added the minor seventh C–B, creating a three-PC whole-tone sonority (A–B–C) spread out in minor sevenths. The two tones of this added interval then each leap up a perfect fourth, to F and E respectively, creating, in combination with the tones already stated, a collection of rising fourths, ordered as such registrally (C–F–B–E–A). The large chord at the end of m. 2 adds G, and thus extends the pattern to six perfect fourths (G–C–F–B–E–A). Notice that the marked return of A in m. 3 is followed by a whole-tone chord that we hear as an altered dominant of F (C–E–G–B), the first cadence in the piece, on the Neapolitan. The flight of fourths returns, and begins the next phrase, (D–G–C–F–B–E). The last PC is held over an augmented triad (G–B–D) in m. 6, comprised of the major third, which helps “modulate” to the whole-tone collection, in which the perfect fourth and perfect fifth are abandoned. In m. 7, the upper woodwinds, horns, and bassoon (indicated by the upper voices of mm. 6–7 in Example 30.21) hold this G augmented triad, while the strings and bass woodwinds move downward in parallel whole tones. Finally, in m. 8, the two collections—quartal and whole-tone—are merged and Schoenberg secures the E-major tonic in m. 11.

PI T C H- C L A S S C OL L E C T ION S W I T H S I X M E M B E R S # 2 : H E X AT O N IC C OL L E C T IO N We can also divide the 12-note chromatic into a different six-note collection by interlocking two augmented triads a half step apart—C–E–G and D–F–A—creating: C–D–E–F– G–A. This collection can be viewed in other ways, such as three minor seconds separated by major thirds. This six-note collection is called hexatonic (or “augmented”). Like others we have encountered, this collection is tonally ambiguous because of the repeating pattern of intervals, 1–3–1–3–1–3, with no differentiation that would help to provide tonal footing. Given the intervallic symmetry, there are fewer than twelve transpositions. For example, transpose an augmented triad by a major third, all PCs are held invariant: T0: T1: T2: T3: T4⫽T0:

C–E–G C–E–G D–F–A E–G–B E–G–B

Because the PCs in an augmented triad return at the major third, then there are only four possible augmented triads. By extension, combining pairs of augmented triads a

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semitone apart also results in only four possible hexatonic scales (Example 30.22), explaining its four unique transpositions.

EXAMPLE 30.22

The Four Possible Hexatonic Scales

Augmented triads on C/Db

&

#œ œ œ bœ œ œ Augmented triads on C#/D

& # œ œ #œ #œ œ bœ Augmented triads on D/Eb

& œ bœ #œ œ #œ œ Augmented triads on Eb/Fb

& bœ bœ œ bœ œ œ

Major and Minor Triads Within the Hexatonic Scale If we consider other subsets of the hexatonic collection, we discover a world of major and minor triads. For example, a hexatonic scale on C (C–D–E–F–G–A; or on E or G, because they contain the same PC content), contains these triads: D major and minor; A major and minor; and F major and minor. We have seen this same progression of major triads by major-third roots (usually falling) in previous chapters. Notice also that these motions can all be generated by smooth and efficient voice leading, using stepwise motion (usually semitonal) and the retention of one or more common tones, a process called parsimonious voice leading. For example, using the hexatonic collection built on C and moving a single PC, a composer can travel all the way around the six possible major and minor triads in the collection (Example 30.23).

EXAMPLE 30.23 Parsimonious Voice Leading: Hexatonic Collection Built on D 

& bbw w w Db major

bbbw w w Db minor

n#nw w w

w nw w

A major

A minor

w w w F major

bw w w F minor

bw w bw (Db major)

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Given that there are four distinct hexatonic collections and each collection has six distinct triads (major and parallel minor triads occur at every major third), there are a total of 24 (4 × 6) major and minor triads: the total possible number of consonant triads. Further, a complete hexatonic collection can be constructed using only two triads, but obviously these triads must not have any pitches in common (the previous examples all had two pitches in common). In the hexatonic collection illustrated in Example 30.23 (C–D–E–F–G–A), D minor and F major together comprise the hexatonic (see Example 30.24).

EXAMPLE 30.24 Hexatonic Poles

& b œ b œ b œ œ nœ œ Db minor + F major

=

b œ nœ œ b œ b œ nœ Hexatonic collection

Any pairing of triads with roots related by a distance of a major third and by the opposite mode generates a hexatonic collection: A major ⫹ F minor and D major ⫹ A minor. As a rule, one must start with a major triad and go down a major third to a minor triad, or start with a minor triad and go up a major third to a major triad (other pairings will not produce a hexatonic collection given pitch redundancies). Pairs of triads that generate the entire hexatonic scale are called hexatonic poles. In such polar pairings, all three voices move by semitone: the outer voices by contrary motion and the inner voice to the required pitch a semitone away.

E IG H T- N O T E C OL L E C T IO N S : O C TAT O N IC We conclude our study of collections with one whose members are again restricted to a single intervallic pattern: a half step followed by a whole step (or vice versa) creating: 1–2–1–2–1–2–1 or 2–1–2–1–2–1–2. And, as we have learned, such symmetrical collections have fewer than 12 transpositions. The twentieth-century French composer, organist, and theorist Olivier Messiaen composed with collections that were symmetrical, allowing for fewer than twelve transpositions. In his treatise The Technique of My Musical Language (1935), Messiaen outlined many such “modes of limited transposition,” including the whole-tone collection as well as the final collection we explore: the octatonic collection. He used this mode more than any others (a mode which some scholars trace back to the Russian composers in the 1850s). It continues to be used today in much jazz and was a favorite collection of composers such as Bartók, Debussy, and Stravinsky. The glorious opening of Messiaen’s “Louange àl’ Éternité de Jésus” (Example 30.25; for the full score, see the Anthology no. 76) unfolds a series of triads, and the relationships between each chord and its voice leading create an ethereal, trancelike effect. The

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EXAMPLE 30.25 Messiaen, “Louange àl’ Éternité de Jésus” from Quatuor pour la fin du temps STR EA MING AUDIO

W W W.OUP.COM/US/LAITZ >> > ? # # # # ‰ >œ- œ œ œ œ œ œ œ œ œ # œ- œ œ œ œ # œ œ œ œ œ œ œ œ œ œ œ œ # œ- œ œ œ #>œ- œ œ œ œ œ œ œ

3

Piano

Infiniment lent, extatique (x = 44 env.)

{

p

? #### ‰ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ nn œœ œœ œœ œœ œœ nn œœ œœ nn œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ nn œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ >>>>>P (etc.) P

P

homophonic progression, detailed by roots, is: E–B–G–B–E. Forming an arch, this ascent and descent involves stepwise voice leading, which explains the B chord in six-four position. As usual, let’s take an inventory of the PCs in the piano part by arranging them in ascending order: D

E

F

G

G

B

B

The pattern of steps unfolds as follows: D

E 2

F 1

G G B B (C) 2 1 2 1 2

We see that the alternating pattern of whole and half steps is yet again a symmetrical collection. Notice that the triadic relationships are by minor thirds and tritone (a combination of two minor thirds). Such relationships reveal a stark contrast between the majorthird root relations of the hexatonic collection. Let’s look at a second example, Bartók’s “From the Isle of Bali” (Example 30.26; for the complete score, see the Anthology no. 68). Notice that this highly dissonant piece contrasts with Messiaen’s triadic movement. Bartók’s “From the Isle of Bali” is a single-line melody in some places, and it consists

EXAMPLE 30.26

Bartók, “From the Isle of Bali” from Mikrokosmos, Book 4, no. 109

Andante e = 134

6 &8

{

?6 8

∑ p dolce

STR EA MING AUDIO

œ bœ œ œ nœ œ

bœ œ œ œ b˙ ™ #œ œ

Ϫ

œ

œ œ œ #œ ™

œ

œ

œ

œ

œ bœ œ œ

j ‰ œ œ J

W W W.OUP.COM/US/LAITZ

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primarily of semitones, perfect fourths/fifths and tritones. Example 30.27 gives a pitch representation of the intervallic pattern, which, again is the octatonic collection.

EXAMPLE 30.27 Octatonic Pattern in Bartók’s “From the Isle of Bali” Andante e = 134

6 &8

{

∑

bœ œ œ nœ œ œ

p dolce

Ϫ

bœ œ œ œ b˙ ™ #œ œ ?6 8

œ

œ

œ

œ œ œ #œ ™

j ‰ œ

œ

œ

œ bœ œ œ

œ J

Scalar representation forms an octatonic collection:

œ

? #œ

2

1

2

œ

œ

bœ

œ

1

1

2

bœ

œ 1

How different the use of the octatonic collection is in Bartók’s hands! Given the remarkable contrast in how the octatonic collection is deployed, let’s look a bit more closely at its potential. The harmonic possibilities of the octatonic collection, compared with collections such as the whole-tone, reveal far more variety and compositional potential, which is why it is arguably the most common collection used in post-tonal music. The 1–2 intervallic pattern beginning on C is C–C–D–E–F–G–A–B. You can conceptualize this as two diminished-seventh chords a half step apart (see Example 30.28A). Reversing the intervallic pattern (2–1: C–D–E–F–G–A–B), the collection can be viewed as two diminished seventh chords a whole step apart (see Example 30.28B). Because the diminished seventh chord partitions the octave into four minor thirds, we know that it has only three distinct forms (see Example 30.28C). Transposing any diminished seventh chord by three half steps will return all of the initial pitches (but in a different rotation).

EXAMPLE 30.28 1–2 Octatonic Collection A.

&

œ # œ b œ nœ #œ

œ

œ bœ

B.

& œ

C.

œ bœ

œ #œ #œ

œ

œ

& bb œœœ œ

bœ nn# œœœ

bb œœœœ

' bnbn œœœœ

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The same is true of the octatonic scale. There are three distinct transpositions, given that it is comprised of two diminished seventh chords within the span of a minor-third (Example 30.29).

EXAMPLE 30.29 Three Transpositions of the Octatonic Scale

œ

bœ

3 ' bœ

& #œ

œ

œ

œ

œ

bœ

bœ

nœ

& œ

bœ

œ

bœ

bœ

nœ

œ

œ

3 ' & bœ

bœ

bœ

nœ

œ

bœ

œ

bœ

&

bœ

bœ

nœ

œ

bœ

≥

If we keep going, the one built on E/F is a repetition of the one built on C–C:  E –F–G–G–A–B–C–D.

Subsets Let’s dissect the version of this octatonic scale to find some of the many subsets embedded in the collection (see Example 30.30).

EXAMPLE 30.30 Subsets of the Octatonic Collection

& œ b œ b œ nœ b œ nœ œ b œ œ

œ bœ œ œ b œ b œ nœ #œ œ

C major and C minor

& œ # œ b œ nœ #œ œ œ b œ œ

œ bœ œ œ # œ b œ nœ #œ œ

A major and A minor

& œ # œ b œ nœ #œ œ œ #œ œ

œ #œ œ œ # œ b œ nœ #œ œ

F major and F minor

& œ b œ b œ nœ b œ nœ œ b œ œ

œ bœ œ œ b œ b œ nœ b œ nœ

E  major and E  minor

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Notice that there are four major and four minor triads, with roots related by minor third. This makes sense given that the pattern of half-step/whole-step occurs four times, covering a span of a minor third, and the triads lie minor thirds apart from one another.

Seventh-Chord Subsets The octatonic collection also contains many seventh chords. In fact, all of the seventh chords we have studied are octatonic subsets. Example 30.31 illustrates seventh chords built only from C; remember, these same types of seventh chords can be built on roots that lie minor thirds away (that is, E, F and A), for a total of 20 different seventh chords in a single octatonic scale!

EXAMPLE 30.31 Seventh-Chord Subsets in the Octatonic Scale

& œ b œ b œ nœ #œ œ œ b œ œ

C Mm7

&

œ bœ œ œ b œ b œ nœ #œ œ

C French 43 chord

&

œ œ bœ œ œ b œ b œ nœ #œ

C mm7

& œ b œ b œ nœ #œ œ œ b œ œ

C dm7

œ bœ œ œ b œ b œ nœ #œ œ

C dd7

&

There are a host of other nontriadic subsets in the octatonic scale, including chords built on major seconds and fourths (a Debussy favorite, mentioned earlier) and members of the pentatonic collection, which lie a tritone apart (see Example 30.32)

EXAMPLE 30.32

& œ

bœ

bœ

nœ

Some Nontriadic Subsets of the Octatonic Collection

#œ

œ

œ

bœ

œ

The “split-third chord,” discussed above in relation to triadic extensions, is also a subset of the octatonic collection, and a popular sonority not only in Stravinsky’s music but also

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with the composers of the Second Viennese School. Example 30.33A shows four of these four-note split third sonorities, one built on C and the other a tritone away on F, followed by an example from the literature (Example 30.33B).

EXAMPLE 30.33 Four-Note Split Third Sonorities A. Split-Third Sonorities within the Octatonic Scale

& b œ b œ nœ #œ œ œ b œ œ œ

=

& nb www w

& b œ b œ nœ #œ œ œ b œ œ œ

=

& n### www w

B. Stravinsky, “Lento” from Le cinq doigts 1

œ

2

3

œ #œ

4

œ

3 & b 4 œ œ œ œ #œ ? b 3 œ œ œ 4

{

#˙ œ

œ œ œ

œ

œ œ #œ œ œ œ œ œ œ œ

œ œ

œ œ

œ œ œ

Some composers prefer the W/H version whose subsets present more tonal possibilities. Example 30.34 shows a version of the octatonic scale—C–D–E–F–F–G–A–B–C— beginning with a minor tetrachord on C (C–D–E–F) followed by another version of the same tetrachord at the tritone (F–G–A–B).

EXAMPLE 30.34 Tower, “Silver Ladders”

? w w

w w bw

w w bw w

w w b w w #w

w w b w nw #w #w

w w w w b w nw #w #w

Finally, members of the octatonic collection often function as ostinati (see Example 30.35).

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EXAMPLE 30.35 Stravinsky, Symphony of Psalms

7 ° 4 &4 Ostinato 1:

Ostinato 2:

Ostinato 3:

œ

œ

˙

˙

œ ‰ #œ œ œ ‰ œ œ œ ‰ #œ pœ . . . . . . . . . 4 &4 œ œ œ ˙ œ œ ‰ # œ œ ‰ œ ˙œ œ ‰ # œ p

œ œj

‰ œ œ‰ œ . . . j‰ œœ œ œ œ ‰

œ

œ

œ œ

œ

œ

8

œ œ

œ

œ

œ œ

œ œ ‰ #œ œ œ ‰ œ œ œ ‰ #œ œ œ ‰ œ œ œ ‰ #œ œ œ ‰ œ . . . . . . . . . . . . . . . . . . œœ œ œ # œ œœ œ œ œ œœ œ œ # œ œœ œ œ œ œœ œ œ # œ œœ œ œ œ ‰ ‰ ‰ ‰ ‰ ‰

4 &4 ‰

‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ ‰ b œ œ nœ œ b œ œ n œ œ b œ œ nœ œ b œ œ nœ œ b œ œ nœ œ b œ b œ b œ b œ b œ p œ œ œ œ œ . œ. . . . œ. . . . œ. . . . œ. . . . . . . . . . b œ b œ b œ b œ œ . ? 44 œ œ . . . œ œ œ . . .œ œ œ . . .œ œ œ . . .œ œ œ . . . œ. b œ œ b œ nœ œ b œ nœ œ b œ nœ œ b œ nœ œ b œ nœ p

j Œ™ j Œ™ ? 44 œ œ œ ∑ œ b œ œ œ œ œ bœ œ œ œ Ó œ bœ œ œ œ œ bœ œ œ œ Ó œ bœ J Œ ™ œ b œÓ n œ J Œ ™ œ b œÓ n œ œ b œ nœ œ b œ nœ œ b œ nœ ¢ p

mf cant.

Ostinato 4:

4 &4 œ

Au

Ostinato 5:

œ

˙

-

ri

7 °? 4 unis. 4 œr‰ ™ b œ. r ‰ ™ . p ? 4 r‰ ™ r ‰ ™ ¢ 4 œ. b œ. p

˙ -

bus

j œ œ ‰ œ per

œ -

œ œ ci

œ -

pe

œ

œ œ lac

œ -

ri

œ

˙

mas me

8 r ‰ ™ r ‰ ™ r‰ ™ r ‰ ™ r ‰ ™œr ‰ ™ r‰ ™ b œr ‰ ™ r ‰ ™œr ‰ ™ r‰ ™ b œr ‰ ™ r ‰ ™œr ‰ ™ r‰ ™ b œr ‰ ™ . œ. . œ. . œ. . œ. . œ. œ. œ. b œ. œ. . œ. r ‰ ™ r ‰ ™ r‰ ™ r ‰ ™ r ‰ ™œr ‰ ™ œr‰ ™ b œr ‰ ™ r ‰ ™œr ‰ ™ œr‰ ™ b œr ‰ ™ r ‰ ™œr ‰ ™ œr‰ ™ b œr ‰ ™ . œ. . . œ. . . œ. œ. œ. b œ. œ. . . . .

r‰™ r‰™ œ. œ. r‰™ r‰™ œ. œ.

F OR M While new formal areas are often distinguished by changes in texture, mood, character, register, and so on, one of the most powerful elements of formal articulation is a change of collections. Debussy often structures his works in just such a way, especially his smaller pieces, such as the prelude “Voiles,” which begins and ends with material derived exclusively from the whole-tone scale on C. However, a contrasting section is based on the pentatonic collection. Let us close this chapter with a brief tour through “Voiles” (see Anthology), given that many of the compositional techniques we have learned in this chapter are found in this remarkable work. The piece begins with a simple third, a bit like Berg’s song “Nacht” in that both works grow from a single whole-tone seed. In Debussy’s piece, the entire whole-tone scale unfolds in three parallel thirds, and all within less than a beat. The contour and rhythmic setting of the opening gesture marks it as a crucial motive. A repetition is lengthened in m. 4, only to lead to a murky B in the low register against the lone right-hand third

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Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

C–E in m. 5. A contrasting idea, with slowly unfolding thirds in octaves, is juxtaposed by the initial motive, which returns in m. 10, almost in ostinato fashion as the rising third A–B–C is thickened by augmented triads (mm. 14ff ). The more frantic, indeed obsessive, section that begins in m. 22 draws on the rhythmic pattern from the opening of the piece. It is only in m. 40 that the exclusively whole-tone material is exhausted and in m. 42, a contrasting section from the pentatonic collection begins. The link between the two collections is remarkable: The incessant A–B–A–G which dominated the first section reappears in m. 42 but is followed by E, the first pitch presented that does not belong to the same whole-tone collection. Debussy marks this special occasion with an accent, making clear that he has taken us to a new land, and from which begins the ecstatic climax of the piece. This brief contrasting section evaporates, leaving only the low B, and signaling the glissando-like return of the opening whole-tone material. The piece ends with the extended C–E, the very pitch classes, indeed, pitches, that occurred in m. 5, which had summoned the appearance of the main melody of the piece.

EX ERCISE INTER LUDE 30.5 Analysis: Identification of collections Identify the pitch class collection in each of the following excerpts. In a sentence or two, describe how the composer is using them in the piece.

WORKBOOK 1 Assignments 30.1–30.5

STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

A.

Debussy, “Et la lune descend sur la temple qui fut” from Images, Book 2

“” # 4 # www & 4

12

{

pp

#4 & 4 Ó

Ɯ

œ-

œ-

œœ

œ

. . . . . . # œ. œ- œ œœ. œ œ œ œ œ œ

un peu en dehors œ m.d.

pp

˙-

m.g.

? # 44 w # ww “‘

B.

œ-

œ œ œ œ œ #œ œ œ . . . . . . . . ∑

œ

œ

3

3

œ œ . .

m.d. -

œ

œ

3 m.d.

œ

m.d.

œ

œœ œ œ œ œ œ #œ . . . . . . ∑

Lutosławski, Bucolic, no. 3

? 83 œ b œ œ # œ # œ œ n œ b œ œ b œ œ # œ # œ œ œ # œ n œ b œ

Ϫ

œ-

cédez œ

œ. œ. # œ. œ- œ. œ. œ. œ œ ˙œ 3

œ œ . .

œ

œ

3

œ œ . . ∑

œ #œ œ œ . . . .

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C. Messiaen “Danse de la fureur, pour les sept trompettes” from Quartet for the End of Time

& #œ nœ b œ œ b œ #œ œ œ ? #œ nœ b œ œ b œ #œ œ œ

{

D.D. Ravel, Jeux d’eau

? ####

{

nœ œ

? #### œ #œ

nœ œ

nœnœ

nœn œ

œ œ#œ

œ

b œ œ- n œ b œ œ b œ # œ nœ œ œ œ b œ nœ b œ b œ #œ nœ

#œ œ b œ nœ b œ œ #˙ #œ œ b œ nœ b œ œ #˙

&

&

nœ œ

nœ œ

nœnœ

nœ

nœ

œ œ#œ

œ œ #œ

#œ œ œ œ b œ #œ œ œ œ b œ

œ

“” nœ

nœ œnœ

nœ

œœ œ

## œœœ

œ œœ

nœ

“”

nœ

œœ œ nœ œ nœ œ œœ œœ

# œœ œ

# œœ œ

œ- ™ # ˙ œ- ™ # ˙-

# œœ œ

# œœ œ

nœ

œœ œ

œœ œ

# œœ œ

fff

tre corde

E. Debussy, “Cloches à travers les feuilles” from Images, Book 2

œ œ œ # œœ # œ ™ # œ œ # œ œ ˙œ œ œ œ #œ œ œ œ œœ

Lent (e = 92)

4 &4

{

∑

∑

3

^ wœ œ bœ bœ b œ œ œ œ œ . . . . -. . . . .

4 & 4 wœ œ b œ b œ b œ œ œ œ pp . . . . -. . . .

#œ #œ ™ œ œ œ #œ œ œ ˙œ œ œ œ œ œ # œ # œ œ œ œ œ &

{

pp

& œ .

œ .

^ b œœ .

3

pp

doucement sonore

b œ˙ -.

bœ .

œ .

bœ .

3

b œ˙ -.

^œ œ .

œ .

3

3

œ .

œ œ œ #œ #œ œ œ #œ œ œ œ œ™ œ œ ^œ œ .

œ .

^ b œœ .

3

3

3

œœ œ œ #œ

œœ œ.

œ .

# œœœ .

# œœœ œ . ## œ. œ

F. Bartók, “Merriment” from Mikrokosmos, Book 3, no. 84 Vivace,

# # 4 œœ & # 4Œ œ

{

q = 152

‰ œœœ

f

# #4 & # 4 œ ™ œj œ ° ## œ œ œ œ & #

{

œœœ J

## & # °

œ œ œ

^ Œ œœœ ‰ œœœ œœœ ‰ J J

œ

œ

Œ

œ˙ ™

œ œ

‰ œj œ œ

^j ‰ œ *

œœ

œ œ œ œ >œ *° *°

œ œ œ

∑

œ

∑ °

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Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

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T ER MS A N D CONCEP TS • aggregate • atonal • blue note • centric • chordal extensions • chromatic collection/universal set • diatonic collection • hexatonic poles • literal complement • octatonic collection • parsimonious voice leading • pentatonic collection • post-tonal • subset • whole-tone scale

CH A PTER R EV IEW 1. Define centricity.

2. True or False: Tonal music is not centric, but twentieth-century music is tonal.

If false, correct the sentence.

3. What is a “split-ninth chord”?

4. Spell a V11 chord in B major by thirds.

5. Arrange the D-major scale into a single extended harmony built in thirds. Then arrange it into two quintal or quartal sonorities, one having three pitches; the other, four.

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THE COMPLETE MUSICIAN

6. A. Spell a Mixolydian scale beginning on B.

B. Spell a Phrygian scale beginning on C.

7. Spell a minor pentatonic scale on F.

8. Write the pitches of the literal complement of the minor pentatonic scale on F.

9. Write a whole-tone scale beginning on A.

10. Given the pitches F–A–D, complete the whole-tone scale.

11. Write a hexatonic scale beginning on E, and then extract as many major and minor triads as possible, listing them in root position.

12. True or False: The octatonic scale is comprised of one whole-tone scale and a minor triad.

13. Two of the sonorities below do not belong to a single octatonic scale. Write out each triad/ seventh chord, and by process of elimination, determine which chords are not members of the same octatonic scale. E major triad D major triad C Mm seventh chord G minor chord A minor chord F mm seventh chord

Chapter 30 Vestiges of Common Practice and the Rise of a New Sound World

14. Notate the octatonic scale that has the following sonorities: B major E minor G major D minor

15. Given the following octatonic scale, extract as many French augmented sixth chords as possible. D–E–F–G–A–B–B–C

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C H A P T E R 31

Noncentric Music: Atonal Concepts and Analytical Methodology OV E RV I E W

In this chapter we explore music that does not project referential pitches or a sense of hierarchical relationships, which are requirements for tonal music and often found in the centric music we studied in Chapter 30. The repertoire taken up in this chapter is often referred to as nontonal or atonal. For this vast body of music we must learn new ways of hearing and develop new tools for analysis to comprehend the types of relationships that composers aurally project. CHAPTER OUTLINE A New Sound World................................................................................................... 791 A First Analysis ............................................................................................................ 792 Limitations ............................................................................................................. 795 Pitch and Pitch-Class Space..................................................................................... 795 Equivalence................................................................................................................... 796 Equivalence in Tonal and Nontonal Music ....................................................... 797 Demonstration of Equivalence in Nontonal Music ......................................... 797 Integer Notation.......................................................................................................... 799 In Pitch Space ........................................................................................................ 799 In Pitch-Class Space .............................................................................................. 799 PC Sets and Modular Arithmetic ........................................................................... 799 The Clock ............................................................................................................... 799

790

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More on Equivalence Classes................................................................................... 802 Transposition ......................................................................................................... 802 Inversion ................................................................................................................. 802 Computing and Comparing: P and PC Space .................................................... 804 Ordered Intervals................................................................................................... 804 Ordered Pitch Intervals ............................................................................... 804 Ordered Pitch- Class Intervals ..................................................................... 804 Unordered Intervals .............................................................................................. 805 Unordered Pitch Intervals ........................................................................... 805 Unordered Pitch- Class Intervals ................................................................. 805 Mod-12 Inverses and Interval Classes ................................................................ 806 P Sets and PC Sets with Three or More Members ............................................. 806 Index Numbers ...................................................................................................... 809 A Systematic Approach.............................................................................................. 814 Step 1: Segmentation → Pitch Collection → Pitch-Class Collection ........... 816 Step 2: Normal Order ........................................................................................... 816 Step 3: Best Normal Order (BNO)..................................................................... 817 Wrinkles .........................................................................................................817 Step 4: Prime Form (PF) and Set Class .............................................................. 818 Enter the Clock: Normal Order Straight to Prime Form...........................818 Symmetrical Sets ......................................................................................................... 819 Invariance ............................................................................................................... 820 Interval Class Vector ............................................................................................. 821 Checking Your Work ............................................................................................. 823 A Curiosity in the PC World ............................................................................... 824 Terms and Concepts ................................................................................................... 825 Chapter Review ........................................................................................................... 826

A N E W S OU N D WOR L D Twentieth-century music must be listened to and analyzed in a piece-by-piece fashion. This is a very different approach than that which we used in the previous sections. In traditional tonal music, the phrase model guided the structure, counterpoint followed specific rules, and all of the other rules and procedures that we have grown so used to were established. The difference becomes apparent when we attempt to apply our knowledge of tonal procedures, modified and centric tonality, added-note sonorities, collections with five to eight notes, and other tools in our analytical arsenal to specific modern works.

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A F I R S T A N A LY S I S Let’s begin by looking at a selection by Anton Webern (Example 31.1; for the full score, see Anthology no. 71). The passage seems impenetrable: It is highly chromatic with no pitches highlighted, and is not based on one of the previously studied collections. For this sort of music, we can benefit from simply taking stock, observing obvious events: texture and repetitions (both literal and transformed). Nontonal music must be listened to and analyzed with a very different approach than that which we used in the first 29 chapters, where the phrase model indicated the structure and counterpoint could be counted on to behave. We can no longer assume and rely on the techniques that we previously used to analyze this music. Webern’s focus is on the total chromatic instead of a (diatonic) subset of it. Seven basic observations can be made as an important analytical first step in our discussion of this work.

EXAMPLE 31.1 Webern, Five Movements for String Quartet, op. 5 STR EA MING AUDIO

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Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

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OBSERVATION #1: Measures 1–2 have a layered structure, with violins 1 and

2 playing eerie sonorities while the cello plays a repeated E. In the middle of m. 2, the viola presents a sort of motive: two repeating PCs (E and F). OBSERVATION #2: By m. 3, an entirely different mood contrasts with the opening idea: an imitative falling gesture, from high in violin 1, to the cello’s low C (the bottom of its range) in m. 5. Because we look for groupings, repetitions, and other gestalt features, these observations are helpful, but limited. OBSERVATION #3: If we keep going, we are rewarded. A new tune is presented

by violin 1 in m. 5; a true melody, although not quite a tonal one. The PC succession is echoed (two octaves lower) an eighth note later in the cello. OBSERVATION #4: We now have something substantive to say: The opening two measures present contrasting ideas while measures 3 through 6 are tightly connected by arguably the most trusted, age-old technique: imitation. Such a grouping of 2  4 is supported by a change in timbre at the end of m. 2: The upper parts play a startling four-note pizzicato chord, bringing into stark contrast the amorphous opening sound of the tremolos that open the piece. Can we call the end of m. 2 a cadence? What about at m. 6, with the conclusion of the imitation and the rests in the upper voices—is this perhaps another cadence? Could the caesura, which plays a subordinate role to cadences in tonal music, now be elevated in stature to serve the important function formerly granted to authentic and half cadences? Might a mere silence or textural change now be considered a structural event? OBSERVATION #5: Our basic observations are paying off. A bit more digging will reveal even more. The opening four-voice tremolo figure presents a sonority composed of major third C–E in violin 1 and tritone F–B in violin 2 (Example 31.2A). Played together, and arranged in ascending order (as we did with collections; see Chapter 30), we get: B–C–E–F. Notice that the sonority can be heard as two half steps a perfect fourth apart, or as a tritone in violin 2 surrounding the major third in violin 1, or as two perfect fourths a half step apart (Examples 31.2B1 and B2).

Let’s look at the second sonority, keeping in mind the information garnered from the first one because the two are clearly related by texture and articulation. The second sonority is sort of the reverse of the first. Now the first violin plays a perfect fifth, B–F, enclosing the second violinist’s perfect fourth which lies inside the larger interval (Examples 31.2B1 and 2). Taken together, we have B–C–F–F, two minor seconds separated by a tritone (or two tritones separated by a half step). The second sonority is a sort of expansion of the first. The interpretation of the two sonorities, the PC content of which we’ll call Sets 1 and 2 respectively, can be read backwards or forwards: Counting half steps, the three intervals of Set 1 (bottom to top) are 1–4–1; Set 2’s intervals are 1–5–1. Two palindromes. Such symmetry is one of Webern’s compositional hallmarks. Notice that the B, C, and F are held in common between the two sonorities, and that the C and B in m. 1 are swapped in a sort of “atonal voice exchange.” Measure 2, with its “cadential” pizzicato, repeats the first sonority, creating a sort of arch of sonorities (Example 31.2B1). Violin 1’s E–F and return to E is heard as a contraction, a kind of neighboring motion. In fact, recall the opening motive in the viola, which can now be identified: It uses the very

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THE COMPLETE MUSICIAN

EXAMPLE 31.2 Webern, Five Movements for String Quartet, op. 5 STR EA MING AUDIO

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E–F that violin 1 presented in mm. 1–2 (Example 31.2B3). Clearly these are important observations because: (1) They are audible; and (2) The chances of such a tightly knit structure being purely coincidental would be astronomical. OBSERVATION #6: With our deepening understanding of the piece, we look at mm. 3 and 4 (Example 31.3). The falling four-note gesture in violin 1 contains the same PCs heard in m. 2, but in falling tritones and perfect fourths/fifths. These are the specific intervals established as important at the beginning of the piece. Violin 2 breaks the expected pattern of repeating its pitch from the opening. However, the

Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

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EXAMPLE 31.3 Webern, Five Movements for String Quartet, op. 5 STR EA MING AUDIO

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“voice exchange” PCs C and B appear juxtaposed on the downbeat of m. 4, and the cello later imitates violin 1 in lockstep with the same PCs. OBSERVATION #7: A crush of dissonance closes the passage as violin 1’s PC

material is imitated in the cello. Notice the prevalence of C–C/D–D, both harmonically (m. 5 beat 2, especially) and melodically (the final four notes of the violin 1/cello melodies). This three-note chromatic unit later proves central to the piece. (refer to Example 31.1, mm. 5–6).

Limitations While our observations are relevant to Webern’s piece, we are still faced with a question, indeed, even a problem: How do we understand and analyze the pitch structure when we don’t understand the vocabulary and syntax? We have no real methodology to understand the pitch combinations that Webern has chosen. Tonality and its fundamental precepts of root progressions, voice leading, and a harmonic palette of just four triad types and six seventh chords guide the analyst when studying music written between 1650 and 1900. Where are these guiding signposts, such as scale degrees, in Example 31.1? Webern’s piece presents a new set of possibilities for the composer, the listener, and the analyst. Thus we need to develop analytical tools that will be appropriate for understanding such music.

PI T C H A N D PI T C H- C L A S S S PAC E Recall from Chapter 1A that pitch is a specific frequency, of which there are an infinite number (that is, C3 is not considered the same as C4, etc.). Pitches exist in pitch space, which is based on their registral placement. On the other hand, a pitch class is a

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representative of all pitches that occur at a distance of one or more octaves and which are enharmonically equivalent (e.g., B3, C3, and D3, all of which are members of the pitch class “C”). These exist in pitch-class (PC) space. The infinite world of pitches has now been reduced to only 12.

E QU I VA L E N C E The analytical approach that we’ve applied to this piece is important, given that it is difficult to work with and distinguish between the millions of possible pitch combinations in the world of atonal music. However, we can group the vast number of sonorities into a surprisingly small number of like groups. For example, given the following sonority (Example 31.4), we see eight groupings of pitches, each of which appears to be different from one another in terms of spacing, register, spelling, texture, and so on.

EXAMPLE 31.4 Equivalence in PC Space A.

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Of course, we view them as being the same sonority: an A-major triad (or an enharmonic equivalent). So, what criteria did we use to be able to say that all of these very different-looking but, to a certain degree, even-sounding sonorities are the same? We invoked the notion of equivalence class. We decided that certain similarities are so important that their differences can be ignored, thus greatly reducing the number of distinct entities. For example, Example 31.4A presents the A-major sonority in close position and in the middle of the keyboard, while Example 31.4B spaces it out over several octaves and even rearranges the order of the pitches. However, given the sonic similarity and the identical PC content, we have decided to ignore the registral differences and call the various locations of, say, A (which in pitch space include A2, A3, A4, and A5), simply as “A,” compressing four As into a single pitch class. We invoked octave equivalence. Such a decision moves us from the very literal pitch world to the more abstract pitch-class world. We have simultaneously invoked order equivalence, in which we are not concerned with the placement of chordal members situated above the bass. Thus, Examples A and B are different pitch sets, but are identical pitch-class sets. The same applies to Example

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31.4C because we have invoked these same equivalences. Example 31.4E spreads out the A-major triad in time over nine beats but we view it as being equivalent to A, B, and C because we have invoked temporal equivalence; when, in time, the same pitch classes occur is not always a consideration in the PC world. Example 31.4D is a bit different than the preceding examples because it does not contain the PC ‘A’ in the bass. In tonal analysis we are very interested in what member of the chord is in the bass. Here the bass is not the root, so we would say that it is an A6. But, if we are concerned only with root names, we do not consider inversions to be enough to distinguish between inverted and noninverted chords. By invoking octave equivalence, spacing, and so on, we would just say that “this, too, is an A-major chord.” Finally, the sonority in Example 31.4F contains F and D, which are in no way related to an A-major chord. But, if we play letter 31.4F and compare it with 31.4A, we hear the identical sonority, including the same spacing and voicing. Thus, in isolation, we might identify it as equivalent to Example 31.4A: an A-major chord. We have invoked enharmonic equivalence. In atonal music enharmonic pitches are considered to be members of the same PC.

Equivalence in Tonal and Nontonal Music Given the numbers of PC combinations in nontonal music, we always try to reduce, simplify, and generalize, in order to grapple with the infinite world of sounds. This is how we can move so quickly from an infinite world of pitches to the tiny world of 12 pitch classes and all of their possible combinations. By invoking octave, order, temporal, and enharmonic equivalences alone, we reduce the nearly infinite pitch world to exactly 4,096 PC combinations (212). If we continue to reduce the tonal pitch world by invoking equivalence classes, it becomes ever more general, and less sensitive to many musical aspects. For example, given an A-major triad and an E-major triad, we would consider them very different, based on their different roots, pitch classes and functions. But, if we were only interested in intervallic content, then, we would say that both the A-major and E-major triads are identical because they have a major third beneath a minor third. By doing this, we have related the two chords by transpositional equivalence, given that each PC of one chord can be transposed by a consistent number of half steps that contain the same PCs as the original chord. However, we have lost many things, with hierarchy being only one. Thus, there is a trade off when we invoke equivalences: the more equivalences (relationships), the fewer the distinctions, and the fewer the distinctions, the less subtle analysis can become. As humans, we try to make sense out of things, to group, to categorize, to simplify. But how far do we go? When do we stop moving from the surface of the music—the pitch world and all of its richness—to the more general and more finite world that allows us to generalize and to make connections? We will use more equivalence classes to understand nontonal music than we do with tonal music because the composers of this music are themselves thinking about other equivalences.

Demonstration of Equivalence in Nontonal Music Let’s apply the concept of equivalence classes to another Webern example (Example 31.5). Again, we will begin with distinct musical gestures, most of which are played by different instruments. The saxophone begins by playing D–B–A, followed by the violin stating B–D–E, and the piano C–C–A and C–B–E. Yes, there are a few repeated pitch classes

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EXAMPLE 31.5 Webern Quartet for Violin, Clarinet, Tenor Saxophone, and Piano, op. 22 STR EA MING AUDIO

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(Note: Webern notates his scores in C, thus the pitches you see are the pitches that sound.) (e.g., B and E) but other than this, each three-note group seems distinct, and all are, in tonal terms, dissonant. Notice, too, that the contour pairs (i.e., sax/violin, and right/left hands of the piano) move in the opposite direction from one another, in mirror fashion, called inversion. We now invoke order and octave equivalences for the sax’s three-note group, and abstract the sonority A–B–D in ascending order from lowest to highest. We do the same for the violin, B–D–E, and for piano, A–C–C and B–C–E. Notice that we have arranged the PCs into a consistent order, based on the intervals of the sonority occupying the smallest span (i.e., the most-compressed form). This is precisely what we do in tonal analysis when adding figures to a bass (i.e., we always write 53 and not 12 10). We will return to this idea of compression, later. Now let’s inventory the specific intervals. Each of the four gestures contains a half step and a minor third with an overall span of a major third (show by number of half steps), either: [4] [4] 1–3 or 3–1 In fact, A–B–D and B–C–E have the same intervallic order: half step followed by minor third. They are therefore the same type of three-PC sonority, or trichord, but they contain different pitch classes. We could make them identical by transposing the first set up a major second or the second set down a major second. Notice that we had to invoke multiple operations on these pitch sets to see these relationships. The other two gestures, B–D–E and A–C–C, have the same interval structure, but reversed from the sets just discussed above. These too, could be turned into or mapped onto one another, just like the first pair of PC sets, by transposing the first trichord down a whole step or transposing the second trichord up a whole step.

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As you can see, we have focused on the world of the interval to see relationships and to learn that Webern is working from a single idea: an intervallic motive composed of a major third with a half step inside. The world of intervals is crucial in twentieth-century analysis.

I N T E G E R N O TAT IO N When we deal with post-tonal music, we use integers to represent pitches (P) and pitch classes (PC).

In Pitch Space Middle C will be assigned the number “0.” Pitches accrue positive numbers based on the number of half steps above middle C and negative value based on those half steps below middle C. So, G above middle C  7. B below middle C  2, and the B one octave lower than that  14.

In Pitch-Class Space The 12 pitch classes exist in pitch-class space, a finite and circular, or “wraparound,” world where we do not differentiate between octaves. Negative numbers don’t exist for PCs because we consider all octave-related pitches to be the same PC. We explore this later in the chapter.

P C S E T S A N D MODU L A R A R I T H M E T IC When we label pitch classes, we again start on C, but this time all Cs—regardless of octave placement—are labeled “0.” Thus, middle C  0, and C above and below also  0. When a system of counting is circular, we call it “modular.” If the number of elements in the system is 12 (as it is in the chromatic PC world), we use only the numbers 0 to 11. Further, since the double digit “10” and “11” could be confused for 1 followed by 0 or two 1s, we use “t” to represent 10 and “e” to represent 11. Thus: 0 1 2 3 4 5 6 7 8 9 t e 0 1 2. A set such as the one opening Webern’s quartet above (D–B–A) is labeled “(1t9).” We used 0 instead of 1 for the base PC because it is the starting point, even though it is the first of the ordered 12 PCs (this will become clear shortly). Mod-12 arithmetic helps us to convert pitches into pitch classes. For example, if we label the interval from C4 (0) up to G5, we call the pitch interval a “19” (i.e., there are 19 half steps between the two pitches), but the pitch-class interval would be “7” because after the upper limit, 11, we start counting at 0 again. We get the high G (19) into the mod-12 space by subtracting 12 from 19, resulting in 7. Now G falls within the range of 0–11 where G  7. The same process can be used with all PC intervals. For example, the distance between F 4 down to D3  16; to convert 16 into a number between 0 and 11, subtract 12 from 16, which is 4.

The Clock The clock face is a handy way of conceiving PC relationships, given that its 12 hours can represent our 12 PC system (see Example 31.6). If you substitute 0 for the 12, you can easily determine the distance between pitch classes. For example, if it’s 4:00 and you wish to know what time it would be three hours later, you would add 4  3 and the result

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THE COMPLETE MUSICIAN

EXAMPLE 31.6 The Clock A.

B. e

0

t 9

3 8

2

9

3 8

4 6

1

t

2

7

0

e

1

4 7

5

4:00 + 3 hrs. = 7:00

6

5

10:00 + 3 hrs. = 1:00 (Note: 13 = 1 mod 12)

would be 7:00. But, if it’s 10:00, what time would it be three hours later? Since the PC world is limited to 0–11, we would need to start over at 12. The answer, then, would be 1:00, not 13:00. On the other hand, we might pose these questions: “It is 4:00. In how many hours will it be 9:00?” (answer: 5). Or, “It is 11:00. In how many hours is it 5:00?” (answer: 6). We have used mod-12 arithmetic to determine answers to these questions. You must be fluent with the numbers assigned to each PC and the ability to determine the intervallic distances using these integers. To learn the PC numbers, slice up the clock into various even segments as we did in Chapter 28. For example, cut into quarters, the numbers 0 3 6 9 represent C–E/D –G/F –A: a diminished seventh chord (Example 31.7A). Further, each of the remaining PCs all lie within one “clock hour” of the 0 3 6 9 hours: e–0–1, 2–3–4, 5–6–7, 8–9–t. Let’s model the octatonic scale on the clock (Example 31.7B) as well as the whole-tone scale (31.7C), which immediately reveals their symmetrical intervallic structures.

EXAMPLE 31.7 Clock Representations of the Diminished Seventh Chord, and Octatonic and Whole Tone Scales A.

B. e

0

1

t

e

9

3 8

4 7

6

5

Diminished 7th

0

1

t

2

STR EA MING AUDIO

C. e

9

3

4 7

6

5

Octatonic

0

1

t

2

8

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2

9

3

4

8 7

6

5

Whole-Tone

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EX ERCISE INTER LUDE EQUIVA LENCIES, PITCH vs. PITCH CL ASS, PITCH- CL ASS NUMBERS 31.1 Determining Types of Equivalencies Label each example below with the applicable equivalence type. Each example exhibits either transpositional, octave, temporal, enharmonic, or order equivalence. Some examples may show multiple equivalences. Example: (C, E, G) and (G, B, D)  transpositionally equivalent 1. C4 and C5 2. (D, A , C ) and (A , C , D) 3. (F, G , B) and (G, A , C ) 4. (E, G, C) and (G , A , D )

31.2 Pitch Numbers vs. Pitch-Class Numbers Label each of the given pitches with the appropriate pitch number and pitch-class number. Example: (C5: pitch  12, pitch class  0) 1. Middle C 2. G 6 3. E 3 4. B4

31.3 Ordered Pitch Interval vs. Pitch-Class Interval For each of the given intervals, determine both the ordered pitch interval and the ordered pitch-class interval. Example: (D4–E5: pitch interval  14, PC interval  2) 1. (G5 –C6) 2. (F4 –E3) 3. (A 2 –A 4) 4. (B5 –D3)

31.4 Practice with Pitch-Class Numbers Rewrite each of the given pitch sets with pitch-class numbers. Example: (F major triad  5, 9, 0) 1. E  major scale 2. F major-minor seventh chord 3. G harmonic minor scale 4. A  fully diminished seventh chord

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THE COMPLETE MUSICIAN

MOR E ON E QU I VA L E NC E C L A S S E S

Transposition We have seen the importance of transposition, an operation that we use to analyze both tonal and nontonal music. Sonorities such as a major triad contain a major third with a minor third above it. We can then reduce the pitch world more by entering the pitch-class world, and transpose the 12 major triads (C major, C major, D major, etc.) to a single member of a major-triad class. Transpositional equivalence is based on interval content. So all major triads can be represented by a major-triad class because even though they may contain different PCs, their intervallic content is identical. Let’s show this by using integers, rather than letter-names. To transform a C-major triad built on middle C (0–4–7) into a G major triad a fifth above (7–e–2), we transpose the C-major triad up seven half steps (this is easy to see, given that a major triad on C begins with 0 and one on G begins on 7). We simply add 7 to each member of the C-major triad, mod 12: 0–4–7 becomes 7–e–2.



0 4 7 (C major triad) 7 7 7 (T7) 7 e 2 (G major triad)

By invoking transpositional equivalence we have reduced the 4,092 possible pitch configurations to just 352, a drastic reduction, indeed.

Inversion Inversion reverses the contour of intervals of a P or PC set such that instead of ascending, they descend or vice versa. For example, an ascending major third (four half steps) followed by an ascending minor third (three half steps) would be inverted if the direction were reversed: the major third would descend, and a descending minor third would follow. Let’s try one using PC names. The inversion of C–E–G (up a major third then up a minor third) would move in the opposite direction: A major third from C falls to A followed by the minor third from A to F, a minor triad. Note: Inversion may take place at any pitch level, not just the literal mirroring around a central note (in this case, it is C). For example, one could invert a major triad beginning on, say, A below C: A falls a major third to F, and a minor third from F to D. Given that the intervals in both sets are identical (but mirror one another), we can relate them by another equivalence class: inversion. In Example 31.8, we see that the inversion of a major triad is equivalent to a minor triad. So, inversion is a process that often occurs in conjunction with transposition. However, inversion as an equivalence class, or relation, is often questioned given that the sound of many inverted pitch sets are very different. Another example of an inversion

EXAMPLE 31.8 Inversion of a C Major Triad Around C (0)

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is the major-minor seventh: C–E–G–B becomes C–A–F–D. Spelled in ascending order, the inverted form of the major-minor seventh is a half-diminished seventh chord: D–F– A–C. Yet both the major/minor triad and the Mm7/dm7 sonorities are inversions of one another. Further, some PC harmonies do sound the same when inverted. This is because the set is composed of the same intervals, like the diminished triad: invert 0–3–6, it becomes 0–9–6; both of these sets are diminished triads. Accepting inversional equivalence class reduces the major- and minor-triad world by half: 12 major triads plus 12 minor triads (24) become 12 entities that contain a major third plus a minor third. If we invoke both inversional and transpositional equivalence, then all 24 major and minor triads are reduced to a single “major/minor” triad. Thus, 24 entities belong to a single representative class, called a set class, which represents all major and minor triads. This makes sense, given that major and minor triads both contain a perfect fifth (or perfect fourth), major third (or minor sixth), and minor third (or major sixth). Let’s return to those four trichords that we discussed in the Webern (see Example 31.9).

EXAMPLE 31.9 Webern, Quartet for Violin, Clarinet, Tenor Saxophone, and Piano, op. 22 STR EA MING AUDIO

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We saw that each of the two pairs of sets were transpositionally equivalent, arranged in ascending order: PAIR #1: Saxophone: A–B–D; Piano right hand: B–C–E (ascending intervals

 1  3) PAIR #2: Violin: B–D–E; Piano left hand: A–C–C (ascending intervals  3  1)

However, given that both pairs of sets have the same intervallic structure, merely reversed, they are all related by inversion and/or transposition. We now explore specific techniques for relating sets in both pitch and pitch-class space.

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C OM PU T I N G A N D C OM PA R I N G : P A N D P C S PAC E We start with methods for manipulating sonorities, the goal being to both generate a new set and to compare given sets. We will begin with the most context-sensitive operations and then move to the most generalized operations, a path that moves from the pitch to the pitch-class worlds.

Ordered Intervals To determine both the intervallic distance and the direction (up or down) between pitches and pitch classes that are stated one after the other, we specify their order using integers. We will determine ordered intervals in both pitch and pitch-class spaces.

Ordered Pitch Intervals • We can find the ordered pitch interval (P int) between two pitches by subtracting the first pitch’s integer from the second pitch’s. For example, C4 up to E4 is an ascending major third, four half steps. We can check this: C4  0 and E4  4, so 4  0  4 (Example 31.10A). We can do the same thing an octave up in the pitch world, 16  0  16, because the P world is infinite, and permits intervals larger than the wraparound PC world of 0 to 11 (Example 31.10B). On the other hand, middle C (0) down to G3 (5)  5, because 5  0  5 (Example 31.10C). A pitch interval gives both magnitude (5) and direction ().

EXAMPLE 31.10 Calculating the Ordered Pitch Interval between Two Pitches A.

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B.

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w

C.

16 - 12 +4

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-5 - 0 -5

Ordered Pitch-Class Intervals We can determine the size and order of pitch-class intervals; but remember: in PC space there are only 12 possible intervals, numbered 0 to 11. For example, to determine the size of a descending interval, subtract the first number from the second, just as in P space: E down to C  4 (0  4  4). However, in PC space there is no “up” or “down.” So we convert the negative number into a positive one in the 0–11 range by adding 12 (recall that on the clockface adding 12 is equivalent to adding 0): 4  12  8. Alternatively, treat the lower pitch as though it were above the higher one (within one octave) and count the semitones between them: E down to C  E up to C  8. The process is shown in Example 31.11 using the clock face.

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Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

EXAMPLE 31.11 Determining Ordered Pitch-Class Intervals C

C

=

-4

+8 E

E

A. Avoid counterclockwise motion since it results in negative numbers

B.

Use clockwise motion since it results in positive numbers

By convention, ordered pitch-class intervals are calculated by moving from one pitch class to another pitch class in the clockwise direction (Example 31.11).

Unordered Intervals Very often, intervals are vertically stacked, making it impossible to determine order, but rather only distance between two Ps or PCs. Such intervals are unordered. Again, we examine such intervals in both the P and PC worlds.

Unordered Pitch Intervals In the P world, unordered intervals represent distance only, not direction or order, so we use only positive integers. The perfect fourth between C4 and F4  5 semitones, and the reverse, F4 to C4  5 semitones. Greater distances are named according to the actual number of half steps spanned. Thus, the distance between C4 and D5 (an octave plus a second)  14 (see Example 31.12).

EXAMPLE 31.12 Calculating Unordered Pitch Intervals

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w 5

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Unordered Pitch-Class Intervals Unordered PC intervals will be the most common method we will use. We use mod 12 (i.e., the clock) to determine the interval: Thus, the distance from any C to any G (or vice versa)  5. The goal is to find the smallest interval between two pitch classes (see Example 31.13).

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EXAMPLE 31.13 The Unordered PC Interval from G to C, or C to G  5 C 00

7 to 0 = 5

0 to 7 = 7

(Perfect 4th)

(Perfect 5th)

G

7

Mod-12 Inverses and Interval Classes

Unordered PC intervals  their inversions always sum to 12. In Example 31.13 we saw that moving clockwise from C to G yielded 7 semitones, while continuing in the same direction, G up to C yielded 5 semitones; both intervals together sum to 12 (7  5). The smaller number, 5, is representative of both 7 and 5 in PC space. This representative number is called an interval class (IC). Numbers that sum to 12 (0) are called mod-12 inverses (Example 31.14). Intervals that are mod-12 inverses of each other have highly similar sounds. For example, clearly a perfect fifth and perfect fourth are similar in sound. The analogy of IC and interval inversion in tonal music is striking: In tonal music, inversions turn seconds into sevenths, thirds into sixths, fourths into fifths, fifths into fourths, etc. These all sum to 9, but the 11 chromatic intervals sum to 12. Notice that the inverse of 6, the tritone, is itself (6←→6). From this point, all interval pairs repeat, but in the opposite order (e.g., 2←→10 becomes 10←→2). These redundant intervals are unnecessary. Therefore, there are only six intervals classes: 1–6. In general, ordered relations are usually associated with melody, because it unfolds in time and we often wish to capture the relationships in pitch space. Unordered relations are usually associated with harmony, where pitches occur simultaneously and order is not possible to determine. We will be working in PC space most of the time. Example 31.15 compares the results of working with intervals in the pitch world (ordered and unordered) and the pitch-class world (ordered and unordered).

P S E T S A N D P C S E T S W I T H T H R E E OR MOR E M E M B E R S A pitch, a pitch interval (two pitches), and a pitch set (3 or more pitches) represent literal musical objects that appear in various registers, timbres, durations, and so on. However, determining relationships between two pitch sets is often difficult because of the sheer number of possible sonorities and distribution of those sonorities in various registers.

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EXAMPLE 31.14 Mod-12 Inverses

e t

t e

The sonorities in Example 31.16 are considered equivalent once they: 1. Both appear in root (“squished”) position; 2. Have the same interval order (if the order is reversed, the two sets are related by inversion); 3. Contain the same PCs (if the intervallic order is the same in both sets, then they are merely transposed). Let’s unpack these three stages. Given: a B-minor triad in first inversion and D-major triad in root position. How do they relate?

Stage 1. Squish and determine PC numbers for B minor and D major. The integers for B minor are e–2–6 and for D major are 1–5–8. Notice that their intervals are reversed: 3–4 for B minor and 4–3 for D. Thus, these sets are related by inversion. By inverting one of the sets, we can compare them because they will have the same intervallic ordering.

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EXAMPLE 31.15 Comparison and Summary of Unordered and Ordered Pitch and Pitch-Class Sets STR EA MING AUDIO

Ordered Pitch Intervals (literal distance and direction)

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Unordered Pitch Intervals

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Unordered Pitch-Class Intervals

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EXAMPLE 31.16 Relating Distantly Related Triads Given:

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F# major transposed up 7 half steps = Db major

Stage 2. We invert B minor: the mod-12 inversion of e–2–6  1–t–6. Note that each PC pairing (e/1, 2/t, 6/6) sums to 12. Reorder in “squished” position (accomplished by reading backwards in this case) and we get 6–t–1, yielding the intervallic pattern 4–3, the same as the major triad. Stage 3. Transpose the F-minor triad (derived from B minor by inversion) by 7 semitones (“T7”) and the original B-minor set will map onto D-major. Thus, to see how inversionally related sets can be mapped onto one another, invert one set, and find the transposition level that will map the inverted set onto the second set. Important Note: When comparing two sets with the same intervallic content in the same order, simply transpose. When comparing two sets with the same intervallic content but in reverse order, invert first, then transpose.

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Index Numbers There is another way to determine relationships and mappings between two inversionally related pitch-class sets, which might be easier for you. To determine inversion and transposition levels in one step, we add their paired integers together as shown in Example 31.17. We return to Webern’s Saxophone Quartet to demonstrate how two inversionally related trichords can be mapped onto another (Example 31.17).

EXAMPLE 31.17 Mapping Two Inversionally Related Trichords A. Webern, Quartet for Violin, Clarinet, Tenor Saxophone, and Piano, op. 22

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Sax.

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≈

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B.

e

2

3

9

t

1

The violin’s pitch-class sets B–D–E (e23) and the saxophone’s A–B–D (9t1) are inversionally related given their reversed intervallic order: 3–1 and 1–3 (note that sets are arranged in ascending order by PC name). Because they are mirrors of one another, we can add the outer integers (e and 1) and then continue inward (2 and t; 3 and 9). There is a consistent resulting number. This single number, called the sum or the index number, reveals the transposition level needed to map two inversionally related sets onto one another. In this case, the sum is 12 (0), because e  1  0, 2  t  0 and 3  9  0. So, we can map the first set onto the second by inverting either of the sets and transposing the inverted set by 0 semitones. Let’s try it the first way that we learned earlier: (e23) and (9t1) are inversionally related. Invert (9t1) using its mod-12 inverse, which is (32e). Now read backwards: (e23). Voilà, we have our first set return. Either method works for inversionally related pairs of sets. You can also use the clock to visually represent the inversion and subsequent mapping. Notice that (e23) and (9t1) are indeed mirrors of one another, which is shown using the clock face (Example 31.18A): the dotted line shows how (9t1) inverts to (e23). Example 31.18B shows the symmetry around the axis 0: If you fold the clock at 0/6, each inversional PC would map onto its mate. The place where the fold occurs is the axis of inversion. Let’s look at another example using the staff. C–D–E can be inverted around the axis of C to produce C–B–A (that is, what was up 1 and up 3 is now down 1 and down 3). Here are the PC integers (Example 31.19A) and their plotting on the staff to show 0 as the axis (Example 31.19B).

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THE COMPLETE MUSICIAN

EXAMPLE 31.18 Using the Clock to Determine Inversionally Related Sets A.

Using the clock e

B.

The axis

1

t

e 2

t 3

9

9

1 2 3

EXAMPLE 31.19 Inverting C–D –E to Produce C–B–A  A. The PC integers 014 0e8 B.

The Axis C = axis

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˙˙

1

1

3

b ˙˙

˙ b˙

3

What happens if we invert a set about a different PC? For example, inverting (t03) with t as the axis? Rather than going through the process of literally inverting the trichord— which could easily introduce errors—let’s simply use the index number. Since we’re inverting around B (t), the inverted set will also contain a t (invert B around itself and you get B). Add the two t’s together (mod 12) to find the index number as we did with Webern’s Quartet (Example 31.17): t  t  20  8 mod 12. So, we can derive the inversion by using integers that add up to 8 (see Example 31.20A and B). Bartók’s “Subject and Reflection” uses these PCs (see Example 31.20C). In this piece, notice that the Bs are not unisons, but rather octaves. We have assumed that the Bs—as unisons—create the axis. But in Bartók’s example, the distance of an octave creates a different literal axis: E4. You can test this on the piano: E lies equidistant from the two Bs. Notice that E is a tritone away and is a secondary axis. Thus, if the axis is a unison, then it is the literal PC from which the axis is generated, but if the axis is an octave distant, the literal axis is a tritone away. Thus, 8 is the index while the literal axis is 4.

Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

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EXAMPLE 31.20 Inverting Around (t03), Abstractly and in Bartók’s “Subject and Reflection” STR EA MING AUDIO

A.

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Given: Inversion around t: Sum:

t03 t85 888

B. Notated in Pitch Space Bb = axis

b ˙˙

b˙ ˙

0+8=8

3+5=8

& b ˙˙ t+t=8

C. Bartók, “Subject and Reflection” Allegro,

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Demonstration: Given a trichord, let’s generate two inversionally related sets, the first of which will be the literal PC inversion around a given PC, and the second, inversion around 0 (C). 1A. Inversion around a given PC: Given the pitch-class set (458), we generate the literal inversion about E (4), which will serve as the axis. Add the first number to itself (in this case, 4), which sums to 8, the index number. Add a corresponding number to each subsequent PC in order for it to sum to 8: thus the literal inversion of (458) is (430). We can check this on the piano. Play (458) (E–F–A ), then, in the opposite direction beginning on E, use the same intervals as the original set: E–E –C, or (430). 1B. Inversion around a given PC using the “rainbow” shortcut (Example 31.21): We can also lay out the first set, (458), and begin the inversion on the far side of the

EXAMPLE 31.21 Inversion About an Axis: “Rainbow” Shortcut

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w

bw

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nw

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THE COMPLETE MUSICIAN

next set in order to maintain the symmetrical inversional structure emanating from the midpoint and again summing to 8: (458) | (034). Play the first set (458) with your left hand and the second set (034) with your right hand. Notice how E is the center point, and the other PCs fan out from E symmetrically. 2. Inversion around 0: We can also generate a set’s inversion around the axis of C, which is common, but does not represent inversion around the literal pitch given. This is easy, because we use the mod-12 complements, which add to 0. The inversion of (458) around C (as axis) is (478). Remember, to find the index number from the axis, which in this case is 0, one must double the axis number (mod 12). This makes sense, since the last member of the first set, A  (8), is a major third below C (the axis), so the inversion then must begin a major third above C, which is E (4), and 8  4  0 (C) (see Example 31.22).

EXAMPLE 31.22 Inversion Around 0

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5

8

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0 0 0

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4

w

w7

b w8

Composers take great advantage of inversion, especially given its properties of symmetry that have made it a hallmark of post-tonal composition. For example, Bartók structured the first movement of his Music for Strings, Percussion and Celesta using mirror inversion at both the surface level of the music and at the deepest levels of the pitch structure. The movement’s pitch events all center around the specific pitch A (440); the rest of the pitch centers in the movement unfold from this pitch. This is accomplished by two simultaneously ascending and descending perfect-fifth patterns, fanning out and expanding pitch space away from the A axis. Because pitches flank A symmetrically, these newly added inversionally-related PCs will always sum to the same index number (6): Every added pitch is balanced by another pitch the same distance from A, but in the opposite direction (see Example 31.23). Notice that the progression by opposing fifths leads inevitably to octave Es, a tritone away from the A: PC 9 plus PC 9  18  6, mod 12, and the arrival on two Es  3  3  6 (mod 12). We see that there are two axes of symmetry, A and E, a tritone apart. The second portion of Bartók’s movement contracts, heading back to A, by rising fourths in the bass and falling fourths in the upper parts. Notice that this reverses the pattern so that the PCs that were above A are now below A, and vice versa (compare the second interval with the next-to-the-last one, etc.). The axis, of course, remains the same given that the pitches remain symmetrical around the A and E. Bartók saturates the surface of the music by inversional relations. But a glance at the closing measures of the movement is particularly instructive, and reveals Bartók’s penchant for projecting audible relationships. The serpentine melodic motive that permeates

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Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

EXAMPLE 31.23 Pitch Analysis of Bartók’s Music for Strings, Percussion and Celesta CLIMAX

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index: 6

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CLIMAX

the piece is crucial: A–B–C–C–B. This motive is imitated in inversion about the A: A–G–F–F–G. Using PC integers we see the very pairs of pitches that were projected at the tonal level of the piece (see Example 31.24). As the piece closes, contracting—almost collapsing—the two inversional strands meet on the unison A.

EXAMPLE 31.24 Bartók, Music for Strings, Percussion and Celesta, closing passage

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# ww

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EX ERCISE INTER LUDE

WORKBOOK 1 Assignment 31.1

TR A NSPOSITION A ND IN V ERSION OPER ATIONS, UNOR DER ED A ND OR DER ED PITCH A ND PITCH- CL ASS INTERVA LS 31.5 Ordered and Unordered Pitch and Pitch-Class Intervals Given the following pitch dyads, provide the ordered pitch interval, the ordered pitch-class interval, the unordered pitch interval, and the unordered pitch-class interval. Example: (A5, C4) ordered pitch interval  21 ordered pitch-class interval  3

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THE COMPLETE MUSICIAN

unordered pitch interval  21 unordered pitch-class interval  3 1. (E4, G5) 2. (C6, A5) 3. (D2, C3) 4. (F4, B3)

31.6 Identify Inversions Are the following pitch-class sets inversionally related? If so, provide the correct index number. If not, correct the second set so that it is inverted around the first set and provide the index number. Example: (2 6) and (2 e) are not inversionally related. (2 6) and (2 t) are inversionally related. Index number  4. 1. (245) and (20e) 2. (036) and (084) 3. (753) and (78t) 4. (147t) and (3096)

31.7 Transpositionally and Inversionally Related Pitch-Class Sets The following pairs of sets are related by either transposition or inversion. Determine whether each pair is transpositionally or inversionally equivalent. If the sets are transpositionally equivalent, label the interval of transposition, mod 12 (e.g., T4). If the sets are inversionally equivalent, provide the index number. Example: (459) and (219)  inversionally related with an index number of 6 (reverse the second to mirror the first). 1. (013) and (679) 2. (135) and (1e9) 3. (347) and (430) 4. (0246) and (468t)

A S Y S T E M AT IC A PPROAC H Because PC space—with its emphasis on interval classes—will be our mainstay in analysis, we close the chapter with a method for you to consistently determine, label, compare, and compose PC sets. We will also see some of the remarkable properties of sets, properties that composers mine in their compositions. To compare two sets of the same cardinality we must maintain a critical balance between the pitch world (the surface and individual pitches) and the pitch-class world (the generalizable world that includes equivalences). Say we wanted to find out if there are PCs in common between two sets, or if their pitch interval contours are related, or if they are inversions of one another; it would not be helpful to determine the most general yet abstract representation of the sets, because this process compresses PCs into a single, generalizable entity, which represents all pitch sets that we have learned are equivalent (e.g.,

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Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

by transposition, and so forth). This compression does not reveal surface-level events, but does reveal interesting properties in a group of pitches that might be hidden in the surface of the music (such as interesting symmetries).

EXAMPLE 31.25 Webern, Five Movements for String Quartet, op. 5, fourth movement, mm. 1–9 STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

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816

THE COMPLETE MUSICIAN

The procedure actually bears significant resemblance to how we determine relationships in tonal music. We return briefly to two excerpts from Webern’s Five Movements for String Quartet, op. 5, fourth movement, the very piece with which we began the chapter (Example 31.25).

Step 1: Segmentation → Pitch Collection → Pitch-Class Collection A. Segmentation: In the first passage (mm. 4–5), violin 1 forms a discrete unit given that it is a single idea, separated by rests on each side, in a single register. It is clearly a complete melodic unit with pitches that belong together: C–F–D –C–D–C . B. Pitch → PC collection. Once segmented, we invoke octave and enharmonic equivalence: 1. Octave equivalence: delete one of the Cs. 2. Enharmonic equivalence: remove the final C , as it duplicates D . C–F–D –D  remain.

Step 2: Normal Order This step allows you to see the intervallic structure of a set and simplifies the comparison of different sets, because it creates a standard for order and arrangement of intervals. To show normal order, we use curly braces: “{ }.” A. Arrange pitch classes in alphabetical order. B. Find the form that squishes the PCs into their most compact form (smallest “boundary interval” between the first and last PC). You can do this through rotation of the set (like finding root position of a triad in tonal music), as shown below. Example: Given set: C, D , D, F First rotation: D, D, F, C (span of a M7, 11 half steps) Second rotation: D, F, C, D (span of a M7, 11 half steps) Third rotation: F, C, D, D (span of a M6, 9 half steps) Final rotation (back to the original form in this case): C, D, D, F (span of a P4, 5 half steps) Clearly the smallest boundary interval—a perfect fourth—turns out to be the initial version of the set. This pitch-class collection is now in normal order, which easily allows us to compare relations between pitch-class sets. C, D, D, F  {0125}, the normal order of the set. If there are two or more rotations that produce the same sized boundary interval, then you choose the rotation that is most “packed to the left.” For example, if we change the F in the above set to a G (C, D, D, G), we’ll find that two rotations span 7 semitones: the original form, and the rotation beginning with G. In this case, we determine which is more compacted to the left by measuring the distance between the first and next-to-thelast PCs of the rotations: C, D, D, (G) (span of 2) G, C, D, (D) (span of 6) C, D, D, G  {0127}, the normal order of the set

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Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

If these two had been equal, we would have continued measuring with the third-to-thelast PC and so on. If two or more rotations are equal all the way through, we choose the one which begins with the lowest PC integer. Another method is probably easier. Use the keyboard or the clock (see Example 31.26) to derive the shortest distance.

EXAMPLE 31.26 The Clock 0

1 2

shortest span = 5

5

Step 3: Best Normal Order (BNO) Once your set is in normal order, the smallest intervals must appear on the left-hand side of the set (i.e., at the beginning of the ascending normal order). This is called best normal order (BNO). Use the interval classes between each member of the normal order to check:

Using pitch names: Using integers: Interval classes:

D 1

C 0 1

D 2 1

F 5 3

In this example, 1–1–3 indicates that the smallest intervals are indeed at the beginning (to the left) of the set. Thus, the normal order of our set is also the best normal order. This step is important because it allows us to compare other sets with our given set. For example, given F, G, A, and B, with an intervallic pattern 1–1–3, we know that this set’s identical intervallic pattern means that it is the same set, but transposed (at the tritone).

Wrinkles What to do when Step 3 (best normal order) reveals that the smallest intervals are packed to the right, rather than to the left, as happens with the major triad (4–3)? We need to invert the set. For example, if the normal order of a set is C, E, F, F, the intervallic pattern is 4–1–1, with the 1s packed to the right. There are two methods used to invert a pitch set; choose one you like and stick with it.

Method 1: Mod-12 inverse Given is the pitch set in normal order: {0456}. However, the smallest intervals appear on the right-hand side of the set (4–1–1).

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THE COMPLETE MUSICIAN

Determine their mod-12 inverse (i.e., find the number that will sum to 12/0):

Original set: Mod-12 complement produces inversion: Note: Inversion sums to 0: Reverse the inverse’s order:

0456 0876 0000 ← 6780

Now the intervals are most packed to the left after inversion. This is the best normal order.

Best normal order:

6780]

Method 2: This variation of Method 1 might be easier. Write the integers of the normal order version and the mod-12 inverse next to it. Normal order: 0 4 5 6

||

0

Inverse: 8 7

6

Reverse the order of the inverse to get to the best normal order:

Reverse: 0 8 7 6, which becomes:

6

7

8

0

Step 4: Prime Form (PF) and Set Class The prime form of a PC set is best normal order transposed to begin on 0. We show prime form with square brackets: [ ]. Prime form represents all transpositions and inversions of a PC set. It is common to use the term set class as a substitute for prime form. Let’s continue with our set, whose BNO is {6780}. The next step is to determine the prime form by transposing the set to begin on 0 by subtracting the first PC integer from each member of the set:

Best normal order: Transpose to begin set on 0: Prime form:

6780]  6666] [0126]

Enter the Clock: Normal Order Straight to Prime Form The clock might be your favorite method to find normal order (NO) and prime form (PF): It is visually verifiable and often more accurate than calculating transformations using integers and it permits shortcuts. It works for about 98 percent of the 220 pitch-class sets (see Examples 31.27 and 31.28). Move clockwise to determine if the smallest intervals are packed to the left (BNO). If the intervals are packed to the right—as in the case above {0456}—we must invert. To invert on the clock, simply: 1. Find the last PC of the set, moving clockwise. (In this case, it is 6.) 2. Subtract all of the PC integers in the set (0456) from this final PC’s integer (6). Work counterclockwise (6  6, 6  5, etc.). This gives [0126].

Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

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EXAMPLE 31.27 Using the Clock to Determine (B)NO A. Step 1A: Plot the PCs on the clock.

STR EA MING AUDIO

Step 1B: Determine the shortest span (this is normal order) 0

0

4

4 6

B.

W W W.OUP.COM/US/LAITZ

5

6

5

Step 2: Determine if smallest intervals are packed to the left 0

4 6

WORKBOOK 1 Assignment 31.2

5

Here’s another example: If the NO is {478}, you can see by glancing at the interval order, 3–1, that inversion is required to find the BNO and the PF. Thus, we take the final PC integer of the set (8), and reading backwards we subtract all the others from it. The prime form would then be [014]. Of course, you can also use the clock for sets that are already in BNO. Moving clockwise, subtract the first PC integer from all of the PC integers in the set, to transpose it to begin on 0. For example, if the BNO is {347}, the prime form would be [014].

S Y M M E T R IC A L S E T S Composers from all eras unified their compositions in many ways, whether through simple variation or by a complex network of motives. Because the vertical and horizontal domains are inextricably connected, one might argue that twentieth-century composers in particular use a minimal amount of materials in as many ways possible. In this section we will learn about PC sets with special properties.

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EXAMPLE 31.28 Converting to Prime Form 0

6

=

= [0126]

4 6

5

2 0

1

Invariance Most pitch sets can be transposed to each of the 12 possible pitch levels without repeating all of their pitch classes. The same can be said for inversions. The major triad is one such set: it has 12 distinct forms, or stated in another way, it has 12 unique transpositions. However, many sets have fewer than 12 distinct transpositions and 12 inversions. Take the whole-tone set (02468t). It has only one distinct transposition (13579e), and no distinct inversion because any level of inversion will reproduce every PC of one of the even or odd transpositions of the whole-tone set. There are then only two distinct versions (versus 24). Sets that possess this property are inversionally symmetrical. Inversionally symmetrical sets are special because they do not have a distinct inversion in normal order. You can tell if a set is inversionally symmetrical if the intervals are in the same order whether they are read from left to right or right to left. Tonal sets that are symmetrical include the diminished seventh chord (intervallic pattern is 3–3–3) and the augmented triad (4–4). We call the PCs held in common when transposed or inverted (usually both operators are required) invariant. However, when all of the original set’s PCs return, such invariance is very important. Composers take advantage of this special property since it provides a path through the piece—an organic component. Let’s look at the tetrachord [0167], arguably Bartók’s favorite pitch-class set. The set is inversionally symmetrical, with the interval pattern 1–5–1. If we invert the set, giving us (56e0), and transpose it 7 semitones, it will map onto itself. The shorthand of these operations is “I7,” where you invert first, then transpose by 7 half steps. Here are four versions of [0167]. Note that all tritone-related transpositions, as well as the inversions at I1 and I7, hold all PCs invariant.

T0: 0167 T6: 6701

I1: 6701 I7: 0167

For this set, T6 reproduces the same PCs as T0 (the original set), which as we’ve seen are also found in I7. This means that if we, say, transpose all these groups up a semitone (T0→T1, T6→T7, I7→I8), then they will still have the same PC content as each other: 1, 2, 7, 8. We could do this again and again to show that, for this set, every T has some

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Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

form of I that produces the same PCs. Thus, since T6 reproduces T0 and all Ts have an I equivalent, there are only six distinct forms of [0167]: T0, T1, T2, T3, T4, and T5 (and their I equivalents).

Interval Class Vector The intervallic makeup of pitch-class sets is crucial. We know that in an interval class, the pair of intervals that are complements of one another are closely related, enough so to be combined into a single interval class resulting in only six ICs, shown in bold followed by their complements: 1/e 2/t 3/9 4/8 5/7 6/6. There is a way to see at a glance every possible pair of intervals within a set. With this tool, we can learn much about the properties of an individual set (such as symmetries) and about relationships between different sets (that is: sets that do not share the same prime form, but which may have very similar intervallic content). Further, we can compare sets with differing numbers of members (or “different cardinalities”), such as a four-note set and a five-note set. We do this by listing the amount of each interval class that occurs between every possible pair of intervals in the set. Thus, if a set contains four pitches, such as A, B, C, D, we would calculate all of the possible pairs of intervals: A to B, A to C, A to D, B to C, B to D, and C to D: a total of six possible intervals. We list the interval classes in an interval class vector, and distinguish it from other labels using angled brackets: “…”. We use the following steps to determine all pairs of ICs and represent them in the IC vector. 1. Given: the following pitch set (F, B , F, G), with integer numbers (5t67). Because we’re determining every possible interval class, there’s no need to arrange them into ascending order or to put them into prime form (which in this case is [0125]). 2. Calculate the IC (unordered PC interval) between all possible pairs of members of the set. Anything larger than 6 will be converted to its mod-12 inverse (e.g., 10 would be represented as 2; see Example 31.29). 3. Write down digits 1–6 from left to right. These will represent ICs. Under each digit, record the number of occurrences of the IC which that digit represents; e.g., there are two semitones in the set, so write “2” below “1”:

Interval class catalogue: Number of occurrences of each IC in (5t67):

1 2

2 1

3 1

4 1

5 1

6 0

The result, displayed as 211110, represents the number of times each interval class appears. Here, all but IC 6 (the tritone) occur at least once, with IC 1 appearing twice. Let’s try one more using the set (014589) (see Example 31.30). Notice that there are neither IC 2 nor IC 6 in this set. There are three instances of ICs 1, 3, and 5, but what stands out are the IC 4s. Let’s write out the set in pitch notation and examine its contents (Example 31.31). The interval pattern of (014589) is 1–3–1–3–1: an inversionally symmetrical set. If you pair up the intervals you discover an important pattern in the set: It is comprised of a combination of two augmented triads a half-step apart, giving us the hexatonic scale we studied

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THE COMPLETE MUSICIAN

EXAMPLE 31.29 Computing the Interval Vector 2 5

5

t

6

7

6

7

1 4

5

t

3 1

5

t

6

7

EXAMPLE 31.30 Computing the Number of Occurrences of Each IC Using the Set (014589)

0

1 1

0

4 4

1

5 4

3 0

1

5

5 4

4

1

4

8 5(7)

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1

4

5

9 5

8 3

0

9

9 4

8

9 1

IC catalog: Occurrences of ICs in (014589):

1 3

2 0

3 3

4 6

5 3

6 0

Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

823

EXAMPLE 31.31 The Set (014589) in Pitch Notation

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in Chapter 30. This feature explains a lot. A single augmented triad contains two major thirds and an augmented fifth (all of which are IC 4); therefore two augmented triads a semitone apart have four major thirds and two augmented fifths, explaining the 6 in IC 4: 303630. Further, if one transposes the set by four semitones, it becomes (458901), revealing that all of the PCs return. In addition to representing a set’s total intervallic content, the IC vector predicts how many common tones will be held invariant under transposition. This is important, because common tones provide connective tissue between harmonies, both in nontonal and tonal music. Conversely, the IC vector also shows variance, the number of PCs that are not held in common when transposing a set by that number. Let’s see how the IC vector does all this. We begin with a logical statement: If a set contains a semitone such that a “1” appears in the first position of the vector, then it makes sense that by transposing that set one semitone, there would be at least one note held in common. The set [013] contains one semitone, so transposing it up a semitone (or 11 semitones) will retain one of the original PCs, C: C, C, E → C, D, E. If we apply this concept to the vector from the set [014589], 303630, we can anticipate that transposing the set by two semitones (or 10 semitones) will hold zero tones invariant (because a zero appears in the IC 2 spot). Let’s see:

014589 T2: 222222 2367te There are no common tones between the original set and its transposition up a major second. On the other hand, the “6” in the “4” column indicates that all six of the original pitch classes will be held invariant at T4 or T8. Let’s see:

T4:

014589 444444 458901

T8:

014589 888888 890145

Every one of the pitch classes returns at T4 and T8.

Checking Your Work You don’t want to overlook any of the pairs of intervals in creating an IC vector. You can make sure that you don’t by using the formula: (n2  n)  2, where n is the number of members (elements) of the set (3-note set, 4-note set, etc.). That is: square the number

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THE COMPLETE MUSICIAN

of elements (the cardinality of the set, the number of wine glasses at a party, etc.) then subtract the number of elements and divide the result by 2. Our present set (014589) contains 6 members: 6  6  36; 36  6  30; 30  2  15. You should have a total of 15 intervals in your IC vector for the 6 PC set (014589). And we do: 303630.

A Curiosity in the PC World You might think that sets with the same intervallic content (i.e., same IC vector) will be in the same set class, and will necessarily have the same prime forms. However, and strangely, this is not always the case. Take the tetrachord [0146], a very special tetrachord because it has the IC vector 111111. A tetrachord has six possible intervals, and in this specific case, it has one of each. It is so special that it is called the all-interval tetrachord. There is only one other tetrachord that also has the same IC vector, and it doesn't have same prime form: its prime form is [0137]. These two tetrachords cannot in any way be mapped onto one another through any transposition or inversion. They are distinct, different tetrachords, but they both have the same intervallic content. These freaks of nature are called Z-related sets. There are actually quite a few of them: 23 pairs (46 set classes, roughly 20 percent of all 220 possible set classes), most of which are found in the hexachords.

EX ERCISE INTER LUDE IN V ERSION, NOR M A L OR DER, PR IME FOR M 31.8 Practice Inverting Sets Invert the following pitch-class sets around the given index number. Example: Invert (235) at I4 (where 4 is the index number)  (21e) 1. (025) at I6 2. (126) at I9 3. (014) at I0 4. (0135) at I5 5. (0236) at It 6. (036) at I4 7. (048) at I8 8. (0134) at I1

31.9 Normal Order Put the following sets in best normal order. Place your answer in curly brackets: { }. Example: (14e) in best normal order  {e14} 1. (2348) 2. (612) 3. (375) 4. (0167)

Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

825

5. (et8) 6. (e129) 7. (1t4) 8. (t109)

32.10 Normal Order and Prime Form The following sets are unordered. First, put each set in best normal order. Then, give the prime form for each set. Example: (165) in best normal order  {67e}, prime form  [015] 1. (2345) 2. (246) 3. (3476) 4. (47t) 5. (et43) 6. (014) 7. (147t) 8. (234)

T ER MS A N D CONCEP TS • all-interval tetrachord • enharmonic equivalence • equivalence class • inversional equivalence • octave equivalence • order equivalence • temporal equivalence • transpositional equivalence • interval class (IC) • interval class vector • invariant/invariance • inversion • mapped; mapping • mod-12 arithmetic • mod-12 inverses • pitch-class set • pitch-class space • pitch interval • pitch set • pitch space

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THE COMPLETE MUSICIAN

• set class • sum/index number • transposition • trichord • Z-related sets

CH A PTER R EV IEW 1. In contrast to the infinite number of pitches in pitch space, the number of unique pitch classes is only _______.

2. In mod-12 arithmetic, we [add/subtract] 12 from a compound interval to make it simple, and we [add/subtract] 12 from a negative interval to make it positive.

3. True or False: Ordered pitch intervals may be positive or negative, but ordered pitch-class intervals may only be positive.

4. Unordered intervals represent distance only, not direction, nor order, so we use only [negative/positive] integers.

5. True or False: The goal of unordered pitch-class intervals is to find the smallest interval between two pitch classes.

6. Ordered relationships are usually associated with: a. melody

b. harmony

7. In contrast, unordered relationships are usually associated with: a. melody

b. harmony

Chapter 31 Noncentric Music: Atonal Concepts and Analytical Methodology

827

8. True or False: When comparing two sets with the same intervallic content but in reverse order, always transpose first, then invert.

9. True or False: The sum or index number reveals the transpositional level needed to map two inversionally related sets onto one another.

10. True or False: The “best normal order” is the version of a pitch set with the largest boundary interval and with the smallest intervals appearing on the right-hand side.

11. True or False: The prime form of a set is the “best normal order” transposed to begin on 0.

12. True or False: To invert a pitch set, find the mod-12 inverse and reverse the order of the integers.

13. True or False: Inversionally symmetrical sets are special because they have a distinct inversion in normal order.

14. PCs held in common when transposed or inverted are called ____________________.

15. How many unique interval classes are there?

16. True or False: The interval class vector predicts how many common tones will be held invariant under inversion.

17. True or False: Z-related sets have the same interval class content, but cannot be mapped onto one another using transposition or inversion.

C H A P T E R 32

New Rhythmic and Metric Possibilities, Ordered PC Relations, and Twelve-Tone Techniques OV E RV I E W

This chapter presents two large topics. The first explores developments in meter and rhythm, focusing on techniques composers use to invigorate and obscure their regularity. Motivated by numerous aesthetic impulses, including the influences of Eastern European folk music and nonWestern music, composers incorporate a vast array of novel techniques to shape their pieces. The second topic focuses on ordered pitch relations within the chromatic or “twelve-tone” world. We will study some of the earliest examples of this technique (1923) through works that might be considered to represent its full flowering in the 1950s. Through various transformations, we will see how composers structure their pieces and control the unfolding of the aggregate, balancing artistry with strict control of the pitch world. CHAPTER OUTLINE Meter and Rhythm ..................................................................................................... 829 Assymetrical Meters .............................................................................................. 830 Added Rhythmic Values ....................................................................................... 832 Nonretrogradable Rhythm ................................................................................... 833 Changing Meters ................................................................................................... 833 Accelerating or Decelerating Tempo: Metric Modulation .............................. 836 (continued)

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Chapter 32 New Directions in Temporality and Pitch

829

Twelve-Tone Music ..................................................................................................... 838 Row as Melody and Harmony ............................................................................ 839 Analyzing Twelve-Tone Music: Schoenberg’s “Walzer,” op. 23, no. 5........... 840 A Cursory Glance at the Rest of the Piece ......................................................... 846 Transforming the Row: Twelve-Tone Operators (TTOs) ................................. 846 Definitions and Properties of TTOs .................................................................. 847 Labeling Row Forms ............................................................................................. 847 Application of Twelve-Tone Rows .......................................................................... 848 Berg, Lyric Suite .......................................................................................................... 852 Contour .................................................................................................................. 852 Ordered PC Intervals ............................................................................................ 853 Unordered P Intervals ........................................................................................... 854 Multiple Row Forms .................................................................................................. 855 The Twelve-Tone Matrix............................................................................................ 856 Shortcuts ................................................................................................................. 859 Simultaneous Row Forms: Combinatoriality ..................................................... 860 Schoenberg’s Signature Procedure: Inversional Combinatoriality ............... 862 Emergence of P9 and I2 ......................................................................................... 864 The Violin Concerto’s Surface.............................................................................. 866 Generalizing Inversional Combinatoriality ....................................................... 866 Variance Versus Invariance ....................................................................................... 867 Invariance and Symmetry..................................................................................... 868 Generalizing Inversional Combinatoriality and Inversional Invariance........ 870 Summary ....................................................................................................................... 872 Terms and Concepts ................................................................................................... 873 Chapter Review ........................................................................................................... 873

METER AND RHY THM Through much of Western classical music history, composers followed relatively fixed rules in using meter and rhythm in their works. For example, a common-practice piece written in 98 is usually grouped into three evenly spaced beats, and the meter can be easily be perceived as notated. Of course, alternative interpretations are possible; in this case, the meter might be interpreted to be #4 with triplets. Our analysis will depend upon musical factors of motives, groupings, texture, and so on. Despite these formal rules, we have already encountered various types of rhythmic and metric irregularities and asymmetries in our tonal studies. These include syncopation and hemiola, which impact the listener’s expectations, and asymmetries in larger units, such as the phrase. For example, phrases that form periods of odd-numbered measures are common in the music of Haydn.

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THE COMPLETE MUSICIAN

However, it became much more common in the twentieth and twenty-first centuries for composers to avoid such regularity, or at least obscure it. Indeed, one encounters distinct and exciting metric and rhythmic techniques throughout the music of this period. We will explore some of the more common techniques, which you will certainly hear as you listen to and perform these works.

Asymmetrical Meters The steady pulse, recurring patterns of strong and weak beats, and general regularity of common-practice music are often displaced, if only temporarily, by irregularity. Some techniques are simple, such as syncopations, or, slightly more complex, including hemiola, but in general, the number of beats in contiguous measures remains constant, and usually are grouped either in twos or threes or their compounds (such as $4, ^8, ~8, etc.) or there is an asymmetry within a given measure. This is not the case with twentieth-century music, much of which unfolds in units that combine twos and threes, such as %8, &8, and ! 8!. We call such meters asymmetrical meters. A good way to describe asymmetrical meters is that they feature measures with one too many or one too few beats or portions of beats. For example, %8 can be heard as $8 plus one eighth note or ^8 minus one eighth note. The best way to internalize these meters is to feel their effect, one of lilting, which weakens the tyranny of the barline. However, the human mind inevitably groups pulses into larger recurring units. For example, in &8 a conductor or performer would not feel seven pulses, but rather would group the events into twos and threes in one of several ways, depending on the specific piece: 3  2  2, or 2  3  2, or 2  2  3. Try conducting these units of threes and twos while strictly maintaining the eighth-note divisions by counting “one-two-three, one-two, one-two . . .” and notice the change in speed of your conducting hand.

Bartók, “Dances in Bulgarian Rhythm” from Mikrokosmos, nos. 5 and 6

EXAMPLE 32.1

A.

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. # œœ

# œœ.

‰

œœ.

. # œœ

# œœ.

‰

. # œœ

# œœ.

‰

Bartók, Bulgarian Dance no. 6 q._q._q = 56

œ^ ™ & 3+3+2 8 # œœ ™™

{

œœ.

f

? 3+3+2 œ 8

^ œœ #œ

œœ^ ™™ œ™ œ œ

œ

œ œ

œ

œœ^ ™™ œ™ œ

œ

Œ œ œ

œ

b simile œœ ™™ œ™

‰ Œ œ œ

œ

œ

œ

œ œ

œ™ n œœ ™™ œ

œ œ

œ

œ

œ

Œ œ œ

œ

‰ Œ œ œ

œ

œ

831

Chapter 32 New Directions in Temporality and Pitch

Further, the upper number of the meter signature need not be five or seven, but could be an integer that is more common, such as 8 (e.g., *8) or 9 (e.g., 98). Béla Bartók in his fifth “Dance in Bulgarian Rhythm” from Mikrokosmos (Example 32.1A) does just this: the measures contain nine eighth notes, but rather than grouping them into three beats of three eighth notes each, he instead groups them asymmetrically as 2  2  2  3. Again, the 3 at the end provides the lilt, or hiccup. And notice that Bartók provides the player with precise rhythmic groupings. See also his sixth “Dance in Bulgarian Rhythm” (Example 32.1B), cast in *8 but grouped asymmetrically as 3  3  2 rather than the more common—and symmetrical—4  4. Another way that composers obscure the regularity of traditionally notated meters (such as $4) is to add accents at irregular intervals. This conflict between the underlying meter and the surface rhythm runs throughout twentieth- and twenty-first-century music. A well-known example by Stravinsky is particularly intriguing. His “Dances of the Adolescents,” from the monumental Rite of Spring (Example 32.2), is cast in a relentless @4. However, the unpatterned accents above the repeated eighth notes obscure the meter. They are attenuated by the similarly abrupt appearances of the E7 chords above the F major chords, which create groupings of 9, 2, 6, 3, 4, and 5. Try clapping the rhythm with the appropriate accents added. You might consider this to be a syncopation that greatly disrupts the meter.

Stravinsky, “Augurs of Spring,” Rehearsal 13, mm. 1–8

EXAMPLE 32.2

13 ° & Hn. in F

¢

?

Tempo guisto h = 50

2 4

I. II. III. IV

∑

VIII 2 V. VI. VII. ∑ 4

∑

‰ bb œœœ ‰ œ.

œœœœ .

∑

∑

‰ b b œœ ‰ œœ b b œœ œœ . .

∑

sf sempre

sf sempre

j ‰ bb œœœ Œ œ. j ‰ b b œœ Œ b b œœ .

j bb œœœœ ‰ Œ . j bb b œœœ ‰ Œ b œ.

j bb œœœœ ‰ Œ . j bb b œœœ ‰ Œ b œ.

j ‰ bb œœœ Œ œ. j ‰ b b œœ Œ b b œœ .

° b b 2 ≥ ≥ ≥ ≥ ≥ ≥ ≥ ≥ sempre simile & b 4 b œœ œœ œœ œœ b œœ œœ œœ œœ b œœ œœ œœ œœ b œœ œœ œœ œœ b œœ œœ œœ œœ b œœ œœ œœ œœ b œœ œœ œœ œœ b œœ œœ œœ œœ . . . . . . . . > > > > > > f sempre stacc. arco (non div.)

Vln. II

≥≥≥ B b b b 42 œœ œœ œœ . . .

≥ ≥≥≥≥ œœ œœ œœ œœ œœ . . . . .

œœ œœ œœ œœ >

œ œ œ œ >œ œ œ œ

œ œ œ œ >œ œ œ œ

≥≥ tutti ? b b 42 b œ œ b œ. œ.

≥ ≥ ≥ ≥ ≥ sempre simile œ bœ œ œ œ bœ œ œ œ bœ œ œ œ bœ œ œ œ œ. œ. œ. œ. œ. œ >œ œ >œ œ œ œ œ œ >œ œ œ sempre stacc.

bœ œ œ œ >œ œ œ œ

bœ œ œ œ bœ œ œ œ >œ œ œ œ œ >œ œ œ

(non div.)

tutti

Vla.

f

≥ œ œ.

sempre stacc.

sempre simile

œœ œœ œœ œœ > >

œœ œœ œœ œœ

œœ œœ œœ œœ >

arco (non div.)

Vc.

f

≥ ≥ ≥ ≥ ≥. ≥. ≥. ≥. sempre>simile> > > > > tutti . . . . ? b b 42 bb œœ œœ œœ œœ bb œœ œœ œœ œœ bb œœ œœ œœ œœ bb œœ œœ œœ œœ bb œœ œœ œœ œœ bb œœ œœ œœ œœ bb œœ œœ œœ œœ bb œœ œœ œœ œœ ¢ b arco (non div.)

Cb.

f

sempre stacc.

832

THE COMPLETE MUSICIAN

Added Rhythmic Values In addition to composer’s manipulation of meter and rhythm, they often incorporate a rhythmic irregularity that impacts the meter of a piece. This simple technique everso-slightly distorts the regularity of metrical patterns within a measure. It results in a free-flowing disturbance of the regular metrical pattern. This is accomplished simply by slightly increasing the length of one beat or a portion of a beat with a dot or tie or even by adding an additional pitch. This technique is referred to as additive rhythm (sometimes called “added value”). For example, a meter of @4, with regular eighth notes as the main rhythmic pattern, can be overturned by adding a dot to any one of the eighth notes. This technique is used by Olivier Messiaen in many of his pieces, including his Vingt Regards sure l’Enfant Jesus (“Twenty Reflections on the Infant Jesus”). To be sure, meter signatures are necessarily absent in this music. The “Regard de la Vierge” (Example 32.3) begins with a measure of #8 (^6), but with the addition of a sixteenth note in the second measure Messiaen creates a measure of &6. The next two measures repeat the pattern from mm. 1–2, but m. 5 has 17 sixteenth notes (! 6&)!

Messiaen, “Regard de la Vierge” from Vingt Regards sur l’Enfant Jesus

EXAMPLE 32.3

n# œœ # œ ##>œœ # œ n# œ>œ # œ ##>œœ # œ n# œœ # œ ##>œœ # œ n# œ>œ # œ ##>œœ # œ n# œœ # œ ## œœ # œ n# œœ # œ ## œœ # œ œœ œ ## œœ n# œœ ™™ œ œ œ œ œ #œ #œ œ #œ #œ #œ #œ & #œ Bien modéré (e = 72)

{

ppp pp

pp tendre et naïf

& # œ # œ #n œœ # œ #œ > ° ° *

#>œ # œ #n œœ # œ #œ > ° ° *

# œ # œ #n œœ # œ #œ

#>œ # œ #n œœ # œ #œ >

# œ # œ #n œœ # œ # œ œ #n œœ œ œœ œ #n œœ ™™ #œ œ # œ-

In Messiaen’s “Dance of Fury, for the Seven Trumpets” (Example 32.4) from Quartet for the End of Time, the $4 measures are distorted by adding a single sixteenth note (C ); the result renders the measure quite lopsided. Clap the measure without the C, then add the sixteenth note and experience the disappearance of meter. Do the same for m. 2, clapping the B first as a sixteenth note, then as an eighth which adds an additional sixteenth to the measure.

EXAMPLE 32.4

& #œ

{

? #œ

œ bœ b-œ œ

Messiaen, “Dance of Fury, for the Seven Trumpets” from Quartet for the End of Time

œ bœ #œ

œ

œ bœ #œ

œ

œ œ

œ #œ nœ bœ nœ bœ #˙ #œ nœ bœ nœ bœ œ #˙

833

Chapter 32 New Directions in Temporality and Pitch

Nonretrogradable Rhythm We have seen various types of palindromes, whether written in the eighteenth century (such as Haydn’s Minuet Rovescio [Appendix 2, Example 2.11], which if played backward is identical to its normal version), or in twentieth-century music (such as the PC sets that have no distinct inversion [e.g., (01478) with the intervallic structure 1  3  3  1]. There are also rhythmic palindromes. A simple case in #4 would be quarter-eighth-eighthquarter: played forward or backward it is identical. Again, it was Messiaen who utilized such nonretrogradable rhythms in his music. Returning to “The Dance of Fury,” we see this technique in effect, whereby the rhythmic pattern in m. 27 and in m. 28 are palindromes.

EXAMPLE 32.5

t 27 Au mouv

™ & œJ

Piano

{

Messiaen, “Dance of Fury . . .” from Quartet for the End of Time (mm. 27–28)

œ

r #˙ œ

#œ

œ # œj™ R

#œ

#œ ™ J

#œ

Ϫ J

nœ ™ J

#œ

œ

œ R

#˙

#œ

œ #œ ™ R J

#œ

#œ ™ J

#œ

Ϫ J

nœ ™ J

#œ

(legato)

Ϫ ? J

Changing Meters Composers often change meters, marking them with new time signatures. Bartók’s “Change of Time” (Example 32.6) is a good example of changing meters: It opens with 19 “changes” after the initial bar! However, a closer look reveals that the metrical pattern that occupies mm. 1–4, @4, #4, #8, %8, recurs every four measures, essentially creating an asymmetrical meter of ! 8* at the four-measure level: (22)  (222)  3  5. (The eighth note receives the beat given Bartók’s metronome marking of 250 for that value.) Polyrhythm refers to the simultaneous statement of two or more different beat divisions. You can think of polyrhythm as two rhythms that are not multiples of each other. The most common types are those that divide the beat into two and three parts, a juxtaposition

EXAMPLE 32.6

Bartók, “Change of Time” from Mikrokosmos, Book 5, no. 126

Allegro pesante e = 250

2 & b 4 œœ

œœ

? b 2 œœ 4

# œœ

{

f

3 4 œœ 3œ 4œ

œœ n œœ

3 œœ œœ œœ 8 œœ œœ œœ œœ 83 œœ

j œœ j œœ

5œ 8œ 5 œœ 8

œœ œœ

‰ 42 œ œ sf j 2 œ 4 œœ

œœ œœ

3 4 œœ 3œ 4œ

3 œœ œœ œœ œœ 8 œœ œœ œ œœ 83

834

THE COMPLETE MUSICIAN

(continued)

EXAMPLE 32.6 7

3 & b 8 œœ ? 3 œœ b8

j œœ j œ

{

14

3 & b 4 œœ ? b 3 œœ 4

5œ 8œ 5œ 8œ

œœ

b œœ

2 j 4œ œ

œœ

sf

œ œ

3 œœ œ œ œ 8 œœ œ œ œ œœ œœ œ œœ 83 œœ

{

‰ 42 œœ p

j œœ j œ

5œ 8œ 5œ 8œ

3 4 œœ 3œ 4œ œœ œœ

œ œ œœ

3 œ œ œ 8 œœ œ œ œ œœ œœ œœ 83 œœ

‰ 42 œœ # œœœ œ sf œ 2 j 4 œ #œ œ

3 4 #n œœœ 3 #n œœ 4

j œ œ j œœ

5œ 8œ 5 œœ 8

œ œ œœ

‰ 42 œ œ œ bœ j 2 œ œ œ 4œ œ

3 œ œ # œœ n œœœ ## œœœ œœœ 8 # œœœ n œœJ œ # œœ n œœ # œœ œœ 3 # œœ n œœJ 8

5 # œœœ 8 œ 5 # œœ 8

œœœ œœœ

3 4 3 4 ‰ j nœ

of simple and compound meter (the simplest form is “two against three”). Three against four and four against five are other common polyrhythms. While the combination of parts creates a mass of sound, one can differentiate the rhythmic lines to hear the recurring beat division. Scriabin’s Prelude in G major (Example 32.7) creates such an effect, with the beat divided into 2’s, 3’s, and 4’s. First, Scriabin places 2 against 3 on beats 1 and 2, and then 3 against 4 on beat 3.

EXAMPLE 32.7

Scriabin, Prelude in G major, op. 11

Vivo M.M. q = 184-192-200

#3 & 4œ œ œ œ œ œ œ œ œ œ p œ œ œ œ ?#3 œ œ 4 œ

{

2:3

œœ œ œ œ - œ œ œ œ ∑

3:4

Polymeter refers to music cast in two or more different meters. Just as polyrhythm pits beat divisions against one another, polymeter pits meters against one another. Polymeter behaves like regular meters: there must be recurring patterns of accented and nonaccented beats. Polymeter can take many forms, including: 1. Overt. Two or more different meters are used from the outset of the piece, often as meter signatures. Example 32.8A presents a simple pairing of ^8 and #4, where the meter aligns after every six eighth notes. This might be considered a simple and very common case of polymeter, given that the underlying two pulses can emerge aurally quite easily. Example 32.8B, on the other hand, combines #4 and $4, with the meter quite obscured (the misaligned bar lines indicate the conflicting meters). Only after 12 beats do the meters align (four measures of 3 and three measures of 4), but these are distant enough from one another to make them very difficult to detect.

835

Chapter 32 New Directions in Temporality and Pitch

Examples of Polymeter

EXAMPLE 32.8

A. 6 œ 8

œ

3 4 œ

œ

œ

œ

œ

œ

œ

œ

Alignment after 12 beats (3 mm. of 4 or 4 mm. of 3)

B. Polymeter 3 œ ì˙ 4 ˙

4 ˙ 4

œ ì˙

œ œ ì˙

œ ì˙

œ œ ì˙

Ä œ ì˙ œ œ ì˙

2. Covert. A single meter appears in the signature, but musical material between voices are grouped in such ways that they create independent meters. Such lines result in layers of sound often called metric strata. Example 32.9, from Stravinsky’s Petrouchka, illustrates this technique.

EXAMPLE 32.9 Stravinsky, “The Masqueraders,” from Petrouchka q._q = 72 +“” œ ° bb 5 ‰ & b8 f 3 “” /04 b 5 œœ œ œœ œœ & b b 8 œœ œ œ œ f 2 8 /0 œ œœœ b 5 œœ œ & b b 8 œœ f

3 4 /0 b 5œ & b b8 œ

œœ

œ

œ

œ

œ J

œ

œ

œ

œ

œ œœ œœ œœ œœ œœ œ œ œ œœ

œœ œœ œ œœ œœ œœ œ œœ œœ œœ œ œ œœ œ œ œœ œ œ

œœ œœ œœ œœ œœ œœ œœ œœ œœ œœ œ œ œ œ œ œ œ

œœœœœ

œœœ œ

œœœœœ

œœœ œ

œœœœœ

œœœ œ

œœœœœ

œœœ œ

œœœœœ

œœœ œ

œœœœœ

œœœ œ

œœœœœ

œœ

œœ

œœ

œœ

œœ

œœ

œœ

œœ

œœ

œœ

œœ

œœ

œœ

f

4 /160 œ œ œ œ œ œ œ œ œ œ bb 5 œ œ œ œ œ œ œ b ¢& 8 œ œ œ f

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

836

THE COMPLETE MUSICIAN

Stravinsky has cast all of the voices in this passage in %8, however, a look at the strata reveals four different meters. Note the added groupings based on pattern repetition, nearly all of which overlap measures. On the other hand, be aware that the presence of two different meter signatures does not necessarily indicate polymeter; it may merely be a notational convenience to reveal a polyrhythm, as shown in Example 32.10. The #4 and 98 meters show the left hand divides the beat into twos while the right hand, in 98, divides it into threes (i.e., two against three). A triplet notation in the right hand would suffice.

EXAMPLE 32.10 Scriabin, Prelude in F minor, op. 17, no. 5 Prestissimo M.M. q. = 100 - 104

Piano

“” œ œ bbb 9 nœ œ œ œ œ œ œ œ œ b & 8 œ œ nœ œ œ œ œ f œ œ œ nœ b œ ? b b b 43 œœ ‰ œ œ nœ b œ b J œ 3 œ

{

“” œ œ œ œœ

œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ

Œ

Œ

Accelerating or Decelerating Tempo: Metric Modulation It is possible to change tempo without using the common-practice method of the imprecise and only relative terms such as “accelerando” or “decelerando.” This is done in one of two ways: maintain the beat and introduce new divisions of the beat; or maintain the division of the beat and introduce a new beat level. When these two techniques are combined it is possible to specify precise tempo changes. This process of tempo change is called metric modulation or tempo modulation. It is a common feature in twentieth- and twenty-firstcentury music, but is most often applied to the music of American composer Elliott Carter. Basic principles: 1. When the tempo of the division of the beat remains unchanged (for example, in #4 the beat divisions are two eighth notes and in ^8 the beat divisions are three eighth notes), then the beat itself would be enlarged (from two eighths in #4 to three eights in ^8, and thus slower) and vice versa when moving from ^8 to #4 (see Example 32.11). Feel how the beat in #4 slows when entering the ^8 measure, then reverse it, moving from ^8 to #4. 2. When the tempo of the beat remains unchanged, the speed of the divisions change, but there is no change of overall tempo. Perform Example 32.12, making sure the speed of the beat is constant between #4 and ^8. Feel how the divisions change while the tempo remains the same. Thus the divisions conform (speed up or slow down) depending upon the beat unit.

837

Chapter 32 New Directions in Temporality and Pitch

Beat Division is Constant

EXAMPLE 32.11

e=e

 œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ 

œ

œ

œ

œ

œ

1 + 2

+

3

+

1

+

2

+

3

+

1 (1

+ +

+ 2

2 +

+ 3

+ +)

EXAMPLE 32.12

 œ 1

Beat Is Constant q = q.

œ œ œ œ

œ œ œ œ œ œ  œ œ œ œ œ œ

œ œ œ œ œ œ

2

1

1

3

2

3

1

2

2

One way of showing these transformations is to provide both a metronome marking and the rhythmic value assigned to it. When the division (note value) of the beat changes as in Example 32.13, the eighth notes move at 60 beats per minute. At the time change, the sixteenth notes become the same tempo as the preceding eighths: the tempo of the beat (the quarter note) is 50 percent slower.

EXAMPLE 32.13

Division of the Beat Changes

q = 60

3 4œ

e = x (q = 30)

œ

œ

œ

œ

œ

2 4œ œ œ œ œ œ œ œ

In Example 32.14 the change from #4 to ^8 maintains the same tempo for the eighth note. This is clarified by both the metronome marking of the beat as well as the equivalence between the eighth-note speed in both meters.

EXAMPLE 32.14 The Tempo of the Eighth Note Remains the Same q = 90

3 4œ

e = e (q. = 60)

œ

œ

œ

œ

œ

6œ 8

œ

œ

œ

œ

œ

838

THE COMPLETE MUSICIAN

Example 32.15 indicates the tempo of the division itself through the rhythm values. The vertical stacking of the rhythm markings over the measure where the time signature changes to ^8 is a particularly precise way to determine the speed of the beat and the division.

The Tempo of the Division Itself

EXAMPLE 32.15

e = 240 e = e (q. = 80)

q = 120

2 4œ

œ

œ

WORKBOOK 1 Assignments 32.1–32.2

œ

œ

œ

œ

6œ 8

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

œ

Usually there is some sort of transition, or pivot (hence the name “metric modulation”) that permits a tempo change. Example 32.16 demonstrates a dramatic increase of tempo. This is accomplished by the rhythm value of quarter note  60 given at the beginning of the example. In m. 2, the beat remains the same, but shifts from two to three divisions. The next stage equates the eighth-note division with the quarter note in the 4# measure. Therefore, the quarter note at the beginning (MM. 60) is, by m. 3, three times faster (MM. 180). The second measure, then, is the “pivot” measure that smoothly transitions from the slow quarter note in m. 1 to the much faster quarter note in m. 3. The actual beat has been transferred from the quarter note to the full measure, which would be conducted in “1.”

EXAMPLE 32.16

q = 60

œ

Pivot in Metric Modulation

q = q.

e = q (mm. 180)

4 œ œ œ œ œ œ œ œ 12 œ œ œ œ œ œ œ œ œ œ œ œ 3 œ 4 8 4

œ

œ œ

œ

œ

œ

T W E LV E -T ON E M U S IC The music that we studied in Chapter 31 is often called “free atonality.” It is characterized by the use of pitch-class motives that composers use to create both melodies and harmonies. We have learned that pitch-class sets—often as small as three and four PCs— function as motives and appear in varied contexts throughout a piece. These motivic cells often are components of larger sets that may support the pitch-class structure of an entire work. We developed tools that allow us to explore properties of individual pitch and pitchclass sets and how to determine relationships between them.

Chapter 32 New Directions in Temporality and Pitch

839

This intervallic-motivic music roughly spanned the decade between 1908 and 1918. By the end of World War I, composers like Arnold Schoenberg and his students Anton Webern and Alban Berg began to focus on ordering PCs, often as few as five or six. By 1920, the complete aggregate was ordered to ensure a consistent presence and balanced circulation of all 12 pitch classes: that is, no pitch may be repeated in one voice until the other 11 had also sounded. The result of this approach provided remarkable compositional possibilities, not the least of which were the increased length of pieces and the creation of an organic, unified structure, a practice that continues to this day. Given the focus on the aggregate and its ordering, such music is called twelve-tone music or serial music. The source material, the specific ordering of the 12 PCs, is often called the row or the twelve-tone row. Schoenberg himself called the row a “basic idea” or Grundgestalt. Once the PCs of a row are deployed in a piece in P space—that is, as contours and grouped as gestures—they could be viewed as motivic: Every melodic figure and harmonic gesture emerges from the ordering of the row and provides a sort of motive or “theme and variations,” although the presentation of the row is not nearly as overt as found in these tonal procedures. Given the 12 pitch classes of the chromatic scale, there are a possible 479,001,600 tone rows: 12! (that is, 12 factorial, or 12 × 11 × 10 × 9 . . .). However, this number comes from all possible ordering of the 12 PCs. (If order were not taken into consideration, using all 12 PCs would only create a single row!) Further, transformations including inversion and transposition of ordered aggregates reduce the number of possible rows to 9,979,200. That said, only a small fraction of these rows are commonly used, perhaps as few as 100. Note the following: 1. Recall that we used the parentheses to show unordered collections, for example (392) and we used square brackets for prime forms, for example [0135]. 2. Since twelve-tone music is ordered, we will label each pitch of a row with an order number (note: this is not a PC integer), from 1 to 12. When we refer to a PC group such as (451), if the PCs are in order, we use angled brackets: 451. (Note that some analysts prefer assigning order numbers 0–11, the same system used for pitch classes.)

Row as Melody and Harmony One might think that, since the 12 PCs are ordered, twelve-tone music is purely melodic. This is not the case. In fact, ordered series of 12 pitch classes can be deployed as verticalities, ranging in size from a single dyad to the aggregate. The use of two, three, or more simultaneously sounding pitches becomes a powerful way of projecting harmony. (Ultimately, this music was never purely melodic, but rather harmonically conceived, and ordering the aggregate was a way of regulating advanced harmony. Schoenberg’s insight was to recognize that such harmony could be understood as the combination of different configurations of the aggregate.) For example, given an unimaginative twelve-tone row—a chromatic ascending scale beginning with C—it can be realized in varied registers and textures: sometimes melodically in one voice and register; other times as an interval such as the E and D in Example 32.17; or as a harmony, such as the trichord 456 in Example 32.17. The trichord is followed by a return to a single pitch, G, in the soprano, and the final four pitches fall in register.

840

THE COMPLETE MUSICIAN

One Setting of a Twelve-Tone Row

EXAMPLE 32.17

& nw

{

nw

nw nw

nw bw

#w

#w

nw bw

bw

?

nw

As you can see, the unfolding of the row occupies both the horizontal (melodic) and the vertical (harmonic) domains of the piece, a feature that Schoenberg called the “unity of musical space.” This crucial idea means that melody and harmony are drawn from the same source but used in varied ways. Indeed, a composer can design a row that has special properties. For example, Alban Berg’s row for his Violin Concerto (Example 32.18A) is conceived as a series of mostly rising thirds, which together form interlocking minor and major triads by rising fifths from G to B (Example 32.18B).

Berg, Violin Concerto

EXAMPLE 32.18 A. Row

&

w

bw

w

nw

nw

#w

nw

nw

#w

#w

bw

nw

B. Embedded triads in the row

& n˙

{

? n˙

b˙

n˙ n˙ n˙

#˙

n˙ n˙

n˙

n˙ n˙ n˙

#˙

n˙

#˙

#˙

n˙

˙

Analyzing Twelve-Tone Music: Schoenberg’s “Walzer,” op. 23, no. 5 So far, we’ve only looked at a given row, but we’ve not really seen how a row is used in a musical work. More importantly, we haven’t discussed how to identify the row and how the tones are arranged. Composers don’t always present the row in a neat and unambiguous way at the beginning of a piece. We will now get our hands dirty by looking at the

841

Chapter 32 New Directions in Temporality and Pitch

opening of one of Schoenberg’s earliest completely serial pieces: Five Piano Pieces, op. 23, no. 5: "Walzer" (1923; for the complete score, see the Anthology no. 65). Listen to Example 32.19.

EXAMPLE 32.19 Schoenberg, “Walzer” from Fünf Klavierstücke, no. 5 (1923) STR EA MING AUDIO W W W.OUP.COM/US/LAITZ

1

&

{

?

q. = 72

3 8

2

# œ.

.r bbn œœœ ™ & ‰

bœ b n œœj™ ≈ b œ ™ nœ . . pp bœ

&

{

nœ ™

nœ ≈ n b œœ

‰ n œ.

mf

? ‰™

‰

nœ . B

nœ

n# œœ

r ≈ #n œœ.

?

C

11

bœ œ> pp

b œ.

œ ™ ^. n œ nœ

12

pp

nœ ™

bœ

nœ ™

‰

p

sfp

& b b œœ

œœ

n œ.

13

bœ

n œ. p

nœ

nn œœ

œ nœ

bœ ™

‰

n œ.

9

nœ

&

‰

r n œ. ≈ b œ sf

bœ

b œ n œ.

f

f

bœ

nœ

‰™ j œ œœ J

?

nœ

‰™

sf

nœ

n œ. J

8

b œ b œ ≈ nœ

4

> ≈ n œr œ n œ b œœ

&

sf

p

nœ ™

r #œ v

bœ ™

7

p

& nœ ™

10

6

≈

n œ.

p

5

{

nœ

nœ ™

A

# œ-

3

‰™

nœ

pp

nœ

nœ ™

#œ œ ™

14

fp

>. . bœ bœ n œ

nœ nœ

bœ

œ ™ bœ J

≈

‰ ( pes.

D

16 17 stacc. . n œ. Ÿ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ . . p n œ n œ 18 n œ. b œ. b œ. b œ b œ ™ . nœ œ œ œ ≈ ‰™ . n œ #œ ® R . . sfpp nœ . . pp . pp . ppn œ ? n œ b œ ™ nœ ≈ ≈ n œ bœ ≈ ≈ J n œ œR ≈ ‰ ∑ & & ≈ bœ ™ œ n œ b œ œ sfp b œ ™ R sfpJ J R sfp tempo) bœ œ pp 19 20 21 22 23 . bœ œ nn œœ n œœœn œ n b pœ ™ n œ . ? n J ‰ bœ ‰ & bn œœ p f b œ. ‰ bœ ? nœ #œ p ‰ ‰ n# œœ j nn œœ ™™ & ‰ nn œœ ™™ # œ n œ . # œ n œ . b œ ™ n œ. dolce v. sf sf

b

4 8

{

∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏∏

{

3 8

∏∏∏∏∏∏∏∏∏∏∏∏∏∏

b œ. 15 & J

842

THE COMPLETE MUSICIAN

EXAMPLE 32.19 (continued)

p

? ‰ nœ n œ.

bn œœ.

25

pp

‰ #nn œœœ n œ ‰ nœ

∏∏∏∏∏∏∏∏∏∏∏∏∏∏

?

{

b œ. nœ

bb œœ.

24

nœ ™ sf

pp

26

5 8

. nn œœ

. bn œœ p

‰ ## œœ .

bœ n œ.

. nn œœ bœ

n œ. b & œ

27

f

&

nœ #n œœ .

b #n œœœ .

?

3 8

rit.

?#

.

.

≈ nœ n œ ™ n# œœ n œ

# œ. œ

. nb œœ nœ . bn œœ

fp

We designate the first complete ordered statement of the row as the prime (P), and all subsequent statements as transformations of the prime. For example, given Berg’s row in Example 32.18, the first complete statement begins on G, so we label it P7 (7 because that is G’s assigned PC integer). Our labeling system refers to the literal PC that initiates the row: If A is the first pitch of the prime form of the row, we called it “P9,” a sort of fixed-doh system where we maintain C as 0, C as 1, etc. Some analysts, however, prefer to label the first statement of the row as “0” regardless of pitch class, a moveable-doh method. Thus, a Prime row that begins on A would be labeled “P0” and a second statement on E would be labeled P7. We will use the fixed-doh system for consistency. As you can see from the opening of Schoenberg’s piece, we’ve run into a problem: If we don’t know what the row is, how can we determine its order when the pitches are presented simultaneously? Schoenberg gives the right hand a waltz tune while the left hand is rather independent, with sporadic trichords and single pitches. It appears that C is the first pitch class of the row, but then what? Does the right-hand A or the left-hand trichord, G–B–D, follow the initial C? If the latter, which member of the trichord precedes another? We must analyze a twelve-tone piece using a global approach, one that includes looking for: a. Single-line melodies. These are spots at which the composer presents pitches in succession, and not as verticalities. However, a row might be distributed between two or more melodies or, conversely, a melody may combine row forms. b. Harmonic markers. Composers control the harmonic content of a row by using recurring sonorities. c. Adding order numbers to each PC. When you encounter purely melodic pitches, even as few as two, you can often safely expect that these are adjacent pitches of the row. Let’s begin with areas that are purely melodic and unharmonized. A sparse texture should reveal ordered members of the row (refer to the marked segments on the score in Example 32.19). The first stretch of single pitches occurs in m. 4: labeled “A”: E–E–C–F. The second melodic marker appears in m. 7: labeled “B” and represented by G–B–D in

Chapter 32 New Directions in Temporality and Pitch

843

the right hand (an augmented triad). It is followed in the left hand with the third melodic marker labeled “C,” that includes E–E. Notice that the E and E occur in both melodic segments. This may indicate that the row is being repeated. The next melodic segment begins at the end of m. 17 to the downbeat of m. 19 and is labeled “D.” This long strand is particularly helpful for two reasons. It presents ten of the twelve PCs, and it confirms that E–E –C–F and G –B –D are ordered portions of the row: E–E appear at the end of the string of ten PCs and the augmented triad G–B–D immediately precedes E and E. Thus, we are missing only C and F to complete the row. This represents a great deal of progress. A summary of the melodic segments appear in Example 32.20.

EXAMPLE 32.20 Order #: 1

&

#w

2

nw

3

nw

Ten of 12 PCs of Schoenberg’s Row 4

nw

5

bw

6

bw

7

bw

8

nw

9

nw

10

bw

11? 12?

We now return to the opening of the piece. The first pitch is C, which is also the first pitch of the staccato passage in m. 17. We also know that the left-hand gesture in m. 1, the augmented triad, appears later in the row in order positions 6–7–8, and is followed by E–E. Thus, the left hand is initially given notes from the second half of the row. Returning to the opening right-hand pitches, we can see that C–A–B–G–A recur in the same ordering in the right hand of mm. 17–18. Continuing our right-hand journey, the following F –A –D augmented triad in mm. 2–3 is enharmonically identical with the G–B–D that followed in m. 18, and the right-hand augmented triad in m. 7. And continuing our path in the melody we encounter a flourish of faster note values: E–E, and the “missing” pitch classes C–F in m. 4. Notice that the C and F are vertical sonorities in m. 19, and as such we cannot discern order, but given their melodic placement early on in the piece, we know their order. Through a bit of detective work we have assembled the row:

C  –A–B–G–A –G –B –D–E–E –C–F At this point, it is a very good idea to: 1. Label each PC with an order number 1 to 12. 2. Study the intervallic structure of the row and the various subsets, particularly trichords and tetrachords, since these usually provide the building blocks of a piece. It is best to include both the IC and the PC intervals because knowing the contour—both abstractly as interval classes and literally, as ordered PC intervals—presents two different types of information.

844

THE COMPLETE MUSICIAN

Example 32.21 provides some of this information.

EXAMPLE 32.21 Schoenberg’s Row with Order Numbers, Interval Classes, and PC Intervals Order #: 1

2

#w

&

4

nw

nw 2 2

4 8

IC: PC-ints:

3

5

bw

nw 4 8

6

1 1

7

bw

bw 2 t

8

4 4

9

4 4

10

nw

nw 2 2

11

bw 1 e

12

nw

nw

3 9

5 5

The many even-numbered ICs in this row (i.e., 2 and 4) indicate that adjacent notes can often be grouped together to form subsets of the whole-tone collection: The PCs in order positions 1 through 4, for example, are members of the whole-tone scale on C (recall there are only two whole-tones scales, one beginning on C and another on C). Order numbers 5 through 9 are members of the whole-tone scale on C. The last three pitches, E, C, and F are members of the pentatonic collection. These collections are shown in Example 32.22.

EXAMPLE 32.22 Order #:

1

& #˙

2

n˙

Distribution of Subsets as Members of Common Collections

3

n˙

whole-tone

4

n˙

5

b˙

6

#˙

7

b˙

8

n˙

9

n˙

10

b˙

11

n˙

12

n˙

pentatonic augmented triad/ whole-tone

Finally, to save time, you need not memorize every pitch of a row nor its representative intervallic collection. Instead, just memorize the first two or three ICs of a row. They will help guide you as to which sorts of transformations the row has been subjected to, including the four main transformations which we’ll describe in the next section of the text. Now that we have the row’s order established, its intervallic properties, and important subsets—only a first step—let’s explore what Schoenberg actually does with this material. We return to the left-hand part, which begins with the augmented triad and occupies the near midpoint of the row, order positions 6–7–8. The rest of the left-hand material in m. 1, E–E, continues the row with order positions 9 and 10. Measure 2 finishes the row in the left hand: C–F are order positions 11 and 12. Notice the “extra” left-hand pitches: D and A, which we recognize as the restart of the row (but rather than rising from C to A as in the beginning, the interval now falls from D to A: don’t forget enharmonic equivalence; see Example 32.23). Measure 3 continues the row in the left hand with B, G, and A.

845

Chapter 32 New Directions in Temporality and Pitch

Schoenberg: Annotated Order Numbers in mm. 1–2

EXAMPLE 32.23 q. = 72

&

{

?

3 8

1

# œ. p

≈

3

2

8 7 6

b bn œœœj™™

4

nœ

nœ ™ bœ

10

nœ . 9

pp

‰

.

≈

5

≈

n œ. 11 12 1

bœ ™

n nb œœœ

2

nœ .

Such observations beg the question: Why would Schoenberg start the left hand midway through the row, on order number 6? Considering the musical gestures, contours, rests, articulations, and dynamics might provide an answer. Schoenberg creates a four-measure phrase given the two two-measure subgroups: mm. 1–2 and mm. 3–4. Measure 5 appears to be a restart, with the left hand given the tune on the downbeat, as the right hand presented it in m. 1. Also, m. 4 ends with the final PCs of the row E–E–C–F. The first two-measure subphrase contains order numbers 1–2–3–4–5 in the right hand while the left hand, which begins with the augmented triad, picks up where the right hand left off, with order numbers 6–7–8–9–10–11–12. In effect, the row overlaps with itself as A appears as the final pitch of the right hand’s first gesture, the left hand is already presenting the remaining pitches, with both portions of the row simultaneously completing their trajectories and the left hand presenting the first two pitches of the next repetition. If mm. 1–2 form a single unit, with both hands unfolding the row in a wraparound manner, then we might hypothesize that the same thing happens in the next two measures. We know already that the right hand alone finishes the row (order numbers 6–7–8–9–10– 11–12) while the left hand also continues and ends with order numbers 3–4–5 in m. 4. Recall that the left hand began with order numbers 6–7–8. Example 32.24 presents the order numbers of the row as distributed between the two hands and arranged by measure. We’ll call order numbers 1–5 “Part 1” of the row and order numbers 6–12 “Part 2” of the row.

EXAMPLE 32.24 Schoenberg, Two Row Presentations (mm. 1–4)

q. = 72

&

{

?

3 8

# œ. p

≈

3

2

nœ

nœ ™ 8 7 6

b bn œœœj™™ pp

bœ

4

≈

n œ.

10

nœ . 9

.

‰

≈

11 12 1

nœ n b œœ

5

n œ. J 8

6

bœ ™ 2

nœ .

‰

&

b œ n œ. . nœ nœ 10

r #œ #œ v 7

1

> ≈ n œr œ n œ b œœ 4

3

5

‰™ j œ œœ J

11

12

9

f

‰

‰

846

THE COMPLETE MUSICIAN

We can summarize the results as follows:

Right hand: Left hand:

mm. 1–2 Part 1 Part 2

mm. 2–4 Part 2 Part 1

This forms what might be viewed as a “segmental voice exchange,” in which the first and second parts of the row are swapped between the hands. Also, pitch repetition (except in the same voice and with no intervening pitches) is avoided in some twelve-tone music, when composers strive for an equal distribution of all PCs such that none is highlighted. One important exception to this rule is that the augmented triad becomes an aural path through the opening four measures. It is so audible, and at the midpoint of the row, that it is marked as the first left-hand event in the first subphrase and then again as the first righthand event in the second subphrase, thus helping the listener hear the musical process.

A Cursory Glance at the Rest of the Piece The piece unfolds as a theme and variations culminating in a return to the opening section’s material in m. 100. Between this is a riotous combination of textures and registers, including the playful mm. 17–19, and the bombastic mm. 58–60. The piece draws to a close with the aggregate formed by two chords within a single beat in m. 112, the first of which contains eight of the row’s pitches, followed by the remaining four. The last measure of the piece is particularly amusing: the first sonority states C, A, B, G, G, followed by F and D. Conspicuously missing is the expected B, the one pitch that would have brought back the “signature” augmented triad. Our analysis of Schoenberg’s early twelve-tone work has served several purposes. The most important shows that “12 counting”—the mere labeling of pitches and order numbers from a twelve-tone row—is only the first step in analysis, comparable with tonal analysis limited to roman numerals. Both are descriptive and not particularly interesting. It is in the second stage when the analyst steps back and asks questions like “how does this fit together?” and “why does the composer present this unusual idea in this context?” We also learned how to extract the row from a serial work that does not present the 12 pitches neatly, as a single line. One must look for clues, including bits of unaccompanied melody, recurring sonorities, and what precedes and follows them. Serial composers before Boulez drew on the past, for it provided wonderful models, but they also forged their own distinct paths.

T R A N S F OR M I N G T H E ROW: T W E LV E -T O N E OPE R AT OR S ( T T O s) In Chapter 31 we learned various operations that allowed us to compare sets. Transposition and inversion were the central operations, but retrograde (reading a set “backwards”) was often implicitly used when we worked with sets that were inversionally related. One final operation, retrograde inversion, reverses the order of the inversion. Together, these four operations are called twelve-tone operators (TTOs).

Chapter 32 New Directions in Temporality and Pitch

847

Some rows have a tonal feel, others are more centric, while still others are atonal. Finally, and arguably most interestingly, composers developed their compositional voices, going their own ways by: 1. exploring different possibilities within a given row; 2. transforming a row; 3. combining different row forms simultaneously. We will explore these topics in the remainder of the chapter, but before we do, let’s define some of our basic terms.

Definitions and Properties of TTOs As previously mentioned, we call the first presentation of the row the prime. The prime can be transformed using one or more of the four twelve-tone operators. 1. Transposition (T). The prime may be transposed to begin on any of the other 11 PCs, thus there are a total of 12 transpositions of the prime (including the prime itself). 2. Inversion (I), the “upside-down” version of the prime, reverses direction of each interval. That is, take the mod-12 inverse of the ordered PC interval of the prime (e.g., 9→3) to calculate the inversion. Like the prime, there are 12 inversions. 3. Retrograde (R) reverses the order of the prime (i.e., read right to left for retrograde and left to right for prime) regardless of transposition. 4. Retrograde Inversion (RI) reverses the order of one of the 12 inversional forms. This brings the total number of row forms derived from a single prime form to 48. These 48 versions of the row are called the “basic forms of the row.”

Labeling Row Forms We label rows to show these transformations. 1. As mentioned, the prime form of the row is labeled according to its first pitch, using our system where C  0, C   1, etc. Thus, if the prime form begins on G, then we call the row form P7. 2. If a following presentation of the row form is inverted and begins on G, we call it I7. (If the inversion begins on C, we call it I0.) 3. If the row appears in its retrograde form, we label it according to the first PC of the prime but use “R.” Thus, if the prime form of the row begins on G (7) and the last pitch is C (0) we label the retrograde R7, not R0. 4. The retrograde inversion would be labeled similarly, based on the first pitch of the inversion. Thus, if an inversional form of the row begins on F (5) and ends on A (9), we label the retrograde of that inversion RI5 (not RI9). In other words, the transpositional level indicated tells us which row form has been retrograded. Let’s examine some examples of each operation applied to a tetrachord, using both pitchclass names and integers. We’ll call the original form of the given tetrachord the prime. Prime: E–C–C–G 4017. Here, both order and intervallic content are important. We use angled brackets to show ordered segments. Maintaining order is crucial, given that serial—ordered—relationships are our focus. The ordered PC intervals are 816.

848

THE COMPLETE MUSICIAN

Inversion (around zero) is easy: use the mod-12 complement of 4017, which is 80e5: A–C–B–F. With C as zero, it is the index number. As a brief review, Example 32.25 shows C (0) as the axis, around which the first tetrachord of the prime form of the tetrachord (E–C–C–G) and inversion (A–C–B–F) are shown.

Tetrachordal Axis

EXAMPLE 32.25

& ˙ b˙

˙ ˙

# ˙˙

œ

Notice the mirror effect: since the prime begins 4–0 (down a major third from E to C), then the inversion would be 8–0, or up a major third, from A to C. Further, inverting again would “undo” itself. If one inverts an already-inverted set, the original PCs return: The inversion of 80e5  4017, which is our original form. Retrograde reverses the order of the prime: G–C–C–E 7104. Retrograde Inversion reverses the order of the inversion: F–B–C–A 5e08.

A PPL IC AT IO N OF T W E LV E -T ON E ROW S Given this background, let’s look at a row by Anton Webern, which illustrates a variety of compositional procedures (see Example 32.26).

Webern, Concerto for Nine Instruments, op. 24: Row and Order Numbers

EXAMPLE 32.26

Order #: 1

&

2

nw

3

nw

bw

4

5

6

bw

nw

#w

7

bw

8

9

nw

nw

10

11

nw

12

#w

nw

Next, we look for relationships between members. The most-important relationships are intervallic patterns, contours, and subsets smaller than the hexachord. Let’s begin with interval classes (Example 32.27).

Webern, Concerto for Nine Instruments: Interval Classes

EXAMPLE 32.27 Order #: 1

&

2

nw

3

nw

bw 1

4

1

4

5

6

bw

nw

#w

4

1

7

bw 2

4

8

9

nw

nw 1

10

11

nw

5

12

#w 1

nw

4

849

Chapter 32 New Directions in Temporality and Pitch

There are two prominent ICs: 1 and 4. By grouping them into trichords, we see that [014] occurs four times, and the four statements of [014]  the aggregate (see Example 32.28).

EXAMPLE 32.28 Order #: 1

2

& n˙

3

n˙

b˙ 1

Webern: [014] Trichord Subsets

4

1

4

5

6

b˙

n˙

#˙

4

014

1 014

7

b˙ º

3

8

9

n˙

n˙

4

1

10

11

n˙

5

014

12

#˙ 1

n˙

4 014

Further, the row is partitioned (segmented) into two groups of six pitch classes with a diminished third (F–A), IC 2, separating the hexachords. The first hexachord B–B–D–E–G–F has the prime form [014589]. We know that hexachords are literal complements of one other. That is, the intervallic content of the first hexachord will be reproduced in the second hexachord, but, of course, with the different PC content in order to complete the aggregate. (That said, although the intervallic content of the two hexachords is the same, they may be Z-related, as discussed in Chapter 31, meaning that they are not members of the same set class.) In Webern’s row the second hexachord, E–F–A–A–C–C, belongs to the same set class as the first [014589].

EXAMPLE 32.29

Index Number for Webern’s Row

hexachord 1: t e 2 3 6 7 hexachord 2: 4 5 8 9 0 1

=

(t e 2 3 6 7) (1 0 9 8 5 4) (e e e e e e)

Displaying these sets in normal order reveals how they map onto one another: by inverting and transposing at Ie. (There are additional mappings possible.) Indeed, working inward and summing the pitch-class numbers of each dyad, we see that the index number is 11 (Example 32.29). Prime form and normal order are great for reducing pitch sets into manageable units that help us see relationships. In this twelve-tone row, we learn that the row is segmented into four trichords, each of which is a member of the same set class. However, prime does not reveal contour relationships between the pitch sets. The order and the contour of each interval within and between each trichord allow us to study the surface events of the music. Thus we will work with P intervals in order to see how Webern deploys the pitch content at the surface of the music.

850

THE COMPLETE MUSICIAN

As we know, Webern’s row is generated by a single trichord: [014]. The three remaining trichords are each generated by one of the three other TTOs. This is not trivial since few trichords allow for such elegant generation of an entire row. Imagine the potential of such a tightly knit row. Let’s look at the ordered pitch intervals to see how Webern does this. The two hexachords are separated by two vertical lines. The trichords are separated by one vertical line. To see the contours (here contours are notated to show relationships to one another) we use ordered pitch intervals (labeled; see Example 32.30).

EXAMPLE 32.30

Hexachord 1: nw & nw b w -1

+4

Webern, Concerto for Nine Instruments: Hexachords 1 and 2, Divided into Trichords and Ordered Pitch Intervals

Hexachord 2:

nw

bw +4

#w -1

bw

nw

nw -4

+1

nw

#w +1

nw -4

Notice that no two trichords (as notated) have the same contour (e.g., trichord 1 contains a minor-second descent followed by a major-third ascent, while trichord 2 rises a major third and falls a minor second, etc.). In Example 32.31, we represent these literal contours (hash marks indicate half steps).

EXAMPLE 32.31 Trichord Contours in Webern’s Concerto for Nine Instruments

Trichord #1: Prime

Trichord #2: Trichord #3: Retrograde Inversion Retrograde

Trichord #4: Inversion

The easiest relationship to see is inversion, which reverses the contour exactly: −1, 4 is answered by 1, −4. Retrograde is also easy. The contour is backward: −1, 4 is answered by 4, −1. Finally, retrograde inversion runs the inversion backward, that is: inversion: 1, −4, so retrograde inversion is: 4, −1. Let’s see what Webern actually does with his row (see Example 32.32). Using octave displacement to create an angular style, Webern assigned each trichord to a different instrument, with an overlap of the last pitch of one trichord with the first pitch of the next as shown in Example 32.33.

851

Chapter 32 New Directions in Temporality and Pitch

Webern, Concerto for Nine Instruments, op. 24 (mm. 1–3)

EXAMPLE 32.32

Etwas lebhaft q = ca 80

b >œ.

° 2 Flute & 4 Œ

2 &4 ‰

Oboe

2 Clarinet * & 4 ¢

nœ

n >œ.

#>œ.

rit.

‰

b œ nœ ≈ ‰

f

∑

Œ

f

∑

∑

# œ-

n œ-

Œ

3

f

Horn *

° 2 &4

∑

Trumpet *

2 &4

∑

Trombone

? 42

∑

° 2 &4

Violin

Viola

Piano

∑ n œp

∑ with mute

#œ nœ f

3

nœ

Œ

Œ

3

∑ ∑

Œ ∑

∑

∑

∑

∑

B2 ¢ 4

∑

∑

∑

2 &4

∑

∑

∑

?2 4

∑

∑

∑

¢

{

* Sounds as written.

EXAMPLE 32.33 Webern, Concerto for Nine Instruments, op. 24: Trichords in Pitch Space (mm. 1–3)

&

n˙

b˙

b˙ n˙

n˙

#˙ #˙

n˙

nn ˙˙

#˙

n˙

852

THE COMPLETE MUSICIAN

B E RG , LY R IC SU I T E Example 32.34 shows the opening melody that comprises the main row of Berg’s Lyric Suite, for string quartet. This row contrasts with Webern’s row shown in Example 32.26 and provides just one of the many ways a composer can construct and project musical elements.

EXAMPLE 32.34 Berg, Opening Melody of Lyric Suite (1927)

nœ nœ 4 b œ ™ 2‰ n œ n œ 4 4 nœ nœ

Allegretto gioviale q = 100

Violin 1

4 &4

∑

b œ. œ. œ. b>œ b>œ b>œ

n˙

poco f

Contour

The melody’s contour reveals a clear arch, featuring a rise from the initial F and E to A in the middle, a tenth higher than F, and then a descent to B at the end. But can we describe precisely the process at this point? No, we will have to use our tool kit that helps us analyze intervals. In previous analyses we usually worked from context sensitive intervallic descriptions ([un]ordered pitch intervals) to most abstract descriptions (interval classes). This method reveals few surface events, but it reveals similarities between what appear to be unrelated events. Let’s now work in the opposite direction, beginning with the most abstract way of viewing intervals: unordered PC intervals—interval classes. Then, we can move ever closer to the notated score: a musically contextual reckoning of the intervals. We begin with the unordered PCs (see Example 32.35). Unordered PC intervals reveal a symmetry, with the tritone between the two hexachords of the row acting as a fulcrum, from which the same interval classes spread out in contrary motion. Notice that all six ICs are represented twice, except for IC 6.

EXAMPLE 32.35 Berg, Lyric Suite: Unordered PC Intervals of the Row and Symmetries

P₅: & nw

nw

nw 1

4

nw

nw 3

2

bw

nw 5

bw

bw 5

2

bw

bw 3

4

nw 1

853

Chapter 32 New Directions in Temporality and Pitch

Ordered PC Intervals This step is a more sensitive reading that identifies order in the PC world, and allows us to learn more about the properties of a row (see Example 32.36).

EXAMPLE 32.36 Berg, Lyric Suite: Ordered PC Intervals

P₅: & nw

nw

nw e

8

nw

nw 9

10

bw

nw 7

6

bw

bw 5

2

bw

bw 3

4

nw 1

This assessment again reveals the symmetry of the row, but given that contour is considered, we see that not only are the pitch class intervals symmetrical but so are the ordered intervals. Moving inward from each end of the row we learn that every possible ordered interval is represented, and done so in mirror fashion. Ordered PC intervals, while revealing the appearance of all 11 intervals, do not fully represent the literal contour. For example, the opening three ordered PC intervals, e–8– 9–t, do not reveal the fact that there are two-note pairs: The second pitch of each of the first three pairs is lower than the first. Because of this, we are unaware that Berg is creating a sort of sigh motif. Also note that the second pitch of each of the next three pairs also falls. Further, ordered P intervals reveal the overall rising line of the first hexachord. Notice that a small falling interval leaps up to a pitch that is much higher, while the second hexachord does the opposite: small rising intervals but large falling ones, thus returning the contour to its initial register (see Example 32.37).

EXAMPLE 32.37

&

P₅: nw

nw

nw -1

Berg, Lyric Suite: Ordered P Intervals and Axial Symmetry

+8

nw

nw -3

+1 0

bw

nw -5

+6

bw

bw -7

+2

bw

bw -9

+4

nw -11

Again we see the mod-12 complements create a strict palindrome. More importantly, ordered P intervals reveal that the contours are identical for each pair; e.g., the outer pair, −1/−11, and both descend from the previous pitch (i.e., F–E and B–B) while the next pair both ascend (i.e., A–E), thus creating the balance of alternating falling and rising. Finally, given a pitch name, such as the F above middle C that Berg starts on, we can construct the row precisely in P space, something we could not do in the PC world.

854

THE COMPLETE MUSICIAN

Note also that the pitch interval distance between each successive interval increases as the pairs rise: F–E, C–A, and G–D, as the pairs unfold the distance between the first and second note rises by 2 (in semitones: 1, 3, and 5). This holds true for the second hexachord but in reverse: each interval pair increases its interval size by 2 as they fall. The intervals unfold in such an order that they enhance the palindrome by each pair summing to 0, from the outside in. What this means is that in each corresponding pair of intervals—from the inside (6/6) out or the outside in (e/1)—the pitches in each pair are equal distance around different center points in PC space. If this is the case, then the first note, F (5) and the last note, B (e), which form a tritone, has the abstract axis of A. Note that A appears as the apex of the arch form of the melody (see Example 32.38).

EXAMPLE 32.38

P₅: & nw

nw

nw

>e

Mod-12 Inverses Between the Hexachords of Berg’s Row

8

nw 9

symmetrical around Ab

nw t

bw

nw 7

6

bw

bw 5

2

bw

bw 3

4

nw 1


œ bn œœ ‰ Œ Œ # œ œ J n˙

863

Chapter 32 New Directions in Temporality and Pitch

(continued)

EXAMPLE 32.47 7

&

bw

‰ nœ b œ b œ

œ

nœ

Ϫ

nœ ˙

‰

#œ

nœ

#œ œ nœ

bœ

nœ

nœ ‰ nœ b œ b œ n œ

dolce

∑

&

{

? œ œ #n œœ ˙˙

Ó Œ #œ ™ n œ ™ #n œœ # œœ

12

&

Ϫ

nœ ˙

?

b˙

‰ ™ nœ ˙ R

nœ

j œ ‰ Œ

EXAMPLE 32.48

b˙ b˙

Ó bœ

Ó

Ó

n˙

Ó œ

bœ

#œ

n˙ b˙

?‰ n

Ó Ó

# œœ n œ J #œ j bœ

nœ ™

b˙ # œ Œ n œ ™™ n œ b œ ™ n œ nœ

œ b œ b œ nœ

f

#œ œ n œ œ ? ‰n œ œ # œ œ ‰ Œ & Ó J

{

‰ j j n œ n œj Œ ‰ j n œ ˙ nœ n œ nœ bœ

Œ

‰ n œj œ bœ œ

œ nn œœ n œ œœ Ó œ bœ bœ b˙ J

nœ ™

∑

n˙ ™

bœ

f

n# œw œ œ œ ˙

∑

Ó

Schoenberg, Violin Concerto: Matrix

P

Opening row form:

I 0 e 6 t 5 3 9 8 2 1 7 4 RI

1 0 7 e 6 4 t 9 3 2 8 5

6 5 0 4 e 9 3 2 8 7 1 t

2 1 8 0 7 5 e t 4 3 9 6

7 6 1 5 0 t 4 3 9 8 2 e

9 8 3 7 2 0 6 5 e t 4 1

3 2 9 1 8 6 0 e 5 4 t 7

4 3 t 2 9 7 1 0 6 5 e 8

t 9 4 8 3 1 7 6 0 e 5 2

e t 5 9 4 2 8 7 1 0 6 3

5 4 e 3 t 8 2 1 7 6 0 9

8 7 2 6 1 e 5 4 t 9 3 0

R

864

THE COMPLETE MUSICIAN

Let’s trace the violin line: 9–t–0–1–2–1 . . . Notice that only 9 and t (order positions 1 and 2) from P9 appear in the opening of the violin. The next PCs played by the violin are 0 and 1 (order position 7 and 8). As we learned in our exploration of Schoenberg’s “Walzer,” the row can circulate between different voices. This is what occurs here: We expect after PCs 9–t, PCs 3–e–4–6, and we find them in the viola and cello. Notice how Schoenberg has deployed these pitches as two dyads, first as a major third, which then expands to a minor seventh. The first hexachord has been stated by this point. The focus returns to the solo violin. The violin plays 01, paralleling the same gesture that opened the piece. As expected, the rest of the row 7825 is assigned to the viola and cello. However, this time the cello and viola’s dyads contract, balancing the expanding dyads in mm. 1 and 2. This completes the first statement of P9. What follows in the violin is D–C. That C appears so close to D in m. 3 is a telltale sign that a new row form has begun, but this time inverted because D–C is a falling half step rather than the prime version, which has a rising half step. Recall that we need not trace all 12 PCs since the matrix presents a path to follow in the score; the new row form begins on D (2), so look for the inversion of the row that starts on 2 (recall that the inversion is read from top to bottom). The inverted form of the row beginning on 2 is: 218075 | et4396. A quick verification of this form reveals that 8075 . . . A–C–G–F . . . occurs in the lower voices, and again complete the first hexachord of I2. The second hexachord, B–B–E–E–A–F, begins in the violin (although the low E precedes the violin’s two pitches by half a beat), and the accompanying instruments complete the hexachord in m. 8. P9 and I2 each unfold over four measures, ending in m. 8. The violin solo is divided into two segments by rhythm (dotted quarter–eighth–tied whole, followed by the same in mm. 2–4), and pitch: the semitones A–B and C–D. Further, the accompaniment is also divided into two parts, just like the melody, but with opposite contours: A third opens to a seventh in mm. 1–2 and in mm. 3–4 a seventh closes to a third, creating an arch.

Emergence of P9 and I2 Here are the two rows, P9 and I2 divided into hexachords:

P 9: I 2:

9t3e46 218075

| 017825 | et4396

The first hexachord of P9 and I2 have no pitch duplications. The same, by extension, is true of the second hexachords of each row form. Thus, the two rows may be combined— are hexachordally combinatorial—because there are no pitch duplications in either of their hexachords. And, of course, the first hexachords from P9 and I2 form secondary aggregates as do the second hexachords. The bassoon enters the fray at the upbeat to m. 9 and presents a melody, which thickens the texture and provides a counterpoint to the solo violin. The violin melody unfolds as follows: A–B–E–B–E–F. We recognize this as the first hexachord of P9. The prominent bassoon begins D–C–G–F. However, no row form—prime, inversion, retrograde, or retrograde inversion—begins or ends with this intervallic pattern. (Primes and inversions begin with a rising or falling semitone and retrogrades begin with a minor third.) Yet, we have encountered a row form that began with D, the I2 version of the row. We return to the matrix: I2  218075 | et4396.

865

Chapter 32 New Directions in Temporality and Pitch

Thus, D should be followed by D–A–C–G–F 18075. Sure enough, the D and A occur, not in the bassoon, but in the viola and cello; now C–G–F in the bassoon makes sense, because these are the next PCs in I2. Schoenberg has completed the first hexachord of P9 and I2, but this time they appear simultaneously. Logically, then, the second hexachords of P9 and I2 should follow. After the eighth-note rest in the solo violin in m. 10, the line continues with C–C–G–  A –D–F 017825, the second hexachord of P9. We thus expect the second hexachord of I2 et4396 to be interwoven with the violin, and indeed it is: In mm. 9–10, the bassoon states B–B–E (et4), while the lower accompanying voices state E and A. The last pitch of the bassoon is the final pitch of I2: F (6). A rest begins the solo violin line in m. 10, and the leap from F (m. 9) up to C (the expected next PC of P9) separates the two hexachords by both register and silence. C is followed by the jagged line, C–G–A–D–F 17825, the expected second hexachord of P9. Here, Schoenberg places the entire opening row form (P9) within a single instrument, the solo violin, rather than distributing it between the lower accompanimental voices of the viola and double bass. As mentioned, beneath the solo violin in m. 8 the bassoon enters on D—a pitch that made its dramatic appearance in m. 4 as the opening of I2. The appearance of something we’ve already heard allows us to expect that I2 will unfold: D–D–A–C–G–F | B– B–E–E–A–F, 218075 | et4396. Indeed, after D, we encounter D and A along with the bassoon’s C–G–F, thus completing the first hexachord of I2. Following a significant rest (1.5 beats) in m. 9, Schoenberg serves up the second hexachord of I2 B–B–E–E–A–F. Recall that in the opening measures of the piece, the row was distributed between the solo violin and the accompaniment. But, because Schoenberg restricted the P9 row form to the violin in mm. 8–11, it is logical that he’ll distribute the simultaneously unfolding of I2 among the remaining instruments, while prioritizing the bassoon. Based on this patterning—P9 stated alone, then I2 stated alone, then P9 and I2 stated together with the violin playing P9 and the other instruments I2—we might expect the reverse: I2 in the solo violin and P9 in the bassoon and accompaniment. Let’s see what actually happens. Clearly the extended caesura that opens m. 11 demarcates the next presentation of row forms. The solo violin begins with D–D–A–C, I2, which is completed in m. 14. The accompaniment, also beginning in m. 11, projects A–B, an indication of P9, finishing, as the solo violin did, in m. 14. Our guess was correct: Schoenberg reversed the row forms in mm. 11–14: now the solo violin is assigned I2 and the accompaniment P9. Here’s a summary of what we’ve observed:

upbeat to m. 1 to downbeat of m. 4 P9 solo violin  accompaniment

mm. 4–8

mm. 8–11

mm. 11–14

I2 solo violin  accompaniment

P9 (solo violin) I2 (bassoon and accomp)

I2 (solo violin) P9 (bassoon and accomp)

Schoenberg’s meticulous step-by-step introduction of row forms, first one at a time (P9 followed by I2) and then their combinations, reveals a musical process that is audible and

866

THE COMPLETE MUSICIAN

elegant. That the two hexachords of P9 and I2 are combinatorial allows this to happen. In fact, the row forms are presented by hexachord and followed by rests, which ensures that no PCs from one row form duplicate those of the other.

The Violin Concerto’s Surface Schoenberg’s musical setting of these two row forms and division into hexachords allows for pitch class invariant motives to emerge. Clearly the half step is ubiquitous. Yet considering the half step, either as part of a line or as PC specific, yields interesting connections that Schoenberg certainly considered. Let’s look at three of these motives. 1. The violin’s opening A–B  (dotted quarter/eighth) is followed by C–D  (same rhythm). Together a rising stepwise line emerges in P space. In order for this line to appear, Schoenberg had to consider the intervallic content of the row so that he could place nonlinear events in the accompaniment. Notice that in order to achieve the ascent, he uses order numbers, 1–2/7–8. Further, the next statement of the row in the violin (I2), descends (mm. 4–8): D–C –B–B , once again, order numbers 1–2/7–8. Further, the connections between the two row forms stress C–D , then D–C , an audible inversion. 2. The direct connection between P9 (A–B , etc.) and I2 (D–C , etc.) and the distance of a perfect fourth between the beginning A (9) in the violin and upper D (2) are generated by the violin’s contour: The line beginning on A does not stop on D , but rather continues to D, at which point I2 begins. Thus, A up to D followed by the descent in the violin from D to B , and ultimately A (up an octave) retraces the perfect fourth in PC space. 3. Interval-imitation draws attention to motivic pitch gestures such as the minor seventh F–E in m. 1 that is overtaken by the violin in m. 9 as it expressively falls a seventh from E to F. In order for Schoenberg to repeat this PC gesture in the accompaniment in m. 10, there must be a leap from the accented A into the accompaniment to state order numbers 10 and 11. This enables Schoenberg to reiterate the final pitch of I2 , F, which occurs in the same falling minor-seventh gesture in the bassoon in m. 10. In m. 11, the simultaneous row forms recur, with the instrumentation switched. The placement of voices is identical to the opening, save for the inversion of the row: the opening of P9 is in the cello and its accompaniment in the upper voices is now played by the violin. These observations reveal but a few of the relationships that Schoenberg develops. Such control of pitch, pitch class, and rhythmic events creates a remarkably tightly knit work.

Generalizing Inversional Combinatoriality But, there is a lingering question: Why does Schoenberg use only these two specific row forms in the opening of the concerto? One answer is that they are combinatorial, but could he have used other pairs of rows that would have yielded the same combinatorial features? The answer is yes, and this process can be generalized. Recall that the interval between the initial notes of P9 and I2 is a perfect fourth (P9 starts on A, and I2 starts on D, up a fourth). There are 5 semitones separating these two row labels. Thus, we can assume that any pair of rows related by inversion and

867

Chapter 32 New Directions in Temporality and Pitch

transposition of a perfect fourth up or perfect fifth down will be combinatorial. Let’s try two pairings:

Pairing 1: P0 and I5. The distance is up a perfect fourth (C up to F) P0 : I5:

016279 34 t e58 54e3t8 217609

The first hexachord of P0 and I5 create a secondary aggregate as do the second hexachords.

Pairing 2: P0 and I2 . The distance is a major second (C up to D), not a perfect fourth. P0 : I 2:

016279 218075

| |

34te58 et4396

Each hexachord from each row form contains numerous PC redundancies (in bold), so they are not feasible for combinatoriality. There is a general rule for inversional combinatoriality: in order to combine two rows whose hexachords have mutually exclusive pitch content, the interval separating the two forms must sum to an odd number. (We will see why this is so after the discussion of hexachords that do not allow for combinatoriality.) The intervallic distance between P9 (which begins on A) and its inversion, I2 (which begins on D) is a perfect fourth up or perfect fifth down; that is, IC 5. We can use the sum, or index number, to check this: 9  5  2  I  I2 (mod 12). It turns out that the majority of Schoenberg’s hexachordally combinatorial rows are separated by a perfect fourth, perhaps a look to the past when imitation and tonal relations occurred most often at the interval of a fourth or fifth.

VA R I A N C E V E R S U S I N VA R I A N C E So far, we have focused on music that avoids PC repetition, in which there is an emphasis on pitch variance. But what if a composer wanted to incorporate invariance, perhaps to project certain pitches and forge interesting compositional relationships throughout the piece, including pitch-class doublings or pitch placement in prominent registers? Although Schoenberg used a single row form in his “Walzer,” the augmented triad became a motivic element, clearly projected in a wide range of musical contexts. In general, invariance refers to the retention of pitch classes permitted by the properties of the row and its interactions with row forms that reinforce pitch-class prominence. These transformations allow pitches to return either as ordered or as unordered pitch sets. For example, C and F transposed at T6 or inverted at I6 return F and C, thus holding these pitches invariant. We have seen this in the tonal world too, of course: The diminished seventh chord D–F–A–C is held invariant at T3, I6, T9, I0, I3, I6, and I9. While variance was a priority to Schoenberg, the equal circulation of the aggregate was central to his compositional process. However, he was also interested in maintaining a pathway through a piece by highlighting pitch classes, a process to which we now turn.

868

THE COMPLETE MUSICIAN

Invariance and Symmetry Let’s look at the contour of the opening two measures of Dallapiccola’s “Contrapunctus secundus” from his Quaderno musicale di Annalibera (Example 32.49). The right hand falls a major seventh from G to A and continues its descent to C. The left hand mirrors the right, rising a major seventh from F to E and continuing its ascent (in the treble clef ) to C. The left hand begins an eighth note before the right hand. The piece continues in this fashion, with the right hand lagging just behind the left, creating a sort of inverted imitation. Further, we can hear and easily see this imitation by inversion.

EXAMPLE 32.49

Dallapiccola, “Contrapunctus secundus” from Quaderno musicale di Annalibera (1953)

Poco allegreo; “alla Serenata” (q = 69 - 72) dolce; espr.

3 &4 Œ

{

nœ -

bœ

(quasi accordando) œfij

Õ À. . . n œ nb œœ œœ n œJ n œ -

ten.

nœ ? 3 ‰ n œ4

n œ œ n œ # œ & J n œ. œ. n œ ÆœJ .

dolce; espr.

ten.

(quasi accordando)

mp Æj .# œ # œ. n œ ‰ b œ > n œ. nœ m.d.

p Æ nn œœ ≈

(movendo p

œœÆ œœÆ Æ nn œœ

# œfij

# n œœ ≈ ≈ # œJ ≈ Œ >.

#nÆœœ J

# œj " n œ.

(a tempo)

>. b >œ b œ j b œœÆ œœÆ œœÆ n œÆ ? n œ b . ‰b œ ≈ & n œ ≈ ≈ ##n œœœ b œ. n œ J b œ-. ÆJ ' mp

≈Œ

fij #n œœ

? #œ ‰ n œJ .

Curiously, however, both hands collide on C, most likely played by the thumbs in spite of it being the same key on the piano. This is a procedure we have not seen before: an apparent serial piece with a prime form of the row against an inversion, but moving toward a unison. In non-twelve-tone works, we have encountered such mirroring in Bartók’s Music for Strings Percussion and Celesta (see Chapter 31). The imitation continues in m. 2 as the left hand presents a minor third below the C (A), followed by G and the grace-note tritone to C with tenuto over that pitch. The right hand adds the minor third above C, and is followed by a falling tritone to B: again, C is the axis. The movendo (accelerando) pits two perfect fifths against one another: E/B and D/A, again, with C5 as literal pitch axis. The pattern continues to the end of m. 4. Here notice that each pair sums to 0, C, which functions as the axis, highlighted by Dallapiccola as unisons. Clearly, this is not combinatoriality, in spite of Dallapiccola’s use of two different row forms related by strict inversion. Rather, Dallapiccola is interested in controlling pitch space and projecting specific pitches (that is, not merely pitch classes, but placement in specific registers). Here is a representation of the two row forms’ pitches, paired as presented:

| t24961 | 2t836e Each pair of PCs remain together when, for example, 7/5 recurs as 5/7, etc. But notice something curious: not every dyad has two different PCs; there are two “singeltons,” the unisons 0 and 6. If we choose another row pairing, say P4 and I6, we see the same thing, P7: I5:

78035e 540971

869

Chapter 32 New Directions in Temporality and Pitch

this time with 5 and e being the singletons. Notice that the two pairs of singletons lie a tritone away from the other (here F and B, and in the P7 and I5 form, C and F):

| 7e163t | 3e9470 Example 32.50A presents the two row forms, P4 and I6, in P space, with C5 the literal axis of inversion, around which all other pitches are symmetrically placed. This not only 459028 651t82

P4: I6:

EXAMPLE 32.50A

The Two Row Forms, P4 and I6, in P Space

7

n˙

8

b˙

&

{

n˙ 4

? n˙ 5

5

3

0

nb ˙˙

˙ 0

# ˙˙

n˙

9

˙

1

7

b ˙8 n˙

2

t

e

bn ˙˙

bn ˙˙

2

t

nb ˙˙

#˙ #˙

4

#˙ b˙

reveals the literal axial symmetry but also explains the unison Cs, and the corresponding endpoint of the other axis, F, occurring together but symmetrically around the C, a tritone away in P space. Example 32.50B presents each of the two row form’s pitches in a single register for easy comparison of their inversional relationships and axes.

EXAMPLE 32.50B

7

&

{

C(0):

?

__ œ

nw

8

bw

nw

nw

5

4

Two Row Form’s Pitches in a Single Register

0

nw nw 0

3

5

bw

nw

nw

nw

9

7

e

nw

t

bw

#w

nw

1

2

2

nw bw t

nw 4

bw 8

9

6

1

nw

#w

#w

bw

#w

nw

3

6

__ œ e

Example 32.50C presents a remarkable relationship between the two row forms in P space. Over the span of the row the upper voice distance from highest to lowest pitch is 27 half steps (a compound major third), which is identically mirrored by the lower voice’s span from lowest to highest, which also comprises 27 half steps. Note that the arrival points occur simultaneously in both voices, immediately following the single point where the two voices each state B–D and D–B, a voice exchange that prepares for the registral arrivals. Each voice then retraces its steps, ending together on the tritone.

870

THE COMPLETE MUSICIAN

EXAMPLE 32.50C

The Relationship Between the Two Row Forms in P Space -6

n˙ &

{

&

n˙

-27

b˙ n˙

˙

b˙

n˙

˙

+2 1

˙ ˙

n˙

#˙

b˙

n˙

n˙

b˙

n˙ b˙

#˙

n˙ b˙

#˙

#˙

b˙

-20

+2 6 +6

Generalizing Inversional Combinatoriality and Inversional Invariance Here is a general rule for combining two inversionally related sets: If complete variance is the goal (no PC redundancy between corresponding hexachords), then an odd index number is required. Conversely, if a composer wishes to project specific PCs and to maintain dyad pairings, an even index number must be used. To see why this is so, let us return to Schoenberg’s combinatorial row forms for his Violin Concerto:

P 9: I2:

9 t3e46 218075

| 017825 | et4396

The index is an odd number (11) and because of this, there are no singletons. And we know that maintaining this relationship (the P form will lie a perfect fourth below or perfect fifth above the I form) will always produce six unique PC pairs. An even index number will always produce five unique pairs and two singletons that lie a tritone away from the other. Let’s see exactly why this is. We return to the clock (see Example 32.51). Each pitch class from Schoenberg’s secondary aggregate—the aggregate resulting from combining the first hexachord of P9 with the first hexachord of I2—reveals a one-to-one correspondence: Each PC from P9 (shown with an “x”) is matched with a PC from I2 (shown with an “o”). Note that every pair has two different PCs. And the single line that bisects the 12 PCs is the axis. Notice, as we discussed earlier, that the axis is precisely half of the sum (in this case it occurs at “5:30” and “11:30”: tritones away). Fold the clock in half along the axis and you will see that it runs between 5/6 and e/0. Thus, no PCs are paired with the same PC: There are no singletons. A glance at the clock plotting Dallapiccola’s row pairings reveals something quite different because it is not combinatorial (see Example 32.52). This time the clock reveals the pairing of all PCs from both row forms. The solid arrows and dotted arrows illustrate dyad pairs between the two row forms, each of which sums to 0 (axis  0/6). This even sum means that there will be two singletons: 0 is paired with itself and 6 with itself. Further, two pairs of dyads t/2 and 7/5 each appear twice in the same hexachord: The 7/5 pairing occurs twice in hexachord 1 (and not at all in hexachord 2) and the t/2 pairing occurs twice in hexachord 2 (and not at all in hexachord 1).

Chapter 32 New Directions in Temporality and Pitch

Schoenberg, Violin Concerto: Inversional Symmetry Plotted on the Clock

EXAMPLE 32.51

0

e t

1

o

x

o

x

9

x

o

o

x

8

871

2 3

x

o o

x

7

4 5

6

Index = 11 Axis = 5.5 (no singletons)

EXAMPLE 32.52

Dallapiccola: Inversional Symmetry of Both P7 and I5 Plotted on the Clock

0 e

1

t

2 in hex. 2 only

9

3 8

4

in hex. 1 only

7

6

5

Clearly, Dallapiccola’s plan is to highlight various Ps and PCs. C, of course, is the literal axis of symmetry, and F/G (5/7) are crucial pitches that establish registral boundaries. Finally, B and D (t/2) are the “fulcrum” PCs that function as reflections of one another through voice exchange.

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SU M M A RY We explored two vast and varied topics in this chapter: rhythm/meter and pitch. The first area of study revealed new elements in the temporal world. Whether a work is cast in #4 or &8, or is not metrical at all because of devices such as added note values, we learned that meter and rhythm become remarkably flexible. Meter can change every measure, tempo change can be delicately and precisely quantified through metric modulation, or meter can be disguised by simultaneously conflicting meters and the pacing of discrete events that are out of sync with surrounding events, and countless other variations of commonpractice temporal processes. The “deregulation” in the temporal sphere is perhaps balanced by the “regulation” of the pitch world through the process of ordering the aggregate. The equal circulation of the 12 PCs often assures that no pitch is singled out or rises to prominence to play anything like the role of “tonic.” Nonetheless, composers manipulated rows by combining various transformations to project certain relationships, perhaps the retention of special PC sets (invariance), and relationships between row forms. The most important types of pairings involve a row form’s hexachords and how they can be combined with other row forms’ hexachords to create new aggregates called secondary sets, in which direct PC duplication is avoided, called “variance.” Yet composers often highlighted specific pitches and in order to do so, pitch space enters the picture, and with it registral symmetries. In such cases, hexachords are constructed and combined such that pairs of unisons might be highlighted as a central point (axis) from which other events symmetrically flank this point. We have now completed our study of music’s processes and structures, ranging from the lament bass of Monteverdi in 1600 to the rhythmic, metric developments in Elliott Carter’s music and twelve-tone techniques in Luigi Dallapicolla’s works in the later twentieth century. We have traveled a long distance from the nascent knowledge required to identify pitches and write scales to discovering the simplicity and generalizability of the diatonic harmonic world and how the phrase model is a commonality in all tonal music. Chromaticism was also simple, growing naturally as applied chords pulling to dominants (tonicization) and mixture processes that focus on the pre-dominant function. Musical construction (form) began modestly with the phrase, but soon progressed to the level of the piece, which ranged in size from small 16-measure binary forms to 300-measure late-Classical rondos and sonata movements, and highly chromatic ternary forms found in the nineteenth century. Thus, our exploration of twentieth-century music, including stylistic traits, compositional techniques, theoretical underpinnings, and a constant comparison and contrast with tonal materials, leads us to this point. Our journey is not complete, however. In the Anthology that accompanies this text, we present several new works by contemporary composers. These works show that composition is a living, breathing art. Some of these composers employ and develop aspects of the modern techniques we’ve discussed in the final section of this book, while some have rejected them. They view the techniques developed during the early twentieth century as providing them with one set of options—but not the only one—that they can use in creating their works. Thus, theory continues to evolve, inspired by both tonal and nontonal traditions, but also forging ahead to create new works.

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T ER MS A N D CONCEP TS • changing meter • even index number • hexachord • metric modulation or tempo modulation • metric strata • nonretrogradable rhythm • odd index number • partitioned/segmented row • pitch variance • polyrhythm • prime • retrograde • retrograde inversion • transposition • twelve-tone operators (TTOs) • variance

CH A PTER R EV IEW 1. True or False: Asymmetrical meters usually subdivide into groups of 2 and 3 pulses together within the same bar.

2. Using the technique of additive rhythms, a bar of #8 with an extra eighth note would change the time signature to __________.

3. Create a nonretrogradable rhythm of five notes (a rhythmic palindrome).

4. True or False: Polyrhythm refers to the consecutive statement of two or more different beat divisions.

5. True or False: Metric strata is a type of polymeter.

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6. Describe two different means to creating a metric modulation.

7. What did Schoenberg mean by the phrase, “unity of musical space”?

8. The first complete ordered statement of the row is called the __________ form.

9. The initial step of labeling pitches, or “12 counting,” in a twelve-tone piece is analogous to what analytical process in tonal music, in that both are purely descriptive?

10. Name the four types of twelve-tone operators (TTOs) which yield the 48 “basic forms of the row.”

11. True or False: Retrograde inversion can be calculated by either reversing the inverted form of the row, or inverting the reverse form of the row.

12. True or False: Retrograde and retrograde inversion forms of a row are labeled by their first pitch.

13. What technique combines two or more different row forms simultaneously without pitch duplication in either of their hexachords?

14. Inversional combinatoriality, a technique associated with Schoenberg, combines a prime form of the row with some [inversionally/transpositionally] related form, while still avoiding pitch-class repetition.

15. If complete variance is the goal (no pitch-class redundancy between corresponding hexachords), then an [odd/even] index number is required.

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16. If invariance is the goal (some pitch-class repetition between corresponding hexachords), then an [odd/even] index number is required.

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G LO S S A RY

IV–ii complex The progression IV–ii (or IV–ii6), viewed as single pre-dominant (PD) function in second-level analysis. Note: ii–IV is a retrogression. 5–6 motion A technique where the upper voice moves in oblique motion from a perfect fifth to a sixth above a bass line, often for better voice leading or to create a consonant neighbor or passing tone in second-species counterpoint. 8–7 A common figured bass symbol indicating the voice an octave above the bass descends by step, creating a seventh above the bass often resulting in a seventh chord. accent A stressed event in musical time that stands out in comparison to nearby events. accented chromatic neighbor (ACN) A threenote figure identical to the chromatic neighbor but occurring on accented beats. accented embellishing tone A metrically stressed embellishing tone. accented incomplete neighbor tone (AIN) A metrically stressed pitch approached by leap and left by step or approached by step and left by leap. See also neighbor tone. accented neighbor (AN) A neighbor tone that occurs in a strong metrical position. accented neighbor tone (ANT) A three-note figure identical to the unaccented neighbor tone but occurring on an accented beat. accented passing tone (APT) A dissonant member of a passing tone that occurs on an accented beat. accidental Symbols (    ) written before a note to raise or lower its pitch. Accidentals apply

to pitches, not pitch classes, and are canceled by bar lines. aggregate See chromatic collection. agogic accent See rhythmic accent. Alberti bass A common broken-chord accompaniment pattern in the Classical era. all-interval tetrachord The tetrachords [0146] and [0137], which have the IC vector ⬍111111⬎, that is, one of each of the six possible intervals. alla breve See cut time. altered dominant seventh chord A dominant seventh chord where 2 is chromatically altered, creating yet another tendency tone which must resolve down by half step. alternating sevenths A D2 sequence where every other harmony is a seventh chord whose dissonant chordal seventh is treated like a suspension (prepared by common tone and resolved down by step). ambitus The interval between the highest and lowest pitch of a melody. amen cadence See plagal cadence. anacrusis An unaccented musical event that leads into an accented musical event, also called an upbeat. antecedent The harmonically open first phrase of a period, ending with a half cadence (HC) or imperfect authentic cadence (IAC). anticipation (ANT) A metrically weak dissonant pitch that is a member of an upcoming chord but enters early, before the rest of the chord members. G-1

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applied (dominant) chord A dominant-functioning chord built on a scale degree other than 1, used for tonicization. A diminished triad cannot be tonicized.

augmented triad A triad that contains two major thirds, spanning an augmented fifth, which is therefore dissonant.

appoggiatura (APP) An unprepared dissonance occurring on a strong beat, resolving by step, usually in the direction opposite the leap.

auxiliary tone See neighbor tone.

arpeggiating six-four chord An unaccented six-four chord resulting from a figurated texture or an accompanimental pattern, common in marches, waltzes, and folk tunes. arpeggiation (ARP) Consonant leaps that occur in the same direction and include all members of the triad or seventh chord. articulation The degree to which each of a succession of notes is separated in performance. articulative accent An accent based on changes of dynamics, articulation, or ornamentation. ascending 5–6 sequence Another label for A2 (⫺3/⫹4) with every other chord in first inversion. ascending-bass arpeggiation See harmonic arpeggiation. ascending-second sequence (2 types) A sequence where each copy is repeated up a second. Two types have different root motions, as described in their labels. Type 1: Either A2 (⫹5/⫺4 or ⫺4/⫹5). The root of each chord moves up the circle of fifths, the opposite of the descending-second sequence. Type 2: A2 (⫺3/⫹4) This type often has every other chord in inversion, utilizing 5–6 motion in the upper voice. asymmetrical meter (1) Meter whose number of beats is not divisible by 2 or 3. (2) Meter whose number of beats combines both 2’s and 3’s. asymmetrical period A period with an uneven number of distinct phrases. atonal music Music that doesn’t gravitate toward a certain pitch or sonority. augmentation The lengthening of all rhythmic values in a melody or motive, usually by the ratio 2:1 or 4:1. augmented interval The largest quality of interval. Perfect intervals and major intervals become augmented when their size is increased by one half step. augmented sixth chord A chromatic pre-dominant chord that always has a bass line 6–5 and upper voices 4–5 and 1–1. The interval between 6 and 4 forms an augmented sixth.

back-relating dominant (BRD) A dominant chord that prolongs a previously sounding tonic without resolving to a following tonic. balanced binary form A binary form where both sections end with similar material (sometimes transposed). bar line A vertical line that defines the borders of a measure. bass clef The clef that indicates the position of F3 (also called an F clef ) and is used by the cello, bassoon, trombone, tenor and bass voices. A bass clef is the lower staff of a grand staff. beat A unit of measurement of the rhythmic pulse of a piece of music. beat division A division of a beat into two parts (simple) or three parts (compound). best normal order See normal order. A refinement of normal order that is defined by having the smallest intervals of the normal order on the left side of the ascending integers. For example, (256) represents a set in normal order, but not best normal order, because the smallest intervals appear on the right side of the set (the interval class content is 3–1 in normal order, but best normal order would require 1–3). The best normal order would be {67t}, derived from mod-12 inversion and reversing the PC order. binary form A form that divides into two sections, each usually with repeat signs. borrowed division The use of simple subdivision in a compound meter (duplets) or compound subdivision in a simple meter (triplets). broken chord A chord whose notes are performed in succession rather than simultaneously. cadence A point of harmonic and melodic arrival that occurs at the end of a phrase. cadential extension The repetition of certain elements of phrase (the pre-dominant area and the dissonant, first part of the cadential six-four chord) after an evaded cadence for greater intensity. cadential six-four chord A root-position dominant harmony whose chordal fifth and third are temporarily postponed by an accented dissonant fourth and sixth. These upper-voice, nonharmonic tones are resolved down by step.

Glossary caesura Any type of pause within or between phrases. cantus firmus (Latin: “fixed song,” plural cantus firmi) A given melody that may not be altered, for use in counterpoint exercises or as the basis of a polyphonic work. cell See intervallic cell. centric music Music that gravitates toward a certain pitch or sonority. chaconne A type of continuous variations built on a repeating harmonic progression. character piece A short, expressive work often with a descriptive title common in the Romantic era. chorale style A four-voice texture in which two notes (voices) are written in the treble clef and two notes (voices) are written in the bass clef and are played with the left hand. chord Any combination of two or more pitches sounding simultaneously. chordal dissonance A dissonant pitch, usually a seventh, added to a triad. chordal extension Adding an additional pitch to a chord, such as a ninth, eleventh, or thirteenth. chordal leap (CL) A leap from one chord tone to another within a single harmony. Chordal leaps may be dissonant if they occur within V7. chromaticism (Latin, chroma: “color”) Any pitch that lies outside the diatonic system. Also two pitches of the same letter name a half step apart (such as C and C). chromatic alteration (1) An accidental. (2) A modification made to a figured bass symbol. (3) Substituting a chromatic pitch for a diatonic pitch, integral to tonicization and modal mixture. chromatic collection In atonal music, all 12 pitch classes (PCs). chromatic common-tone harmonies There are two types: common-tone augmented sixth chords and common-tone diminished seventh chords. Both types embellish the prevailing harmony. chromatic common-tone modulation A type of modulation using a common tone that links two nondiatonic keys usually lying a third above or below one another.

G-3 chromatic neighbor tone (CN) A neighboring tone creating a half step between a diatonic pitch and a nondiatonic pitch. chromatic passing tone (CPT) A pitch that fills in the space between two diatonic tones a major second apart. chromatic pivot-chord modulation A chromatic modulation employing a pivot chord, which must always result from modal mixture. chromatic scale A symmetrical scale consisting of all 12 chromatic pitches arranged by half step. There is only one unique chromatic scale. chromatic sequence A sequence where all the odd chords (the first, third, fifth, etc.) contain altered scale degrees. The mere presence of accidentals does not guarantee that a sequence is chromatic (such chromaticism usually indicates an applied chord sequence). The roots of the chords in a chromatic sequence move by equidistant, rather than diatonic, intervals. chromatic voice exchange A voice exchange where one pitch is altered chromatically, resulting in a cross relation, which can be softened by intervening passing tones. circle of fifths The arrangement of the tonics of the 12 major or minor keys by ascending or descending perfect fifths, making a closed circle. clef A symbol placed on the far left of every staff, indicating the location of pitches in a specific octave. close position A compact type of spacing where it is not possible to insert an additional chord tone between the upper three voices (soprano, alto, and tenor). closely related keys The set of keys that are one accidental away from the tonic key. In a major mode: ii, iii, IV, V, vi. In minor: III, iv, v (V), VI, VII. coda Extra musical material that occurs beyond the point at which a piece could have ended. codetta A small coda at the end of the exposition in sonata form. common time A meter signature indicating four quarter notes to a bar: . common tone A pitch that is held over in the same voice in the same octave through a change in harmony.

chromatic half step A half step of two of the same letter names (e.g., G and G).

common-practice period The Baroque, Classical, and Romantic periods of Western art music (ca. 1650–ca. 1900), in which the prevailing musical language was tonal.

chromatic modulation Modulation to a chromatically related key, which is any key more than one accidental away from the tonic, such as C major and A major.

common-tone augmented sixth chord (c.t.⫹6) An augmented sixth chord that usually prolongs tonic by holding 1 as a common tone.

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common-tone diminished seventh chord (c.t.o7) A diminished seventh chord that shares a common tone with the prevailing diatonic harmony. composite form A large form constructed of multiple compound form sections that are self-contained (e.g., ternary and rondo forms). composite phrase A phrase that comprises three or more subphrases, but still has only one large cadence. compound form A smaller, nested section contained in a larger composite form (i.e., binary form or rondo). compound intervals Intervals larger than an octave. compound melody The impression of two independent voices or the implication of a fuller harmony with only a single melodic line.

contour The rise and fall (shape) of a melodic line. contour accent An accent based on a change in direction of a melodic line. contrapuntal cadence A contrapuntally weak imperfect authentic cadence (IAC) where the bass does not move 5–1 (but rather 7–8 or 2–1). Another way to describe this phenomenon is to say I or V (or both) inverted. contrapuntal expansion The prolongation of a functional area (tonic, pre-dominant, or dominant) within the phrase model through use of contrapuntal harmonies. contrapuntal framework The contrapuntal foundation between soprano and bass that is fleshed out with inner voices.

compound meter Meters in which the beat is divided into three parts.

contrapuntal motion The contours produced between two or more voices (i.e., contrary, parallel, similar, or oblique).

conjunct motion Motion by step.

contrapuntal texture See polyphonic texture.

consequent The harmonically closed final phrase of a period, which ends with strong authentic cadence (AC).

contrapuntal voice The added voice that is composed against the cantus firmus.

consonant/consonance The quality in an interval or chord that seems complete and stable.

contrary motion Contrapuntal motion where voices move in opposite directions.

consonant intervals Stable intervals, including the unison, third, fifth (perfect only), sixth, octave, and their compound versions.

contrasting period A period with phrases that are melodically dissimilar (ab).

consonant leap A leap from one consonance to another, both of which are usually part of a single triad.

copy The repetition of the two-chord model in a harmonic sequence at a given ascending or descending interval.

consonant neighbor A neighboring tone that creates a consonance within the prevailing harmony (a third, perfect fifth, sixth, or octave). consonant passing tone A pitch that is consonant with the cantus firmus or prevailing harmony and is approached and left by step, usually filling in the interval of a third. continuous binary form A binary form where the first section ends away from the tonic. continuous period A period with an antecedent that ends with a half cadence (HC) and a consequent that begins away from tonic, ending with an authentic cadence (AC) in tonic. continuous ternary form A type of ternary form where both the A and B sections close away from their respective tonic chords (ABA′). continuous variations A type of variation set with a relatively short theme that is often harmonically open to facilitate repetition. Examples: ground bass, chaconne, passacaglia.

counterpoint The relationship between and movement of two or more voices. courtesy accidental An optional accidental placed in parenthesis as a reminder to performers. cross relation A chromatic pitch occurring directly after its diatonic version in another voice. Cross relations are the result of unprepared chromaticism. cut time A meter signature indicating two half notes to a bar: . da capo (Italian: “from the head”) aria An important ternary form in the Baroque era, usually incorporating instrumental ritornellos. The repeat of the A section is often embellished. da capo form A type of ternary form where the performer repeats the A section by simply returning to the beginning of the piece. deceptive motion The progression V–vi (V–VI in minor), when V–I (V–i in minor) is expected.

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Glossary dependent transition (DTr) A transition that begins with a restatement of the initial theme from the first tonal area (FTA) in sonata form. descending-bass arpeggiation See harmonic arpeggiation. descending-fifth sequence Another term for the descending-second sequence, because each chord’s root moves down the circle of fifths. descending-second sequence A very common sequence where each copy is repeated down a second. The label is either D2 (⫺5/⫹4 or ⫹4/⫺5) or falling fifths depending on the root motion of each chord. descending-third sequence A sequence where each copy is repeated down a third. The label is always D3 (⫺4/⫹2), and is the same progression as Pachelbel’s Canon in D major. descriptive analysis See first-level analysis. development The second section of a sonata that presents material from the exposition (and sometimes new material) in various harmonic and melodic contexts. It ends with a retransition (RTr) to prepare the return of tonic at the beginning of the recapitulation. The development of sonata form is analogous to the digression in binary form.

diminution (1) Embellishing a melody by filling in the steps in a larger interval (e.g. eighth or sixteenth notes added to a primarily quarter-note chorale texture. (2) The shortening of all rhythmic values in a melody or motive, usually by the same ratio (i.e., by half ). direct intervals Similar motion to a perfect interval. It is forbidden in strict counterpoint unless the upper voice moves by step. direct step-descent bass The bass line 8–7–6–5 in major or minor, which can be harmonized in a variety of ways. direct modulation See unprepared chromatic modulation. disjunct motion Motion by leap. dissonance Musical events that are unstable (e.g., a tritone). dissonant intervals Unstable intervals, including the second, fourth (can be consonant), and seventh, their compound versions, and all diminished and augmented intervals. dissonant neighbor A neighboring tone that creates a dissonance within the prevailing harmony (a second, fourth, seventh, or any augmented or diminished interval).

developmental repetitions Restatements of a motive that are significantly altered, and consequently more difficult to recognize.

dominant Scale degree 5, or the triad built on scale degree 5.

diatonic Literally “through the tones,” meaning the collection of seven pitches in a major or minor scale with each letter name represented once, as distinct from chromatic pitches of the same letter name.

dominant substitute A harmony other than V or V7 that has a dominant function (e.g., viio6).

diatonic collection A collection including all seven pitch names. diatonic half step A half step of two different letter names (e.g., G and A, as in the E major scale). diatonic intervals Intervals found in the major, minor, and other modes (without chromatic alteration). diminished interval The smallest quality of interval. Perfect intervals and minor intervals become diminished when their size is decreased by one half step. diminished seventh chord A chord containing a diminished triad and diminished seventh (dd7, or o7). This is the most dissonant seventh chord. diminished triad A triad containing two minor thirds, spanning a diminished fifth, which is therefore a dissonant triad.

dominant seventh chord See major-minor seventh chord.

dot A mark placed adjacent to a note that lengthens the value of a note or rest by half its original value. double counterpoint See invertible counterpoint. double flat An accidental () that lowers a natural pitch (e.g., B, F, or C) by two half steps (or an already-lowered pitch by one half step). double period A period with large antecedent and consequent phrases that themselves divide into smaller antecedent and consequent phrases. double sharp An accidental () that raises a natural pitch by two half steps (or an already-raised pitch by one half step). double suspension Two simultaneous suspensions in two different voices. double tonality Two keys that simultaneously vie for supremacy or simply coexist as tonic.

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double-neighbor figure (DN) Stepwise ascent or descent from a chord tone, followed by a leap by third to the opposite neighbor and return to the initial chord tone. doubling When two or more voices share the same pitch at the unison or octave. downbeat The first and strongest metrically accented beat of a measure, where a conductor’s baton goes down. duple A subdivision of the measure into two parts (strong–weak). duplets Two-note groups appearing in a compound meter. durational accent See rhythmic accent. dyad Any two pitches. dynamics The loudness or softness of a sound. échappé See escape tone. eleventh The compound version of the interval of a fourth, often found in the music of the twentieth century as a chord tone. The interval of a third built above a seventh is called a chordal extension: a third above the seventh is a ninth chord; a third above the ninth is an eleventh chord. elided resolution When normal dissonance resolution is omitted, as in V7→I→V7/IV: V7→V7/IV. elision The technique of combining two independent phrases to create one large phrase, often with an evaded cadence. Elision also occurs in spoken language, as in “thisnake,” an elision of “this snake.” embedded phrase model Miniature “Tonic–PreDominant–Dominant–Tonic” models that occur anywhere in the tonic prolongation portion of a phrase. embellished suspension A suspension using figurations to embellish the dissonant note. embellishing chord (EC) A metrically weak chord that ornaments the prevailing harmony. embellishing tone A general term for neighboring tones, consonant leaps, passing tones, etc., that may be consonant or dissonant. embellishment The process of adding neighboring tones, consonant leaps, passing tones, etc. to a contrapuntal framework. enharmonic equivalence Two notes that differ in name but not in pitch, such as C and D.

modulation to remote keys, especially when applied to symmetrical harmonies. episode (rondo form) The alternating B and C sections that provide variety, separated by recurrences of the refrain. equal divisions of the octave Intervals (minor second, major second, minor third, major third, and tritone) that partition the octave equally. equivalence class The grouping of elements, usually pitch classes based on one or more relationships, such as transposition and inversion. See also inversionally symmetrical; octave equivalence; temporal equivalence; transpositional equivalence. escape tone A type of incomplete neighbor that is approached by step and left by leap. evaded cadence A general term for a cadence that deviates from the expected arrival on root-position tonic. A contrapuntal cadence is an example, where a passing seventh in the bass resolves to I6 or i6. Deceptive motion (V– vi) is also an evaded cadence. even index number When combining two inversionally related sets, an even index number will maintain dyad pairings. See also index number ; odd index number. expectation/fulfillment The Gestalt principle of creating an event requiring resolution. Sometimes resolution of an established pattern is delayed for dramatic effect. exposition The first large section of a sonata containing the first tonal area (FTA), transition (Tr), second tonal area (STA), closing material (CL), and perhaps a codetta. extended third-related second tonal area (STA) A second tonal area (STA) in sonata form, which remains in the mediant for the entire exposition, delaying the dominant until the retransition at the end of the development. extended tonicization A tonicization involving multiple applied chords. false recapitulation A harmonic anomaly sometimes used at the end of the development where the first tonal area (FTA) occurs, but in the “wrong” key. The real recapitulation, in the tonic, usually follows soon after. figured bass A shorthand notation used between 1600 and 1800 to describe the intervals above the bass note, also called thoroughbass. Figured bass always contains a bass note and a figure (unless the figure is purposely omitted, indicating a root-position triad).

enharmonic pun See enharmonic reinterpretation.

first inversion When the third of a triad or seventh chord is in the bass.

enharmonic reinterpretation Rewriting a pitch as its enharmonic equivalent (e.g., G as F), allowing

first tonal area (FTA) The material in the tonic key at the beginning of the exposition in sonata form.

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Glossary first-level analysis The objective process of identifying each sonority with roman numerals and figured bass.

half step The smallest interval, corresponding to the distance between any two adjacent keys on the piano.

first-species counterpoint (1:1 counterpoint) Two or more voices that move at the same rate.

harmonic arpeggiation A harmonized bass line that moves by thirds (e.g., the descending harmonic arpeggiation: 1–6–4 or the ascending harmonic arpeggiation: 1–3–5).

flag A curved line placed on the stem of a notehead to shorten its value. One flag ⫽ 8th note; two flags ⫽ 16th note, etc. fragmentation A transformation that develops only a portion of a motive, such as a neighbor figure or even a single interval. French augmented sixth chord (Fr43) The fourth voice has 2. See augmented sixth chord for the other three voices. full score See open score. full sectional ternary form A type of ternary form where each of the three sections closes in its respective tonic (A || B || C). fully diminished seventh chord See diminished seventh chord. gap-fill The Gestalt principle that a leap creates the expectation of stepwise motion in the opposite direction that fills the gap created by the leap. generic size A numerical label for an interval that identifies the distance between letter names, measured by including the first and last notes.

harmonic interval Any interval played simultaneously. harmonic minor scale One of the three forms of the minor scale, using a minor sixth above tonic for 6 (e.g., in C minor, A) and a major seventh above the tonic for 7 (e.g., in C minor, B). harmonic mixture A type of modal mixture employing chromatic alteration of a chord’s root. harmonic paradigm A short chord progression, or even just outer voices, that serves as a contrapuntal framework for embellishment in many tonal pieces. harmonic rhythm The rate at which harmonies change. harmonic sequence A repeating pattern containing a two-chord model, whose copies are repeated at a given ascending or descending interval. Sequences can have every other chord in first inversion, alternating or interlocking seventh chords, or applied chords. harmonized neighbor A neighboring tone made consonant by a supporting harmony. helping chords See voice-leading chord.

German augmented sixth chord (Gr65) The fourth voices has 3. See augmented sixth chord for the other three voices.

hemiola A type of syncopation where the established meter is temporarily displaced by a competing meter (e.g., duple meter imposed on triple meter).

German diminished third chord (Gr7) An inversion of the augmented sixth chord with bass line 4–5 and upper voices 6–5 and 1–1.

hexachord A grouping or set of six pitch classes. See also hexatonic.

good continuation The Gestalt principle that established patterns of texture, mood, or harmonic rhythm tend to continue. Gradus ad Parnassum A treatise on counterpoint by Johann Fux (1660–1741) summarizing the style of Palestrina into various “species,” or rhythmic ratios. grand staff The combination of treble and bass clef connected by a brace, used in keyboard music. gravitational center The tonic pitch, toward which other seem to be pulled. ground bass A type of continuous variations built on a repeating bass line, often a direct step-descent bass. half cadence A cadence that ends on the dominant. half-diminished seventh chord A chord containing a diminished triad and minor seventh (dim7, or ø7).

hexatonic A scale or collection consisting of six notes. Ordered as a scale its pattern is 1–3–1–3–1–3. See also hexachord. hexatonic poles Pairs of triads that generate the entire hexatonic scale (e.g., C major and A minor triads). hidden intervals See direct intervals. hidden motivic repetitions See motivic parallelism. hierarchy Grouping musical events based on their relative importance. Hollywood cadence A chromatically altered IV–I cadence that uses 5–6 motion to change IV to iiø65, labeled as plagal motion (PL) and which leads directly to the tonic. homophonic texture A cross between monophony and polyphony, usually containing a melody and accompaniment (e.g., a chorale in four voices).

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illegal doubling A doubling that will result in parallel octaves (e.g., doubling the leading tone in a dominant chord). imitation The repetition of a motive in a different voice. imperfect cadence See half cadence. imperfect authentic cadence (IAC) A type of authentic cadence that is weaker than a perfect authentic cadence (PAC). An IAC ends with the soprano on 5 or 3. imperfect consonances Moderately stable intervals: major thirds (M3), minor thirds (m3), major sixths (M6), minor sixths (m6). incomplete neighbor (IN) A leap to a note that neighbors a chord tone, followed by resolution to that chord tone by step. incomplete neighboring chord A harmonized incomplete neighbor tone, as in the bass of the progression i6– V6–i. independent transition (ITr) A transition that uses new thematic material, avoiding a restatement of the initial theme from the first tonal area (FTA) in sonata form. index number The sum of the intervals of two inversionally related pitch class sets, revealing the level of transposition needed to make them equivalent. See also even index number; odd index number. indirect step-descent bass The bass line 8– 7–6–5–4–5 in major or minor, which can be harmonized in a variety of ways. interlocking sevenths A sequence where every harmony is a seventh chord. Their dissonant chordal sevenths are treated like a suspension (prepared by common tone and resolved down by step). interpolation The substantial addition of pitches to a motive, creating the effect of an insertion rather than a mere embellishment. interpretive analysis See second-level analysis. interrupted period A period with an antecedent that ends with a half cadence (HC) and a consequent that restarts on tonic, ending with an authentic cadence (AC) in tonic. interruption A term that captures the procedure in which the dominant that closes a phrase (half cadence) does not continue to the following tonic, but rather it interrupts the motion to the expected authentic cadence. It is only in the restart of the following phrase that the dominant leads to the tonic. The moment of interruption is shown by two vertical slashes. The interruption can occur at deeper levels, as in a binary form, where the tonic ultimately moves to the dominant at the end of the digression.

The restart on tonic and continuation to the authentic cadence allows the dominant to finally move to and be resolved by the tonic. For example: I→V–|| I–V–I). Notice the distinct correlation between this model and that of sonata form, where the end of the retransition is the point of interruption and the beginning of the recapitulation in the tonic restarts the tonal motion and ultimately leads to an authentic cadence. interval The musical distance between two pitches. interval class (IC) The measurement of the smallest distance between two pitch classes regardless of their order using mod-12 inverses; e.g., a minor seventh ⫽ 10 half steps but the interval class is 2, since order is not taken into account, only the shortest span. interval class vector The number of each of the six interval classes that appears in a pitch-class set. intervallic cell A high-profile intervallic motive that permeates a piece. These motives generate more abstract collections of pitches defined by their intervallic content and contour, instead of relying on period structures and singability. invariant/invariance The retention of pitch classes following one or more operations (e.g., transposition and inversion). inversion (harmonic) A chord with any chord tone other than the bass is said to be in inversion. inversion (intervallic) A process applied to an interval where the lower pitch is moved up an octave, or the upper pitch is moved down an octave. The inversion of a generic interval always sums to 9. inversion (motivic) A transformation that projects each interval in a motive in the opposite direction (e.g., up a third becomes down a third). inversionally symmetrical A pitch-class set in which the intervallic pattern is the same read from left to right or right to left. invertible counterpoint A procedure where contrapuntal lines are swapped between voices. irregular division A division of the beat into something other than two or three parts. Italian augmented sixth chord (It6) The fourth voice doubles 1. See augmented sixth chord for the other three voices. key (1) A musical composition based on a certain scale is said to be in that key, identified by its tonic pitch. (2) The lever on an instrument depressed by the finger. keyboard style A four-voice texture in which three notes (voices) are written in the treble clef within the space of

Glossary an octave and are played with the right hand, and one note (voice) is written in the bass clef and played with the left hand. lament bass A step-descent bass in the minor mode. law of recovery The tendency for a leap to be followed by step in the opposite direction. See gap-fill. leading tone Scale degree 7 (raised 7 in the minor mode), a half step below tonic. leading-tone chord A triad or seventh chord that is built on the leading tone: viio6 or viio7. leap Motion by intervals larger than a third, usually requiring stepwise motion in the opposite direction. ledger lines Short horizontal lines above or below a staff to accommodate pitches that exceed its range. Lied [plural: Lieder] German for “song,” usually referring to the art songs of the Romantic era. linkage A technique to smooth the connection between contrasting sections of a piece, whereby a motivic element is retained in both sections but is necessarily transformed in order to fit into the new musical environment. literal complement A collection that can be combined with another one to form an aggregate. lower neighbor (LN) A neighboring tone a step below a chord tone. major mode The scale organized with in the following steps: W–W–H–W–W–W–H major seventh chord A chord containing a major triad and a major seventh (MM7). major triad A consonant triad that contains a major third stacked below a minor third, spanning a perfect fifth. major-minor seventh chord A chord containing a major triad and a minor seventh (Mm7). Also called a dominant seventh, this chord appears regularly built on 5 in both the major and minor modes. major/minor (M/m) A category of intervals including the second, third, sixth, and seventh, or a possible quality for such intervals. mapped/mapping Relating two pitch-class sets through an operation (e.g., transposition or inversion). marked for consciousness An event that receives the listener’s attention. measure A unit of musical time with a fixed number of beats. mediant Scale degree 3, or the triad built on scale degree 3.

G-9 melodic cadence The approach to a stable pitch, most often scale degrees 7–1 or 2–1. melodic climax The high point of a melody, often approached slowly and by step. melodic fluency The underlying scalar patterns that support the infinite variety of melodic embellishments that lie on the music’s surface. melodic interval Any interval played consecutively. melodic minor scale One of the three forms of the minor scale. The scale uses two intervallic patterns, one ascending and one descending. When ascending, a major sixth occurs above the tonic for 6 (e.g., A above C) and a major seventh above the tonic for 7. When descending both 6 and 7 are lowered one half step (forming a minor sixth and minor seventh above the tonic, respectively). melodic mixture A type of modal mixture employing chromatic alteration of a chord’s quality (chordal third or fifth), but not its root. meter The grouping of both strong and weak beats into recurring patterns. meter signature Two numbers, one on top of the other, written at the very beginning of the piece. Top number ⫽ number of beats in a measure (simple) or number of beats in a measure once divided by three (compound); bottom number ⫽ note value of the beat. Also called time signature. metric modulation Changing the meter through: (1) maintaining the beat and introducing new divisions of the beat; or (2) maintaining the division of the beat and introducing a new beat level. metric strata Two or more simultaneously sounding lines that feature independent meters. metrical accent An accent that occurs through the natural hierarchy of a measure. Downbeats almost always receive a strong metrical accent. metrical figuration An embellishing figure with a duration of one beat. minor mode A seven-pitch collection characterized by a minor third above 1. minor seventh chord A chord containing a minor triad and a minor seventh (mm7). minor triad A consonant triad that contains a minor third above the root and a major third above the third, spanning a perfect fifth. minuet A Baroque dance in simple triple meter that became a standard inner movement in Classical symphonies and chamber pieces.

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THE COMPLETE MUSICIAN

minuet-trio form A common inner movement in the Classical era. The minuet is followed without pause by a trio with a da capo marking. This creates a large ternary form when the minuet is repeated. Each section is usually in binary form. mirror inversion See inversion (motivic). mod-12 arithmetic A numbering system used in posttonal music to label each pitch using an integer between 0 to 11, with C as 0, C/D as 1, etc. mod-12 inverses Two interval classes whose total number of half steps sum to 12; e.g., C to G (7) and G to C (5) equals 12. modal mixture The technique of borrowing harmonies from the parallel mode. Usually elements of the minor mode are imported to the major mode. model The initial pair of chords that form the basis for sequential repetition. modified motivic repetition Restatements of a motive in which elements of the pitch and/or rhythm are varied. modified period A period that does not fit the antecedent/consequent model. Common modified periods may take the form aab or abb. modulation A large tonicization, which occupies an entire section of a piece, usually confirmed by a strong cadence in the new key.

neighbor tone (N) Stepwise ascent or descent from a chord tone, followed by a change in direction and return to the initial chord tone. neighboring chord A harmonized neighbor tone. nesting of sentences Miniature 1:1:2 relationships within a larger sentence; e.g., 1 ⫹ 1 ⫹ 2, with the 2 being structured as 1/2 ⫹ 1/2 ⫹ 1. ninth The interval of a ninth or a second above a harmony, such as C–E–G–B–D, with D sounding as either a ninth or as a second above C. nonchord tone A pitch that is not a member of the prevailing harmony. nondominant seventh chord A seventh chord without dominant function (i.e., IV7, ii7, vi7, etc.). These chords do not have a dominant (Mm7) or leading-tone (dd7) quality. nonretrogradable rhythm A rhythm pattern that is the same when played forward or backward. normal order The first step in determining the intervallic content of a set of pitch classes. Obtained by determining a set’s most compact form (smallest intervallic span) and arranging the pitch class integers in ascending order from smallest to largest. note-against-note counterpoint See first-species counterpoint.

monophonic texture A single-line melody with no accompaniment (e.g., a cantus firmus alone).

notehead A filled or unfilled oval placed on a staff to indicate both pitch and rhythm.

monothematic sonata form A sonata form where the second tonal area (STA) restates the same theme (although often varied) as the first tonal area (FTA).

oblique motion Contrapuntal motion where one voice is stationary and the other moves (as in second-species counterpoint).

motive The smallest formal unit of musical organization, used to create melodies and even harmonies.

octatonic collection A collection of eight pitch classes.

motivic nesting The hierarchical interconnection between large-scale and small-scale motives. motivic parallelism Repetitions of a motive in different musical contexts and at different structural levels. motivic saturation The appearance of many statements of a motive, often varied, within a short time span. musical texture The general density of a piece, based on the number of voices and their relative activity. natural A symbol () that cancels previous accidentals and returns a pitch to its unaltered form. natural minor scale One of the three forms of the minor scale, using lowered 6 and lowered 7. Minor key signatures refer to the natural minor scale. Neapolitan chord II with a pre-dominant function, usually written in first inversion.

octatonic scale A symmetrical scale consisting of eight pitches, alternating half steps and whole steps. There are three unique octatonic scales: C–D–E–F…; C–C– D–E…; and C–D–E–F…. Restatements beginning on any other pitches are members of one of these three forms. octave The interval between two pitches of the same letter name with frequencies that are related by the ratio 2:1. octave displacement Transposition of a melodic fragment or motive by an octave. octave equivalence Identifying all pitches of the same name as identical pitch classes, no matter what their registral placement. octave sign A symbol that indicates that a passage should be played an octave higher (8va) or lower (8vb) than notated.

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Glossary octuplet A division of the beat into eight evenly spaced parts.

passing tonic A tonic chord that elaborates a predominant or dominant function.

odd index number An odd number sum resulting from two inversionally related pitch sets. See also even index number ; index number.

pedal (PED) A sustained pitch, most often in the bass, with tonic or dominant function. Surface harmonic activity usually occurs above.

off-tonic beginning Postponing tonal stability at the beginning of the piece to create ambiguity and a heightened sense of expectation. Off-tonic beginnings are common in nineteenth-century music.

pedal six-four chord An unaccented harmony resulting from two simultaneous neighboring figures or passing figures in upper voices with the bass sustained.

omnibus A type of prolongation (usually of the dominant function) where one or more upper voices move chromatically and in contrary motion to the bass, which ascends or descends chromatically. The result is a symmetrical division of the octave by minor thirds. open position Any voicing where there is a missing chord tone between any two of the three upper voices. There are innumerable ways of writing a chord in open position. open score A score where each voice has its own staff and clef. ornamentation How a melody is varied or embellished in a score or performance. ostinato A repeated rhythmic and/or pitch pattern.

pentatonic collection A collection of five pitch classes. perfect authentic cadence (PAC) The strongest type of authentic cadence where the soprano moves 7–8 or 2–1 and the bass moves 5–1. perfect consonances The most stable class of intervals: perfect unisons (P1), perfect fifths (P5), and perfect octaves (P8). perfect interval (P) A category of intervals including the unison, fourth, fifth, and octave. period One or more antecedent phrases with weak cadences (e.g., IAC, HC) paired with a consequent phrase that closes more definitively (e.g., PAC). phenomenal accent See articulative accent.

outer-voice counterpoint The relationship between the soprano and bass voices.

phrase A self-contained musical event ending in a cadence.

parallel keys Major and minor keys with the same tonic.

phrase group A series of phrases containing unrelated material, punctuated by weak cadences or caesuras. Only the last cadence is strong enough to close the group.

parallel motion Contrapuntal motion where voices move in the same direction by the same intervals (e.g., both voices move up a step). parallel perfect intervals Parallel motion to or from two perfect intervals of the same size (e.g., P5 to P5) is forbidden.

phrase model The paradigm that all harmonies fall into one of three functional categories (tonic, pre-dominant, and dominant). They tend to progress in the order T– PD–D–T within a phrase.

parallel period A period with phrases that are melodically similar (aa or aa′).

phrasing slur A curved horizontal line connecting two different pitches that are intended as a single musical idea, usually played legato.

parsimonious voice leading Voice leading that uses stepwise motion (usually semitonal) and the retention of one or more common tones.

Phrygian half cadence A half cadence iv6–V in minor.

part See voice (contrapuntal). part exchange A multiple-pitch voice exchange. partitioned row A row that is broken into more than one section, usually divided by 3, 4, or 6.

Picardy third A major tonic triad that ends a piece in a minor mode. pitch (1) A frequency generated by a vibrating body. (2) A musical tone or note.

passacaglia A type of continuous variations built on a repeating harmonic pattern and a repeating bass pattern.

pitch accent An accent based on the instability of certain pitches, such as the leading tone (7), which require resolution.

passing chord A harmonized passing note, as in the bass line of the progression I–viio6–I6.

pitch class (PC) All pitches related by one or more octaves including enharmonic equivalents (e.g., B and C).

passing six-four chord An unaccented harmony resulting from a passing figure in the bass.

pitch (or pitch-class) center A pitch in a collection toward which all others gravitate.

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THE COMPLETE MUSICIAN

pitch-class (PC) set A collection of pitch classes arranged by invoking various equivalences (e.g., transposition, inversion, enharmonicism, etc.) defined by their intervallic relationship. pitch-class (PC) space A modular, circular world that permits only 12 pitch classes. pitch invariance See invariant/invariance. pitch set A collection of different pitches. pitch space A space where an infinite number of pitches can occur. Pitch space does not admit equivalents (e.g., register, enharmonicism, etc.). pivot area See pivot chord. pivot chord A chord used in a modulation that is diatonic to the old key and the new key. The best pivot chords function as pre-dominant in both the original key and the new key. plagal cadence A cadence involving IV–I, often used at the end of hymns at the text “Amen.” plagal motion A subdominant-function harmony leading to tonic, often using modal mixture, as in the “Hollywood cadence” (iiø65–I). plagal relation The increasingly important function of plagal motion (especially iv–i and iiø65) in nineteenthcentury chromaticism. polyphonic texture The combination of two or more independent melodies such that there is no clear distinction between melody and accompaniment (e.g., a Bach fugue). polyphony See counterpoint. polyrhythm The simultaneous statement of two or more different beat divisions. post-tonal music Music of the twentieth and twentyfirst centuries that does not exhibit the hallmarks of tonal music, including a harmonic hierarchy with a single pitch or chord to which other pitches or chords are drawn, use of vertical sonorities comprised of thirds, and a clear distinction between consonance and dissonance. pre-dominant (PD) A chord that leads to the dominant (IV, ii, vi, and their inversions). preparation The way a pitch is approached, usually in reference to a dissonance, such as the suspension, which must be approached by common tone. prime (1) See unison; (2) The first ordered presentation of a row in a twelve-tone composition. prime form (or set class) The best normal order of a PC set transposed to begin on zero. Square brackets identify sets in prime form ( [ ] ). The prime form of the 236 and 67t are both [014].

progressive period A period whose final phrase closes in a key other than tonic. prolongation See contrapuntal expansion. prolongational sequence A harmonic sequence that expands one function (e.g., tonic). pulse Undifferentiated (e.g., same quality, loudness, and so forth) and equally spaced impulses. quadruple Usually associated with meter, specifically a division of the measure into four equally spaced beats (strong–weak–semistrong–weak). quality The type of interval or chord (e.g., major, minor, augmented, diminished). quintuplet An irregular division of one or more beats into five parts. range (1) The interval between the highest and lowest notes in a melody; (2) The total span of pitches that a voice can sing, roughly the interval of a twelfth. real transposition Transposition that maintains the specific interval (both size and quality) between each pitch and its transposed repetition. recapitulation The third and last section of a sonata, containing the same material as the exposition, except with the second tonal area (STA) now in the tonic. There may also be a final coda. That the recapitulation follows the development, where a large-scale retransition leading to a structural HC, creates the overall division into two large sections: exposition/development (I–V) and recapitulation (I–I). reciprocal process The blurring of harmonic function (Tonic, Pre-Dominant, Dominant) caused by chromaticism and the plagal relation (e.g., iv–I interpreted as i–V). reduction The process of removing neighboring tones, consonant leaps, passing tones, etc., to reveal the underlying contrapuntal framework. refrain (rondo form) The recurring material from the opening of the piece (A section) that is usually untransposed and provides unity between contrasting sections. registral accent An accent based on pitch frequency, with higher notes receiving greater emphasis. reharmonization Placing a melody or small motive in a new harmonic environment. relative keys Major and minor keys with the same key signature. resolution The point of rest after a dissonance, often a suspension, which must resolve down by step, to a consonance (usually a chordal member).

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Glossary restruck suspension A suspension that omits the tie after the preparation.

score Musical notation representing two or more staves, each staff containing a clef and key signature.

retardation A suspension that resolves up by step, rather than down by step. Much less common than the suspension.

second An interval consisting of one pitch and another that lies above or below by one or two half steps. Usually the letter name of the pitches differ by one, such as C–D, C–D, C–D, etc.

retransition (RTr) Musical material that bridges from a contrasting key back to tonic. In sonata form, the retransition is the last section of the development and expands this harmonic function in preparation for the recapitulation. retrograde (1) A transformation that reverses the order of a motive’s pitches: the first pitch becomes the last, and vice versa. (2) In twelve-tone theory, the reverse of the prime order of a pitch or pitch class set; i.e., playing the notes right to left instead of left to right. retrograde inversion (1) A transformation that combines retrograde and inversion (motivic). (2) In twelvetone theory, the reverse of the inverted order of a pitch or pitch-class set. retrogression Awkward or weak harmonic progressions that contradict the phrase model (Tonic–Pre-Dominant– Dominant–Tonic), such as Dominant–Pre-Dominant. rhythm Durations of pitches and silences. rhythmic accent A surface-level accent based on duration, with longer notes receiving greater emphasis. ritornello Instrumental interludes in a da capo aria. rondeau/rondo French for “rondo,” a popular form for Louis and François Couperin, among other composers, in the French Baroque era. See rondo form. rondo form A composite form alternating self-contained sections called refrains (A) and episodes (B or C), either in five parts (A1 B A2 C A3) or seven parts (A1 B1 A2 C A3 B2 A4). root The lowest pitch of a triad or seventh chord when stacked in thirds. root motion The progression of chords based on their roots. There are three standard root motions in tonal music: descending fifth (D5), ascending second (A2), and descending third (D3). The root is not always in the bass. root position When the root of a triad or seventh chord is in the bass. rounded binary form A binary form where the return of tonic is accompanied by restatement of some or all of the first section’s melodic and motivic material (a⬘). scale degrees The numbering of the seven pitch classes in the diatonic scale, beginning with the tonic as 1. Each is marked by a caret. scherzo (“joke” or “jest”) A more spirited version of a minuet often used by Beethoven.

second inversion When the fifth of a triad or seventh chord is in the bass. second tonal area (STA) The material in the second key (usually in the dominant for major keys and in the relative major in a minor key) after the first tonal area (FTA). second-level analysis The interpretive process of distinguishing ornamental function from structural function. second-species counterpoint (2:1 counterpoint) Counterpoint wherein there are two notes in the contrapuntal voice for each single pitch in the cantus firmus. secondary dominant chord See applied (dominant) chord. sectional binary form A binary form in which the first section ends on tonic. sectional period A period with an antecedent that ends with an imperfect authentic cadence (IAC), and a consequent that ends with a perfect authentic cadence (PAC). sectional ternary form A type of ternary form where either the A section (AB || A) or the B section (A || BA) closes away from its respective tonic. sectional variations A type of variations with a longer theme (often in binary form), employing more substantial changes between each variation. segmented row See partitioned row. semitonal voice-leading A type of voice-leading where two or more voices move by half step while usually keeping one common tone in another voice. See also hexatonic. sentence structure The rhetorical device of “shortshort-long,” usually in the ratio 1:1:2. septuplets An irregular division of the beat into seven parts. sequence The immediate restatement of a musical idea (including harmony and other elements) on different scale degrees. sequential progression (1) A passage in which the harmonic structure follows a sequential pattern but the melodic structure does not. set A group of pitches or pitch classes that are often significant in the overall structure of a nontonal composition.

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THE COMPLETE MUSICIAN

set class An abstract representative of a group of pitch classes that are related by various equivalences, including transposition and inversion. For example, 2,3,5 and 6,7,9 and 4,2,1 all belong to the set class 013. The concept is best applied to post-tonal music. seventh chord A chord that in root position contains three stacked thirds, spanning the interval of a seventh. All seventh chords are dissonant, though to varying degrees. short score A score containing two to four staves that represents as closely as possible multiple instruments. Usually instrumental doublings are omitted but the goal is to replicate as closely as possible the medium for which the piece is conceived. For example, a Beethoven symphony of 20 staves, one for each instrument, could be reasonably approximated in bass and treble staves, although multiple parts would appear on each staff. similar intervals See direct intervals. similar motion Contrapuntal motion where voices move in the same direction by different intervals (e.g., one voice moves up a step, the other up a third). simple binary form A binary form where the two sections share no melodic material (ab). simple intervals Intervals an octave or smaller. simple meter A meter in which the beat is divided into two parts. six-four chord A triad consisting of a bass note with a sixth and fourth above. skip A consonant leap of a third, not requiring stepwise motion in the opposite direction. slow introduction A common initial section in a movement cast in sonata form. It usually begins on tonic, but soon moves through foreign harmonic territory, and ultimately leads to the dominant, to prepare the exposition that begins on the tonic. sonata form A three-part piece (expositiondevelopment-recapitulation) with a two-part tonal structure incorporating elements of balanced and rounded continuous binary form. sonata principle The principle that material presented in the later portion of the exposition in a contrasting key will return at the analogous spot in the recapitulation in the tonic key. sonata-rondo form A hybrid form using a seven-part rondo (A1 B1 A2 C A3 B2 A4) where B2 is transposed to the tonic (like the STA in the recapitulation) and C is expanded (like the development). Additionally, the borders between sections are blurred for greater continuity. A2 in

tonic (analogous to the closing section in dominant) is often shortened or destabilized, because it undermines traditional sonata form. spacing The distribution of voices into various registers. species A five-step pedagogical method of learning sixteenth-century counterpoint created by Johann Fux in his Gradus ad Parnassum. specific size A label for an interval that includes both the generic name and the quality. For example, perfect (quality) and fifth (quantity) ⫽ perfect fifth (specific size). staff (plural: staves) The five horizontal lines with a clef, on which pitches are notated. step The distance between two adjacent pitches. Steps may be half steps or whole steps. stretto The overlapping of motivic repetitions so that one voice begins a new statement before the previous voice has finished. strict motivic repetition Restatements of a motive in which the same pitch-and-rhythm structure is maintained. subdivision of the beat The beat is divided into two or more hierarchical levels. subdominant Scale degree 4, or the triad built on scale degree 4. subdominant return A harmonic anomaly in sonata form where the first tonal area (FTA) returns in the subdominant, rather than the tonic, at the recapitulation. This provides harmonic variety because the original transition can still modulate up a fifth, returning to tonic. submediant Scale degree 6, or the triad built on scale degree 6. submetrical figuration An embellishing figure whose duration occupies less than one beat. subphrase A relatively independent part of a phrase marked by a caesura and/or by the repetition and variation of short melodic gestures. subset A portion of a larger PC collection or set, usually used in reference to post-tonal music. subtonic Lowered scale degree 7, a whole step below tonic. sum See index number. supermetrical figuration An embellishing figure that extends beyond the value of the beat. supertonic Scale degree 2, or the triad built on scale degree 2.

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Glossary suspension (S) The most important accented embellishing tone. A stepwise melodic descent is temporarily postponed while the other voices move to the next chord, creating a dissonance before the line continues. Suspensions have three parts: a consonant weak-beat preparation (P) by common tone, a dissonant accented suspension (S), and a resolution (R) down by step to a consonance.

three-key exposition An alternate harmonic strategy in sonata form where the second tonal area (STA) is not in the dominant, but in a third-related key (usually diatonic, but, as in the case of Beethoven’s “Waldstein,” a chromatic third-related key). The closing material (CL) is then in the dominant, creating the shape I–iii–V in a major key and i–III–v in a minor key.

suspension chain A series of interlocking suspensions, where the resolution of the first suspension forms the preparation for the next suspension.

tie A curved horizontal line connecting two notes of the same pitch and whose duration is combined and performed as a single sustained note.

suspension with change of bass A suspension in an upper voice where the bass moves to another chord tone at the same time that the suspension resolves.

time signature See meter signature.

symmetrical tonal motion Harmonic motion by symmetrical intervals (e.g., by major third: C–E–A–C). symmetrically constructed harmonies Chords that possess the special ability to partition the octave into identical intervals (i.e., augmented triads and diminished sevenths). They are especially suited for enharmonic reinterpretation. syncopation A musical accent that occurs on a metrically unaccented beat or part of a beat. tempo The speed of the beat, often given in beats per minute (bpm) for use with a metronome. tempo modulation See metric modulation. temporal equivalence Identifying all pitches of the same name as identical pitch classes, no matter where they occur in a composition over time. tendency tone An unstable pitch that requires resolution, such as 7 or 4. ternary form A form with a three-part melodic design (ABA or ABA′) and a three-part tonal structure (original key–contrasting key–original key). tessitura The average (not total) range of a melody, especially for voice. tetrachord A group of four notes. textural accent An accent based on a change in the number of voices or overall patterning of a piece. third The interval between two pitch names separated by one letter name (for example C–E, F–A) third inversion A seventh chord in which the chordal seventh is in the bass. thirteenth A chordal extension of a triad created by adding the interval of a thirteenth (compound sixth) above the root of the chord. thoroughbass See figured bass.

tonal ambiguity A by-product of increasing chromaticism and the plagal relation in the Romantic era, where the location of the tonic or a harmonic motion is deliberately obscured. tonal music Hierarchically organized music using functional harmony and scale degrees centered around a tonic pitch (as distinct from modal or nontonal). tonal transposition Transposition that maintains the generic (numerical) size of the intervals, but alters the quality in order to remain diatonic. tonality The hierarchical relationship of pitches in a scale around a definite center or tonic pitch. tonic The gravitational center of a set of pitches, called scale degree 1, or the triad built on scale degree 1. tonic substitute The mediant triad or submediant triad can have tonic function, because they both share two common tones with the tonic triad. tonicization Brief emphasis on a key other than tonic by means of one or more applied chords. tonicized half cadence A half cadence incorporating an applied chord that precedes the dominant. total chromatic See chromatic collection. transition (Tr) Musical material that bridges between tonic and a new key. In sonata form, a transition occurs between the first tonal area (FTA) and second tonal area (STA). transitional sequence A sequence that moves from one function to another (for example, leading from a tonic harmony to a pre-dominant harmony: T–PD). transposition (1) The process of moving musical material up or down by a fixed interval. (2) In nontonal music, the transformation whereby all members of a pitch set are moved up or down by a consistent interval. transpositional equivalence In nontonal theory, pitch or pitch-class collections are transpositionally equivalent if all members of the collection can be mapped onto one another by the same transpositional level.

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THE COMPLETE MUSICIAN

treble clef The clef that indicates the position of G4 (also called a G clef ). It is used by violin, flute, oboe, and soprano and alto voices. A treble clef is the upper staff of a grand staff.

voice (1) In vocal music, the individual vocal line, indicated by pitch range as soprano, alto, tenor, bass. (2) In instrumental music, the individual line or part performed by each instrument or instrument type.

triad A chord comprised of three different pitches able to be stacked in thirds.

voice (contrapuntal) A single melodic line, usually combined with one or more other voices.

trichord A three-note grouping or set.

voice crossing adjacent voices that swap ranges (i.e., the tenor sings below the bass voice). Voice crossings are difficult to sing and obscure the independence of parts, and should therefore be avoided.

trio A section of lighter texture played after a minuet, usually ending with a da capo marking. triple suspension Three simultaneous suspensions in three different voices. triplets Three-note groups appearing in a simple meter. tritone An interval of three whole tones. Sometimes called “the devil’s tone” because of its dissonance. The tritone is a key-defining interval given that it appears only once in a diatonic collection. twelve-tone operators The processes used to transform groups of PCs ranging in size from two to twelve and include: transposition, inversion, and retrograde inversion. two against three Simple and compound divisions of the beat appearing simultaneously. two-reprise form See binary form. unaccented embellishing tone A metrically weak embellishing tone. unaccented passing tone A metrically weak passing tone. unequal fifths Two voices that proceed from perfect fifth to diminished fifth, allowable if the diminished fifth resolves to a third. unison The interval from a pitch to the same pitch in the same octave. universal set See chromatic collection and aggregate. unprepared chromatic modulation A modulation that occurs without the aid of a pivot chord. upbeat The beat where a conductor’s baton goes up. See anacrusis. upper neighbor (UN) A neighboring tone a step above a chord tone. variation set A type of piece incorporating variations on the same theme.

voice exchange Two voices that swap pitches usually involving the shift of third to sixth or vice versa. This may occur with or without intervening passing tones. voice overlap A lower voice that leaps above the previous pitch of an upper voice, or an upper voice that leaps below the previous pitch of a lower voice. Voice overlaps are difficult to sing and obscure the independence of parts, and should therefore be avoided. voice leading The way that individual voices, or lines of counterpoint, move. voice-leading chord A chord inserted between two other chords to prevent unwanted parallel fifths or octaves, often used in sequences. For example, in the step progression I to ii, V is usually added between the chords to avoid illegal parallels. voicing See spacing. waltz six-four chord See arpeggiating six-four chord. whole step An interval made up of two adjacent half steps, corresponding to the distance between any two keys on the piano separated by one intervening key. whole-tone scale A symmetrical scale consisting of six pitches, all a whole step apart. There are two unique whole-tone scales, one built on C and the other on D. whole-tone track A chromatic sequence (or sequential progression) where each model is repeated at the interval of a whole step. Z-related sets Two distinct tetrachords that share the same intervallic content but cannot be mapped onto each other through any common operators such as transposition and inversion.

C R E DI T S

5 MOVEMENTS FOR STRING QUARTET, OP. 5 By Anton Webern Used with kind permission of European American Music Distributors Company, U.S. and Canadian agent for Universal Edition AG, Vienna 44 Duos for 2 Violins, SZ98 By Béla Bartók © 1933 Boosey & Hawkes, Inc. Copyright renewed. Reprinted by permission of Boosey & Hawkes, Inc. Allegro Barbaro By Béla Bartók © Copyright 1918 by Editio Musica Budapest Reprinted by permission of Boosey & Hawkes, Inc. ALTENBERG LIEDER, OP. 4, NO. 1 By Alban Berg Copyright © 1953 by Universal Edition AG, Vienna Copyright © renewed Used by permission of European American Music Distributors Company, U.S. and Canadian agent for Universal Edition AG, Vienna Concerto for Orchestra, SZ 116 By Béla Bartók © Copyright 1946 by Hawkes & Son (London) Ltd. Reprinted by permission of Boosey & Hawkes, Inc. CONCERTO FOR SIX By Tan Dun Copyright © 1998 G. Schirmer, Inc. (ASCAP) International Copyright Secured. All Rights Reserved. Used by Permission. Diminishing Return By David Rakowski Copyright © 2009 by C.F. Peters Corporation. Used by permission. For Children, SZ42 By Béla Bartók © Copyright 1998 by Boosey & Hawkes Music Publishers Ltd. Reprinted by permission of Boosey & Hawkes, Inc.

Fourteen Bagatelles, op. 6 By Béla Bartók © Copyright 1998 by Editio Musica Budapest Reprinted by permission of Boosey & Hawkes, Inc. SUITE FOR PIANO, Op. 25 By Arnold Schoenberg Copyright © 1925 by Universal Edition AG, Vienna Copyright © renewed All Rights Reserved Used by permission of Belmont Music Publishers, Los Angeles. Used in Australia, New Zealand, Brazil and Japan by permission of European American Music Distributors Company, agent for Universal Edition AG, Vienna Giant Steps By John Coltrane Copyright Jowcol Music, LLC All rights reserved. Used by permission. Louange a l’Eternite de Jesus from Quartet for the End of Time By Olivier Messiaen © 1942 Éditions Durand, Paris. All rights reserved. Reproduced by kind permission of MGB Hal Leonard s.r.l. Mikrokosmos, SZ107 By Béla Bartók © Copyright 1940 by Hawkes & Son (London) Ltd. [Definitive corrected edition © Copyright 1987 by Hawkes & Son (London) Ltd.] Reprinted by permission of Boosey & Hawkes, Inc. Music for Strings, Percussion, and Celesta By Béla Bartók © Copyright 1937 by Boosey & Hawkes, Inc. for the USA, Copyright renewed. Reprinted by permission of Boosey & Hawkes, Inc. PIANO ETUDES 1 & 2 from SIX ETUDES FOR PIANO By Augusta Read Thomas Copyright © 2006 G. Schirmer, Inc. (ASCAP)

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THE COMPLETE MUSICIAN

International Copyright Secured. All Rights Reserved. Used by Permission. PIERROT LUNAIRE, Op. 21 By Arnold Schoenberg Used by permission of Belmont Music Publishers, Los Angeles. Used in Australia, New Zealand, Brazil and Japan with kind permission of European American Music Distributors Company, agent for Universal Edition AG, Vienna QUADERO MUSICALE DI ANNALIBERA, No. 5 “Contrapunctus secundus” By Luigi Dallapicolla Copyright © 1953 Edizioni Suvini Zerboni, Milan Copyright © renewed Used with kind permission of European American Music Distributors Company, U.S. and Canadian agent for Edizioni Suvini Zerboni, Milan QUARTET, OP. 22 By Anton Webern Copyright © 1930 by Universal Edition AG, Vienna Copyright © renewed All Rights Reserved Used by permission of European American Music Distributors Company, U.S. and Canadian Agent for Universal Edition AG, Vienna STOMP By John Corigliano Copyright © 2011 G. Schirmer, Inc. (ASCAP International Copyright Secured. All Rights Reserved. Used by Permission. Symphony of Psalms By Igor Stravinsky © Copyright 1931 by Hawkes & Son (London) Ltd. Revised Version © Copyright 1948 by Hawkes & Son (London) Ltd. U.S. copyright renewed. Reprinted by permission.

THREE SONGS on poems by Hildegard Jone, Op. 25 No. 1 “Wie bin ich froh” By Anton Webern Copyright © 1934 by Universal Edition AG, Vienna Copyright © renewed All Rights Reserved Used by permission of European American Music Distributors Company, U.S. and Canadian agent for Universal Edition AG, Vienna VARIATIONS, Op. 27 By Anton Webern Copyright © 1936 by Universal Edition AG, Vienna Copyright © renewed All Rights Reserved Used by permission of European American Music Distributors Company, U.S. and Canadian agent for Universal Edition AG, Vienna Vocalise, pour l’Ange qui annonce le fin de Temps from Quartet for the End of Time By Olivier Messiaen © 1942 Editions Durand-Paris. All Rights Reserved. Reproduced by permission of MGB Hal Leonard. What’s Hairpinning By David Rakowski Copyright © 2009 by C.F. Peters Corporation. Used by permission. WHITE WATER By Joan Tower Copyright © 2012 Associated Music Publishers, Inc. (BMI) International Copyright Secured. All Rights Reserved. Used by Permission.

INDEX OF TERMS AND CONCEPTS

Accented dissonances. See Tones of figuration Accented six-four chords. See Cadential six-four chords Accents, 5 agogic, 65 anacrusis, 64–65 analysis of, 75–76 articulative, 67 bass, 252 beats, 49 chromatic neighbor tones, 298 contour, 70 downbeat, 65 durational, 65 embellishing tones, 283 incomplete neighbor, 288 as marked for consciousness, 64 metrical, 49, 64–65, 261 musical, 64 neighbor notes, 194–95 neighbor tones, 286, 298 nontemporal, 65–71 passing tones, 283–85, 287– 88, 298, 309–10 pitch, 6, 71 registral, 67 rhythm, 65, 831 syncopation, 72–73, 829 temporal, 64–65 tendency tones, 71 textural, 69–70 tones of figuration, 282–83 upbeat, 64–65 Accidentals. See Chromatic alterations Added rhythmic values, 832

Additive rhythm, 832 Aeolian mode, 763, 764 Affect, 69 Aggregate. See Chromatic collections Agogic accents, 65 Alberti bass, 133 alla breve. See Cut time All-interval tetrachord, 824 Altered dominant seventh chords, 687–89 Altered mediant harmony, 516–17 Altered tonic harmony, 514–15 Alternating sevenths, 422, 426, 450–52 A-Major scale, 15–16 Ambiguity, tonal. See Tonal ambiguity Ambitus, 176 Anacrusis, 64–65 Analysis. See also Gestalt psychology of accents, 75–76 of chromatic modulations, 542–43 context and, 148 of contrapuntal cadences, 332–33 of embellishing tones, 162 of embellishment, secondlevel, 190, 193–95 of figured bass, 111–12, 116–17 harmonic and melodic, 150 of harmony, 162 interpretive, 195 of intervals, 38–39 of melodic fluency, 162 of melody, 83–84

of Neapolitan chords, 564 nondominant seventh chords, 327–28 of outer-voice counterpoint, 102–3 of periods, 387–89, 405–6 of rhythm, 48 of second species counterpoint, 101–2 of sentences, 405–6 of sequences, 418–21 of seventh chords, 127, 129 of tonicization and modulation, 469–70 of triads, 122 of voice-leading, 183 Antecedent, 380, 400–401. See also Periods; Phrases Anticipation, 295–97 Applied chords, 369 composition with, 445, 447–48 diatonic progressions with, 437 dominant, 436–38, 443 dominant substitute chords, 450 in inversions, 438–39, 454 leading tones and, 443–44 modal mixture and, 532 part writing, 441 phrases and, 444–48 recognizing, 440–41, 448–49 sequences with, 450–59 shorthand, 444–45 voice-leading and, 440–41 writing, 445, 447–48, 450 Applied triads, 455 Appoggiatura, 288–89, 298. See also Tones of figuration I1-1

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THE COMPLETE MUSICIAN

Arch, 157–59. See also Melody Arpeggiating six-four chords (waltz six-four chords), 307–8 Arpeggiations, 146–47, 253, 297, 514 ascending-bass, 367 IV6 chords and, 223–24 mediant in, 367–69 melodic bass, 351–52 of vi, 349 Art, 174 Articulative accents, 67 Ascending and Descending, 411 Ascending-bass arpeggiation, 367 Ascending-seconds, 348, 351–55 Ascending-second sequences, 416– 18, 426, 453–54, 458–59 Ascending sequences, 412, 420–21 Asymmetry balanced music based on, 680– 81 fifths and, 682 meters, 59, 830–32 periods, 404 Atonal, 737 Attwood, Thomas, 86–87 Augmented collections. See Hexatonic collections Augmented fifths, 683 Augmented intervals, 32–34 Augmented sixth chords, 507 chromatic stepwise bass descents and, 705–6 common-tone, 690–91 components of, 571 definition of, 569, 583 derivation of, 570–71 diatonic progressions and, 570 doubly, 573 elided resolution of, 573 French, 571, 688 function of, 568 German, 571–72, 575, 675 German diminished third chords, 578–81 Italian, 571 in major, 572, 573 in minor, 572 modal mixture and, 570 parallel fifths and, 572–73 Phrygian cadence and, 570 pivot chords and, 583–87 pre-dominants and, 575–81 prolonging, 579

Swiss, 573 tonicization and modulation of, 570, 581–87 types of, 571–72 voice exchange and, 577–78 writing, 572–73 Augmented triads, 107–8, 683–84, 774, 776–78 Authentic cadences, 172, 311. See also Cadences Auxiliary tone. See Neighbor tone Axial symmetry, 853–54, 869 Axis, 809–10, 848 Back-relating domains, 373 Balance, 345 Balanced binary form, 488–89. See also Binary form Balanced continuous binary form, 488, 489 Bar lines, 5, 49 Baroque period, 69, 75, 411 neighbor tones, 287 suite, 483 Bass. See also Chromatic stepwise bass descents; Figured bass of V6 chords, neighboring tones in, 216–17 accented, 252 Alberti, 133 arpeggiations, ascending, 367 chordal leaps in, 212–15 clef, 7–8 direct step-descent, 359–61 ground, 359, 495 harmonic paradigms, 318–19 indirect step-descent, 361 lament, 359 lines, 446–47 melodic arpeggiation in, 351–52 pre-dominants and ascending, 268 scale degrees, 220 step-descent, 358–62 suspensions with change of, 293 of vii°6 chords, passing tones in, 221–23 Beams, 59–61 Beats, 45 accented, 49 division of, 836–38 downbeats, 65 groupings, 58 meter signature and, 55

subdivision, 51, 56 syncopation, 72–73, 829 unaccented, 49 upbeat, 64–65 weak-beat consonance, 97–98 weak-beat dissonance and, 98–99 Best normal order, 817–18 Binary form balanced, 488–89 balanced continuous, 488, 489 definition of, 483 digressions, 486, 488 interruptions, 486 rounded, 596–97, 601 rounded continuous, 487–88, 489 rounded sectional, 485–86, 489 simple continuous, 484–85, 489 simple sectional, 483–84, 489 sonata form and, 632 ternary form and, 596 Binary model, for sonata form, 632–38 Blue notes, 755–56 Borrowed divisions, 61–62 Bridging sections, 597. See also Transitions Broken chords, 254 Cadences. See also Cadential sixfour chords; Half cadences authentic, 172, 311 contrapuntal, 172, 325, 332–33 counterpoint and, 94 deceptive, 355, 415 definition of, 171 evaded, 236–37, 312–14 in folk melodies, 204–5 Hollywood, 522 identification of, 204–5 imperfect authentic, 172 melodic, 82 pedal point and, 296 perfect authentic, 172 in phrase model, 273–75 Phrygian, 295, 417, 570 plagal, 317 structural, 332–33, 350–51 Cadential extension, 312–14 Cadential phrase models, 329 Cadential six-four chords authentic cadences and, 311 elision and, 312–14 evaded cadences and, 312–14 extension and, 312–14

Index of Terms and Concepts half cadences and, 310–11 within phrases, 311–12 preceding V 7 chords, 311 preparing, 310 root position of, 310 suspensions and, 308–9 in triple meter, 314–15 writing, 315 Caesura, 338, 636 Cantus firmus (pl. cantus firmi), 87 C Clef, 7–8 Cells. See Intervallic cells Centricity, 737–41, 757–61 Chaconnes. See Ground bass Changing meters, 833–36 Character piece, 605 Chorale style, 121, 176 Choral texture, 253 Chordal dissonance, 182 Chordal dissonance, dominant seventh chords and, 197– 204 Chordal extensions, 752–57, 761– 62 Chordal leaps, 147, 283, 297, 559 in bass, 212–15 suspensions and, 293 Chordal sevenths, neighboring motion and, 199 Chordal skips, 272 Chord progressions elaboration and, 253–54 with seventh chords, 123 tonicization and modulation of, 479 Chords, 107. See also Seventh chords; Triads V, 167–68 applied, 369 broken, 254 chart of, 227 compositional impact of contrapuntal, 246–48 first-inversion, 214 I, 167–68 neighboring, 216, 217, 325 passing, 221 pivot, 469–73, 476–77, 479 split-third, 783 substitute, 221, 450 voice-leading, 272, 413 Chord tones doubled, 179 embellishing tones and, 147–48

omitted, 179 texture and, 133 Chromatic adjustment and intervals, 38 contrary motion, 708–11 half steps, 13 neighbor tones, 287, 297, 298 passing tones, 284–86, 298 scales, 12–13, 861 system, 12–13 thirds, 523 voice exchange, 520–21, 578–79 Chromatic alterations (accidentals), 12, 436 double flat, 11 double sharp, 11 figured bass and, 113–14, 115 flat, 11 intervals and, 29–30 in major keys, 23 in minor keys, 23 natural, 11 sharp, 11 Chromatic collections, 763 Chromaticism, 261 cross relations, 441–42 diatonicism and, 436 in eighteenth and nineteenth century, 510 expressive, 507 figured bass and, 113–14 leading tones and, 433 passing tones and, 433, 436 pre-dominant and, 507 tonicization and modulation of, 510, 524 types of, 433 Chromatic modulations analysis of, 542–43 common chords, 532–34 common tones, 539–41 pivot chord, 532–37 unprepared, 537–41 writing, 536 Chromatic passing chords tritone voice exchange using, 710 voice exchange using, 709 Chromatic sequences A2 (⫺3/⫹4), 701–2 applied A2, 702–3 D2 (⫺5/⫹4), 698–99 D2 (⫺P4/⫹m3), 697 D2 (Falling-Fifth) Sequence (three-chord model), 700

I1-3 D2 (Falling-Fifth) Sequence (two-chord model), 700 definition of, 696 diatonic context of, 697–98 writing, 707 Chromatic stepwise bass descents, 577–78 with 7-6 suspensions, 704 augmented sixth chords and, 705–6 diminished seventh chords and, 705–6 in major, 520–21 in minor, 520–21 six-three chords and, 704 Circle of fifths, 17–18. See also Root motion in major keys, 24 in minor keys, 24 sequences and, 413–14 submediant and, 349–51 Classical period, 69, 483 folk melodies in, 206–7 neighbor tones in, 287 rondo form in, 617–28 style, 133 Clef bass, 7–8 C, 7–8 treble, 7–8 Climax, 144 Clock as analytical tool, 799–801, 810, 817, 819, 871 Closed position, 108, 137, 180–81 Closely related keys, 18, 468–69. See also Tonicization and Modulation Coda rondo form, 619–20 sonata form, 637 Codettas, 637 Cognition, 154–55 Collections. See Pitch classes Combinatoriality, 860 inversional, 862–67, 870–71 retrograde, 861 transpositional, 861–62 Common chords, chromatic modulations, 532–34 Common-practice period, 4 Common time, 55 Common-tones augmented sixth chords, 690–91 chromatic modulations, 539–41

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THE COMPLETE MUSICIAN

Common-tones (continued ) diminished seventh chords, 689–90 Complete chords, 179, 182 dominant seventh chords, 201–2 I chords, 201–2 voice-leading, 179, 182 Compliments, literal, 768 Composite forms, 595, 617. See also Rondo form; Ternary form Composite phrases, 339–41 Compound intervals, 28–29 Compound melody, 97 Compound meter, 51–55. See also Meter beams and, 60 meter signature for, 56–58 Compound rondo form, 620–22 Compound ternary form, 600–602 Conducting gestures. See Anacrusis; Downbeat Conjunct motion, 82 Consequent, 380, 400–401 Consonance, 259 dissonance and, 144, 727 embellishing tones, 283 imperfect, 40–41, 145–46, 424– 25 intervallic, 98 intervals, 40–41, 90, 145–46 leaps, 97–98, 147 neighbor tones, 97, 146 passing tones, 97–99 perfect, 40–41, 99–100, 145–46 skips, 97 weak-beat, 97–98 Continuous harmonic motion, 338 Continuous periods, 382, 386. See also Periods Continuous ternary form, 596. See also Ternary form Continuous variations, 494–99 Continuous variation sets, 494 Contour, 7, 28, 722–23, 852 of accented neighbor tones, 286 of accented passing tones, 285 accents, 70 arch, 157–59 literal, 853 nested lines, 157–59 row and intervallic, 859–60 trichord, 850 Contrapuntal cadences, 172, 325, 332–33

Contrapuntal chords, compositional impact of, 246–48 Contrapuntal expansion (prolongation), 248–50, 316–18 dissonance, 708 of dominant, using V6, 224–25 chromatic contrary motion and omnibus, 708–11 IV6, 224–25 through invertible counterpoint, 604–5 metric placement, 285–86 of pre-dominant, 333–35, 439, 710 prolongational harmony, 218 of tonic, using chordal skips, 272 double-neighbor figures, 297 embedded phrase model, 329–32 I6 chord, 223–24 inversions of V 7, 232–38 invertible counterpoint, 604–5 multiple, 225 step-descent bass, 358–62 of viiø7, 245 Contrapuntal independence, 178 Contrapuntal motions, 90–91, 95–96 Contrapuntal texture, 130 Contrapuntal voice, 87 Contrary motion, 90–91, 712–13 chromatic, 708–11 outer-voices, 265 Contrasting continuous periods, 387 Contrasting periods, 380, 382 Controlling harmonies, 376 Counterpoint, 85. See also First species; Second species counterpoint cadences and, 94 cantus firmus, 87 contrapuntal motions, 90–91, 95–96 contrapuntal voice, 87 contrary motion, 90–91 definition of, 86 direct intervals, 92, 100 error detection in, 96 harmony and, 86, 345 hidden intervals, 92

history of, 86–87 intervals and, 86 invertible, 604–5 outer-voice, 102–3, 107 parallel motion, 90–91 parallel perfect intervals, 91–92, 100 passing tone: consonant and dissonant (unaccented), 97–99 perfect consonances, 40–41, 99– 100, 145–46 role of, 78 rules and guidelines, 87, 94–95, 101 similar intervals, 92 similar motion, 90–91, 92 six centuries of, 88–89 treatment of leaps, 93 Covert polymeter, 835 Cross relation, 441–42 Cut time (alla breve), 55 Da Capo Aria, 602 Da Capo Form, 600–602 Deceptive cadences, 355, 415. See also Cadences Deceptive motion, 352–53, 355 Dependent transitions, 636 Derivation of augmented sixth chords, 570– 71 melody and, 198–200 Descending 5-6 sequences, 415–16 Descending fifths, 348–51, 354, 514. See also Root motion Descending-second sequences, 413–14, 425–26, 450–52, 455–56 Descending sequences, 412, 418– 19 Descending thirds, 348–49, 354 Descending-third sequences, 414– 16, 425, 451–53, 457 Development, 632, 637, 650–51, 653–55 Diatonic collections, 763–68 descent with 7-6 suspensions, 704 half steps, 13 harmonies, 410 intervals, 31–32 modes, 763–68

Index of Terms and Concepts passing chords, voice exchange using, 709 scales, 12–13 sequences, 425–26, 451–53, 680, 695–96 seventh chords, sequences with, 421–22 thirds, 526 triads, 455 voice exchange, 709 Diatonicism, chromaticism and, 436 Diatonic progressions with applied chords, 437 augmented sixth chords and, 570 Digression, 486, 488 Diminished fifths, 202 Diminished intervals, 32–34 Diminished scales. See Octatonic scales Diminished seventh chords, 674–79 chromatic stepwise bass descents and, 705–6 clock and, 800 common-tone, 689–90 half, 123–24 parallel, 706 Diminished triads, 108, 110, 118, 683–84 Diminution, 31–32. See also Contrapuntal expansion; Tones of figuration definition of, 30 as pitch embellishments, 21–22 rhythmic, 718 Direct intervals, 92, 100 Direct modulations. See Unprepared chromatic modulations Direct step-descent bass, 359–61. See also Indirect step-descent bass Disjunct motion, 82, 151 Dissonance, 71, 259 consonance and, 144, 727 dominant seventh chords and chordal, 197–204 embellishing tones, 283 intervals, 40–41, 123, 145–46 neighbor tones, 146 passing tones, 98–99, 557 prolongation, 708 suspensions and, 292 weak-beat, 98–99

Distant harmonic relation, 668 Distantly related triads, 808 Dominant. See also Applied chords applied chords, 436–38, 443 applied substitute chords, 450 back-relating, 372–73 closure on, 170 expansion, 224–25, 227, 710 harmony, 522 instability of, 168–69 substitute, 221 tonic and, 167–70, 680 triads, 173 unaccented six-four chords and, 305 Dominant seventh (Mm7) chord. See also Seventh chords altered, 687–89 approaching, 202 chordal dissonance and, 197–204 complete, 201–2 incomplete, 201 part writing, 201 resolution of, 201 scale degree, 14–15 Dorian mode, 763, 764 Dots and ties, 46–49, 832 Double counterpoint. See Invertible counterpoint Doubled chord tones, 179 Doubled fifths, 180, 218–19 Double flat, 12 Double-neighbor figures, 297 Double periods, 400–402 Double sharp, 11 Double suspensions, 294 Double tonality, 670–73 Double unisons, 218–19 Doubling v6 chord, 219 fifths, 180, 218–19 in four-part writing, 174 i6 chord, 219 triads, 109–10 Downbeat, 65 Duple meter, 50, 52, 57, 63–64, 73–74 Duplets, 61–62 Durational accents, 65 Durational symbols. See Notation Dyad, 27 Dynamics, registral accents and, 67

I1-5 Echappée, 153. See also Incomplete neighbor Eighteenth Century, 681 Eighths, parallel, 178 Eight-note collections. See Octatonic collections Elaboration broken chords and, 254 chord progressions and, 253–54 figured bass and, 253–54 harmonic rhythm and, 255 inner voices and, 254 voice-leading, 253–56 writing, 253–56 Elided resolution, 573 Elision, 312–14 E-Major key signature, 15 scale, 15 Embedded phrase models, 325, 329–32, 349–50, 513 Embedded triads, 840 Embellished suspensions, 293 Embellishing chords, 316–17 Embellishing tones, 146–47, 154, 188–90 accented, 283 analysis of, 162 chord tones and, 147–48 consonant, 283 dissonant, 283 function of, 281 most common, 297 omitting, 253 structural and, 190–91, 218 unaccented, 282–83, 297–98 Embellishment accented neighbor notes, 194–95 deepest level of, 195–96 forms of, 191 harmonized accented neighbor notes, 195 interpretive analysis of, 195 levels of, 193–96 of melody, 154–55 metrical figuration, 193 metrical passing tones, 193 reduction and, 192–93 second-level analysis of, 190, 193–95 stages of, 188–90 submetrical figuration, 194 submetrical passing tones, 194

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Embellishment (continued ) supermetrical figuration, 193 of tonic and first inversion, 212 Enharmonic, enharmonicism equivalence, 797 intervals, 39 modulations, 674–76 pitches, 13–14 reinterpretation, 583–86, 675–76 symmetry and, 675 Episodes, 617. See also Rondo form Equal divisions of the octave. See also Chromatic sequences in nonsequential progressions, 715–18 in sequential progressions, 713– 15 Equivalence, 801 class, 796 enharmonic, 797 inversions and, 802–3 in nontonal music, 797–99 octave, 796 order, 796 registral, 796 temporal, 797 in tonal music, 797 transposition and, 797, 802 Escape tone, 153 Escher, M. C., 411 Evaded cadences, 236–37, 312–14 Even-numbered intervals, 30 Expansion. See Contrapuntal expansion Expansion, of Neapolitan chords, 559–62 Expectation/fulfillment, 156, 160–61. See also Gestalt psychology Exposition, 632, 642, 648–50, 652–53 Extended third-related second tonal areas, 642–45 Extension cadential, 312–14 chordal, 752–57 phrase, 331–32 triadic, 752–57, 761–62 Falling fifths D2 (Falling-Fifth) Sequence (three-chord model), 700 D2 (Falling-Fifth) Sequence (two-chord model), 700

harmony and, 200 False recapitulations, 640 Fifths. See also Falling fifths asymmetry and, 682 augmented, 683 circle of, 17–18, 349–51, 413–14 descending, 348–51, 354, 514 diminished, 202 doubling, 180, 218–19 parallel, 178, 273, 327, 357, 572–73 of triads, 107 unequal, 202 Figuration, 261 accented tones of, 282–83 metrical, 193 submetrical, 194 supermetrical, 193 unaccented tones of, 281–83 Figured bass (thoroughbass), 115 abbreviations, 112–13 analysis of, 111, 116–17 chromatic alterations and, 113– 14, 115 chromaticism and, 113–14 elaboration and, 253–54 horizontalized, 254 key signatures and, 113 melodic motion and, 114 realization of, 111–12 suspensions and, 291 First inversion chords, 214, 225– 26. See also Six-three chords First inversion triads, 109–10, 212–13 First-level analysis, 218 First species (note-against-note counterpoint), 87, 88–96 beginning and ending, 94 motion within and between voices, 90 rules and guidelines for, 94–95 First tonal area, 632, 653 Five-note collections: Pentatonic, 768–71 Five-part rondo, 619 Five-six motion (5-6). See also Semitonal voice leading figured bass chromaticism and, 113–14 5–6 technique, 97–99 in IV–ii complex, 272–73 mixture and, 522

parallel fifths and, 357 in sequences, 415–16 vi6 and, 357–58 Flags, 45 Flats double, 12 in major keys, 23 in minor keys, 23 Florid melodies, harmony and, 318–21 Fluency melodic, 154–59, 162 texture, 133–35 F-Major scale, 16–17 Folk melodies cadences in, 204–5 in classical period, 206–7 harmony and, 204–7 identification of cadences in, 204–5 identification of harmonic rhythm in, 205–6 Folk music, 59 Form as process, 379 twentieth and twenty-first century, 741–44, 784–86 Four-phrase piece, in minor, 375– 76 Fourths, perfect, 144–45 Four-voices style, 121 suspensions in, 290–91, 293 texture, 174–78 Free atonality, 838 French augmented sixth chords, 571, 688 Frequency, 9 Full score. See Open score Full sectional ternary form, 596, 603. See also Ternary form Functions, harmonic. See Dominant; Pre-dominants; Tonic Fux, Johann, 86–87 Gap-fill, 156–57. See also Gestalt psychology Generic intervals, 27–29 Generic sixths, 28 German augmented sixth chords, 571–72, 575, 675 German diminished third chords, 578–81

Index of Terms and Concepts German Lied. See Lied Gestalt psychology. See also Motive ambiguity, 155 balance, 155 expectation and realization/ fulfillment, 156, 160–61 gap-fill, 156 good continuation, 159–60 Gesture, 5 Good continuation, 159–60 Gradus ad Parnassum (Fux), 86–87 Grand staff, 8 Gravity, tonal, 4 Ground bass, 359, 495–98. See also Passacaglia Half cadences, 172, 214, 382. See also Cadences; Interruptions cadential six-four chords and, 310–11 Phrygian, 265–67, 570 tonicized, 439–40 Half-diminished seventh chords, 123–24 Half step, 10–11, 13 Harmonic anomalies, 640–42 Harmonic arpeggiations. See Root motion Harmonic chromatic passing tones, 436 Harmonic function, 261 Harmonic interruption, 385 Harmonic intervals, 28 Harmonic markers, 842 Harmonic minor scales, 20–21 Harmonic mixture, 513–– 514 Harmonic motion continuous, 338 independent, 339 Harmonic paradigms, 246 bass, 318–19 soprano, 318–19 Harmonic reduction, 135–36 Harmonic rhythm, 66–67, 159. See also Contrapuntal expansion; Metrical figuration; Metric placement elaboration and, 255 in folk melodies, identification of, 205–6 meter and, 188, 196 reduction and, 252 rhythm and, 188, 196

roman numerals and, 133 in sequences, 411 Harmonic sequences. See Sequences Harmonic verticalization, 160 Harmonized accented neighbor notes, 195 Harmony, 85–86. See also Contrapuntal expansion altered mediant, 516–17 altered tonic, 514–15 analysis of, 162 bass lines and, 446–47 controlling, 376 counterpoint and, 86, 345 dominant, 522 falling fifths and, 200 florid melodies and, 318–21 folk melodies and, 204–7 good continuation, 159–60 implied, 133 initial, 385 keyboard and, 120–21 levels of I-V, 194 melody and, 159–62, 226, 380– 84 in minor and major, diatonic, 410 nineteenth century, 661 ornamental, 218 parallel motion and, 181 passing, 334 pedal point, 296 periods and, 380–84 pre-dominant, 512–13 progressional, 218, 232 prolongational, 218 revoicing tonic, 191 row and, 839–40 scale degrees and, 321 seventh chords and, 200 structural and embellishing, 190– 91, 218 of submediant, altered, 513–14 symmetrical, 675 in twentieth and twenty-first century, 744–52 Hemiola, 73–75, 829, 830 Hendrix chords, 756 Hexachords, 849–50, 854, 860–62, 864–66, 869 Hexatonic collections, 776–78. See also Whole-tone collections Hexatonic poles, 778 Hexatonic scales, 776–78

I1-7 Hidden intervals, 92 Hierarchy, 141, 144–46. See also Motive illustrated in analysis, 6–7 of phrase model, 410 phrases and, 151 tonal music and, 6–7 Hollywood cadences, 522 Homophonic chords, horizontalizing, 253 Homophonic texture, 131, 133–34, 135, 150 Human interaction, 393–94 Human nature, 616 Human perception, 155–56 Hypermeter, 680 I6 chord, 212 V6 and, 248 doubling, 219 expanding, 334 tonic expansion of, 223–24 voice-leading and, 219 I chords, 167–68 expanding, 214–15 incomplete, 201 vi overshadowing, 356 ii, 267–68, 334 ii°, 267–68 ii6, 334 ii°6, 267–68 ii65 chords, 327–28 ii7 chords. See Supertonic seventh chords Imperfect authentic cadences, 172 Imperfect consonances, 40–41, 145–46, 424–25 Imperfect intervals, 30–31 Implied harmony, 133 Implied resolution. See Resolution Incomplete chords. See also Seventh chords; Triads dominant seventh chords, 201 I chords, 201 neighboring, 217 voice-leading, 179, 182 Incomplete neighbor, 153, 288, 297 Independent harmonic motion, 339 Independent transitions, 636 Index numbers, 809–13, 849, 870 Indirect step-descent bass, 361 Initial harmony, 385

I1-8

THE COMPLETE MUSICIAN

Inner voices elaboration and, 254 reduction and, 252 Instinct, 155–56. See also Gestalt psychology Integer notation, 799 Interlocking sevenths, 422, 426, 450–52 Interrupted periods, 380–81, 382, 386 Interruptions, 486 Interval classes, 806, 844 Interval class vector, 821–23 Intervallic cells, 718, 724. See also Motive Intervallic consonance, 98 Intervallic contour, row and, 859–60 Intervals all-interval tetrachord, 824 analysis of, 38–39 augmented, 32–34 chromatic adjustment and, 38 chromatic alterations and, 29–30 compound, 28–29 consonant, 40–41, 90, 145–46 counterpoint and, 86 diatonic, 31–32 diminished, 32–34 direct, 92, 100 dissonant, 40–41, 123, 145–46 dyad, 27 enharmonic, 39 even numbered, 30 generating all, 36–38 generic, 27–29 half step, 10–11 harmonic, 28 hidden, 92 imperfect consonances, 40–41, 145–46 inversion, 34–35, 37 major and minor, 30–32 melodic, 28 melody and, 79, 82 notation of, 39 octave, 28, 145 odd-numbered, 29 ordered pitch, 804, 808, 813– 14, 853 ordered pitch-class, 804–5, 808, 813–14, 853 parallel perfect, 91–92, 100 perfect and imperfect, 30–31, 91–92, 99–100

perfect consonances, 40–41 pitch and, 37 pitch-class, 844 prime, 28 quality, 30–31 similar, 92 simple, 28–29 specific, 30–31 stability of, 40–41 stacking, 756–57 transforming, 32–36 tritone, 35 unison, 28 unordered pitch, 805, 808, 813– 14, 854–55 unordered pitch-class, 805–6, 808, 813–14 whole steps, 10–11 in whole tone scale, 774 Invariance, 820–21 symmetry and, 868 variance and, 867–71 Inversional combinatoriality, 862– 67, 870–71 Inversional equivalence class, 803 Inversional symmetry, 871 Inversional variance, 870 Inversions, 718, 798, 858–59. See also Interval classes; Mod-12 inverses; Six-three chords around 0, 812 of V 7, spelling, 240 of V 7, voice-leading and, 237 of V 7 chords, 232–40 of V 7 chords, combining, 237–38 applied chords in, 438–39, 454 chords, first, 214, 225–26 descending-second sequences in, 414 descending-third sequences in, 415–16 equivalence and, 802–3 first inversion chords, 214, 225– 26 first inversion triads, 109–10, 212–13 index numbers, 809–13 intervallic, 34–35, 37 “Rainbow” shortcut, 811 retrograde, 847–48, 850, 859 second inversion triads, 109–10 sequences with seventh chord, 422–23

of seventh chords, 124–25, 128– 29 triads, 109–10, 212–13, 802–3 triads, first, 109–10, 212–13 of viiø7, 241–43 Invertible counterpoint, 604–5 Ionian mode, 763, 764 Italian augmented sixth chords, 571 IV65 chords, 327 IV6 chords, 250 arpeggiation and, 223–24 dominant expansion with passing tones, 224–25 IV 7, 325 IV 7 chords. See Subdominant seventh chords IV chords contrapuntal expansion with, 316–18 as embellishing chords, 316–17 plagal cadences and, 317 root position of, 320 IV–ii complex, 272–73 Jazz notation, 754 Keyboard style, 120–21, 175–76 Keys, 12 closely related, 18, 468–69 parallel and relative (major and minor), 23–24 relative key-relations, 23–24 relative major and minor, 22–25 remote, 667–70 three-key expositions, 642 Key signatures, 18 E-Major, 15 figured bass and, 113 minor, 22 relative major and minor, 23–24 symbols, 17 triads and, 119 twentieth and twenty-first century, 775 Labeling suspensions, 291–92 Lament bass, 359. See also Stepdescent bass Laws. See also Gestalt psychology melodic fluency, 154–59, 162 of recovery, 82 Leading tones, 81, 82, 180 on V 7 chords, 240–45 applied chords and, 443–44

Index of Terms and Concepts chromaticism and, 433 scale degree, 14–15 temporary, 440–41 Leaps, 6. See also Chordal leaps consonant, 97–98, 147 treatment of, 93 tritones, 417 voice-leading and, 178 Ledger lines, 8 Legal cross relations, 442 Legato, 47 Lied (pl. Lieder), 543–52 Lines, in twentieth and twenty-first century, 744–52 Linkage (motivic). See Motive Literal compliments, 768 Literal contour, 853 Locrian mode, 763, 764 Long-range pitch structure, 152–53 Lower neighbors, 146 Lydian mode, 763, 764 Major augmented sixth chords in, 572, 573 chromatic stepwise bass descents in, 520–21 closely related keys in, 469 diatonic harmonies in, 410 intervals, 30–32 scales, 15–19, 117 seven-part rondo form in, 623 submediant in, 348, 354 tonicization and modulation in, 469 triads, 107–8, 118, 777–78 Major keys chromatic alterations in, 23 circle of fifths in, 24 flats, 23 parallel and relative, 23–24 relative minor and, 22–25 seventh chords in, 126 sharps in, 23 Mapping, 798, 809 Marked for consciousness, 64 Matrix. See Twelve-tone matrix Measure (m., plural, mm.), 5, 49 Medial caesura, 636 Mediant, 345, 366 in arpeggiations, 367–69 harmonic contexts of, 368 harmony, altered, 516–17 modal mixture, 516–17

part writing for, 370–71 scale degree, 14–15 voice-leading for, 370 Melodic bass arpeggiation, 351–52 Melodic cadences, 82 Melodic fluency, 154–59, 162 Melodic intervals, 28 Melodic minor scales, 20–21 Melodic mixture, 512–14. See also Mixture Melodic motion, figured bass and, 114 Melody. See also Contour; Counterpoint; Harmony; Motive analysis of, 83–84 arch, 157–59 characteristics of, 79–83 climax of, 82–83 compound, 97 conjunct motion of, 82 continuous, 339 criticism of, 84 derivation and, 198–200 disjunct motion of, 82 embellishment of, 154–55 expectation/fulfillment in, 160–61 florid, 318–21 gap-fill, 156–57 gesture, 5 harmonizing folk, 204–7 harmony and, 159–62, 226, 380–84 intervals and, 79, 82 melodic fluency, 154–59, 162 in minor mode, 21–22 nested lines, 157–59 outer voices, 84, 102–3 over a thousand years, 79–81 periods and, 380–84 phrases and, 385 range of, 82 reduction of, 154 row and, 839–40 single-line, 842 in twentieth and twenty-first century, 744–52 uniqueness of, 81 voices or parts of, 84–86 writing, 82 Meter, 45, 49–51, 829. See also Accent; Compound meter; Simple meter accent, 49

I1-9 asymmetrical, 59, 830–32 building clear, 50 changing, 833–36 clarifying, 59–61 correspondence of rhythm and, 61 determining, 58 disturbance of, 72–76 duple, 50, 52, 57, 63–64, 73–74 harmonic rhythm and, 188, 196 hemiola, 73–75, 829, 830 hypermeter, 680 metric modulation, 836–38 polymeter, 834–35 quadruple, 50, 52, 57 syncopation, 72–73, 829 triple, 50–52, 53, 57, 63–64, 73–74, 314–15 types of, 52 Meter signature beats and, 55 commonly used, 57 common time, 55 for compound meter, 56–58 cut time, 55 for simple meter, 56 Metrical accent, 49, 64–65, 261 Metrical figuration, 193 Metrical passing tones, 193. See also Embellishment Metric modulation, 836–38 Metric placement accented neighbor tones, 286 of accented passing tones, 285 Metric strata, 835 Minor augmented sixth chords in, 572 chromatic stepwise bass descents in, 520–21 closely related keys in, 469 diatonic harmonies in, 410 four-phrase piece in, 375–76 intervals, 30–32 preparing three chord in, 369 seven-part rondo form in, 623 sixths, 144 submediant, 348, 354 tonicization and modulation in, 469 triads, 107–8, 118, 777–78 Minor keys chromatic alterations in, 23 circle of fifths in, 24 flats in, 23

I1-10

THE COMPLETE MUSICIAN

Minor keys (continued ) parallel and relative, 23–24 relative major and, 22–25 seventh chords in, 126 sharps in, 23 Minor mode building scales in, 19–20 melody in, 21–22 Minor scales, 15 harmonic, 20–21 melodic, 20–21 natural, 20–21 triads and, 117–18 Minuet, 483. See also Binary form; Ternary form Minuet-trio form, 602–6 Missing double bars and repeats, 623–24 Missing pitches, 253 Mixolydian mode, 763, 764 Mixture, 511–12, 524–26, 661 applied chords and, 532 augmented sixth chords and, 570 embedded phrase models and, 513 five-six motion and, 522 harmonic, 513–– 514 lied and, 543–52 mediant, 516–17 melodic, 512–14 part writing, 518 poetic drama and, 547 pre-dominants and, 512–13, 524 submediant, 513–14 tonic harmony, 514–15 voice-leading, 517–18 Mm7. See Dominant seventh chord Mod-12 arithmetic, 799–801. See also Pitch-classes Mod-12 inverses, 806, 807, 854 Modal mixture. See Mixture Model and copy. See Sequences Modes, 15 building scales in minor, 19–20 determining, 765 diatonic, 763–68 identification of, 769–71 transposition of, 765 Modified periods, 402–5 Modulations. See Tonicization and Modulation Monophonic texture, 130. See also Texture Monothematic sonata form, 638

Mood, affect, 69 Motive. See also Intervallic cells saturation, 31 in twentieth and twenty-first century, 744–52 Multiple row forms, 855–56 Musical texture. See Texture Must sum to an odd number, 867 Natural, 11 Natural minor scale, 20–21 Neapolitan chords analysis of, 564 characteristics, effects, and behavior of, 554–56 common contexts of, 556 definition of, 556 expansion of, 559–62 pivot chords and, 562–63 sequences and, 562 sixth, 507 tonicization and modulation of, 559–60 writing, 556–57 Neighbor, stabilizing, 216 Neighboring chords, 216 incomplete, 217 pre-dominants and, 325 Neighboring motion, 216–18 V43 chords and, 235–36 chordal sevenths and, 199 Neighboring sevenths, 199–200 in V65 chords, 234 Neighbor notes accented, 194–95 harmonized accented, 195 Neighbor tones (auxiliary tones), 146, 259. See also Appoggiatura accented, 286, 298 accented chromatic, 298 in Baroque period, 287 in bass of V6 chords, 216–17 chromatic, 287, 297, 298 in Classical period, 287 consonant, 97, 146 dissonant, 146 double, 297 incomplete, 153, 297 lower, 146 unaccented, 286 upper, 146 Nested lines, 157–59 Nesting of sentences, 396

Nineteenth century aesthetics, 664 harmony, 661 ternary form in, 605–11 tonal paths, 681–82 Ninth chords, 755–56 Noncadential phrase models, 329 Nondominant seventh chords, 325–29 Non-harmonic tones. See Tones of figuration Nonretrogradable rhythm, 833 Nonsequential progressions, equal division of octave and, 716–18 Nontemporal accents, 65–71 Non-tertian sonorities, 756 Nontonal music, 792, 797–99 Nontriadic subsets of octatonic collection, 782 Normal order, 816–17, 824–25 Notation. See also Chorale style; Keyboard style beams, 59–61 dots and ties, 46–49, 832 flags, 45 of four-voice texture, 174–76 integer, 799 of intervals, 39 jazz, 754 notehead, 45–46 notes and rests, 46 pitch, 823 of rhythm, 45–49 Notehead, 45–46 Oblique motion, 97 Octatonic collections, 778–84 Octatonic scales, 778–84, 800 Octave, 218–19 designations, 9 displacement, 850 equal division of, 711–18 equivalence, 796 interval, 28, 145 major-third division of, 712, 714 nonsequential progressions and equal division of, 716–18 octave sign (“ottava” 8va or 8vb), 8 parallel, 179 pitch and, 9 Octuplet, 63 Odd-numbered intervals, 29

Index of Terms and Concepts Off-tonic beginning, 507, 670 Omitted chord tones, 179 Omnibus, 710–11 Open position, 108–9, 137, 180 Open score, 174 Operations, 847 Ordered pitch-class intervals, 804– 5, 808, 813–14, 853 Ordered pitch intervals, 804, 808, 813–14, 850, 853 Order equivalence, 796 Ordering pitch-classes, 839, 842 Order numbers, 839 Ornamental harmony, 218 Ostinatos, 359, 494–95, 497, 741, 742, 757–61 Outer-voices contrary motion, 265 counterpoint, 107, 424–25 of melody, 84, 102–3 reduction and, 252 Overt polymeter, 834 Palindromes, 833, 853–54 Parallel diminished seventh chords, 706 Parallel eighths, 178 Parallel fifths, 178, 273, 327, 357, 572–73 Parallel interrupted periods, 387 Parallel major keys, 23 Parallel minor keys, 23 Parallel motion, 90–91, 181, 215 Parallel octaves, 179 Parallel perfect intervals, 91–92, 100 Parallel periods, 380, 382 Parallel progressive periods, 387 Parallel sectional periods, 387 Parallel six-three chords, 294 Parsimonious voice leading, 777. See also Hexatonic collections Part exchanges, 238. See also Invertible counterpoint; Voice exchange Partitions, 849 Parts, of melody, 84–86 Part writing applied chords, 441 ascending-seconds, 355 dominant seventh chord, 201 for mediant, 370–71 modal mixture, 518

nondominant seventh chords, 328 pre-dominants, 268–70 submediant as pre-dominant, 355 supertonic seventh chords, 327 Passacaglia, 495, 499, 741 Passing chords, 221. See also Contrapuntal expansion between ii and ii6, 334 between IV6 (IV65) to ii65, 334 between IV and IV6, 334 pre-dominants and, 325, 334 seventh, 198–99 Passing dissonance. See Counterpoint Passing harmony, 334 Passing sevenths, 198–99, 233 Passing six-four chords, 306 Passing tones, 259. See also Supermetrical figurations accented, 283–85, 287–88, 298, 309–10 in bass of vii°6 chords, 221–23 chromatic, 284–86, 298 chromaticism and, 433, 436 consonant, 97–99 dissonant, 98–99, 557 dominant expansion with IV6, 224–25 harmonic chromatic, 436 metrical, 193 submetrical, 194 unaccented, 98, 283–84 unaccented six-four chords as, 304–5 Passing vii°6 chord, 306 Pauses, subphrases and, 337–38 Pedal (pedal point), 296, 298, 304–5 Pentatonic collections, 768–71 Perception, 154–55 Perfect authentic cadences, 172 Perfect consonances, 40–41, 99– 100, 145–46 Perfect fourths, 144–45 Perfect intervals, 30–31, 91–92, 99–100 Perfect symmetry, 680 Periods, 374 analysis of, 387–89, 405–6 asymmetrical, 404 composing, 389

I1-11 continuous, 382, 386 contrasting, 380, 382 contrasting continuous, 387 definition of, 379 double, 400–402 harmony and, 380–84 interrupted, 380–81, 382, 386 labels, 385–86 melody and, 380–84 modified, 402–5 parallel, 380, 382 parallel interrupted, 387 parallel progressive, 387 parallel sectional, 387 phrases and, 384 progressive, 384, 386 sectional, 383, 386 sentences and, 398 writing, 389 Phenomenal accents. See Articulative accents Phrase elision, 312–14 Phrase extension, 331–32 Phrase groups, 403 Phrase model, 261, 321. See also Submediant cadences in, 273–75 cadential, 329 diversity within, 276–77 embedded, 325, 329–32, 349– 50, 513 error detection in, 277–78 flexibility of, 273–74 four-measure, 275 hierarchy of, 410 noncadential, 329 pacing of, 379 refinements of, 325 tonal music and, 325 Phrases, 151. See also Cadences applied chords and, 444–48 cadential six-four chords within, 311–12 composite, 339–42 definition of, 379 melody and, 385 periods and, 384 subphrases, 325, 337–41, 345 tonicization and modulation of, 471 Phrasing slurs, 47 Phrygian cadence, 295, 417, 570 Phrygian half cadences, 265–67, 570

I1-12

THE COMPLETE MUSICIAN

Phrygian mode, 763, 764 Picardy third, 172, 511, 688 Pitch accents, 6, 71 collection, 816 definition of, 9 dyad, 27 enharmonic, 13–14 frequency, 9 intervals, ordered, 804, 808, 813–14 intervals and, 37 missing, 253 notation, 823 octave and, 9 prominence, 5–7 register, 10, 176, 869 sets, 796, 798 space, 795–96, 799 structure, long-range, 152–53 variance, 867 Pitch-classes, 10, 762–63 chromatic collections, 763 collection, 816 diatonic collection, 763–68 five-note collections: Pentatonic, 768–71 hexatonic collections, 776–78 octatonic collections, 778–84 ordering, 839, 842 row and, 843–44 sets, 796, 824 seven-note collections: diatonic modes, 763–68 six-note collections, 771, 776–78 space, 795–96, 799 whole-tone collections, 771–76 world, 796 Pitch-class intervals, 844 ordered, 804–5, 808, 813–14, 853 unordered, 805–6, 808, 813–14, 852 Pivot area, 473–76 Pivot chords, 469–73, 476–77, 479 augmented sixth chords and, 583–87 chromatic modulations, 532–37 Neapolitan chords and, 562–63 Pivot measure, 838 Plagal cadences, 317 Plagal motions, 522–24 Plagal relation, 661

Poetic drama, modal mixture and, 547 Polymeter, 834–35 Polyphonic texture, 130, 135 Polyphony. See Counterpoint Polyrhythm, 833 Post-tonal, 737 Pre-dominants, 261, 264–65 ascending bass and, 268 augmented sixth chords and, 575–81 checklist for function, 276 chordal skips, 272 chromaticism and, 507 expansion, 333–35, 439, 710 extending, 272 harmony, 512–13 mixture and, 512–13, 524 neighboring chords and, 325 part writing, 268–70 passing chords and, 325, 334 seventh chords, 326 submediant as, 353, 355 Preparation-resolution, 199 cadential six-four chords, 310 seventh chords, 328 of suspensions, 290, 298 Prime, 850, 858 form, 818–19, 820, 825, 849 intervals, 28 row and, 842, 847 Progressional harmony, 218, 232 Progressive periods, 384, 386 Prolongational harmony, 218 Prolongational v. transitional sequences. See Sequences Psychology, Gestalt. See Gestalt psychology Pulses, 45, 49, 830 Quadruple meter, 50, 52, 57 Quality (intervallic), 30–31 Quartal chords, 756, 776 Quintal chords, 756 Quintuplets, 62 “Rainbow” shortcut, 811 Range, 82 long-range pitch structure, 152– 53 unrestricted, 176 vocal, 174, 176 Realization, of figured bass, 111–12

Recapitulation, 632, 637, 640, 651–52 Reciprocal process, 665 Reduction. See also Embellishment composition and, 250–53 embellishment and, 192–93 harmonic, 135–36 harmonic rhythm and, 252 inner voices and, 252 of melody, 154 outer-voices and, 252 spacing and, 252 upper voices and, 252 voice-leading, 250–53 writing, 250–53 Refrains, 617 Register, 10, 176, 869 Registral accents, 67 Registral equivalence, 796 Registral independence, 177 Relative key-relations, 23–24 Relative major and minor keys, 22–25 Remote keys, semitonal voice leading and, 667–70 Renaissance Period, 411 Repetition, 345 Resolution, 199. See also Preparation-resolution of dominant seventh chord, 201 elided, 573 of suspensions, 290, 292 of viiø7, 243 Restruck suspensions, 294 Rests, 46 Retardations, 294 Retransitions rondo form, 619–20 of sonata form, 637 ternary form, 597 Retrograde, 847–48, 850, 858–59 Retrograde combinatoriality, 861 Retrograde inversion, 847–48, 850, 859 Retrogression, 372–73 Rhythm, 7, 45, 829. See also Accent accents, 65, 831 additive, 832 analysis of, 48 borrowed divisions, 61–62 correspondence of meter and, 61 duplets, 61–62 harmonic, 66–67 harmonic rhythm and, 188, 196

Index of Terms and Concepts nonretrogradable, 833 notation of, 45–49 octuplet, 63 polyrhythm, 833 quintuplets, 62 rhythmic accents, 65 septuplets, 62 triplets, 61–62 two against three, 63–64 values of, 48 Rhythmic augmentation, 718 Rhythmic diminution, 718 Ritornellos, 602. See also Ternary form Roman numerals harmonic rhythm and, 133 seventh chords and, 126–27 triads and, 118–19 Rondeau, 617 Rondo form, 593. See also Sonatarondo form in Classical era, 617–28 coda, 619–20 compound, 620–22 definition of, 616 episodes, 617 five-part, 619 missing double bars and repeats, 623–24 refrains, 617 retransitions, 619–20 sections of, 617 seven-part, 623, 645 transitions, 619–20 Root of V 7 chords, 232 doubled, 218–19 of triads, 107, 110, 119 Root motion, 348 by descending thirds, 349 principles and composition of, 374–76 submediant and, 348–49 Root position of cadential six-four chords, 310 inverted applied chords versus, 438 of IV chords, 320 seventh chords, 328 triads, 109–10 Rounded binary form, 596–97, 601. See also Binary form Rounded continuous binary form, 487–88, 489

Rounded sectional binary form, 485–86, 489 Row, 842–44, 849, 852, 854. See also Twelve-tone operators harmony and, 839–40 intervallic contour and, 859–60 melody and, 839–40 multiple forms, 855–56 pitch-classes and, 843–44 prime and, 842, 847 register and, 869 simultaneous row forms, 860–62 twelve-tone music, 839 Scale degrees bass, 220 dominant seventh chord, 14–15 harmony and, 321 soprano, 220 subdominant, 14–15 submediant, 14–15 Scales chromatic, 12–13, 861 diatonic, 12–13 error detection, 19, 26–27 hexatonic, 776–78 in minor mode, 19–20 natural minor scale, 20–21 octatonic, 778–84, 800 parallel and relative (major and minor), 23–24 scale degrees, scale degree numbers and names, 14–15 symmetry and, 682–83 triads and, 117–18 types (chromatic, diatonic), 12–13 whole tone, 771–76 writing, 25–27 writing fragments, 19, 26 Scherzo, 483, 602. See also Minuettrio form Scores, 7 Secondary aggregate, 860–61, 870 Secondary dominant chords. See Applied chords Second inversion triads, 109–10 Second-level analysis, 218 Seconds ascending, 348, 351–55 ascending-second sequences, 416–18, 426, 453–54, 458–59 Second species counterpoint, 87

I1-13 analysis of, 101–2 beginning and ending, 100–101 5–6 technique, 97–99 intervallic consonance and, 98 oblique motion, 97 perfect consonances, 40–41, 99– 100, 145–46 perfect intervals in, 99–100 rules and guidelines for, 101 weak-beat consonance and, 97– 98 weak-beat dissonance and, 98–99 Second tonal area, 632, 642–45, 653 Sectional binary form. See Binary form Sectional harmonic period. See Periods Sectional periods, 383, 386 Sectional ternary form, 596, 602. See also Ternary form Sectional variations, 494, 499–500. See also Variations Segmentation, 816 Semitonal voice leading, 667–70 Sentences analysis of, 405–6 nesting of, 396 periods and, 398 structure and, 394–400 Septuplets, 62 Sequences, 153 analysis of, 418–21 with applied chords, 450–59 ascending, 412, 420–21 ascending-second, 416–18, 426, 453–54, 458–59 circle of fifths and, 413–14 components and types of, 412–18 copies, 412 definition of, 410–11 descending, 412, 418–19 descending 5-6 sequences, 415– 16 descending-second, 413–14, 425–26, 450–52, 455–56 descending-third, 414–16, 425, 451–53, 457 diatonic, 425, 451–53, 680, 695–96 with diatonic seventh chords, 421–22 harmonic rhythm in, 411 imperfect consonances and, 424–25

I1-14

THE COMPLETE MUSICIAN

Sequences (continued ) inserting, 410 labels, 412 model, 412 Neapolitan chords and, 562 outer-voice counterpoint and, 424–25 with seventh chord inversions, 422–23 stasis of, 700 terminology, 412 tonicization and modulation of, 473–76, 478 triadic, 427–29 voice-leading, 424 writing, 423–26 Sequential progressions, 713–15 Serial music. See Twelve-tone music Series, 174 Set class, 803, 818–19 Seven-note collections: diatonic modes, 763–68 Seven-part rondo form, 623, 645 Seventh chords altered dominant, 687–89 alternating, 422, 426, 450–52 analysis of, 127, 129 analytical tips for, 125 chord progressions with, 123 definitions of, 123–24 harmonic analysis of, 126 harmony and, 200 interlocking, 422, 426, 450–52 inversions of, 124–25, 128–29 in major keys, 126 in minor keys, 126 musical characteristics of, 124 neighboring, 199–200, 234 nondominant, 325–29 omnibus and, 710–11 passing, 198–99 pre-dominant, 326 preparing, 328 roman numerals and, 126–27 root position, 328 sequences with diatonic, 421–22 sequences with inversions of, 422–23 subsets, 782 types (Mm, MM, mm, dm, dd), 123–24 writing, 127–28, 137 Sharp ninth chords, 756

Sharps double, 11 in major keys, 23 in minor keys, 23 Short score, 174 Similar intervals, 92 Similar motion, 90–91, 92, 215. See also Contrapuntal motions; Counterpoint Simple continuous binary form, 484–85, 489 Simple intervals, 28–29 Simple meter, 51–55, 58 beams and, 60 meter signature for, 56 Simple sectional binary form, 483– 84, 489 Simultaneous row forms, 860–62 Single-line melodies, 842 Six-four chords. See Arpeggiating six-four chords; Cadential six-four chords; Passing six-four chords; Unaccented six-four chords Six-note collections, 771, 776–78 Six-three chords, 259 alternating, 699 ascending-second sequences with, 418 chromatic stepwise bass descents and, 704 descending-second sequences with, 414 descending-third sequences with, 416 expanding, 214–15 parallel, 294 Sixths generic, 28 minor, 144 Slurs, 192–93 Smoothness, 177 Sonata form, 593 basic, 646 binary form and, 632 binary model for, 632–38 closing section of, 636–37 coda, 637 definition of, 630 dependent transitions, 636 development, 632, 637, 650–51, 653–55 exposition, 632, 642, 648–50, 652–53

false recapitulations, 640 first tonal area, 632, 653 historical context and tonal background of, 631 Independent transitions, 636 medial caesura, 636 monothematic, 638 recapitulation, 632, 637, 651–52 retransitions of, 637 second tonal area, 632, 642–45, 653 slow introduction of, 638 sonata principle, 632 three-key expositions, 642 transitions, 636 Sonata-rondo form, 645 definition of, 646 structure of, 646 Soprano harmonic paradigms, 318–19 scale degree, 220 Spacing, 180 reduction and, 252 triads, 108–9, 116 Species. See First species; Second species counterpoint Spelling, inversions of V 7 chords, 240 Split-third chords, 783 Split-third ninths, 755–56 Stabilizing neighbor, 216 Staff, (pl. staves), 7–8 Step-descent bass, 358–62 Structural cadences, 332–33, 350– 51 Structural harmony, 190–91, 218 Structure, 141, 394–400 Style chorale, 121, 176 classical period, 133 four-voices, 121 keyboard, 120–21, 175–76 in twentieth and twenty-first century, 730–37 Subdivision, of beats, 51, 56 Subdominant, 264–67 contrapuntal expansion with IV chords, 316–18 return, 641–42 scale degree, 14–15 tonic and, 680 Subdominant seventh chords (IV 7), 327

Index of Terms and Concepts Submediant, 345 altered harmony of, 513–14 apparent, 356–57 in ascending-seconds, 351–55 circle of fifths and, 349–51 contradictory behavior of, 350 descending fifths and, 348–51, 354 in descending-thirds progression, 348–49, 354 in major, 348, 354 in minor, 348, 354 modal mixture, 513–14 as pre-dominant, 353, 355 root motion and, 348–49 scale degree, 14–15 tonic and, 351–53 voice-leading for, 353–55 Submetrical passing tones, 194 Submetrical/supermetrical. See Figuration Subphrases, 325, 337–41, 345 Subsets, 777, 781–82, 844, 849 Substitute chords, 221, 450 Subtonic, 21 Sum. See Index numbers Supermetrical figurations, 193 Supertonic, 14–15, 267, 335–36 Supertonic seventh chords (ii7), 325–27 Suspensions, 298 adding, 293 additional techniques, 293–95 cadential six-four chords and, 308–9 chains, 294–95 with change of bass, 293 characteristics of, 289 chordal leaps and, 293 chromatic descent with 7-6, 704 components of, 290 diatonic descent with 7-6, 704 dissonance and, 292 double, 294 embellished, 293 figured bass and, 291 in four voices, 290–91, 293 labeling, 291–92 most common, 292 preparation of, 290, 298 resolution of, 290, 292 restruck, 294 retardations, 294 stages of, 290, 298

triple, 294 in two voices, 289 writing, 292–93 Swiss augmented sixth chords, 573 Symbols. See Notation Symmetrical harmony, 675 Symmetrical sets, 819–25 Symmetry, 852 axial, 853–54, 869 enharmonicism and, 675 invariance and, 868 inversional, 871 perfect, 680 scales and, 682–83 six-note collections, 771 thirds and, 682 tonal ambiguity and, 682–83 Syncopation, 72–73, 829 Tempo, 45, 836–38 Tempo modulation. See Metric modulation Temporal accents, 64–65 Temporal equivalence, 797 Temporary tonic. See Applied chords; Tonicization and Modulation Tendency tones, 82, 168 V 7 chords and, 232 accents, 71 voice-leading, 179–80, 182 Tenuto marks, 73 Ternary form, 593. See also Da Capo Form binary form and, 596 characteristics of, 595–97 compound, 600–602 continuous, 596 Da Capo Aria, 602 Da Capo Form, 600–602 definition of, 596 full sectional, 596, 603 Minuet-trio form, 602–6 in nineteenth century, 605–11 retransitions, 597 sectional, 596, 602 seven-part rondo form and, 623 transitions, 597 Tessitura, 82, 176 Tetrachordal axis, 848 Texture accents, 69–70 analytical method of, 133–36 chorale, 253

I1-15 chord tones and, 133 contrapuntal, 130 definition, 130 fluency, 133–35 four-voice, 174–78 harmonic reduction, 135–36 homophonic, 131, 133–34, 135, 150 implied harmonies and, 133 monophonic, 130 polyphonic, 130, 135 Thematic design, 483, 488 Themes, 494 Thirds chords, split, 783 chromatic, 523 descending, 348–49, 354 descending-third sequences, 414– 16, 425, 451–53, 457 diatonic, 526 extended third-related second tonal areas, 642–45 German diminished third chords, 578–81 major-third division of octave, 712, 714 nonsequential progressions that divides octave into, 716 Picardy, 172, 511, 688 relations, tonic and, 526 split-third ninths, 755–56 symmetry and, 682 of triads, 107, 110 Three chord, 369 Three-key expositions, 642 Ties, 192 Time signature. See Meter signature Tonal ambiguity, 664. See also Augmented sixth chords; Diminished seventh chords; Mixture; Reciprocal process; Semitonal voice leading semitonal voice leading, 667–70 symmetry and, 682–83 Tonal clarity, 670 Tonal gravity, 771 Tonality, 4, 13, 795 Tonal music, 4 check and balances in, 187–88 complexity of, 140 equivalence in, 797 hierarchy and, 6–7 phrase model and, 325 Tonal vs. post-tonal, 737

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THE COMPLETE MUSICIAN

Tones of figuration, 282–83 Tonic, 7, 13 dominant and, 167–70, 680 first inversion and embellishment of, 212 harmony, altered, 514–15 harmony, revoicing, 191 off-tonic beginning, 507, 670 stability of, 168 subdominant and, 680 submediant and, 351–53 third relations and, 526 transposed to supertonic, 335–36 unaccented six-four chords and, 305 Tonic expansion, 227, 236, 710 of i6 chord, 223–24 multiple, 225 of viiø7, 245 Tonicization and Modulation, 436, 661. See also Pivot chords analysis of, 469–70 augmented sixth chords and, 570, 581–87 chord progressions and, 479 chromaticism and, 510, 524 chromatic pivot-chord modulations, 532–37 closely related keys, 18 definition of, 467–68 extended, 461–67 half cadences, 439–40 in major, 469 in minor, 469 Neapolitan chords and, 559–60 phrases and, 471 pivot area, 473–76 sequences and, 473–76, 478 short, 479 writing, 470–71, 478–79 Total chromatic. See Chromatic collections Transitions dependent, 636 independent, 636 rondo form, 619–20 sonata form, 636 ternary form, 597 Transposition, 718, 847–48, 858– 59 combinatoriality, 861–62 equivalence and, 797, 802 of modes, 765

of octatonic scale, 781 Treble clef, 7–8 Triadic extensions, 752–57, 761–62 Triadic sequences, 427–29 Triads. See also Figured bass analysis of, 122 applied, 455 augmented, 107–8, 683–84, 774, 776–78 closed position, 108, 137 definition of, 107 diatonic, 455 diminished, 108, 110, 118, 683–84 distantly related, 808 dominant, 173 doubling, 109–10 embedded, 840 fifths of, 107 first-inversion, 109–10, 212–13 harmonic analysis of, 118–21 identification of, 110 inversions, 109–10, 212–13, 802–3 key signatures and, 119 major, 107–8, 118, 777–78 major scales and, 117 minor, 107–8, 118, 777–78 minor scales and, 117–18 open position, 108–9, 137 qualities of, 107 relative stability of root-position and inverted, 212–13 roman numerals and, 118–19 root of, 107, 110, 119 root-position, 109–10 scales and, 117–18 second inversion, 109–10 spacing, 108–9, 116 thirds of, 107, 110 types of, 108 voicing, 108–9 writing, 121–22, 137 Trichords, 798, 803, 809, 849, 850 Trios, 602. See also Minuet-trio form Triple meter, 50–52, 53, 57, 63–64, 73–74, 314–15 Triple suspensions, 294 Triplets, 61–62 Tritones intervallic, 35 leaps, 417

voice exchange using chromatic passing chords, 710 Twelve-tone matrix, 856–60 Twelve-tone music, 838–39 Twelve-tone operators, 846, 847 Twelve-tone row. See Row Twentieth and Twenty-first century, 727–28 centricity, 737–41 diversity of style in, 730–37 form and process, 741–44, 784– 86 key signatures and, 775 melody, motives, harmony, and line in, 744–52 Two against three, 63–64 Two-reprise form. See Binary form Two voices, suspensions in, 289 Unaccented beats, 49 Unaccented embellishing tones, 282–83, 297–98 Unaccented neighbor tones, 286 Unaccented passing tones, 98, 283–84 Unaccented six-four chords dominant and, 305 as passing tones, 304–5 pedal, 304–5 tonic and, 305 writing, 315 Unaccented tones of figuration, 281–83 Unequal fifths, 202 Unison intervals, 28 Unity, of musical space, 840 Universal set. See Chromatic collections Unordered pitch-class intervals, 805–6, 808, 813–14, 852 Unordered pitch intervals, 805, 808, 813–14, 854–55 Unprepared chromatic modulations, 537–41 Unrestricted range, 176 Upbeat, 64–65 Upper neighbors, 146 Upper voices, reduction and, 252 V42 chords, 236–37, 249 V43 chords, 241, 246, 249 neighboring motion and, 235–36 passing motion and, 235

I1-17

Index of Terms and Concepts V65 chords, 249 neighboring sevenths in, 234 passing sevenths in, 233 V6 chord, 212, 233 doubling, 219 I6 chord and, 248 neighboring tones in bass of, 216–17 voice-leading, 219 V 7 chords cadential six-four chords preceding, 311 combining inversions of, 237–38 inversions of, 232–40 leading tones on, 240–45 root of, 232 tendency tones and, 232 viiø7 and, 241 Variance, 862 invariance and, 867–71 inversional, 870 pitch, 867 Variation form, 493 composition in, 500–501 ostinatos and, 742 Variation sets, 494 V chords, 167–68 expanding, 214–15 vi overshadowing of, 355 Vertical alignment, 130 Vertical stems, 192 vi harmonic arpeggiations of, 349 overshadowing I chords, 356 overshadowing of V, 355 vi6, 357–58 VII, as V/III, 370 Vii42, 241 Vii43, 241, 249 Vii65, 241, 246, 249 Vii°6 chords, 246, 248 common settings of, 221 passing tones in bass of, 221–23 voice-leading for, 222–23 V/III, VII as, 370 viiø7, 244–45, 249 V 7 and, 241 contrapuntal functions for, 242 inversions of, 241–43 resolution of, 243 tonic expansion of, 245

voice-leading for, 241–43 V–IV6–V6, 225 Vocal music, 60 Vocal ranges, 174, 176 Voice crossing, 178, 182 Voice exchange, 181, 214–15, 334, 335 augmented sixth chords and, 577–78 chromatic, 520–21, 578–79 diatonic, 709 part exchanges, 238 using chromatic passing chords, 709 using chromatic passing chords, tritone, 710 using diatonic passing chords, 709 Voice leading. See also Tendency tones Voice-leading v6 chord, 219 analysis of, 183 applied chords and, 440–41 chords, 272, 413 closed position, 180–81 complete chords, 179, 182 crossing, 178, 182 definition of, 174 doubling, 180 elaboration, 253–56 error correction in, 178 in four-part texture, 177 I6 chord and, 219 incomplete chords, 179, 182 indirect step-descent bass, 361 inversions of V 7 and, 237 leaps and, 178 for mediant, 370 modal mixture, 517–18 open position, 180 overlaps, 177, 182 parsimonious, 777 reduction, 250–53 rules and guidelines, 182 semitonal, 667–70 sequences, 424 for submediant, 353–55 tendency tones, 179–80, 182 texture and register (ambitus, range, and tessitura), 174– 76

for vii°6 chords, 222–23 for viiø7, 241–43 V–IV6–V6, 225 vocal ranges, 174, 176 Voice overlaps, 177, 182 Voices, of melody, 84–86 Voicing, 180, 754, 756. See also Doubling; Spacing Waltz six-four chords. See Arpeggiating six-four chords Weak-beat consonance, 97–98 Weak-beat dissonance, 98–99 Whole step, 10–11 Whole-tone collections, 771–76 Whole tone scale, 771–76, 800 Wrinkles, 817 Write (voice lead; compose) applied chords, 445, 447–48, 450 augmented sixth chords, 572–73 cadential six-four chords, 315 chromatic modulations, 536 chromatic sequences, 707 diatonic intervals, 32 elaboration, 253–56 impact of contrapuntal chords, 246–48 intervallic identification, 38 intervallic transformation, 35–36 melody, 82 Neapolitan chords, 556–57 periods, 389 reduction and, 250–53 rhythmic values, 48–49 root-motion principles and, 374–76 scale fragments, 19, 26 scales, 25–27 sequences, 423–26 seventh chords, 127–28, 137 step-descent bass, 360–61 supertonic seventh chords, 327 suspensions, 292–93 toniciziation and modulation, 470–71, 478–79 triads, 121–22, 137 unaccented six-four chords, 315 variation form, 500–501 Z-related sets, 824

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INDEX OF MUSICAL EXAMPLES AND EXERCISES

Exercises are identified with “*” to distinguish them from Examples Arlen, Harold (1904–1986) “It’s Only a Paper Moon,” 73 “Over the Rainbow,” 81 Bach, C.P.E. (1714–1788), Flute Sonata no. 6 in G, Wq 134 H548, Allegro, 579 Bach, Johann Jacob (1682– 1732), *Flute Sonata in C minor, Allegro, 228 Bach, Johann Sebastian (1685– 1750) “Allemande” from Sonata no. 2 for Solo Violin in A minor, BWV 1003, 160 “Bereite dich, Zion,” from Christmas Oratorio, 80 “Chaconne” from Partita no. 2 in D minor for Solo Violin, BWV 1004, 496 *“Christus, der ist mein Leben,” 519 C minor Prelude, from WellTempered Clavier, Book 1 BWV 847, 69 Flute Sonata no.1 in B minor, BWV 1030, Largo, 363 Flute Sonata no. 2 in E major, BWV 1031, Siciliano, 52 French Suite in B minor Gigue, 55 Menuet, 55

Fugue in C minor, from The Well-Tempered Clavier, Book 1, BWV 847, 296 Fugue in G minor, from The Well-Tempered Clavier, Book 1, BWV 861, 130–31 *Gavotte, French Suite no. 5 in G major, BWV 816, 419 *Geistliches Lied, “Beschränkt ihr Weisen,” 362 “Gerne will ich mich bequemen” (“Gladly Will I Take My Portion”), St. Matthew Passion, BWV 244, 335 *“Des heil’gen Geistes reiche Gnad,” 336 *“In allen meinen Taten,” 336 Invention in C minor, 88 “O Haupt voll Blut und Wunden,” 131, *336 “O Welt, ich muss dich lassen” from St. Matthew Passion, 175, 330 “O World, I Now Must Leave Thee” from St. Matthew Passion, 85 Partita no. 2 in D minor for Solo Violin, BWV 1004, Chaconne, 496 Partita no. 3 in E major, BWV 1006, Prelude, 5–6

Prelude in C minor, from The Well-Tempered Clavier, Book 1, 69 Prelude in E Major, The Well-Tempered Clavier, Book 2, BWV 876, 372–73 Sonata for Solo Violin in G minor, Presto, 159 “Verleih’ uns Frieden gnädiglich,” 22 “Wo soll ich fliehen hin,” Cantata no. 5, BWV 5, 266 Bartók, Béla (1881–1945) Allegro Barbaro: 1911, 730 “Boating” from Mikrokosmos, Book 5, no. 125, 756–57 “Change of Time” from Mikrokosmos, Book 5, no. 126, 833–34 “Dances in Bulgarian Rhythm” from Mikrokosmos, nos. 5 and 6, 830–31 “From the Isle of Bali” from Mikrokosmos, Book 4, no. 109, 779–80 “Introduzione” from Concerto for Orchestra, Andante non troppo– Allegro vivace, mm. 1–6, 757 “Little Study” from Mikrokosmos, Book 3, no. 77, 765–66

I2-1

I2-2

THE COMPLETE MUSICIAN

Bartók, Béla (continued ) “Merriment” from Mikrokosmos, Book 3, no. 84, 786 Music for Strings, Percussion and Celesta, 813 “Ostinato” from Mikrokosmos, Book 6, no. 146, 738 “Subject and Reflection,” 811 “Tale” from Mikrokosmos, Book 3, no. 95, 767–68 Beethoven, Ludwig van (1770– 1827) *Andante in F major, WoO 57, 588 *Bagatelle, op. 119, no. 9, 558 Bagatelle in C major, op. 119, 685 Klavierstück, WoO 82, 388 “Lustig-Traurig,” WoO 54, 395 *Piano Concerto no. 1 in C major, op. 15, Allegro con brio, 163 *Piano Concerto no. 2 in B, op. 19, Rondo, 399 Piano Concerto no. 4 in G major, op. 58, Allegro moderato, 272, 334 Piano Sonata in A major, op. 26, Andante, 401 Piano Sonata in C major, op. 2, no. 3, Trio, 306 Piano Sonata in C major, “Waldstein,” op. 53, Allegro con brio, 81, 644–45 Piano Sonata in C minor, “Moonlight,” op. 27, no. 2 Adagio, *557 Trio, 452 Piano Sonata in C minor, op. 13, I, 677–78 Piano Sonata in C minor, “Pathetique,” op. 13, Rondo, 402 Piano Sonata in D major, “Pastorale,” op. 28 Andante, 23–24 Rondo, Allegro ma non troppo, 56 Piano Sonata in D minor, “Tempest,” op. 31, no. 2 Largo/Allegro, 68, 307 Allegretto, 192–93, 202–3 Piano Sonata in E major, op. 27, no. 1, Andante, 463

Piano Sonata in E major, op. 81A, “Das Lebewohl” (Les Adieux), 93 Piano Sonata in F minor, op 2, no. 1, Trio, 605 *Piano Sonata in F minor, op. 2, no. 1, Adagio, 322 Piano Sonata in G major, op. 31, no. 1, Allegro vivace, 643 *Piano Sonata in G major, op. 14, no. 2, Andante, 271 Piano Sonata in F minor, op 2 no. 1, Trio, 605 Allegro, 395–96; Menuetto-Trio: Allegretto, 603–4 Piano Sonata no. 11 in B major, op. 22, Menuetto, 381 Piano Sonata no. 13 in E major, op. 27, no. 1, Allegro vivace, 577 Piano Sonata no. 14 in C minor, “Moonlight,” op. 27, no. 2, Piano Sonata no. 19 in G Minor, op. 49, no. 1, Andante, 633–35 *Piano Sonata no. 23 in F minor, “Appassionata,” op. 57, Allegro assai, 565 Piano Sonata no. 27 in E minor, op. 90, Nicht zu geschwind und sehr singbar vorzutragen, 534 Piano Trio in C minor, op. 1, no. 3, ii, Andante cantabile, 134 Piano Trio in E major, op. 1, Finale, 440 Piano Trio in G major, op. 1, no. 2, Largo, con espressione, 158 *Piano Trio no. 5 in D major, “Ghost,” op. 70, no. 1, Presto, 528 “Rage Over a Lost Penny,” op. 129, 584 String Quartet no. 8 in E minor, op. 59, no. 2, Allegro, 560–61 String Quartet no. 9, op. 59, no. 3 Andante con moto, 47 Menuetto: Grazioso, 444 String Quartet no. 13 in B major, op. 130, Alla danza tedesca, 364

Symphony no. 1 in C major, op. 21 Adagio molto, 85, 639–40 Finale, 299 Symphony no. 3 in E major, “Eroica,” op. 55 Allegro vivace: Trio, 379 Finale, 168–70 Trio, 308 Symphony no. 4 in B major, op. 60, Adagio/Allegro vivace, 197–98 Symphony no. 5 in C minor, op. 67, Allegro, 170, 238 Symphony no. 6 in F major, “Pastorale,” op. 68, Allegro ma non troppo, 170 Symphony no. 7 in A major, op. 92 Allegretto, 54, 216 Assai meno presto, 234 Symphony no. 9 in D minor, op. 125, Adagio molto, 175 Theme and Variations in G major, WoO 77, Thema: Andante, quasi Allegretto, 684 Thirty-two Variations on an Original Theme, in C minor, WoO 80, theme and two variations, 497 *Violin Concerto in D major, op. 61, Rondo: Allegro, 399 Violin Sonata in A major, op. 12, no. 2, Allegro piacevole, 468 Violin Sonata in A major, op. 23, Allegro molto, 89 *Violin Sonata in G major, op. 30, no. 3, Allegro assai, 390–91 *Violin Sonata in G major, op. 96, Scherzo, 96 Violin Sonata no. 3 in E major, op. 12, no. 3, Adagio con molto espressione, 134–35, 239 Violin Sonata no. 5 in F major (“Spring”), op. 24, Allegro, 350–51 *Violin Sonata no. 8 in G major, op. 30, no. 3, Minuet, 228–29 Berg, Alban (1885–1935) Lyric Suite (1927), 852

Index of Musical Examples and Exercises “Nacht” from Seven Early Songs, 772–73 “Ü ber die Grenzen” from Five Orchestral Songs: 1912, 733 Violin Concerto, 840 Berlioz, Hector (1803–1869), L’Enfance du Christ, recitative of the Father, scene 2, 60 Brahms, Johannes (1833–1897) *“Dämmrung senkte sich von oben” (“Twilight sank from high above”), op. 59, no. 1, 673 “Es hing der Reif ” (“Hoarfrost was hanging”), op. 106, no. 3, 671–73 “Es wohnet ein Fiedler,” from German Folk Songs, vol. 6, 120 “Gunhilde,” German Folk Songs, vol. 1, 120 “Heimweh III” (“Homesickness III”), op. 64, no. 9, 690 *Horn Trio, Andante, 239 *“Immer leiser wird mein Schlummer” (“Ever More Peaceful Grows My Slumber”), op. 105, no. 2, 717–18 Intermezzo in A minor, op. 118, no. 1, 719–20 *Intermezzo in A minor, op. 116, no. 2, 406 “Parole” (“Password”), op. 7, no. 2, 668–69 Romanze in F, Six Piano Pieces, op. 118, no. 5, 597–99 Symphony no. 3 in F major, op. 90 Allegro con brio, 523 Andante, 523 Symphony no. 4 in E minor, op. 98 Allegro energico e passionato, 498, 688–89 *Allegro giocoso, 372 “Unüberwindlich,” op. 72, no. 5, 89, 103 “Vom verwundeten Knaben,” op. 14, no. 2, 213–14 “Von ewiger Liebe,” op. 43, no. 1, 62

*Waltz in A major, op. 39, no. 15, 390 Byzantine Chant, 79 Chopin, Frederick (1810–1849) Etude in A, op. posth., 158 Etude in A major, op. 25, no. 1, 132 Etude in A major, op. posth., Allegretto, 64 Etude in C minor, “Revolutionary,” op. 10, no. 12, 664 Etude in F major, op. 10, no. 8, BI 42, 246–47 Impromptu in A, 705 Impromptu no. 1 in A major, op. 29, BI 110, 247 Mazurka in A minor, 609–10 Mazurka in A minor, op. 17, no. 4, 607–9 Mazurka in A minor, op. 59, no. 1, BI 157, 701 Mazurka in B major, op. 56, no. 1, BI 153, 586–87 *Mazurka in C minor, op. 30, no. 4, BI 105, 558 Mazurka in F minor, op. 68, no. 4, 610–11 Nocturne in B major, op. 9, no. 3, 63 Nocturne in B major, op. 62, no. 1, 326 Nocturne in B minor, op. 9, no. 1, 561 Nocturne in C minor, op. 48, no. 1, Bl 142, 528, 564–65 Nocturne in E minor, op. posth. 72, no. 1, 157 Nocturne in F major, op. 15, no. 1, 156 Nocturne in F minor, op. 48, no. 2, 269 Nocturne in F minor, op. 55, no. 1, 157, 400 *Nocturne in G major, op. 37, no. 2, 466 Nocturne in G minor, op. 15, no. 3, 157 Prelude, op. 28, no. 2, 720–24 Prelude in A minor, op. 28, 706–7 Prelude in C minor, op. 28, no. 6, 85

I2-3 Scherzo no. 3 in C minor, op. 39, 353 Waltz in A major, op. 42, 64 *Waltz in A major, op. 64, no. 3, 76 Waltz in A minor, BI 150, 66 *Waltz in B minor, op. posth. 69, no. 2, 75 *Waltz in D major, op. 64, no. 1, 75 *Waltz in E minor, B1 56, 75 Clementi, Muzio (1752–1832), *Prelude in A minor, op. 19, 466 Coltrane, John (1926-1967), “Giant Steps,” 714–15 Corelli, Arcangelo (1653–1713) Concerto Grosso in D major, op. 6, no. 7, Allegro, 255 Concerto Grosso no. 8 in G minor, Allegro no. 2, 217 Sonata for Two Violins in E major, op. 2, no. 11, Giga, 281–82 Sonata for Two Violins in E minor, op. 2, no. 4, Preludio, 282 Sonata no. 7, op. 5, Sarabande in D minor, 161 *Sonata no. 11 in F for two flutes, after Violin Sonata in E major, op. 5, Allegro, 150 *Violin Sonata, op. 2, no. 3, Preludio, Largo, 331 Violin Sonata in A minor, op. 1, no. 4, Presto/Adagio, 267 Violin Sonata in B minor, op. 2, no 8, Tempo di Gavotta, 226–27 Violin Sonata in F major, op. 5, no. 4, Grave, 227 Violin Sonata no. 11 in D minor, op. 1, Adagio, 296 Corrett, Michel (1709–1795), *Sarabanda in E minor for Flute and Continuo, 331 Costeley, Guillaume (1531–1606), “Allon gay, gay,” 80 Couperin, François (1668–1733) Les Goûts-réunis, Concert no. 8, “Air tendre,” 618–19 “Les Nations,” Premier Ordre: La Francoise, XIV, Chaconne, 422

I2-4

THE COMPLETE MUSICIAN

Dallapiccola, Luigi (1904–1975), “Contrapunctus secundus” from Quaderno musicale di Annalibera, 868 Debussy, Claude (1862–1918) *“Cloches àtravers les feuilles” from Images, Book 2, 786 “Engulfed Cathedral,” from Preludes, Book 1: 1910, 735 *“Et la lune descend sur la temple qui fut” from Images, Book 2, 785 “Footprints in the Snow” (“Des pas sur la neige”) from Préludes, Book 1, 744 “La puerta del Vino” from Preludes, Book 2, no. 3, 740 “Reflets dans l’eau” from Images, Book 1, 769 Donizetti, Gaetano (1797–1848), Lucrezia Borgia, act 1, no. 3, 156, 237 Dufay, Guillaume (1397(?)–1474), Missa Sancti Jacobi, Communion, 88 Dvořák, Antonin (1841–1904), *Symphony no. 9, “New World,” Largo, 674 Dykes, John (1823–1876), “Holy, Holy, Holy,” 318 Fauré, Gabriel (1845–1924), Pavane, op. 50, 360 Foster, Steven (1826–1864), “Beautiful Dreamer,” 264 Franck, César (1822-1890), *Violin Sonata, movement 1, 761 Gaultier, Denis (1603–1672), “Piece for Lute,” 80 Geminiani, Francesco (1687–1762), The Art of Playing the Violin, op. 9, no. 8, 521 Giardini, Felize, (1716–1796), *Six Duos for Violin and Cello, no. 2, 299 Gluck, Christoph Willibald (1714– 1787) *“Bettet den Vater,” from Alceste, act 1, 588 Orfeo, act 1, no. 1, 241 Grieg, Edvard (1843–1907) “Illusion,” Lyric Pieces VI, op. 57, 686

“Morning” from Peer Gynt Suite, op. 46, no. 1, 524–25 Gruber, Franz (1786–1863) “Stille Nacht” (“Silent Night”), 305, 403 Handel, George Friedrich (1685– 1759) “Comfort Ye,” from Messiah, HWV 56, 223–24 *Concerto Grosso, op. 6, no. 9, Largo, 278 *Concerto Grosso in B major, op. 3, no. 2, HWV 313, Largo, 478 Concerto Grosso in C minor, op. 6, no. 8, HWV 326, Allegro, 27 *Concerto Grosso in F major, op. 3, no. 4, HWV 315, Allegro, 492–93 Concerto in B major for Harp, op. 4, no. 6, Larghetto, 414 Flute Sonata in B minor, HWV 367b, 222 Keyboard Suite no. 7 in G minor, Passacaglia, *427, 499 Prelude in G major, 472–73 “Since by Man Came Death,” Messiah, HWV 56, 569 *Trio Sonata in G minor, op. 2, no. 5, HWV 390, Allegro, 421 *Water Music, Minuet, 103 Haydn, Franz Joseph (1732–1809) Divertimento, “St. Anthony Chorale,” 316 Divertimento in G major, Hob XVI.11, Presto, 600–601 *Piano Sonata in A major, Hob XVI.12, Trio, 491–92 *Piano Sonata in C major, Hob XVI.10, Menuet and Trio, 611–12 *Piano Sonata in C major, Hob XVI.35, Finale: Allegro, 88, 626–28 *Piano Sonata in D major, Hob XVI.4, Menuetto, 299 Piano Sonata in E minor, no. 53, Hob XVI.34, Vivace molto, 469 Piano Sonata in G minor, Hob XVI.44, 332

Allegretto, 312 *Piano Sonata no. 29 in E major, Hob XVI.45, Moderato, 342 Piano Sonata no. 30 in D major, Hob XVI.19, Moderato, 341 Piano Sonata no. 37 in E major, Hob XVI.22, Tempo di Menuetto, 295 Piano Sonata no. 38 in F major, Hob XVI.23, Adagio, 396 Piano Sonata no. 48 in C major, Hob XVI.35, Allegro con brio, 648–52 Finale: Allegro, 88 *Piano Sonata no. 50 in D major, Hob XVI.37, Presto ma non troppo, 490 Sonatina no. 4 in F major, Hob XVI.9, Scherzo, 485–86 String Quartet in A major, op. 55, no. 1, Hob III.60 Allegro, 448, 638–39 Menuetto, 582 String Quartet in B, op. 33, no. 4, Allegretto, 161–62 String Quartet in B major, op. 64, no. 3, Hob III.67, 449 Menuetto, 340 *String Quartet in B major, “Sunrise,” op. 76, no. 4, Adagio, 399 String Quartet in B minor, op. 33, no. 1, 640–41 *String Quartet in B minor, op. 64, no. 2, Hob III.68, Adagio ma non troppo, 271 String Quartet in C major, “Emperor,” op. 76, no. 3, Hob III.77, 606 Poco adagio; cantabile, 80, 404–5 String Quartet in C major, op. 54, no. 2, Hob III.58, Vivace, 538 *String Quartet in C major, op. 20, no. 2, Hob III.32, Trio, 428 String Quartet in D major, op. 33, no. 6, Hob III.42, Finale, 624–26 String Quartet in D major, “The Frog,” op. 50, no. 6, Hob III.49, Menuetto, 274

Index of Musical Examples and Exercises String Quartet in D minor, op. 76, no. 2, Andante o piú tosto allegretto, 228 String Quartet in D minor, “Quinten,” op. 76, no. 2, Hob III.76, Andante o più tosto allegretto, 228, 352 String Quartet in E major, op. 64, no. 6, Trio, 206–7 *String Quartet in E major, op. 20, no.1, Hob III.31 Allegro, 449 Finale, 449 *String Quartet in E major, op. 50, no. 3, Allegro con brio, 162 String Quartet in F minor, op. 20, no. 5, Hob III.35, Allegro moderato, 269 *String Quartet in G major, op. 33, no. 5, iii, 300 *String Quartet in G minor, op. 74, no. 3, ii, Largo assai, 257 *Symphony no. 92 in G major, “Oxford,” Hob I.92, Adagio, 343 Symphony no. 100 in G major, “Military,” Allegretto, 338 Symphony no. 101, “Clock,” Finale, 224 Hummel, Johann Nepomuk (1778– 1837), Bagatelle in C major, op. 107, 483–84 Joel, Billy (1949–), “Piano Man,” 81 Josquin des Pres (1450–1521), Missa Pange Lingua, Kyrie, 88 Kabalevsky, Dmitri Borisovich (1904-1987), *Toccatina, 770 Lamm, Robert (1944–), “Saturday in the Park,” 679 Leclair, Jean Marie (1697–1764) Sonata in C major for Flute and Continuo, op. 1, no. 2, Corrente, 451 Sonata in G minor for Two Violins and Basso Continuo, op. 4, no. 5, Andante, 244 Trio Sonata in D major, op. 2, no. 8, Allegro, 424

Liszt, Franz (1811–1886) “Aux cypres de la Villa d’Este I: Threnodie” (“To the cypresses of the Villa d’Este”), from Anneés de Pèlerinage (Years of Pilgrimage); Third Year, 699 “Nuages gris” (“Gray Clouds”), S199, LW 305, 686–87 “Sursum corda” from Années de Pèlerinage, Year 3, 8–9 Loeillet, Jean-Baptiste (1680–1730), Sonata for Oboe in A minor, op.5, no.2, 235 Lutosławski, Witold (1913-1994), *Bucolic, no. 3, 785 Mahler, Gustav (1860–1911) Song of the Earth, 755 Symphony no. 2 in C minor (“Resurrection”), “Urlicht,” 353, 369 Marcello, Benedetto (1686–1739), *Sonata in A minor, no. 8, Presto, 371 Mascagni, Pietro (1863–1945), “A casa amici” (“Homeward, friends”), Cavalleria Rusticana, scene 9, 510–11 Mendelssohn, Felix (1809–1847) *Elijah, opening of Part I, 363 Lieder ohne Worte (“Songs Without Words”) op. 19, no. 5, 276 *no. 20 in E major, op. 53, 331 op. 30, no. 2, 277 *no. 48 in C major, op. 102, 337 Midsummer Night’s Dream, Overture, 85 *“Weh mir!” Ariette, from Elijah, no. 18, 588 Messiaen, Olivier (1908-1992) “Dance of Fury, for the Seven Trumpets” from Quartet for the End of Time, 785, 832–33 “Louange àl’ Éternité de Jésus” from Quatuor pour la fin du temps, 779 “Regard de la Vierge” from Vingt Regards sur l’Enfant Jesus, 832 Meyerbeer, Giacomo (1791–1864), “Se non ti moro allato,”

I2-5 Sei canzonette italiane, no. 5, 264 Monteverdi, Claudio (1567–1643), “Lamento della ninfa” (“Lament of the Nymph”), Madrigali guerrieri et amorosi, 494–95 Montrose, Percy (1851–1893), “Clementine,” 151–54 Mozart, Wolfgang Amadeus (1756– 1791) Act I, Finale, from The Magic Flute, K. 620, 387 *Adagio in C major, K. 356, 587 Bassoon Concerto in B major, K. 191, Rondo, Tempo di Menuetto, 315 Clarinet Quintet in A major, K. 581, I, 352 Concerto in E major for Horn and Orchestra, K. 447, Larghetto, 311 *Cosi fan tutte, act 1, scene 5, 209 Eine Kleine Nachtmusik, K. 525 Menuetto, 74–75 Trio, 204 *“In diesen heiligen Hallen,” from The Magic Flute, 321 “Madamina,” Don Giovanni, act 1, no. 4, 135–36 Menuett in D major, K. 94, *103, 515 Piano Concerto in C major, K. 467, ii, Andante, 132 Piano Concerto in D minor, K. 466 Allegro, 72 Andante, 381 *Piano Concerto in G major, K. 453, Allegretto, 477 Piano Sonata in A major, K. 331, Andante grazioso, 274–75 Piano Sonata in A minor, K. 310 Allegro maestoso, 71 Presto, 83 Piano Sonata in B major, K. 281 Allegro, 383 Rondeau: Allegro, 397–98 Piano Sonata in B major, K. 333 *Allegretto grazioso, 390 Allegro, *278, 652–55 Piano Sonata in B major, K. 570, Allegretto, 285

I2-6

THE COMPLETE MUSICIAN

Mozart, Wolfgang Amadeus (continued ) Piano Sonata in C major, K. 545, Allegro, 12–13, 25, 132, 236 Piano Sonata in C minor, K. 457, Allegro, 50 Piano Sonata in D major, K. 284, Polonaise en Rondeau, 21 Piano Sonata in D major, K. 284, Thema, Andante, 470, 487–88 Piano Sonata in D major, K. 311, Rondeau, 647 Piano Sonata in D major, K. 576, Allegro, 335–36, 374 *Piano Sonata in D major, K. 284 Theme: Andante, 405 “Variation VII, Minore,” 271 *Piano Sonata in D major, K. 576, Allegretto, 406 Piano Sonata in E major, K. 282, Allegro, 233 Piano Sonata in F, K. 280, Presto, 238 Piano Sonata in F major, K. 332, Allegro, 71 *Piano Trio in G major, K. 496, Allegretto, 490–91 Quintet “Hm! Hm! Hm!” from The Magic Flute, act I, 313–14 *Rondo, in F major, K. 494, 256 Rondo in C major, K. 373, 171 *Serenade in D major, K. 204, 362 *Sonata for Violin and Piano in B major, K. 372, 419 String Quartet in B major, K. 159, Andante, 357 String Quartet in B major, K. 159, Rondo, 234 *String Quartet in B major, K. 172 Adagio, 299 Allegro assai, 239 String Quartet in C major, “Dissonance,” K. 465, Adagio, 667 *String Quartet in C major, K. 157, Andante, 219 *String Quartet in D minor, K. 173, Menuetto, 219

*String Quartet in F major, K. 590, Andante, 219 *String Quintet in C minor, K. 406, iii, 427 Symphony 35 in D major, “Haffner,” K. 385, Menuetto, 273 Symphony in A major, K. 114, Allegro moderato, 313 Symphony in A major, K. 385, Menuetto/Trio, 305 Symphony in D major, K. 97, Trio, 245 *Symphony in D major, “Prague,” K. 504, Presto, 467 Symphony in E major, K. 132, Andante, 245 Symphony in G major, K. 74, Allegro, 423 *Symphony in G major, K. 124, Allegro, 429 Symphony in G minor, K. 183, Allegro con brio, 72 Symphony no. 28 in C major, K. 200, Allegro, 251 *Symphony no. 36 in C major, “Linz,” K. 425, Poco adagio, 337 Symphony no. 39 in E major, K. 543, Menuetto, 317 *Symphony no. 39 in E major, K. 543, Allegretto, 390 Symphony no. 41 in C major, “Jupiter,” K. 551, Andante cantabile, 158 *Variations on “Ah vous diraisje, Maman,” K. 265, 300 Viennese Sonatina in B major, Five Divertimenti for Two Clarinets and Bassoon, K. Anh. 229, Allegro, 620–22 Violin Sonata in C major, K. 14, Menuetto secondo en Carillon, 397 Violin Sonata in F major, K. 377, Minuet, 356 Violin Sonata in G major, K. 379, Adagio, 363 *Violin Sonata in G major, K. 379, Andantino cantabile, 427 *“Wer ein Liebchen,” from Abduction from the Seraglio, 574

Mussorgsky, Modest Petrovich (1839–1881), *“Bydlo” from Pictures at an Exhibition, 559 Pachelbel, Johann (1653–1706), Canon in D major, 415, 500 Paganini, Niccolo (1782–1840) *Caprice for Solo Violin, op. 1, no. 11, 575 Caprice for Violin, op. 1, no. 12, 93 *Caprice no. 20, from 24 Caprices, op. 1, 613 Pergolesi, Battista, Giovanni, (1710–1736), *“Il nocchier nella Tempesta,” from Salustia, act 2, scene 9, 428 Pinkard, Maceo (1897–1962), “Sweet Georgia Brown,” 670–71 Platti, Giovanni Benedetto (1692– 1763), *Sonata in C Major, Six Sonatas for Harpsichord, op. 4, no. 4, 655–57 Poulenc, Francis (1899-1963), *Waltz, 771 Prokofiev, Sergei (1891-1953) Sarcasms, op. 17, no. 3, 740 Visions Fugitives, op. 22, no. 16, 743 Purcell, Henry (1649–1695), Ground in G, theme and two variations, 495–96 Quantz, Johann Joachim (1697– 1773), *Duet no. 4, from Six Duets for Two Flutes, 95 Rachmaninoff, Sergei (1873–1943) Moment Musical, op. 16, no. 3, 753–54 *Prelude in G minor, op. 32, no. 12, 566 Rameau, Jean Philippe (1663– 1733), *Rondino, 163 Ravel, Maurice (1875–1937) Daphnis et Chloe: 1912, 732 *Jeux d’eau, 786 “Passacaille” from Piano Trio in A minor, 741 “Rigaudon” from Le Tombeau de Couperin, 754

Index of Musical Examples and Exercises Sonatine “Animé,” 752, 753 “Modere,” 745–49 “Mouvement de Menuet,” 749–51 Roman, Johann Helmich (1694– 1758), *Flute Sonata in B minor, op. 1, no. 6, Grave, 256 Scarlatti, Domenico (1685–1757) Sonata in D major, K. 96, 93 *Sonata in G minor, K. 64, 477 Schoenberg, Arnold (1874–1951) Chamber Symphony no. 1, 775 Drei Klavierstück, op. 11, no. 1, 743 “Gavotte” from Suite for Piano, op. 25, 742 “Nacht” from Pierrot Lunaire, 731–32, 738–39 Violin Concerto, op. 36, mm. 1–16, 862–63 “Walzer” from Fünf Klavierstücke, no. 5 (1923), 841–42 Schubert, Franz (1797–1828) *“Am Frühling,” D. 882, 371 “Am Meer” (“By the Sea”), Schwanengesang, D. 957, no. 12, 691 “An den Mond,” D. 193, 54 “Der Atlas,” from Schwanengesang, D. 957, no. 8, 685 “Der Lindenbaum,” from Winterreise, 69–70, 148–49 “Der Müller und der Bach” (“The Miller and the Brook”), Die schöne Müllerin, D. 795, no. 19, 555 *“Du bist die Ruh,” op. 59, no. 3, 520 “Erlkönig,” D. 328, 674 Frühlingstraum” (“A Dream of Springtime”), Winterreise, D. 911, no. 11, 351 “Gute Nacht” from Winterreise, 15–16 Impromptu in A, from Four Impromptus, D. 935, Trio, 542 Impromptu in B major, Thema, Andante, 214–15

Impromptu in G major, op. 90, no. 3, D. 899, 132 Impromptu no. 3 in B, D. 935, 287–88 “Die Krähe,” from Winterreise, 333 “Lachen und Weinen” (“Laughter and Tears”), D. 777, 543–45 Ländler, D. 734, op. 67, no. 16, 307 “Die liebe Farbe” (“The Beloved Color”) and “Die böse Farbe” (“The Evil Color”), from Die schöne Müllerin, 543, 546–47 *“Die Liebe hat gelogen,” 589 *Minuet in A minor, from 20 Minuets, D. 41, no. 8, Trio, 208 Minuet in D major, D. 41, 305 *“Morgengruss,” from Die schöne Müllerin, 239 “Des Müllers Blumen” (“The Miller’s Flowers”), from Die schöne Müllerin, 235, 338 Piano Sonata in A major, D. 959 Andantino, 217 *Trio, 400 “Schwanengesang” (“Swan Song”), op. 23, no. 3, D. 744, 515–16 Sonata in B major, op. posth., D. 960, Molto moderato, 539–41 Sonatina in D major for Piano and Violin, op. posth. 137, no. 1, D. 384, Allegro molto, 582–83 String Quartet in A minor, D. 804, I, 678 String Quartet in C minor, “Quartettsatz,” D. 703, 563 String Quartet in G major, D. 887, Allegro molto moderato, 698 String Quartet no. 3 in B major, D. 36, Menuetto-Trio, 539 *String Quintet in C major, D. 956, Adagio, 420

I2-7 Symphony no. 4 in C minor, D. 417, “Tragic,” Andante, 339 Symphony no. 9 in C major, D. 944, “Great,” 81 Andante, 130 Scherzo, 342 Violin Sonata no. 2 in G minor, D. 408, Andante, 275 Waltz in A minor, from 12 Grazer Walzer, D. 924, no. 9, 308 *Waltz in B major, from 36 Originaltänze, op. 9, no. 24, D. 365, 208 Waltz in C major, Valses sentimentales, D. 779, no. 16, 576 *Waltz in C minor, no. 27, from 36 Original Dances, D. 365, 300 Waltz in D major, 34 Valses Sentimentales, op. 50, no. 12, D. 779, 689 Waltz in F major, 36 Original Dances, D. 365, no. 33, 535–36 Waltz in G minor, Die letzte Walzer, op. 127, no. 12, D. 146, 569 “Wasserfluth” (“Torrent”), Winterreise, op. 89, no. 6, D. 911, 199–200, 235 Schumann, Clara (1819–1896) “Andante espressivo,” Quatre pièces fugitives, op. 15, no. 3, 464 *“Les Ballet des Revenants,” from Quatre pièces caractéristique, op. 5, 174 Schumann, Robert (1810–1856) (Untitled), from Album for the Young, op. 68, 328 “Am leuchtenden Sommermorgen,” from Dichterliebe, op. 48, 284 “Armes Waisenkind,” from Album for the Young, op. 68, no. 6, 85 “Auf einer Burg” (“In a Castle”), Liederkreis, op. 39, no. 7, 665–66 “Ich grolle nicht” (“I bear no grudge”), Dichterliebe, op. 48, no. 7, 512–13

I2-8

THE COMPLETE MUSICIAN

Schumann, Robert (continued ) *“Kind im einschlummern,” Kinderszenen, op. 15, no. 12, 400 *Kreisleriana, op. 16, no. 7, 428 “Mit Myrthen und Rosen” (“With Myrtle and Roses”), Liederkreis, op. 24, no. 9, 465 “Sängers Trost” (“Singer’s Consolation”), Fünf Lieder und Gesänge, op. 127, no. 1, 464 “Schlummerlied,” from Albumblätter, op. 124, 62 *Symphony no. 2, op. 61, Allegro Vivace, 679 “Talismane,” Myrten, op. 25, no. 8, 462–63 “Waldesgespräch,” from Liederkreis, op. 39, no. 3, 93, 547–51 *“Wichtige Begebenheit,” from Kinderscenen, op. 15, 96 “Winterzeit,” from Album for the Young, op. 68, 328 Schütz, Heinrich (1585–1672), “Nacket bin ich von Mutterleibe kommen” (“Naked I have come from my mother’s womb”), Musicalischen Exequien, op. 7, SWV 279, 359 Scriabin, Alexander (1872–1915) Etude in C minor, op. 2, no. 1, 81 Prelude for Piano, op. 74, no. 2: 1912, 735 Prelude in F minor, op. 17, no. 5, 836 Prelude in G major, op. 11, 834 Smetana, Bedrich (1824–1884), “Moldau,” from My Country, mm. 40–47, 154 Strauss, Richard (1864–1949), *“Ach lieb, ich muss nun scheiden,” op. 21, no. 3, 256 Stravinsky, Igor (1882–1971) *Firebird Suite, Finale, 762 “In Petrushka’s Room” from Petrushka, 734

“Lento” from Le cinq doigts, 783 “The Masqueraders,” from Petrouchka, 835–36 *Les Noces, 758–59 The Rite of Spring 759–61 “Augurs of Spring,” Rehearsal 13, mm. 1–8, 831 Symphony of Psalms, 739, 784 Tchaikovsky, Peter (1840–1893) Sleeping Beauty *act 1: La Fée des Lilas, 679 Pas de Six, “Violente,” 585–86 scene 2, 580–81 *“Sweet Reverie,” Children’s Pieces, op. 39, no. 21, 406–7 “Za oknom v teni mel’kajet” (“At the window, in the shadow”), op. 60, no. 10, 362 Telemann, Georg Philipp (1681– 1767) “Domenica,” from Scherzi Melodichi, Vivace, 215 Sonata for Flute in B major, Dolce, 226 Thomas, Ambroise (1811–1896), *Gavotte, from Mignon, 240 Traditional “Adeste,” 53 “Down in the Valley,” 53 “Erie Canal,” 360 “Flow Gently,” 53 “God Save the King,” 152–54 “Greek Folk Song,” 59 “A Mighty Fortress Is Our God,” 54 “My Gentle Harp,” 320 “Oh, Susanna,” 52 “Simple Gifts,” 204–5 *Türk, Daniel Gottlob (1750– 1813), Serenade, *322 Verdi, Giuseppe (1813–1901) Overture to La forza del destino, 265 *“Se mami ancor,” from Il trovatore, no. 19, 574–75 *“Si, la stanchezza m’opprime, o figlio,” from Il trovatore, no. 21, 575 Victoria, Thomas Luis (1548– 1611), *Kyrie, 95

Vivaldi, Antonio (1678–1741) The Four Seasons, “Spring,” 191 *Sonata in C minor for oboe, 150 Sonata in C minor for Oboe and Basso Continuo, Allegro, 147 Trio Sonata in C minor, Allegro, 474–75 Violin Concerto in C minor, “Il Sospetto,” RV199, Allegro, 410 *Violin Sonata in F major, RV 176, 173 Wagner, Richard (1813–1883) “Der Augen leuchtendes Paar” (“Those eyes so lustrous and clear”) (Wotan’s Farewell), Die Walküre, act 3, scene 3, 364 “Mögst du mein Kind,” from The Flying Dutchman, act 2, 358 Das Rheingold Prelude, 168 *scene 1, 257 Weber, Carl Maria von (1786– 1826), Six Ecossaises, no. 2, J. 30, 484–85 Webern, Anton (1883–1945) Concerto for Nine Instruments, op. 24 (mm. 1–3), 848–51 Five Movements for String Quartet, op. 5, 736–37, 792–95, 815 Quartet for Violin, Clarinet, Tenor Saxophone, and Piano, op. 22, 798, 803, 809 Willaert, Adrian (1490–1562), *”And if out of jealousy you are making me such company,” 103 Williams, Vaughan, “Greensleeves,” 766–67 Wipo of Burgundy (995?–1048?), “Victimae paschali laudes,” 79 Yarrow, Peter (1938–), “Puff the Magic Dragon,” 368