Engineering of Music for the Digital Age: Creativity in Musical Composition 9788770041072, 9788770042505, 9788770042529, 9788770042512

Table of contents :
Cover
Half Title
Series Page
Title Page
Copyright Page
Table of Contents
Preface
Acknowledgement
List of Figures
List of Tables
List of Abbreviations
Chapter 1: Music Maker: Introduction
1.1: Themes of the Book
1.2: Democratization of Creation
1.3: Is Music a Science or an Art?
1.4: The Rest of the Book
1.5: Sidebar – Music and Limitless Possibilities
Chapter 2: Form in Composition
2.1: Introduction
2.2: Form
2.3: One-part Forms
2.4: Binary Form
2.5: Variation Form
2.6: Ternary Form
2.7: Rondo Form
2.8: Sonata Form
2.9: Song Forms
2.10: Fantasia
2.11: Other Structural Elements
2.12: Sidebar – Creative Sources for Musical Composition
2.13: Summary
Chapter 3: Phrase, Period, and Expression
3.1: Introduction
3.2: The Phrase
3.3: Ingredients: Rhythm–Melody–Harmony
3.4: Connecting Phrases
3.5: Emerging Patterns
3.6: Digitally Calculable Possibilities
3.7: Sidebar – How Being an Omnivore Aids in Musical Composition
3.8: Summary
Chapter 4: Rhythm/Motive
4.1: Introduction
4.2: Meter
4.3: Rhythmic Devices
4.4: Motive
4.5: Sidebar: Creative Sources for Musical Composition
4.6: Summary
Chapter 5: Melody and Harmony
5.1: Introduction: Melody and Harmony
5.2: Chord Progression
5.3: Melody and Harmony in Texture
5.4: Harmonic and Non-harmonic Tones
5.5: Sidebar: Patterns for Creating Music
5.6: Summary
Chapter 6: Tonal Center
6.1: Introduction
6.2: Tonality
6.3: Modality
6.4: Atonality
6.5: Sidebar
6.6: Summary
Chapter 7: Mode Mixture and Modulation
7.1: Introduction
7.2: Mode Mixture
7.3: Borrowed Chords
7.4: Tonicization
7.5: Chromaticism
7.6: Modulation
7.7: Obscuring the Key
7.8: Sidebar
7.9: Summary
Chapter 8: Accompaniment/Instrumentation/ Orchestration
8.1: Introduction
8.2: Texture
8.3: Accompaniment
8.4: Orchestration/Arrangement/Instrumentation
8.5: Sidebar
8.6: Summary
Chapter 9: Compositional Techniques
9.1: Introduction
9.2: Variation
9.3: Development
9.4: Transformation
9.5: Sidebar
9.6: Summary
Chapter 10: Notation Document Creation
10.1: Introduction
10.2: Types of Notation
10.3: What Time Signature?
10.4: Other Notational Concerns
10.5: Sidebar: Music as a Document
10.6: Summary
Chapter 11: Application (Democratization of Creation)
11.1: Introduction
11.2: Bach’s Prelude in C Major BWV 846
11.3: Selected Mozart Sonata Movements
11.4: Tárrega Capricho Árabe
11.5: Paganini Caprice Op. 1, No. 1
11.6: Debussy Prelude “Voiles”
11.7: Sidebar
11.8: Summary
Chapter 12: WWWD?
12.1: Sky Echo the Blue Whale
12.2: Dances with Traffic
12.3: Siri-ously? That’s All It Takes?
12.4: Headband Harmony
12.5: My What Big Hands You Have
12.6: Modern Mozart and Musical Meaning
Index
About the Authors

Citation preview

Engineering of Music for the Digital Age Creativity in Musical Composition

RIVER PUBLISHERS SERIES IN DOCUMENT ENGINEERING Series Editor: STEVEN SIMSKE Colorado State University USA Document engineering is an interdisciplinary set of processes and systems concerned with the analysis, design, development, evaluation, implementation, management, and/or use of documents and document corpora in order to improve their value to their users. In the era of the Internet, the millenniaold concept of a document is rapidly evolving due to the ease of document aggregation, editing, re-purposing, and reuse. In this series of books, we aim to provide the reader with a comprehensive understanding of the tools, technologies, and talents required to engineer modern documents. Individual documents include web pages and the traditional print-based or print-inspired pages found in books, magazines, and pamphlets. Document corpora include sets of these documents, in addition to novel combinations and re-combinations of document elements such as mash-ups, linked sets of documents, summarizations, and search results. In our first set of books on document engineering, we will cover document structure, formatting, and layout; document structure; summarization; and classification. This set will provide the reader with the basis from which to go forward to more advanced applications of documents and corpora in subsequent years of the series. The books are intended to cover a wide gamut of document engineering practices and principles, and as such will be suitable for senior undergraduate students when using the first 2/3 of each book (core topics), and be extensible to graduate students, researchers and professionals when the latter 1/3 of each book is also considered (advanced topics). Students and graduates of data analytics, information science, library science, data mining, and knowledge discovery will benefit from the book series.

For a list of other books in this series, visit www.riverpublishers.com

Engineering of Music for the Digital Age Creativity in Musical Composition

Jeff Ewing Fort Collins, CO, USA

Steve Simske Fort Collins, CO, USA

River Publishers

Published 2024 by River Publishers

River Publishers Alsbjergvej 10, 9260 Gistrup, Denmark www.riverpublishers.com Distributed exclusively by Routledge

605 Third Avenue, New York, NY 10017, USA 4 Park Square, Milton Park, Abingdon, Oxon OX14 4RN

Engineering of Music for the Digital Age / by Jeff Ewing, Steve Simske. 2024 River Publishers. All rights reserved. No part of this publication may be reproduced, stored in a retrieval systems, or transmitted in any form or by any means, mechanical, photocopying, recording or otherwise, without prior written permission of the publishers.

©

Routledge is an imprint of the Taylor & Francis Group, an informa business

ISBN 978-87-7004-107-2 (hardback) ISBN 978-87-7004-250-5 (paperback) ISBN 978-87-7004-252-9 (online) ISBN 978-87-7004-251-2 (master ebook) While every effort is made to provide dependable information, the publisher, authors, and editors cannot be held responsible for any errors or omissions.

Contents

Preface

ix

Acknowledgement

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List of Figures

xiii

List of Tables

xxxix

List of Abbreviations 1

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xli

Music Maker: Introduction 1.1 Themes of the Book . . . . . . . . . . . . . 1.2 Democratization of Creation . . . . . . . . 1.3 Is Music a Science or an Art? . . . . . . . . 1.4 The Rest of the Book . . . . . . . . . . . . 1.5 Sidebar – Music and Limitless Possibilities

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Form in Composition 2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . 2.2 Form . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 One-part Forms . . . . . . . . . . . . . . . . . . . . 2.4 Binary Form . . . . . . . . . . . . . . . . . . . . . . 2.5 Variation Form . . . . . . . . . . . . . . . . . . . . 2.6 Ternary Form . . . . . . . . . . . . . . . . . . . . . 2.7 Rondo Form . . . . . . . . . . . . . . . . . . . . . . 2.8 Sonata Form . . . . . . . . . . . . . . . . . . . . . . 2.9 Song Forms . . . . . . . . . . . . . . . . . . . . . . 2.10 Fantasia . . . . . . . . . . . . . . . . . . . . . . . . 2.11 Other Structural Elements . . . . . . . . . . . . . . . 2.12 Sidebar – Creative Sources for Musical Composition 2.13 Summary . . . . . . . . . . . . . . . . . . . . . . .

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Phrase, Period, and Expression 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 The Phrase . . . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Ingredients: Rhythm–Melody–Harmony . . . . . . . . . . . 3.4 Connecting Phrases . . . . . . . . . . . . . . . . . . . . . . 3.5 Emerging Patterns . . . . . . . . . . . . . . . . . . . . . . . 3.6 Digitally Calculable Possibilities . . . . . . . . . . . . . . . 3.7 Sidebar – How Being an Omnivore Aids in Musical Composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . Rhythm/Motive 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . 4.2 Meter . . . . . . . . . . . . . . . . . . . . . . . . 4.3 Rhythmic Devices . . . . . . . . . . . . . . . . . . 4.4 Motive . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Sidebar: Creative Sources for Musical Composition 4.6 Summary . . . . . . . . . . . . . . . . . . . . . .

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Melody and Harmony 5.1 Introduction: Melody and Harmony 5.2 Chord Progression . . . . . . . . . 5.3 Melody and Harmony in Texture . . 5.4 Harmonic and Non-harmonic Tones 5.5 Sidebar: Patterns for Creating Music 5.6 Summary . . . . . . . . . . . . . .

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Tonal Center 6.1 Introduction 6.2 Tonality . . 6.3 Modality . . 6.4 Atonality . 6.5 Sidebar . . 6.6 Summary .

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Mode Mixture and Modulation 7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 Mode Mixture . . . . . . . . . . . . . . . . . . . . . . . . . 7.3 Borrowed Chords . . . . . . . . . . . . . . . . . . . . . . .

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Contents vii

7.4 7.5 7.6 7.7 7.8 7.9 8

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Tonicization . . . . Chromaticism . . . Modulation . . . . Obscuring the Key Sidebar . . . . . . Summary . . . . .

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Accompaniment/Instrumentation/ Orchestration 8.1 Introduction . . . . . . . . . . . . . . . . . . 8.2 Texture . . . . . . . . . . . . . . . . . . . . 8.3 Accompaniment . . . . . . . . . . . . . . . . 8.4 Orchestration/Arrangement/Instrumentation . 8.5 Sidebar . . . . . . . . . . . . . . . . . . . . 8.6 Summary . . . . . . . . . . . . . . . . . . .

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Compositional Techniques 9.1 Introduction . . . . . . 9.2 Variation . . . . . . . . 9.3 Development . . . . . 9.4 Transformation . . . . 9.5 Sidebar . . . . . . . . 9.6 Summary . . . . . . .

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10 Notation; Document Creation 10.1 Introduction . . . . . . . . . . 10.2 Types of Notation . . . . . . . 10.3 What Time Signature? . . . . 10.4 Other Notational Concerns . . 10.5 Sidebar: Music as a Document 10.6 Summary . . . . . . . . . . .

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11 Application (Democratization of Creation) 11.1 Introduction . . . . . . . . . . . . . . . 11.2 Bach’s Prelude in C Major BWV 846 . 11.3 Selected Mozart Sonata Movements . . 11.4 Tárrega Capricho Árabe . . . . . . . . . 11.5 Paganini Caprice Op. 1, No. 1 . . . . . 11.6 Debussy Prelude “Voiles” . . . . . . . . 11.7 Sidebar . . . . . . . . . . . . . . . . .

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viii

Contents

11.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 12 WWWD? 12.1 Sky Echo the Blue Whale . . . . . . . 12.2 Dances with Traffic . . . . . . . . . . 12.3 Siri-ously? That’s All It Takes? . . . . 12.4 Headband Harmony . . . . . . . . . . 12.5 My What Big Hands You Have . . . . 12.6 Modern Mozart and Musical Meaning

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317 317 320 322 325 328 331

Index

333

About the Authors

337

Preface

“Engineering of Music for the Digital Age – Creativity in Musical Composition” Musical scores – like literature, poetry, and technical manuals – are documents. The central thesis of this book is that musical composition in the digital age is a form of document engineering. Music, in essence, shares with other forms of creative content generation – from poetry to prose, and from science to science fiction – the needs for structure, flow, and sources for creativity. Musical composition can be thought of as the creative process of engineering documents with regards to its arrangement, form, texture, and instrumentation, etc. This document then instructs a performance or the creation of an alternative document, such as a recording. In this book, the arrangement of phrases, patterns, and structures seen in music will be illustrated to give new composers a starting point to begin planning and making decisions about their own compositions. The book will also guide those who need assistance in completing a piece. While this is a book about musical composition per se, it is not a manual on music theory. Instead, the book keeps its focus on the structural elements of a composition. Its aim is to give the audience a structural road map for composing; whether they are starting a piece from the first note, having a melody in mind already, or need help overcoming a creative hurdle. The book examines compositions that clearly define a form or technique. Targeted examples cover all stages of writing a piece, helping to build the reader’s composition from the first note into a complete work without promoting a style or harmonic practice. Each chapter contains a sidebar addressing helping the composer to add creative sources for the music making process. Finally, the book concludes with a chapter on creativity in terms of how composed music can affect our lives and even our fairy tales.

ix

Acknowledgement

Thank you to Steve (and Tess, Kieran, and Dallen) for many great musical years and friendship. Steve, thank you for planting the seed and suggesting that we should write this book. It was a rewarding journey, and I look forward to more in the future. Thank you to Nicki Dennis for providing a framework in which to include this book in a larger series of books about content creation; Junko Nakajima for patience, assiduousness, and encouragement in the publishing process; and River Publishers for giving us the opportunity to include this book as part of the Document Engineering Series. I would like to acknowledge Dr. Morton J. Achter, Dr. Craig R. Johnson, Dr. Lyle T. Barkhymer, Dr. Michael Haberkorn, and Dr. Jack D. Jenny from my time at Otterbein University. Hopefully, this book will serve new musicians in a way that lives up to the map of the musical world that they provided me with and that I continue to explore. Thank you to Mrs. Eleanor Popper (“Boss”), Dirk Kraus, Penny Popper, Kevin Wines, and Bill Van Sickle; all who have had a tremendous impact on me with opportunities and guidance from the beginning of my professional teaching career and beyond. Thank you to the many students and their families whom I’ve been able to work with through the years. Through them, I’ve visited the entire globe from within my teaching studio. And finally, to my wonderful wife, Bethany, and our amazing kids, Sam and Amélie, thank you for the support and patience through this whole process. Here’s to it, and to it again. . . Jeff Ewing Wow, was this book fun to put together! Thanks to Jeff, who patiently guided me through all of the musical elements of the book, and also patiently wait for me to unsplit infinitives, tuck in the odd Oxford comma, and otherwise fuss and fret over every text element in a book that is, instead, on music. What follows is a good picture of how the book came together. Steve:

xi

xii

Acknowledgement

“We could really use an example of a major work that has no accidentals, but surely there is no such thing.” Jeff: “How ‘bout Scriabin, Op. 11, No. 15?” Steve: “You clearly just made that up.” Steve looks it up, taking 100 times as long to find it online as Jeff found it in his head. Yes, that’s how it went. In addition, a huge thanks to my now long-standing publisher and editor, Nicki Dennis, at River Publishers for her tireless energy, perpetual encouragement, and ability to work through difficulties (hopefully not augmented by Jeff and myself). Thanks to Douglas Heins and Ellis Gayles for their continual support as knowledgeable friends. Thanks to my Thursday morning Zoom buddies, Paul Ellingstad, Mick Keyes, Gary Moloney, and Margie Sherlock, for always listening to the latest chapter plan. Thanks to many other friends who’ve put up with my sharing of ideas. Finally, thanks most of all to Tess, Kieran, and Dallen, who as always have supported me throughout the effort. Steve Simske

List of Figures

Figure 1.1

Figure 2.1 Figure 2.2

Figure 2.3

Figure 2.4 Figure 2.5 Figure 2.6 Figure 2.7

Figure 2.8 Figure 2.9 Figure 2.10 Figure 2.11 Figure 2.12

The ADSR (attack–decay–sustain–release) pattern for a note. The x-axis is time, and the y-axis is the loudness of the sound. The upper curve (A) is an idealized representation, while the lower curve (B) represents a more realistic curve (there are time constants for the curve to reach each of its inflection points). Please see text for more details. Score to Lavender’s Blue. . . . . . . . . . . . . . Simple diagram with Section A shown to be composed of two equal-length (horizontal length is proportional to time) phrases, the antecedent and the consequent. This is a graphic representation of the Lavender’s Blue score shown earlier. . . . . . Simple diagram with Section A shown to be repeated four consecutive times. This corresponds to AAAA, or strophic, form, as discussed in the text. . . . . . . . . . . . . . . . . . . . . . Score to Das Neugeborne Kindelein. . . . . . . . Score to Chopin’s Prelude in A. Major, Op, 28, No. 7. . . . . . . . . . . . . . . . . . . . . . . . . Score to Quinciani’s Udite lagrimosi spirti d’Averno, udite. . . . . . . . . . . . . . . . . . . Simple diagram with Section A and Section B of equal length. This corresponds to AB, or binary, form, as discussed in the text. . . . . . . . . . . . Score to Catches and Glees. . . . . . . . . . . . . Simple diagram for “Catches and Glees” as performed. Please see text for details. . . . . . . . . . Score to Johann Krieger’s Minuet. . . . . . . . . . Score to Bach’s English Suite BWV 808. . . . . . Diagram for ABA’ structure. . . . . . . . . . . . .

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xiv

List of Figures

Figure 2.13 Figure 2.14 Figure 2.15 Figure 2.16 Figure 2.17 Figure 2.18 Figure 2.19 Figure 2.20 Figure 2.21

Figure 2.22

Figure 2.23 Figure 2.24 Figure 2.25 Figure 2.26 Figure 2.27 Figure 2.28 Figure 2.29 Figure 3.1 Figure 3.2 Figure 3.3 Figure 3.4 Figure 3.5 Figure 3.6

Figure 3.7

Figure 3.8

Diagram for ABACADA rondo structure. . . . . . Diagram for ABACABA rondo structure. . . . . . Diagram for sonata structure. . . . . . . . . . . . Diagram for a simple, “generic,” song form. . . . Score to Bach’s Chorale Nicht so Traurig. . . . . Diagram for Texas Flood by Larry Davis. . . . . . Diagram for Texas Flood by Stevie Ray Vaughan. Diagram for Santa Claus is Comin’ to Town as arranged by Bing Crosby. . . . . . . . . . . . . . Diagram for Santa Claus is Comin’ to Town as original written by Haven Gillespie and J. Fred Coots. . . . . . . . . . . . . . . . . . . . . . . . Diagram for “Quiet Nights of Quiet Stars (Corcodovo),” by Antônio Carlos Jobim, as performed by Stan Getz and João Gilberto. . . . . . . . . . . Diagram for the Fantasia. . . . . . . . . . . . . . Diagram for Wolfgang Mozart’s Fantasy in C minor K. 475. . . . . . . . . . . . . . . . . . . . Diagram for a rondo with a coda. . . . . . . . . . Diagram for a sonata with a coda. . . . . . . . . . Diagram for a ternary form with a coda. . . . . . . Diagram for a form with multiple transitions. . . . Diagram for an Exposition in a Sonata form with a transition. . . . . . . . . . . . . . . . . . . . . . Beginning of the seasonal song, Jingle Bells. . . . First two phrases in Jingle Bells. . . . . . . . . . Phrase in Amy Beach’s In Autumn Op. 15, No. 1. . Phrase in Giuseppe Verdi’s La Donna e Mobile, illustrating relaxation. . . . . . . . . . . . . . . . Phrase in Ravel’s Pavane pour une Infante Défunte, illustrating relaxation. . . . . . . . . . . Phrase in Haydn’s String Quartet in Eb Major, Op. 50, No. 3, III. Menuetto, Allegretto, illustrating tension and relaxation. . . . . . . . . . . . . . . . Phrase in Isaac Albeniz’s Capricho Catalan from the suite Espana, further illustrating tension and relaxation. . . . . . . . . . . . . . . . . . . . . . Phrase in Erik Satie’s First Gymnopedie, again illustrating tension and relaxation. . . . . . . . . .

30 30 31 32 32 33 33 34 34 35 35 36 37 37 37 37 38 50 51 51 52 52 52 52 53

List of Figures xv

Figure 3.9

Figure 3.10 Figure 3.11 Figure 3.12 Figure 3.13 Figure 3.14 Figure 3.15 Figure 3.16 Figure 3.17 Figure 3.18 Figure 3.19 Figure 3.20 Figure 3.21 Figure 3.22 Figure 3.23

Figure 3.24

Figure 3.25

Figure 3.26

Phrase in Vivaldi’s Concerto in E Major: La Primavera, RV 269, I. Allegro, illustrating a phrase of one measure. . . . . . . . . . . . . . . . . . . . . Phrase of one measure in Scarlatti’s Sonata in G Minor, K. 88 L. 36. . . . . . . . . . . . . . . . . . One-measure phrase in Mozart’s Piano Sonata in C Major K. 309 (284b) II. Andante un poco adagio. One-measure phrase in Schoenberg’s Verklärte Nacht Op. 4. . . . . . . . . . . . . . . . . . . . . Phrase of three measures in the Christmas hymn, O Come O Come Emmanuel. . . . . . . . . . . . Three-measure phrase in the 15th century chorale melody Allein zu dir, Herr Jesu Christ. . . . . . . Complicated phrase from Bach’s Invention in C Minor BWV 773. . . . . . . . . . . . . . . . . . . Stripping back of the complicated phrase from Bach’s Invention in C Minor BWV 773. . . . . . . The Kyrie eleison from Palestrina’s Missa Brevis. . Re-engineering of the Kyrie eleison from Palestrina’s Missa Brevis to be a four-measure phrase. . Opening phrase from Beethoven’s Piano Sonata, Opus 2, No. 1. . . . . . . . . . . . . . . . . . . . Manipulated opening phrase from Beethoven’s Piano Sonata, Opus 2, No. 1. . . . . . . . . . . . Reworked opening phrase from Beethoven’s Piano Sonata, Opus 2, No. 1. . . . . . . . . . . . . . . . Repetition of a one-measure phrase from Alexander Scriabin’s Desir Op. 57. . . . . . . . . . . . . The initial phrase from the first movement of Ravel’s Sonatine, I. Modere. Note the pick-up beat at the onset. . . . . . . . . . . . . . . . . . . . . Phrase from Scarlatti Sonata in B Minor K.197, L. 147, featuring an irregular phrase duration of one and a half measures. . . . . . . . . . . . . . . . . Phrase from J.S. Bach’s Prelude in Eb Major BWV 852 from “The Well-Tempered Clavier, Book One,” illustrating a pleasing wholeness. . . . . . . Phrase from Scott Joplin’s ragtime waltz, Pleasant Moments. . . . . . . . . . . . . . . . . . . . . . .

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xvi

List of Figures

Figure 3.27 Figure 3.28 Figure 3.29 Figure 3.30 Figure 3.31 Figure 3.32 Figure 3.33 Figure 3.34 Figure 3.35 Figure 3.36 Figure 3.37 Figure 3.38

Figure 3.39 Figure 3.40 Figure 3.41 Figure 3.42 Figure 3.43 Figure 3.44 Figure 3.45 Figure 3.46 Figure 3.47

Figure 3.48 Figure 3.49 Figure 3.50

Period from the third movement of Wolfgang Mozart’s Horn Concerto in Eb, K.417. . . . . . . Section diagram from “Have Yourself a Merry Little Christmas.” . . . . . . . . . . . . . . . . . Period from Beethoven’s Piano Sonata, Opus 2, No. 1. . . . . . . . . . . . . . . . . . . . . . . . . Period from Verdi’s La Donna e Mobile. . . . . . Period from Amy Beach’s In Autumn Op. 15, No. 1. Period from Albeniz’s Capricho Catalán. . . . . . Period from Scarlatti’s G Minor Sonata. . . . . . Period from Mozart’s Piano Sonata K. 309 (284b). Period from Ravel’s Pavane. . . . . . . . . . . . . Period from Vivaldi’s La Primavera concerto. . . Period from Haydn’s Minuet from String Quartet Op. 50, No. 3. . . . . . . . . . . . . . . . . . . . Period from Haydn’s Minuet from String Quartet Op. 50, No. 3., reimagined into a 4 + 4 + 4 + 4 arrangement. . . . . . . . . . . . . . . . . . . . . Section diagram of ternary form of Haydn’s Minuet from String Quartet Op. 50, No. 3. . . . . . . Section of Mozart’s Piano Sonata K. 309 (284b). . Section from Isaac Albeniz’s Capricho Catalan from the suite Espana. . . . . . . . . . . . . . . . Section from Amy Beach’s In Autumn Op. 15, No. 1. Section from Vivaldi’s La Primavera. . . . . . . . Melody riff diagram for Van Halen’s Jump. . . . . Theme from Muzio Clementi’s Sonata in Bb Major, Op. 24, No. 2. . . . . . . . . . . . . . . . Overall theme from Muzio Clementi’s Sonata in Bb Major, Op. 24, No. 2. . . . . . . . . . . . . . . Mozart’s restructuring of the theme from Muzio Clementi’s Sonata in Bb Major, Op. 24, No. 2, used in the Overture to his opera The Magic Flute. . . . Phrase sequences available for compositions of two, three, or four phrases. . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in its (actual) AAB structure. . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in AAA structure. . . . . . . . . . . . . . . . . . . .

62 64 64 65 65 66 66 67 67 67 68 69 69 70 70 71 72 72 74 74 74 75 75 76

List of Figures

Figure 3.51 Figure 3.52 Figure 3.53 Figure 3.54 Figure 3.55 Figure 3.56 Figure 3.57 Figure 3.58 Figure 3.59 Figure 3.60 Figure 3.61 Figure 3.62 Figure 3.63 Figure 3.64 Figure 3.65 Figure 3.66 Figure 3.67 Figure 3.68 Figure 3.69

Vivaldi’s opening phrase for La Primavera in ABA structure. . . . . . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in ABB structure. . . . . . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in ABC structure. . . . . . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in an alternative ABC structure. . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in AA structure. . . . . . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in AB structure. . . . . . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in AAAA structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in AAAB structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in AABA structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in AABB structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in AABC structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in ABAA structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in ABAB structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in ABAC structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in ABBA structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in ABBB structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in ABBC structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in ABCA structure. . . . . . . . . . . . . . . . . . . Vivaldi’s opening phrase for La Primavera in ABCB structure. . . . . . . . . . . . . . . . . . .

xvii 76 77 77 77 78 78 78 78 79 79 79 79 79 80 80 80 80 80 81

xviii List of Figures Figure 3.70 Figure 3.71 Figure 3.72

Figure 4.1 Figure 4.2

Figure 4.3

Figure 4.4 Figure 4.5 Figure 4.6 Figure 4.7 Figure 4.8 Figure 4.9 Figure 4.10

Vivaldi’s opening phrase for La Primavera in ABCC structure. . . . . . . . . . . . . . . . . . . 81 Vivaldi’s opening phrase for La Primavera in ABCD structure. . . . . . . . . . . . . . . . . . . 81 Vivaldi’s opening phrase for La Primavera in ABBB structure with dynamics (piano, p, and forte, f) indicated for a different “feel” than Figure 3.66. . . . . . . . . . . . . . . . . . . . . . . . . 82 The first movement of Beethoven’s Piano sonata Op. 27, No. 2, “Moonlight.” . . . . . . . . . . . . 95 Full realization of the piano score of the first movement of Beethoven’s Piano sonata Op. 27, No. 2, “Moonlight.” . . . . . . . . . . . . . . . . . . . . 95 Graphic allowing one to focus on the rhythmic notation without the use of a traditional musical score. The simple meters of 4, 3, and 2 (left, center, and right, respectively) are depicted as quadrangular hatched shapes. Simple meter refers to time signatures where the main pulses are divided into smaller even divisions (halves). The highlighted (hatched) shapes represent the main pulse of the meter with some of the smaller subdivisions below, or longer overarching note values above. Please see the text for further details. . . . . . . . . . . . 97 Time signature of 44 with representation down to the 32nd notes. . . . . . . . . . . . . . . . . . . . 98 Phrase from the Bach Prelude in Bb minor, BWV 867. . . . . . . . . . . . . . . . . . . . . . . . . 99 Time signature of 34 with representation down to the 32nd notes. . . . . . . . . . . . . . . . . . . . 99 An example of 34 time from the Adagio movement of Mozart’s Piano Sonata K. 576. . . . . . . . . . 100 Time signature of 24 with representation down to the 32nd notes. . . . . . . . . . . . . . . . . . . . 101 An example of 24 time from Mendelssohn’s Spring Song, Op. 62, No. 6. . . . . . . . . . . . . . . . . 101 Graphic allowing one to focus on the rhythmic notation without the use of a traditional musical score, applied to 68 time (left) and 24 time (right).

List of Figures

Figure 4.11 Figure 4.12

Figure 4.13 Figure 4.14 Figure 4.15 Figure 4.16 Figure 4.17

Figure 4.18

Figure 4.19

Figure 4.20 Figure 4.21 Figure 4.22 Figure 4.23 Figure 4.24

Each graphic shows how we get two pulses in the meter, and that for 68 time the main pulse has a subdivision in three instead of the subdivision in two of 24 time. Note that further subdivisions for both meters are in twos. . . . . . . . . . . . . . . Time signature of 68 with representation down to the 32nd notes. . . . . . . . . . . . . . . . . . . . An example of 68 time from Franz Liszt’s Les Cloches de Genève: Nocturne from Années de Pèlerinage, Première année: Suisse. . . . . . . . . Time signature of 98 with representation down to the 32nd notes. . . . . . . . . . . . . . . . . . . . An example of 98 time from Beethoven’s Andante movement from Piano Sonata Op. 79. . . . . . . Time signature of 12 8 with representation down to the 32nd notes. . . . . . . . . . . . . . . . . . . . An example of 12 8 time from Chopin’s Nocturne in Eb Op. 55, No. 2. . . . . . . . . . . . . . . . . . An example of asymmetrical meter, 58 time, where the pulses are felt in a 3 + 2 (first measure) and in a 2 + 3 (second measure) structure. . . . . . . . . An example of asymmetrical meter, 58 time, where the pulses are felt in a 3 + 2 structure: Scriabin’s Prelude Opus 67, No. 1. . . . . . . . . . . . . . . An example of asymmetrical meter, 54 time, in Tchaikovsky’s Symphony No. 6 in B minor, Op. 74. The first two antecedent phrases from the principle theme are shown, with Tchaikovsky dividing the measure in a 2 + 3 arrangement. . . . . . . . . . . Two-measure phrase with a pick-up beat (anacrusis) having zero pick-up beats. . . . . . . . . . . . Two-measure phrase with a pick-up beat (anacrusis) having one pick-up beat. . . . . . . . . . . . Two-measure phrase with a pick-up beat (anacrusis) having two pick-up beats. . . . . . . . . . . . Two-measure phrase with a pick-up beat (anacrusis) having three pick-up beats. . . . . . . . . . . Example of beat 1 pick-up in the Gavotte I of Bach’s English Suite in G Minor, BWV 808. . . . .

xix

102 102 103 104 104 105 105 105 106

106 107 107 107 108 108

xx List of Figures Figure 4.25

Figure 4.26

Figure 4.27

Figure 4.28 Figure 4.29

Figure 4.30

Figure 4.31 Figure 4.32

Figure 4.33 Figure 4.34 Figure 4.35 Figure 4.36 Figure 4.37

Example of multimetric composition, seasonal holiday song “Here We Come A-Wassailing.” Please see text for details. . . . . . . . . . . . . . Example of idiosyncratic change in meter from Albéniz’s Rondena from Iberia Suite Book 2. Here, the location of the main pulse changes across the two meters, from two dotted-quarter note pulses in 6 3 8 time to three quarter note pulses in 4 time. . . . Example of syncopation in the opening strings section of Mozart’s Piano Concerto in D Minor K. 466. . . . . . . . . . . . . . . . . . . . . . . . . Example of ragtime syncopation in Scott Joplin’s Maple Leaf Rag. . . . . . . . . . . . . . . . . . . Example of tuplets in a 44 time signature, indicated with a numeral (“3,” “5,” “6,” and “7” below) above the beaming of notes. Quarter, eighth, 16th, and 32nd notes require no indication as they are on beat with the time signature. . . . . . . . . . . . . Example of tuplets in a compound ( 12 8 ) time signature, where the normal division of the beat is in three with their even divisions (6 and 12), meaning that the tuplets occur in other numerical divisions (“2,” “4,” “5,” “7,” “8,” etc.). . . . . . . . . . . . . Example of tuplets in Debussy’s Claire de Lune where a “duplet” rhythm is used in the main theme. Example of tuplets in the Pastorale from Liszt’s Annes de Pelerinage, Premiere Annee: Suisse. Please see text for details. . . . . . . . . . . . . . Septuplet example from Bach’s Toccata from Partita in E Minor BWV 830. . . . . . . . . . . . . . Polyrhythm example from Debussy’s Arabesque No. 1. . . . . . . . . . . . . . . . . . . . . . . . . Polyrhythm 3 vs. 5 example from Rachmaninov’s Prelude in G Major, Opus 32, No. 5. . . . . . . . Polyrhythm 3 over 7 over 4 example from the Andante from Scriabin’s Piano Concerto, Opus 20. Example of a left-hand piano score for a 12-bar blues composition in which the swung rhythm is implicit but not explicit. . . . . . . . . . . . . . .

109

109 110 111

111

112 112 113 114 115 115 116 116

List of Figures

Figure 4.38

Figure 4.39

Figure 4.40

Figure 4.41 Figure 4.42

Figure 4.43

Figure 4.44

Figure 5.1 Figure 5.2 Figure 5.3

Figure 5.4

Figure 5.5

Figure 5.6

Score indicating how the first two measures of the 12-bar composition of Figure 4.37 might be realized in performance (notated to make the swung nature of its performance explicit). . . . . . . . . Excerpt from the first movement of Mozart’s Piano Sonata in F Major, K.332 (330k), where the emphasis on the perceived beat 1 is changed over the course of the phrase. . . . . . . . . . . . . . . Characteristic two-measure phrase creating the rhythmic motive for Ernesto de Curtis’s Torna a Surriento. . . . . . . . . . . . . . . . . . . . . . Varying the melodic motion across different harmonies in Ernesto de Curtis’s Torna a Surriento. . Rhythmic motive, “and-two-and one,” used throughout the entirety of the first movement Beethoven’s Symphony No. 5 in C Minor, Op. 67. . . . . . . . Rhythmic character maintenance with change in melodic interval distances and across different harmonies in the first movement of Beethoven’s Symphony No. 5 in C Minor, Op. 67. . . . . . . . Rhythmic motive with an extension, creating a phrase that introduces the secondary theme, in the first movement of Beethoven’s Symphony No. 5 in C Minor, Op. 67. . . . . . . . . . . . . . . . . . . London Bridge with a traditional harmonization. . London Bridge with a reharmonization. . . . . . . Harmonic scheme from the traditional harmonization of London Bridge in an eight-measure layout with single chord for each measure; namely, {D, D, A7, D} repeated twice. . . . . . . . . . . . . . Harmonic scheme from the reharmonization of London Bridge in an eight-measure layout with two chords for each measure. . . . . . . . . . . . New melody derived from the tradition harmonization of the London Bridge nursery rhyme using the “cakewalk” rhythm with its characteristic syncopation as a basis for the melody. . . . . . . . . . . . New melody derived from the reharmonization of the London Bridge nursery rhyme changing from double meter to quadruple meter. . . . . . . . . .

xxi

117

117 118 118 119

120

121 126 127

127 128

129 129

xxii

List of Figures

Figure 5.7 Figure 5.8 Figure 5.9 Figure 5.10 Figure 5.11 Figure 5.12 Figure 5.13

Figure 5.14

Figure 5.15 Figure 5.16 Figure 5.17 Figure 5.18

Figure 5.19

Figure 5.20

Figure 5.21

Figure 5.22

Figure 5.23

Harmonic scheme for a 12-bar blues. . . . . . . . Harmonic scheme for tonic dominant toggle. . . . Primary chords in F Major. . . . . . . . . . . . . Primary chords in E Minor. . . . . . . . . . . . . Progression including other diatonic chords (ii, vi) from the key added along with the primary chords. Chords taken from two phrases within Fredric Chopin’s Ballade in G Minor Op. 23. . . . . . . . Lili Boulanger’s D’un Vieux Jardin showing a progression of chords where each new chord defines its own tonal center instead of relating together in the same key with the others. . . . . . . . . . . . Debussy’s La fille aux cheveux de lin, based on a stepwise motion with diatonic chords straddling the keys of Gb and Cb Major. . . . . . . . . . . . Major chord cycle based on an ascending movement in minor thirds. . . . . . . . . . . . . . . . . Descending intervals of the fourth. . . . . . . . . Descending intervals of the fifth. . . . . . . . . . Chords moving based on chromatic movement where the bass note in each successive chord descends a half step. . . . . . . . . . . . . . . . . Different arrangement possibilities (24 in total) for the I, IV, V, and VI chords (in C Major) in a four-measure loop progression. A similar set of 24 could be presented for each major and minor key. The first two phrases of Alexander Scriabin’s Etude in A Major, Op. 8, No. 6, demonstrating a harmonic rhythm of one chord per measure (please see text for details). . . . . . . . . . . . . . . . . Robert Schumann’s “Of Foreign Lands and Peoples” from the Scenes of Childhood, Op. 15, No. 1 showing two chords per measure. . . . . . . . . . Chopin’s Prelude in C Minor Op. 28, No. 20 showing multiple harmonies per one measure of music. . . . . . . . . . . . . . . . . . . . . . . . Mozart’s “alla turca” from the Sonata in A Major, K. 331, giving an example of one harmony over a four-measure run. . . . . . . . . . . . . . . . . .

131 131 131 131 132 132

132 133 133 133 133 133

134

135 135 136 136

List of Figures xxiii

Figure 5.24

Figure 5.25

Figure 5.26

Figure 5.27 Figure 5.28 Figure 5.29 Figure 5.30 Figure 5.31 Figure 5.32 Figure 5.33 Figure 5.34

Figure 5.35 Figure 5.36 Figure 5.37 Figure 5.38 Figure 5.39 Figure 5.40

Figure 5.41

First section of Robert Schumann’s “Of Foreign Lands and Peoples,” from the Scenes of Childhood, Op. 15, No. 1, composed in a homophonic texture for piano (please see text for details). . . . . . . . Diagram of the composition showing the pathway of the melody through the note choices from each chord harmony. The chords are above the modified scores in Lighter text; for example, G/B is the G chord with the B in the bass. . . . . . . . . . . . . The “A” section of the Allemande from the Partita for unaccompanied flute in A Minor BWV 1013 by J.S. Bach (please see text for details). . . . . . . . Bugle Assembly score. . . . . . . . . . . . . . . . Bugle First Call score. . . . . . . . . . . . . . . . Bugle Reveille score. . . . . . . . . . . . . . . . Bugle Taps score. . . . . . . . . . . . . . . . . . Frere Jacques, monophonic texture. . . . . . . . . Frere Jacques, homophonic setting with accompaniment. . . . . . . . . . . . . . . . . . . Frere Jacques, stacked representation. . . . . . . . Diagram of melodic figures (four in total) overlaid with the others forming the harmony of C Major on the main beats (1 and 2). The notes in the off-beat count (the “+” of beat one) themselves create a similar relationship based on the G7 harmony. Multiple melodies cover all the notes of the harmony (chords) in this composition. . . . . . . Frere Jacques, realized in the polyphonic round setting. . . . . . . . . . . . . . . . . . . . . . . . Jolly Old Saint Nicholas. . . . . . . . . . . . . . Richard Wagner’s Ride of the Valkyries from the third act of the opera Die Walküre. . . . . . . . . The “Blue Danube Waltz” by Johann Strauss II. . “Lavender’s Blue” with accented passing tones. . . . . . . . . . . . . . . . . . . . . . . . . “Lavender’s Blue” with altered rhythm and the notes “C” and “A” moved forward to off-beat positions. . . . . . . . . . . . . . . . . . . . . . . “Lonesome Road.” . . . . . . . . . . . . . . . . .

138

138 139 140 141 141 141 141 142 142

143 144 144 145 145 146 147 147

xxiv

List of Figures

Figure 5.42

Figure 5.43 Figure 5.44 Figure 6.1

Figure 6.2

Figure 6.3

Figure 6.4

Figure 6.5

Figure 6.6

Figure 6.7

Figure 6.8 Figure 6.9

The first phrase of Robert Schumann’s melody to “Traumerie,” from the Scenes of Childhood, Op. 15, No. 7. . . . . . . . . . . . . . . . . . . . . . . Mozart’s Rondo K. 494. . . . . . . . . . . . . . . The Bourree from the Lute Suite in E Minor WV 996 by J.S. Bach. . . . . . . . . . . . . . . . . . Score for the first period of François Couperin’s Les Baricades Misterieuses (1717). Note the lack of accidentals. . . . . . . . . . . . . . . . . . . . Score for Scriabin’s Prelude in Db Major, Opus 11, No. 15 (1895). Note the lack of accidentals (but the very common occurrence of black keys). . . . . . The traditional French nursery composition, “Alouette,” showing the return of lines 1 and 3 to the starting note, F. The second line ends with the fifth note, C, of the F Major scale. Without any specified harmony, this tone leaves the listener wanting to continue on with more music, looking for a final resolution on F. Unintentionally, this song also incorporates no accidentals. . . . . . . . The traditional French nursery composition, “Ah! vous dirai-je, maman,” showing the gravity of the phrases aiming toward their starting note, A. . . . C Major scale and its corresponding chords as triads of notes derived from the scale − the basis of traditional tonal centeredness (the composer’s “palette”). . . . . . . . . . . . . . . . . . . . . . Alouette with harmonization (with C7) at the end of the second line that leaves you in expectation of resolution by harmonization with F at the end of the third line. . . . . . . . . . . . . . . . . . . . . Alouette with harmonization (with F) at the end of the second line that no longer leaves you in expectation of resolution with the additional third line of Figure 6.6 (because this line ended with F already, of course − thank you, Department of Redundancy Department). . . . . . . . . . . . . . Steven Foster’s Camptown Races. . . . . . . . . . Auld Lang Syne (traditional Scottish tune). . . . .

147 148 148 159 160

162 162

164

165

166 167 167

List of Figures

Figure 6.10

Figure 6.11 Figure 6.12 Figure 6.13

Figure 6.14 Figure 6.15 Figure 6.16 Figure 6.17

Figure 6.18

Figure 6.19

xxv

Auld Lang Syne redirected toward the V chord (more commonly used), but here changing the feel of the familiar tune. . . . . . . . . . . . . . . . . 168 Ludwig van Beethoven’s Piano Sonata Op. 14, No. 2.168 C (Natural) Minor scale, also known as the Aeolian mode (more to come on this). . . . . . . . . . . . 169 The C harmonic minor scale. Note that it is spelled C, D, Eb, F, G, Ab, B, C, instead of C, D, Eb, F, G, Ab, Bb, C in the natural minor scale. . . . . . . . 169 Beethoven Piano Sonata in C Minor Op. 10, No. 1. 170 Seventh chords generated beyond the basic triads in the key of C Major. . . . . . . . . . . . . . . . 171 Nikolai Medtner’s Six Tales Op. 51, No. 3. . . . . 172 A section of the “Ode to Joy” theme from Beethoven’s Ninth Symphony. The melody for this composition uses an antecedent/consequent pairing as discussed in Chapters 2 and 3 as a way of providing tension (by the F# [upper line] or E [lower line] dotted quarter note at the beginning of the last measure of each line) followed by resolution of the tone. The eighth note (the E in the upper line or D in the lower line, last measure) is an anticipation note that foreshadows the harmony and melody coming together on the last half note. . . . . . . . . . . . . . . . . . . . . . . 173 The “Ode to Joy” section of Beethoven’s Ninth Symphony without the tension (delayed resolution) created by the F# [upper line] or E [lower line] dotted quarter note at the beginning of the last measure of each line as shown in Figure 6.17. Here, the harmony and melody track more predictably than in Figure 6.17, but perhaps musically this arrangement is “less interesting?” Undoubtedly, it was to Beethoven, as he chose Figure 6.17. . . . . . . . . . . . . . . . . . . . . . . . . 173 Mozart Minuet in F Major K.2. Here, the lower “suspension” note E holds off the expected note of resolution, F. . . . . . . . . . . . . . . . . . . . . 174

xxvi

List of Figures

Figure 6.20

Figure 6.21 Figure 6.22 Figure 6.23 Figure 6.24 Figure 6.25 Figure 6.26 Figure 6.27 Figure 6.28

Figure 6.29 Figure 6.30

Figure 6.31 Figure 6.32 Figure 6.33 Figure 6.34 Figure 6.35 Figure 6.36

Figure 6.37 Figure 6.38

Mozart’s Minuet K. 2 with its deceptive cadence (fourth measure) upending and delaying the resolution. Please see text for details. . . . . . . . . . Ionian mode. . . . . . . . . . . . . . . . . . . . . Dorian mode. . . . . . . . . . . . . . . . . . . . . Phrygian mode. . . . . . . . . . . . . . . . . . . Lydian mode. . . . . . . . . . . . . . . . . . . . . Mixolydian mode. . . . . . . . . . . . . . . . . . Aeolian mode. . . . . . . . . . . . . . . . . . . . Locrian mode. . . . . . . . . . . . . . . . . . . . Noel Nouvellete in Dorian mode. A typical harmonization is given in which a D7 chord (which incorporates a note not in the Dorian scale) is used to create an authentic cadence (V7 to i). . . . . . . Noel Nouvellete in harmonic minor mode. . . . . The first line of Noel Nouvellete employing the Ionian mode. The root chord, G, is a major sound (as opposed to the minor sound, Gm, in Figures 6.28 and 6.29). . . . . . . . . . . . . . . . . . . . The first line of Noel Nouvellete employing the (unmodified) Dorian mode. . . . . . . . . . . . . The first line of Noel Nouvellete employing the Phrygian mode. . . . . . . . . . . . . . . . . . . The first line of Noel Nouvellete employing the Lydian mode. . . . . . . . . . . . . . . . . . . . . The first line of Noel Nouvellete employing the Mixolydian mode. . . . . . . . . . . . . . . . . . The first line of Noel Nouvellete employing the Aeolian (natural minor) mode. . . . . . . . . . . . The first line of Noel Nouvellete employing the Locrian mode. The tonality of the root chord is based on a diminished G. . . . . . . . . . . . . . Arnold Schoenberg’s Sechs Kleine Klavierstücke, Op. 19, No. 4 (1911). . . . . . . . . . . . . . . . Color wheel with 12 colors, each 30 degrees apart from its neighbors. The entire wheel is 360 degrees in total, for 12 colors. Red, at top, is normally considered to be at 0 degrees. . . . . . . . . . . .

174 176 176 177 177 177 178 178

179 179

180 180 180 181 181 181 181 183

185

List of Figures xxvii

Figure 6.39

Figure 6.40

Figure 7.1 Figure 7.2 Figure 7.3

Figure 7.4

Figure 7.5

Figure 7.6

Figure 7.7

Color wheel with 12 colors, each 30 degrees apart from its neighbors. Here the colors are named with their common, rather than graphics/printing names (e.g. “Lime” instead of “Green,” “Aqua” instead of “Cyan,” “Azure” instead of “Blue-Cyan,” etc.). . . 186 Color wheel with 12 colors, each 30 degrees apart from its neighbors. The 12 notes of the scale are written to the 12 colors, using sharps for all of the accidentals. . . . . . . . . . . . . . . . . . . . . . 187 Mode mixture Mozart on display. Mozart’s Sonata for Keyboard Four-hands in D Major, K. 381/123a. 193 Example chord progression borrowing in D Major. Please see text for details. . . . . . . . . . . . . . 195 Diagram illustrating the chord progression borrowing of Figure 7.2 within their respective scales (D Major borrowing from D natural minor). . . . 195 Score of the Andante un poco adagio from Mozart’s Sonata in F Major, K. 309/284b, Second Movement. The lower line of the score is annotated with the chord progression and shows Mozart borrowing the Bb Minor chord from the minor mode and returning to the major mode with the C7 chord (second measure, lower line). . . . . . . . . . . . 196 Diagram illustrating the chord progression borrowing of Figure 7.4 within their respective scales (F Major borrowing from F natural minor). . . . . 196 Score of the Rondeau allegretto grazioso from Mozart’s Sonata in F Major, K. 309/284b, Third Movement. The upper line of the score is annotated with the chord progression and shows Mozart borrowing the Bdim7 chord (starting in the first measure, upper line; note the use of the Ab, which is the indicator of the borrowing) from the harmonic minor mode and returning to the major mode with the C chord (second measure, lower line).197 Diagram illustrating the chord progression borrowing of Figure 7.6 within their respective scales (C Major borrowing from C harmonic minor). . . 197

xxviii

List of Figures

Figure 7.8 Figure 7.9

Figure 7.10

Figure 7.11

Figure 7.12

Figure 7.13

Figure 7.14

Figure 7.15

Figure 7.16

Figure 7.17

Example of a sequence of chords all derived from C Major. . . . . . . . . . . . . . . . . . . . . . . 198 Example of secondary dominant in C Major, where A7 is the V7/ii of this scale, and Dm is the ii chord of C Major. . . . . . . . . . . . . . . . . . . . . . 198 Diagram illustrating the chords derived from the scale of C Major (center line). The line above indicates how to use secondary dominants derived from the V chord of the given chord (e.g. A7 is derived from the V chord of Dm), while the line below indicates how to use secondary leading tone chords derived from the vii chord of each given chord (e.g. C#◦7 is derived from the vii chord of Dm). Please see text for more details. . . . . . . . 199 Example of a secondary leading tone chord in C Major, where C#◦7 is the vii◦7 /ii of this scale, and Dm is the ii chord of C Major. . . . . . . . . . . . 200 Main theme of Scott Joplin’s The Easy Winners. This ragtime composition tonicizes Eb in measure 7 and returns to (re-tonicizes) Ab Major in measure 9.200 Chords derived from the Ab major scale with the secondary dominant (Bb7) that is used to tonicize Eb major in Scott Joplin’s The Easy Winners. . . . 200 Bach’s Prelude in D Major BWV 850, showing two tonicizations of the IV and V chords (please see text for details). . . . . . . . . . . . . . . . . . . 201 Chords derived from the D Major scale with the secondary dominant and secondary leading tone chords (D7 and G#◦7 ) that are used to tonicize the IV and V (G and A) chords in Bach’s Prelude in D Major, BWV 850. . . . . . . . . . . . . . . . . . . 201 Julius Fuˇcík’s “Grande Marche Chromatique,” introduction and first main phrase. The chromatic scale is used in context of the harmony, which is tonally C Major. . . . . . . . . . . . . . . . . . . 202 Chopin Prelude in E Minor Op. 28, No. 4, where the harmony chromatically changes, one chromatic step at a time, with generally one note of the chord for each change. . . . . . . . . . . . . . . . . . . 203

List of Figures

Figure 7.18

Figure 7.19

Figure 7.20

Figure 7.21

Figure 7.22

Figure 7.23

Figure 7.24

Schumann’s Knecht Ruprecht Op. 68, No. 12, illustrating phrase modulation from A Minor (“A” section) to F Major (“B” section). . . . . . . . . . Score of O Little Town of Bethlehem by Lewis Redner, showing modulation within the core melodic structure of AA’BA”. Please see text for details. . . . . . . . . . . . . . . . . . . . . . . . Beethoven’s Piano Sonata Op. 79 2nd movement, illustrating modulation from G Minor to Eb Major. Please see text for details. . . . . . . . . . . . . . Opening of Beethoven’s Symphony #1 in C Major, Op. 21. The opening chord sequence of C7 to F obfuscates the actual key that Beethoven is purportedly (according to the key signature) composing in, giving it a feel of F (since this is a tonicization of F). Given the contents of the sidebar for this chapter, it can also be thought of as a musical metamerism, where it appears to be in C Major from one light, and F Major from another. . Brahms’ Intermezzo Op. 118, No. 1, illustrating obfuscation of key altogether. Please see text for details. . . . . . . . . . . . . . . . . . . . . . . . Musical metamerism illustrated by two songs (dashed curves) of greatly different content from Music Styles A, B, and C but the same relative overlap with the musician’s expertise (solid curve). Based on the areas under the curves, we can see that Song A is 50% Music Style A, 40% Music Style B, and 10% Music Style C. Song B is 25% Music Style A, 41.5% Music Style B, and 33.5% Music Style C (see Table 7.1). The musician, Musician 1, meanwhile, has relative expertise of 10% for Music Style A, 85% for Music Style B, and 5% for Music Style C. Please see text for details of how this results in musical metamerism. Musical metamerism illustrated by two songs (dashed curves) of greatly different content from Music Styles A, B, and C but the same relative overlap with the musician’s expertise (solid curve).

xxix

205

207 208

210 211

214

xxx

List of Figures

Figure 7.25

Figure 7.26

Figure 8.1

Figure 8.2

Figure 8.3

Figure 8.4 Figure 8.5

Here, the areas of the different sections under the curves are labeled 1−7. See text for details. . . . . 215 Musical metamerism illustrated by two songs (dashed curves) of greatly different content from Music Styles A, B, and C but the same relative overlap with the musician’s expertise (solid curve). Here, the areas of the different sections under the curves are labeled 1−7, and it is shown that the areas under the musician curve for Song A (1 + 2 + 4 + 5) and Song B (2 + 5 + 6 + 7); that is, (4 + 5) and (5 + 6), respectively, are equal. The musician thus classifies each song to have the same style. . 216 Musical metamerism illustrated by two songs (dashed curves) of greatly different content from Music Styles A, B, and C but the same relative overlap with two different musician’s expertise (solid curves). Please see text for details. . . . . . 217 Debussy’s Syrinx L. 129. The opening section of this composition offers an example of a solo instrument monophonic texture of a single melody. 223 Giovanni Pierluigi da Palestrina’s Kyrie Eleison from the Missa Brevis, an example of polyphonic music where each voice (text not shown) is its own independent line, yet all four voices work together to create harmony. From a compositional standpoint, Giovanni has given a meaningful melodic part to each voice, allowing each of them to contribute to the main musical texture. . . . . . . 224 Edward MacDowell’s To a Wild Rose from Woodland Sketches, Op. 51, No. 1, exemplifying homophonic texture with a single melody (upper staff, stems up) having harmonic support (upper and lower staff, stems down). . . . . . . . . . . . . . 225 Bach’s Gavotte en Rondeau from Violin Partita No. 3 in E Major BWV 1006 (please see text for details). 226 Mozart’s Andante amoroso, 2nd movement from Piano Sonata K. 281 (189f) (please see text for details). . . . . . . . . . . . . . . . . . . . . . . . 227

List of Figures

Figure 8.6

Figure 8.7

Figure 8.8 Figure 8.9 Figure 8.10

Figure 8.11

Figure 8.12

Figure 8.13

Figure 8.14

Figure 8.15

Figure 8.16

Beethoven’s 2nd Movement of Piano Sonata Op. 27, No. 2 (“Moonlight Sonata”), illustrating homorhythmic texture (please see text for details). Mozart’s 1st Movement of Piano Sonata K. 310 (300d), illustrating the use of full chords below the main melodic content to “drive” the musical phrase forward. . . . . . . . . . . . . . . . . . . . . . . Albeniz’ Granada from Suite Española, with repetitive chords above the melody. . . . . . . . . A phrase from Beethoven’s Piano Sonata Op. 13 “Pathétique” (please see text for details). . . . . . Six possibilities for four-note voicings of a C Major chord spaced in close and open positions (please see text for details). . . . . . . . . . . . . Debussy’s Soirée dans Grenade gives an example of chords voiced with the same interval structure moving in a parallel fashion (please see text for more details). . . . . . . . . . . . . . . . . . . . . Chord-to-chord progression example using parallel leaping and voice leading or smooth progression between the notes of each chord, taken from Mozart’s Piano Sonata in C Major K. 279 (189d) (please see text for details). . . . . . . . . . . . . Arpeggio, or broken chord, accompaniment, taken from Mozart’s Piano Sonata in C Major K. 279 (189d) (please see text for details). . . . . . . . . Liszt Consolation No. 3 in Db Major, S. 172, showing harmonic pattern repeating from measure to measure (please see text for details). . . . . . . . Claude Debussy’s Claire de Lune from Suite Bergamesque, showing the use of a harmonic figure that repeats rhythmically but progresses chordwise (as arpeggio notes here) (please see text for details). . . . . . . . . . . . . . . . . . . . . . . . Scriabin’s Etude Op. 8, No. 8 in Ab Major, illustrating melody, harmony, and bass in a single piano score (please see text for details). . . . . . . . . .

xxxi

227

228 228 229 230

231

232 232 233

234 235

xxxii

List of Figures

Figure 8.17

Figure 8.18

Figure 8.19

Figure 8.20

Figure 8.21

Figure 8.22

Figure 8.23

Figure 8.24

James Scott’s Great Scott Rag, showing the melody (right hand, upper score) and the dual bass/chord march rhythm (left hand, lower score) (please see text for details). . . . . . . . . . . . . Chopin’s Waltz in Ab Major Op. 34, No. 1, with its characteristic bass-chord-chord notes comprising each measure of the waltz in the left hand (lower score). . . . . . . . . . . . . . . . . . . . . . . . Beethoven’s String Quartet Op. 130 in Bb, Second Movement, Presto, illustrating the use of high to low registries within the same instrument family (strings). . . . . . . . . . . . . . . . . . . . . . . Mozart’s Serenade K.361/370a Adagio, illustrating the use of high to low registries within the same instrument family (woodwinds). In the woodwind ensemble, roles range from melody (oboes and clarinets) to bass (bassoon and contrabassoon). . . Johann Strauss Jr.’s The Blue Danube, main theme, illustrating melody and accompaniment roles dispersed across multiple sections of instruments (please see text for details). . . . . . . . . . . . . Rimsky-Korsakov’s The Sea and Sinbad’s Ship, from the first movement of the symphonic suite Scheherazade, illustrating multiple instruments playing the melody together initially and shortly thereafter splitting into very different roles, thus providing strong musical contrast between these subsequent phrases. . . . . . . . . . . . . . . . . Rimsky-Korsakov’s Theme from the Young Prince and the Young Princess, from the third movement of the symphonic suite Scheherazade, illustrating the use of only one section (strings), with the common use of the higher tones (violin) as melody and the lower tones (viola through contrabass) as harmonic accompaniment. . . . . . . . . . . . . . Repetition (in a different key) of the Theme from the Young Prince and the Young Princess of the third movement from Rimsky-Korsakov’s symphonic suite Scheherazade with a complete

235

236

238

239

241

242

243

List of Figures

Figure 8.25

Figure 8.26

Figure 9.1

Figure 9.2 Figure 9.3

Figure 9.4

Figure 9.5

Figure 9.6

Figure 9.7

Figure 9.8

reworking of the orchestration (please see text for details). . . . . . . . . . . . . . . . . . . . . . . . Gustav Holst’s first movement, Mars, The Bringer of War, from the orchestral suite The Planets, Op. 32, illustrating the full power of the orchestra. . . The figurative chart of the ill-fated Russian campaign of Napoleon’s army in 1812−1813, made in 1869 by graphical artist Charles Minard [Mina69], and celebrated by Edward Tufte as an example of how to convey massive amounts of information in a single graphic. . . . . . . . . . . . . . . . . . . The melodic content A, A’, A”, and A”’ sections from Chopin’s Nocturne in E-flat Major, Op. 9, No. 2, lined up one over the other (without the accompaniment), illustrating the use of varied repeats. . Mozart’s Variations on “Come un agnello” by Sarti, K. 460/454a, illustrating variation. . . . . . Opening two measures of Mozart’s Adagio, K. 540, illustrating the use of fragment material for development. This phrase includes three highlighted fragments, labeled A, B, and C, above the top line (treble staff). . . . . . . . . . . . . . . . . Phrase from later in Mozart’s Adagio, KV 540, illustrating the development of fragment B from Figure 9.3. . . . . . . . . . . . . . . . . . . . . . Phrase from later in Mozart’s Adagio, KV 540, illustrating the development of fragments B and C from Figure 9.3. . . . . . . . . . . . . . . . . . . Phrase from still later in Mozart’s Adagio, KV 540, illustrating the development of fragments A and B from Figure 9.3. . . . . . . . . . . . . . . . . . . The beginning of the formal development section from Mozart’s Adagio, KV 540, illustrating the combination of the primary opening phrase and the secondary theme exploring new harmonies and tonal centers. . . . . . . . . . . . . . . . . . . . . Sequencing of fragments from the subject of Bach’s Fugue in C Minor BWV 847 from the Well-Tempered Klavier, Book 1. . . . . . . . . . .

xxxiii 244 245

247

254 255

258 258 259 259

260 261

xxxiv

List of Figures

Figure 9.9

Figure 9.10

Figure 9.11 Figure 9.12 Figure 9.13 Figure 9.14

Figure 9.15

Figure 9.16 Figure 9.17

Figure 10.1

Beethoven’s Ode to Joy melody from his Symphony No. 9 in D Minor, Op. 125, using his original rhythmic and notational incarnation of the melody. The notes are superscripted by their scale degree, so that D is note 1 (since the key is D Major). . . . . . . . . . . . . . . . . . . . . 262 Beethoven’s Ode to Joy from his Symphony No. 9 in D Minor, Op. 125, incorporating the same notational incarnation as the original (Figure 9.9) but with a rhythmic change to produce a marchlike feeling. The transformation here also includes a change in key and an octave displacement in the second line of the example. The notes are superscripted with an identical sequence to Figure 9.9, showing that the notation is sequentially identical even though the music feels quite different. . . . . 262 Scriabin’s Prelude to Opus 2, No. 2, illustrating transposition upward by a fifth. . . . . . . . . . . 263 Twelve-tone matrix (please see text for explanation). 264 Bach’s Musical Offering, BMV 1079, original theme as supplied by Frederick II of Prussia. . . . 265 Bach’s Musical Offering, BMV 1079, showing the crab canon “palindrome” that reads forward and backward identically in the notes. The voices playing the notes switch at the midpoint (end of measure 3 of line 2). . . . . . . . . . . . . . . . . 266 Bach’s The Art of Fugue, BMV 1080. This is the subject that forms the basis for the transformations Bach employs to illustrate compositional variance and creativity. . . . . . . . . . . . . . . . . . . . 266 Bach’s The Art of Fugue, BMV 1080, showing an inversion of the original subject (Figure 9.15). . . 267 Bach’s The Art of Fugue, BMV 1080, using various combinations of inversion, diminution, and augmentation of the original subject (Figure 9.15), as labeled by the small text. . . . . . . . . . . . . 268 Mozart’s Great G Minor Symphony No. 40, Second Movement, Andante, K. 550, demonstrating traditional staff notation. . . . . . . . . . . . . . . 280

List of Figures xxxv

Figure 10.2

Figure 10.3

Figure 10.4 Figure 10.5

Figure 10.6

Figure 11.1

Figure 11.2

Figure 11.3

Figure 11.4

Figure 11.5

Mozart’s Great G Minor Symphony No. 40, Second Movement, Andante, K. 550, demonstrating lead sheet notation. The melody is shown explicitly on the staff, while the harmony is shown by the chord notation above the staff. . . . . . . . . . . . . . . Ludwig van Beethoven’s Piano Sonata No. 8 in C Minor, Op. 13, (Sonata Pathétique) in traditional score notation. Note the “shorthand” notation for the lower staff, which simplifies the notation of eight eighth notes in each measure. . . . . . . . . Beethoven’s Piano Sonata No. 8 in C minor, Op. 13, (Sonata Pathétique). . . . . . . . . . . . . . . Rhythmic notation with accuracy to the sounding of notes but in notation that is difficult to read due to the beaming and choice in note duration. . . . . Corrected rhythmic notation of the music from Figure 10.5, making the location of the main beats clearer with corrected beaming and note duration. Bach’s Prelude in C Major BWV 846, first four measures, with all of the notes in the (broken) chords indicated explicitly. . . . . . . . . . . . . Bach’s Prelude in C Major BWV 846, illustrating a harmonic plan realized. Here, block chords are used to facilitate the viewing of the harmonic structure, but the actual notes comprising the chord are played sequentially, as in Figure 11.1, as “broken chords” in performance. . . . . . . . . . . . . General diagram of an overall ternary form ABA, with a sub-structure within each division of binary form. . . . . . . . . . . . . . . . . . . . . . . . . The melody from the first of eight minuets from Mozart’s K. 315a (315g), where each section of the macro ternary form (ABA) is made up of binary (AB) structure. Realization in performance consists of playing the minuet (A) with repeats, followed by the trio (B) with repeats, and finally the minuet (A) without repeats. . . . . . . . . . . Mozart’s Menuetto, the second movement of his Piano Sonata in A Major K. 331 (300i). . . . . . .

281

283 284 284 284 295

296 299

300 301

xxxvi

List of Figures

Figure 11.6

Figure 11.7 Figure 11.8 Figure 11.9 Figure 11.10

Figure 11.11 Figure 11.12

Figure 11.13

Figure 11.14 Figure 11.15

Figure 11.16

Mozart’s Andante Cantabile, the second movement of the Piano Sonata in C Major K.330 (300h). . . . . . . . . . . . . . . . . . . . . . . . Mozart’s Alla turca, the third movement from the Piano Sonata K. 331 (300i). . . . . . . . . . . . . Mozart’s Tempo di Menuetto, the second movement from the Violin Sonata K. 304 (300c). . . . . Form diagram of Tárrega’s Capricho Árabe. . . . Tárrega’s introductory interludes for Capricho Árabe. These interludes break up repetitions of the melody and their placement within the composition can be seen in the form diagram of Figure 11.9. . . . . . . . . . . . . . . . . . . . . . . . . Main theme of Tárrega’s Capricho Árabe. . . . . . Theme of Tárrega’s Capricho Árabe in F Major, similar to its appearance in D Minor. Note, however, the chromatic scale ascending at the end of the phrase. . . . . . . . . . . . . . . . . . . . . . Two successive occurrences of the theme from Tárrega’s Capricho Árabe set in the key D Major without an interlude to break up the repetition. These are the fourth and fifth repeats of the theme as seen in Figure 11.9. . . . . . . . . . . . . . . . Paganini’s Caprice no. 1, illustrating ricochet technique for the violinist (please see text for details). Paganini’s Caprice no. 1, showing additional variation by continuing upward arpeggiation with 16th notes followed by a cadenced closure of the idea with three of the four “ricochet” notes played simultaneously instead of sequentially (end of upper line and start of lower line). Mode mixture (switching from E Major to E Minor) then follows, with the key change indicated near the beginning of the lower line. . . . . . . . . . . . . . . . . . . Paganini’s Caprice no. 1, here illustrating developmental material incorporating contrasting scale figures in triplet rhythm and the continual changing of keys. . . . . . . . . . . . . . . . . . . . . .

301 302 303 304

305 305

306

306 307

308

309

List of Figures

Figure 11.17 Figure 11.18 Figure 11.19

Figure 11.20

Figure 12.1 Figure 12.2 Figure 12.3 Figure 12.4

xxxvii

Opening theme to Debussy’s prelude Voiles, illustrating the use of the whole tone scale. . . . . . . Second phrase in Debussy’s prelude Voiles, “B.” . A later section of Debussy’s prelude Voiles, illustrating incorporation of both the “A” and “B” of Figures 11.17 and 11.18. . . . . . . . . . . . . . . Two recurrences of the secondary theme (Figure 11.18) from prelude Voiles, illustrating how it can continue to be used throughout the piece without stifling further creativity. . . . . . . . . . . . . . . Noise. . . . . . . . . . . . . . . . . . . . . . . . Anti-noise. . . . . . . . . . . . . . . . . . . . . . Sum of noise and anti-noise. . . . . . . . . . . . . Section of Mozart’s Cosi Fan Tutti, contra I venti.

309 310 311

312 321 321 322 331

List of Tables

Table 1.1

Table 1.2

Table 5.1

Table 5.2

Table 5.3

Table 6.1 Table 6.2

The list of three-phrase and four-phrase musical piece arrangement patterns. These are the 20 patterns possible. Note that the possible arrangements of (A,B,C,D) in each of these 20 scenarios greatly increase the total number of arrangements from the four phrases (or pieces). Please see text for more details. 13 The list of three-phrase and four-phrase musical sequences corresponding to the patterns from Table 1.1. In parentheses is the total number of possibilities for sequencing within each pattern, if you have composed four phrases, A, B, C, and D. Please see text for details. . . . . . . . . . . . . . . . . . . . . . . 14 Table of similarities between poems A (Emily Dickinson 479), B (Two halves make a whole), and C (The breath of God below). Based on the similarity scores, poems B and C are much more similar than either is to poem A. . . . . . . . . . . . . . . . . . . . . . . 152 Table of distances between songs based on the objective function of notes, rhythm, instruments, sequence, etc. The range of distances is 0−8, with songs C and D being considered “nothing alike.” . . . . . . . . . 154 Table of distances between songs from Table 5.1, arranged by distance. One cluster of more closely related songs has distance < 5, while a second cluster of less related songs has distance > 5. . . . . . . . . 154 The seven modes, from Ionian to Locrian mode. . . 175 The seven modes, from Ionian to Locrian mode, showing the pattern of whole and half steps for consecutive notes. Each sequence is unique from the other six. The adjustment of the Aeolian mode, the harmonic minor mode, is added as an additional row here for comparison. . . . . . . . . . . . . . . . . . 180 xxxix

xl List of Tables Table 7.1

Musical metamerism illustrated by two songs and musician 1 in Figure 7.21, with the percentage of each curve corresponding to each of the three music styles (A, B, and C) indicated in Columns 2, 3, and 4 from the left. The product of Column 2 and Column 3 is given in Column 5, and the product of Column 2 and Column 4 is given in Column 6. Note that the area under each curve (Musician 1, Song A, and Song B) is normalized to 1.0 (SUM at bottom), and that the SUMs of Column 5 and Column 6 are each 0.395. That equality is the musical metamerism. . . . . . . 215

List of Abbreviations

ADSR AI CD CGI CIE DAW DIA E.T. EDM ELP GAI LP N.T. P.T. WWMD WWWD

Attack, decay, sustain, and release Artificial intelligence Compact disc Computer-generated imagery International commission on illumination Digital audio workstation Denver international airport Escape tone Electronic dance music Emerson, lake, and palmer Generative artificial intelligence Long play Neighbor tone Passing tones What would Mozart do? What would Wolfgang do?

xli

1 Music Maker: Introduction

Without music, life would be a mistake – Friedrich Nietzsche If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which he hears, however measured or far away. – Henry David Thoreau

Abstract With the advent of the Arduino, Raspberry Pi, ThingIVerse, and additive manufacturing, the power to make is in the hands of a larger percentage of the population than ever before. This democratization of manufacturing – or the “maker movement” for initiates – unleashes pent-up creative energy that was temporarily on hiatus as tinkerers lost their way in an analog world gone digital. Benny Landa famously said, “Everything that can become digital will become digital and that includes printing.” The same is clearly true for music. Pianos have become electronic keyboards, and drum kits have become synthesizers. Sheet music has become a set of swipe-able glyphs on a pad, and musical selection is performed by web services, which handle, presumably legally, the digital rights management behind the scenes. After the conversion to digital, however, where is the “music maker movement”? With all this technology in hand, music is an important – and why not the most important? – beneficiary of this digital design availability. In this book, we empower musicians to be makers by providing them with the patterns, processes, and practicalities needed to create great music. In so doing, we hope to help create a generation of great musicians. Keywords: Music, Composition, Democratization, Creator, Maker. 1

2

Music Maker: Introduction

1.1 Themes of the Book The maker movement is a reaction to a digital world in which software and hardware manufacturers, effectively, are declaring, “you can’t modify this device because it is a security risk if you do, and even if it isn’t just don’t or your warranty is void!” The maker movement rallies behind the idea that anyone can make something that is of interest or value to at least someone. Given this “democratization of creation,” we believe that anyone who can learn to play a musical instrument can also learn to compose for a musical instrument. Moreover, we believe that learning to compose can, and perhaps should, be an integral part of the curriculum for learning music in general. Rather than solely learning to memorize music (which is still a vital element in performance), we argue for composition to be a peer-level element of the music curriculum with theory, performance, and improvisation. Composing while you are learning to play a piece, in fact, will assist you in later improvisation, since the composer has already explored logical, and hopefully listenable, alternatives to the score sheet. This book is part of the River Series in Document Engineering. As part of this series, as elaborated in Chapter 10, we view composition as the engineering of music; that is, the design, construction, testing, and maintenance of music over time. In Chapter 10, we make this definition explicit, noting that “music engineering is the discipline that investigates systems for musical creation in any form and in all media. Musical engineering is concerned with principles, tools and processes that improve our ability to create, manage, and maintain music.” Aside from the engineering part, let us consider for a moment what the “document” part really means. A text document is one that contains alphanumeric and punctuational symbols, carefully arranged to create “chunks” such as words, expressions, sentences, and paragraphs. Musical notes are the same, except that the chunks are chords, measures, phrases, and movements. Engineering a musical piece is not unlike engineering a document. Instead of a sonnet, assemble a sonata. Ditch the diary, and define a divertimento. Forget the fable, and fashion a fugue. The point is, composing is a specialized form of writing, and music is a specialized form of document. As soon as you learn to type, you learn to write. The same should apply to music.

1.2 Democratization of Creation Not only is “democratization of creation” an expression of inclusivity; it is also an expression of reality. Before social media, echo chambers, and

1.2 Democratization of Creation

3

confirmation bias became such important factors for internet usage, the Internet offered the possibility of being able to find any useful information on any topic instantaneously. That has not changed. Sure, it is fashionable to chuckle over the occasional inaccuracies of Wikipedia, let alone the opinesaplenty places like Quora, Reddit, and Pinterest. But, the fact is, well, that the fact is on the Internet, if you just know where to trust finding it. I, for one, could not be happier. It was not too many years ago (well, close to 30, so maybe that is too many?) when, if you were putting together an important document like a thesis, dissertation, or even (imagine that!) a book chapter, the hardest part of the task was performing the literature search. But not anymore. Need a literature search? Try Google Scholar? Need to learn how to do almost anything with your hands? Try YouTube, and almost certainly there is a video for you. With the possibilities available to you online, the hardest decision is not what to choose from but rather how to find out what you need. Democratization of creation, therefore, is as much a filtering operation as it is an accumulation operation. Sensory overload needs to be followed by a little quiet time. Information overload needs to be followed by a little knowledge consolidation. In this book, both the expansion of possibilities to provide a wide set of possible musical compositions and the consolidation of a particular musical instance to create a listenable piece of music will be considered together. Democracy means rule by the people. Democratization of creation, therefore, means the people (in other words, everyone) can create music. Anyone who has the tools to create music – which in the digital age is, frankly, everyone – has the possibility (if not the ability) to create great music. The way to achieve greatness is to practice, and one important aspect of composing while learning music is its ability to enhance the efficacy of practice. Composing, therefore, is a democratization of practice. Creativity stems from the juxtaposition of the possible with the impossible, which, like a chemical reaction, produces end products often entirely different in properties from their individual reagents. Think of a good recipe − cooking is applied chemistry, after all. Sometimes the simplest recipes are the best. A peanut butter cup is essentially chocolate and peanut butter, two ingredients heterogeneously distributed in a single item. Substitute “loud” for the “peanut butter” and “quiet” for the “chocolate,” and now you have the music of the Pixies (e.g. “Tame” from Doolittle) or Nirvana (e.g. “Lithium” from Nevermind). Music so quiet it coaxes you into a trance, and then suddenly a wall of noisy, boisterous notes that jar you into agitation.

4

Music Maker: Introduction

In addition to loudness, we have four other key tools to vary to create a huge range of music: tempo, pitch, duration, and timbre. Tempo is the pace, or speed, of the music. Pitch is the frequency of the note. These two can easily be related. If a recording is sped up, with the spacing between notes reduced, then the frequency is sped up in inverse proportion. That is, the following equation holds: Frequency = k/Spacing. (1.1) For example, if the spacing between the notes is 0.5 seconds and the frequency of the note is 440 Hz, then the constant k = (440)(0.5) = 220. Now, suppose the note was originally recorded on an old-fashioned LP record at 33 rpm (revolutions per minute) but played back on an even more old-fashioned LP player at 78 rpm. The spacing between the notes is thus reduced to (0.5) × (33/78) seconds, or 0.2115 seconds. Plugging this into eqn (1.1), the frequency at this higher speed is 220/0.2115, or 1040 Hz. You can certainly hear this “chipmunk” effect any time you play an old LP at a higher speed. Duration is how long a note is held. The length of the note dictates how fast we count off the notes to synchronize when two or more people are making music together. For example, you may count “one, two, three, four” for the quarter notes in 4/4 time just before starting a piece of music. The duration, of course, does not by itself describe how the loudness of a note is held over time. A staccato note is punctuated but quickly fades in loudness. A legato note transitions into its following note with nary a change in intensity. Thus, we can consider both absolute duration (the beat) and relative duration (the progression of loudness during the beat). Timbre is a measure of the color and quality of a note. The purely scientific aspect of timbre largely consists of the harmonic spectrum; in specific, the nature of the harmonic frequencies (odd or even multiples of the base frequencies) of the notes. Additionally, the timbre is determined by the envelope of the notes. This includes the attack time (how fast the note goes from quiet to peak loudness), the decay (half-life of loudness), the sustain (how flat the peak note’s modal loudness is), and the release (how fast the sound fades at the end of the note). Combined, the envelope comprises an attack, decay, sustain, and release (ADSR) curve. The ADSR curve is shown in idealized form in Figure 1.1.A, and in a more realistic form (with time constants for the signal to reach each inflection point in the curve) in Figure 1.1.B. The attack portion is the speed at which the sound moves from its onset to its peak magnitude. On a piano, for example, the attack is more about how

1.2 Democratization of Creation

5

fast your finger pushes down the key, rather than how hard the key is hit. On a woodwind, it may be about how fast the “puff” occurs, rather than how much breath is used. Once the peak loudness is reached, the loudness decays. For the piano, this is mostly related to how the hammer releases after striking the string, meaning the piano player does not have much input on it while playing. A key held firmly will have a slower and/or lesser delay than a key held softly. A long puff will have a slower/lesser decay than a short, quick puff. The next part of the ADSR curve (Figure 1.1) is the sustain. This is how well the loudness of the sound is held over time. For staccato articulation, the sustain section will continue dropping quickly, as for the delay section. For legato articulation, the sustain section will hold close to the loudness at the end of delay (as shown in Figure 1.1). On a piano, sustainment is accomplished by holding down the key. On a woodwind, sustainment is attained by keeping the breath flowing into the mouthpiece. The final portion of the ADSR curve is release. Here, the finger is lifted off the note or the breath is ended into the mouthpiece and the natural inertia of the instrument’s mechanism – e.g. vibration of the string or continuation of the breath through the length of the instrument’s tube – is allowed to govern the fading of the loudness. The force creating the loudness is released, and so the instrument’s structural harmonics dictate the evanescence of the fading sound. Since the human ear is very good at discerning frequency differences, the human ear is good at determining different arcs in the ADSR curve. Even at the most basic frequency comparisons, humans can discern between (relative to the overall tempo of the music) fast, moderate, and slow attack, decay, sustain, and release. With only three such possibilities for each element of the ADSR, we have 34 = 81 different ADSR curves or “sound architectures” to each note. The human ear (strictly, the cochlea and all of its sound receptors, but we will skip over the physiological details here) can discern all of these differences, but auditory understanding occurs in the brain (primarily, at least initially, in the temporal lobe). There, the delay, sustain, and release parts of the ADSR curve are usually “chunked” together, and so the human brain differentiates less than 81 different ADSR curves, at least in the flow of the music itself. Offsetting these, there are other aspects of the envelope that are important to human auditory processing. For example, the bandpass of frequencies around the key frequency of a musical note determines how much of the cochlea is recruited at the same time. If a middle C is chimed on a tuning fork, there is a tight bandpass around 262 Hz, the frequency of middle C. If it is played on a woodwind or a piano, there will be a broader bandpass around 262 Hz. In other words, more frequencies, say from 245−280 Hz

6

Music Maker: Introduction

A

Decay Sustain

Attack

Release

ADSR (Idealized)

B

Decay Sustain

Attack ADSR (Realistic)

Release

Figure 1.1 The ADSR (attack–decay–sustain–release) pattern for a note. The x-axis is time, and the y-axis is the loudness of the sound. The upper curve (A) is an idealized representation, while the lower curve (B) represents a more realistic curve (there are time constants for the curve to reach each of its inflection points). Please see text for more details.

instead of from 260−265 Hz, will be heard. This changes the signal sent to the brain by the cochlea, and thus changes the “fatness” of the ADSR envelope. Coming back to the democratization of creation, at the highest level, composing can be viewed as the proposing of two or more musical pieces at the same time, and from them arriving at a combination that seems optimal. As with any other form of document creation, musical composition benefits from each of the following: (1) Editing and versioning − the first draft is often full of errors (2) Feedback − a second pair of ears, whether from a music sophisticate or from a musical novice, can often identify rough spots in the music

1.3 Is Music a Science or an Art?

7

(3) Experimentation − instead of changing the notes, why not change the instrument? This in turn changes the envelope and the harmonics (relative loudness of frequencies that are integer multiples of the key frequency of the note) Is there anything in this list that you, or anyone you know for that matter, cannot do? No! It is truly no more difficult than voting (thus, it is democratization), and just like voting you should absolutely do it. Some argue that we are in a “post-literate” age, where learning is less important than knowing where to find the learning of others. For example, now that the Internet is populated with almost every imaginable salient fact, you no longer have to remember that the capital of North Dakota is Bismarck or that your favorite crazy aunt and uncle can be reached at [email protected]; instead, you need only know what search window to type a simple query (or speak a simple query) into. This indirection, or dereferencing in computer lingo, means that we do not hold the knowledge in our heads but instead the knowledge of how to find the knowledge. However, not holding the actual knowledge does not make you less intelligent; rather, it frees your mind up to select among more knowledge in a more efficient manner. Since the mechanics of musical creation are more readily accomplished, your mind is freer to compose from among this broader and more readily accessed collection of musical options. Think of it this way: does an engineer have to build a computer every time they need to write a program? Does a carpenter need to build a hammer every time they need to attach two pieces of wood? Of course not − in both of these cases, the expert uses more and most sophisticated tools as they build up more expertise. Music makers are musical engineers and carpenters, and it is natural that their toolset will become more sophisticated over time. Composition is, perhaps, more sophisticated than sight reading (though not necessarily harder), and given the greater sophistication of tools available to any and all musicians, musical engineers and carpenters will naturally move into composition that much earlier and that much more successfully than in times past.

1.3 Is Music a Science or an Art? Not surprisingly, the answer is yes to both. Music is both a science and an art, and likely always will be. Some of the music that is popular today would have been considered mere noise a few decades ago. The band Skinny Puppy sued the US Government for $666,000 (the 666 from the famous Book of

8

Music Maker: Introduction

Revelation 13:15-18 passage on the number of the beast) after finding out that their music was being used to torture prisoners at Guantánamo [Mich14]. One person’s music is another person’s emergency broadcast system meets nails on a chalkboard meets fork on a glass. The point is, it is likely always going to take the evaluation of humans to distinguish music from noise. The science of music centers on turning theory into practice. Science is experimental, which means based on experience. Theory does not have to be so; that is, theory can lack any empirical input whatsoever. But, when most people like music, they like it in its totality, not just because of the theory it embodies. When music “works,” it works generally through some combination of the experience and the understanding that goes with it. Knowing your audience matters, and the musicians who give their audience what they want are generally more successful than those who provide the same output for every audience. Since every performance can be expected to be available on Spotify in this connected era, performers can gear their music to match multiple audiences, thus increasing their appeal. As we will see in other sections of this book, a simple change of key, of instrument, of meter, and of loudness, among many other factors, can provide a different “feel” to the music. Improvisation to meet the mood, expectation, and desire of your audience is a huge talent in an era in which pitch-shifting and a myriad of music automation mechanisms are available. The ability to improvise, therefore, is perhaps the most important musical skill of all. Composing music from the very beginning of your musical education, therefore, is a key talent for any musician since composition and improvisation are partners in musical creativity. One of Mozart’s greatest talents was his ability to hear a piece of music being played, sit down and play, and while doing so improve upon it. Mozart innately improvised all of his music. As an absolute musical prodigy, Mozart might seem out of reach for the average musician. Not so! When thinking about your own learning and composition, the simple acronym/mnemonic WWMD is enough to get you past any roadblock. WWMD = what would Mozart do? If Mozart were alive today, he would be learning every possible new sound-generator. Would he replace clarinets with congas, cymbals with synthesizers, or oboes with oscillators? Maybe. But far more likely, Mozart would simultaneously consider the use of all six instruments – along with other instruments like the saxophone and electric guitar that were not available to him – for consideration in his compositions. WWMD? He would be open-minded to any, and likely all, new instrumentation. Remember that ragtime, rock and roll, reggae,

1.4 The Rest of the Book

9

and rap were all new once, and many people were initially uncomfortable with these musical genres and in some case with their signature instruments. Patrick Star once asked, “Is mayonnaise an instrument?” [Spon04]. Squidward, his long-suffering frenemy, replied in the negative. Squidward, for once, was correct. Mayonnaise is not an instrument − it is a family of instruments. Mayonnaise spread over cellophane, rubber-banded to the top of a bowl, changes the harmonics of the simple cellophane-and-bowl drum that would otherwise form. Blowing a recorder into mayonnaise produces another family of sounds. Mayonnaise, processed by the human gastrointestinal system, may cause the same body (especially if it has an egg allergy) to produce a unique form of music. Yes, we are being a bit facetious here, but the point is well-taken: mayonnaise, like pretty much anything else you can get your hands on, can be used in a creative way to produce intentional sound. In other words, you can make mayonnaise music. From the above, it is clear that any musician will incorporate (a) new instruments, which in the case of Mozart were the French horn, the clarinet, and the glass harmonica, and (b) new styles. The music maker is a music taker, a polymath, a polyglot, and an omnivore. When asked which style of music you should use, remember it is an AND not an OR. You do not have to use mayonnaise in your compositions (and, quite frankly, we rather discourage this), but the point here is that if it works within the context of your creation, please do.

1.4 The Rest of the Book The remainder of the book will follow in the pattern set by this chapter. Following the introduction of one or more important musical concepts, we will explore ways of adding creativity to your musical learning, re-learning, or even mastery by complementing the musical playing with musical composition. Sure, there will be musical notation, as that is generally an important part of learning for most of us, even if many genius musicians over time were at least anecdotally incapable of reading musical notation. Notation is simply another tool for the composer. A “complete” composer will sometimes use notation, and other times improvisation, depending on the situation. Most musicians have a certain hybridization of the two, assuming herein that improvisation includes simply playing around with the instrument. The goal is, as in most learning situations, to find the right mix that works for you. We hope to provide enough tools and insights to help you decide the right balance. Regardless, both notation and improvisation tie in nicely with the

10 Music Maker: Introduction sort of musical composition approach that we champion in this book; that is, where it is customized to the individual tastes of the composer. We thus try to provide a more or less all-inclusive view from which you can carve out a path best aligned with own unique tastes and talents. We trust you to make those decisions. Are there a set of rules, or “design patterns,” that we can provide a musician to create good music? As in, is there a set of patterns, processes, and practicalities along the lines of the patterns for creating hybrid intelligent systems from sets of individual intelligent systems [Sims13]? There should be, right, because music is in some sense an intellectual (intelligent) output comprising multiple intelligent inputs. So, to some extent, yes, such patterns exist, although they are more like techniques than specific patterns per se. What we are really interested in is helping each musical student become a composer. A music baker knows the theory, that is, uses a set of rules or patterns as a recipe to “cook” up a composition. This is not always creative enough to generate good new music. A music shaker, on the other hand, knows the experimental methods to innovate with but might not know enough recipes to create a satisfying, balanced meal of music. We are interested in the music maker, who knows composition is not just about writing new music − it is also about new ways to write new music. Your musical muse (if we are allowed to use such redundant language) changes all the time. A sure way to be unsuccessful in composing is to try to compose the same way each time. To paraphrase a famous quote, insanity in composition is trying to do the same thing the same way and expecting it to sound new. Maybe this is the most important element of this book: providing a roadmap to create new roadmaps. Each song, tune, or symphony can be viewed as an excursion, and some may be as mundane as a trip to the office, while others are as scintillating as a trek along the North Yungas Road. Either way, no two journeys should be or really ever are the same, and no two of your compositions should be. Will composition be replaced by bots that generate tunes and, trained by humans, know beforehand which ones will be hits and which will be ignored? We hope not: we aim to create composers, so that the human being still rules the digital age, and not the converse. Besides, bots are going to produce music that is so yesterday. And trust me, we only need one Yesterday. In future chapters, we will address such topics as “what would Mozart do?”; new instruments and styles; and the “AND,” not the “OR,” of music, in what we call “sidebars” of each chapter. These will provide the numerical and inspirational underpinnings of continued musical composition experimentation. Within the main part of each chapter, the breadth of creative composition will

1.5 Sidebar – Music and Limitless Possibilities

11

be led by a music teacher (Ewing) who has taught more than 35,000 lessons to guitar, bass guitar, and piano students ranging from the toddler neophyte to the middle-age proficient, with a sprinkling of professionals in the mix. Teaching to students of all levels means coming up with learning strategies of many different types. If what you are currently reading does not work for you, please turn the page and keep experimenting. In the rest of the book, we will address the theory, experimentation, and composition aspects of musical phrase, scale, harmony, form, and rhythm. The combination of formal and informal approaches is conducive to increased creativity. Along the way, we will frame the future of the music maker using a wide variety of perspectives, including: (1) the Hegelian dialectic as applied to musical synthesis (come up with a song, then write its opposite, and then make the two of them work together somehow), and (2) the effective infinity (infinities!) of music . . . how many possible songs are there? In (2), we consider what makes a song a song − the role of sampling, using different instruments, different vocal or instrumental styles, and what constitutes an “atomic unit” of music. We could readily apply the concept of typewriting monkeys creating Hamlet to the digital means of creating songs − except that we are not going to! What we really aim to show is that there is an unending need for musical creativity and that music is inexhaustible. The future looks very good indeed for music makers.

1.5 Sidebar – Music and Limitless Possibilities Music is perhaps the greatest source (and sink) of inspiration on Earth. When someone asks you to “follow your muse,” are they not simply asking you to listen to your favorite music? Why not write your favorite music? Think of how amazing that would be! Set to writing, playing, and mixing, and all of a sudden, you can leave Spotify on “OFF” and jive to your own creation. How hard can it be? Even if you come up with just four different phrases, you have a lot of variability in terms of how you put them together as a sequence of phrases. If you only choose one phrase to play, you have four choices from which to choose. If you put two of the phrases together in sequence, you have 16 options, if we allow repeats, and 12 if you do not. If we name the four phrases A, B, C, and D, then the 12 non-repeating sequences are AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB, and DC. The repeating additional four sequences are, of course, AA, BB, CC, and DD. However, there are only two patterns possible for this type of arrangement. Either you repeat the same phrase or you sequence two phrases.

12 Music Maker: Introduction We shorthand these patterns AA and AB, recognizing that the “AA” pattern describes all four sequences AA, BB, CC, and DD, and the “AB” pattern describes all 12 sequences AB, AC, AD, BA, BC, BD, CA, CB, CD, DA, DB, and DC. We simply use the minimum set of alphabetic characters possible to describe the pattern. Think of the old Genesis song, “ABACAB,” which originally described its sequence of phrases. Note that “A” is the first character appearing in this sequence, followed by “B” and then “C.” Thus, “ABACAB” is a legitimate pattern for phrase sequencing. Note that if we used phrase B first, followed by “D,” and then “A” in this pattern, the particular sequence of this general pattern would be “BDBABD.” This is reflected in the patterns of Table 1.1 and sequences of Table 1.2. Often musical terms are used in place of alphabetical characters for patterns or sequencing. Instead of “AB,” you might see “verse-chorus.” No worries − this is just like poetry notation, wherein a rhyming scheme (sequence) of a Shakespearean sonnet might be listed as ABBA CDDC EFFE GG. An “ABABCB” sequence might be described as “verse-chorus-versechorus-bridge-chorus.” No worries − they are the same musical progression, no matter what they are called. An alien might call ABABCB “glip-glorpglip-glorp-glop-glorp,” but the same sequence would be easy to recognize. In Table 1.1, we expand from two-phrase patterns to three-phrase and four-phrase musical phrase arrangements. There are, instead of 2, either 5 or 15 patterns. Note that the possible arrangements of (A,B,C,D) in each of these 20 scenarios greatly increase as the number of phrases used in the pattern increases. In Table 1.2, we expand these patterns into the entire set of unique for three- and four-phrase compositions corresponding to the patterns from Table 1.1. In parentheses in Table 1.2 are the total number of possibilities for sequencing within each pattern, if you have composed four phrases, A, B, C, and D, and wish to put them together in any possible order. Of course, these add up to 4 × 4 × 4 × 4, or 44 , or 256. The difference between the number of patterns, 5 and 15, in Table 1.1 and the number of sequences, 64 and 256, in Table 1.2 is compelling. We have many more sequences possible than the patterns possible, and the number of patterns quickly exceeds the number of phrases as we increase the length of the composition. What this all means is that, when it comes to composition, there are various levels of infinity. As we will show in other sidebars in the book, there are quickly an infinite number of primary compositions, by which I mean the set of individual phrases that are combined to create the musical piece. In our example here, the primary composition is the set of four phrases, A, B,

1.5 Sidebar – Music and Limitless Possibilities

13

Table 1.1 The list of three-phrase and four-phrase musical piece arrangement patterns. These are the 20 patterns possible. Note that the possible arrangements of (A,B,C,D) in each of these 20 scenarios greatly increase the total number of arrangements from the four phrases (or pieces). Please see text for more details. List item Three-phrase musical Four-phrase musical pattern pattern 1 AAA AAAA 2 AAB AAAB 3 ABA AABA 4 ABB ABAA 5 ABC ABAB 6 – ABBA 7 – AABB 8 – ABBB 9 – AABC 10 – ABAC 11 – ABCA 12 – ABCB 13 – ABCC 14 – ABBC 15 – ABCD

C, and D, each of which have an effective infinity of possibilities to choose from in their creation. So, any combination or sequence of these phrases would generally be recognizable as a variant of the same composition. But, the number of patterns (Table 1.1) and sequences of patterns (Table 1.2) are many times greater than the number of primary compositions. If there is an effective infinity of primary compositions, then there are many infinities of patterns and many more infinities of sequences of these phrases to choose from for the final composition. To close this chapter, it is worth exploring a little further the comment that “any combination or sequence of these phrases would generally be recognizable as a variant of the same composition” from the perspective of musical plagiarism (or copyright infringement). This is an area of arbitration that may actually be assisted by artificial intelligence in the future (maybe even by the time this book is available!). A musical recognition application (more formally, an intelligence engine), such as Shazam or SoundHound, or the equivalent of a jury of such applications, can be used to perform the plagiarism testing. If your new musical composition piece is not “recognized” as the song from which it is supposedly plagiarized, then the case for plagiarism may be found in error. Of course, it is not that simple. The degree of

14 Music Maker: Introduction Table 1.2 The list of three-phrase and four-phrase musical sequences corresponding to the patterns from Table 1.1. In parentheses is the total number of possibilities for sequencing within each pattern, if you have composed four phrases, A, B, C, and D. Please see text for details. List item Three-section musical sequence Four-section musical sequence (first (first in each list is the pattern in each list is the pattern from from Table 1.1) Table 1.1) 1 AAA, BBB, CCC, DDD (4) AAAA, BBBB, CCCC, DDDD (4) 2 AAB, AAC, AAD, BBA, BBC, AAAB, AAAC, AAAD, BBBA, BBD, CCA, CCB, CCD, DDA, BBBC, BBBD, CCCA, CCCB, DDB, DDC (12) CCCD, DDDA, DDDB, DDDC (12) 3 ABA, ACA, ADA, BAB, BCB, AABA, AACA, AADA, BBAB, BDB, CAC, CBC, CDC, DAD, BBCB, BBDB, CCAC, CCBC, DBD, DCD (12) CCDC, DDAD, DDBD, DDCD (12) 4 ABB, ACC, ADD, BAA, BCC, ABAA, ACAA, ADAA, BABB, BDD, CAA, CBB, CDD, DAA, BCBB, BDBB, CACC, CBCC, DBB, DCC (12) CDCC, DADD, DBDD, DCDD (12) ABAB, ACAC, ADAD, BABA, 5 ABC, ABD, ACB, ACD, ADB, BCBC, BDBD, CACA, CBCB, ADC, BAC, BAD, BCA, BCD, CDCD, DADA, DBDB, DCDC (12) BDA, BDC, CAB, CAD, CBA, CBD, CDA, CDB, DAB, DAC, DBA, DBC, DCA, DCB (24) 6 – ABBA, ACCA, ADDA, BAAB, BCCB, BDDB, CAAC, CBBC, CDDC, DAAD, DBBD, DCCD (12) 7 – AABB, AACC, AADD, BBAA, BBCC, BBDD, CCAA, CCBB, CCDD, DDAA, DDBB, DDCC (12) 8 – ABBB, ACCC, ADDD, BAAA, BCCC, BDDD, CAAA, CBBB, CDDD, DAAA, DBBB, DCCC (12) 9 – AABC, AABD, AACB, AACD, AADB, AADC, BBAC, BBAD, BBCA, BBCD, BBDA, BBDC, CCAB, CCAD, CCBA, CCBD, CCDA, CCDB, DDAB, DDAC, DDBA, DDBC, DDCA, DDCB (24) 10 – ABAC, ABAD, ACAB, ACAD, ADAB, ADAC, BABC, BABD, BCBA, BCBD, BDBA, BDBC, CACB, CACD, CBCA, CBCD, CDCA, CDCB, DADB, DADC, DBDA, DBDC, DCDA, DCDB (24)

1.5 Sidebar – Music and Limitless Possibilities 11

–

12

–

13

–

14

–

15

–

TOTAL

64

15

Table 1.2 Continued ABCA, ABDA, ACBA, ACDA, ADBA, ADCA, BACB, BADB, BCAB, BCDB, BDAB, BDCB, CABC, CADC, CBAC, CBDC, CDAC, CDBC, DABD, DACD, DBAD, DBCD, DCAD, DCBD (24) ABCB, ABDB, ACBC, ACDC, ADBD, ADCD, BACA, BADA, BCAC, BCDC, BDAD, BDCD, CABA, CADA, CBAB, CBDB, CDAD, CDBD, DABA, DACA, DBAB, DBCB, DCAC, DCBC (24) ABCC, ABDD, ACBB, ACDD, ADBB, ADCC, BACC, BADD, BCAA, BCDD, BDAA, BDCC, CABB, CADD, CBAA, CBDD, CDAA, CDBB, DABB, DACC, DBAA, DBCC, DCAA, DCBB (24) ABBC, ABBD, ACCB, ACCD, ADDB, ADDC, BAAC, BAAD, BCCA, BCCD, BDDA, BDDC, CAAB, CAAD, CBBA, CBBD, CDDA, CDDB, DAAB, DAAC, DBBA, DBBC, DCCA, DCCB (24) ABCD, ABDC, ACBD, ACDB, ADBC, ADCB, BACD, BADC, BCAD, BCDA, BDAC, BDCA, CABD, CADB, CBAD, CBDA, CDAB, CDBA, DABC, DACB, DBAC, DBCA, DCAB, DCBA (24) 256

matching of individual phrases in the music might be the most important, just as matching elements of text in a text-based plagiarism technology is not defined by the entire body of text. Regardless, music recognition technology will increasingly be used not just to find you that song you want to hear all of but also to tell you if that song was stolen from an earlier performer.

References [Mich14] Michaels S, “Industrial Band Skinny Puppy Demand $666,000 After Music is Used in Guantánamo Torture,” The Guardian

16 Music Maker: Introduction Online, https://www.theguardian.com/music/2014/feb/07/skin ny-puppy-payment-guantanamo, 7 February 2014, accessed on 12 December 2020 [Sims13] Simske S, “Meta-Algorithmics: Patterns for Robust, Low-Cost, High-Quality Systems”, Singapore, IEEE Press and Wiley, 2013. [Spon04] SpongeBob SquarePants: The Complete 2nd Season (“Band Geeks” credits) (DVD). United States: Paramount Home Entertainment/Nickelodeon. October 19, 2004.

2 Form in Composition

Beauty of expression is so akin to the voice of the sea – George Matthew Adams My music is the spiritual expression of what I am – my faith, my knowledge, my being – John Coltrane

Abstract This chapter will provide a macro view of the variety of structures, or forms, from which finished musical compositions are written. Diagrams will be used to illustrate the different parts or sections of a work, and their functions are discussed. The objective of the chapter will be to provide readers with templates to begin conceiving and producing their own compositions. We present the general forms that music is composed (binary, variation, ternary, rondo, and sonata), leading to the more variable song and fantasia structures. This chapter’s sidebar will focus on how creative sources result in musical advancement. Keywords: Binary Form, Expression, Fantasia, Form, Homophony, Rondo, Sonata, Song, Style, Templates, Ternary Form, Variation Form.

2.1 Introduction We start off the composition in this book in earnest with a consideration of style and form. Form is the structure behind your composition, while style is the superficial feel or sound of the form as you have personally constructed the music. This is an important distinction, because you can use a form from some musty, worm-laden volume of music long forgotten by the human ear and still superimpose your own sounds and feelings. If you take a sonata form,

17

18 Form in Composition for example, you do not have to compose something that sounds like Mozart or Beethoven. It can sound more like Dua Lipa or Kendrick Lamar, if you so choose. Aaron Copland noted this separation of form and style, complaining that an earlier composer “Scriabin. . . put this really new body of feeling into the straight jacket of the old classical sonata form” [Copl53, p. 153]. Straight jackets (or straitjackets) are traditionally used for the mentally unbalanced, which may in fact be your choice of mood for composing (think of how mentally altered John Lennon might have been whilst writing LSD, or Lucy in the Sky with Diamonds, even if it really was just based on Julian Lennon’s drawing of his classmate, Lucy), but likely are not in general something you want to adopt as your normal clothing. Lose the straight jacket, and separate form and style. This chapter will help you get started.

2.2 Form All composed music has some sense of organization to it. The listeners may have varying degrees of expertise they bring to their perception of the structure of a piece of music. There may be a piece of music considered a “masterpiece” that a casual listener finds so magical that they may claim to not understand how it possibly could have been composed. But upon analysis of these “masterpieces,” we may find that they follow conventional forms in their use of structure. Not that any of this should negate the fact that these compositions can still be seen as works of genius, but like great humor, they do not survive dissection. That is, even a genius in music can be analyzed logically and thereafter understood. Then, it can be used as a template for your own composition. All of this should mean music keeps getting better and better, right? Right? With certain genres of music, there may be an expectation for the structure. A pop song has certain criteria in its construction so as to merit the title “song” (verse, chorus, and bridge). There is certainly flexibility in this expectation, and it may evolve decade after decade, century after century. An architect has parameters they work within and certain expectations to fulfill in order to have a design qualify as a house. When you enter a bathroom or kitchen, there are definite expectations as what to find within. Yet, you may find different arrangements, shapes, and sizes to these rooms and the buildings that contain them. So with music also, there is flexibility within the structure. Yet, we may still meet listener expectations or, perhaps in some instances, even surprise them despite employing a familiar form.

2.2 Form

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One essential component of the structure of music depends on the treatment of repetition. Upon the creation of a perhaps “catchy” phrase or theme, the composer must make a choice: repeat it or go on to something new. There are many possibilities, and through many centuries of composing, different forms have taken hold, which have different shapes in their construction. The aim here is not to give a thorough historical evolution on form in music. Instead, we will look at a few forms common in the western music tradition, which help illustrate the compositional process. We do not have to cover every style to provide meta-cognition that will help you create in any form. That is to say, you do not need to write in a particular style to write in a particular form. You could use the form from a Baroque composition for a Hip Hop song, for example, even though anyone listening would not think the two pieces relate in any way. In the analysis of a composition, it is useful to label the first occurrence of material in the structure of the work with the alphabetical lettering A and proceed with each new section of material in sequential order (A, B, C, etc.). Hence, the first major section of a work would be labeled “A” and upon entering into a new section of material, the lettering becomes “B,” a notation we will adopt throughout the book. So, an overall shorthand for the structure of a composition might be ABA. If the repeated section is not exact and has some difference(s) from the original, it can be labeled A’. The labeling is applicable not only to the overall (or “macro”) view of the composition but also to a “micro” view within a section. Inside the macro view’s “A” section, you might find a sub-structure of AABA. This labeling gives a visually concise graphic of the structure, and it is useful to the theorist analyzing a composition as well as the composer creating them. Having a “road map” to work from can be an essential tool for a composer as they begin any new creative endeavor. A composer can change their mind at any point. They can expand or reduce a portion of a work at any point, as well. Song forms dominate the music created today, and probably always have throughout history. We remember the troubadours and minstrels, and their songs survive to this day. In fact, looking back to Shakespeare’s plays, the Folios are filled with fonts, but only slightly suggestive of song. When songs are integral to his plays (think of Midsummer Night’s Dream for one), the audience is so familiar with the tune that no score is included (nor needs to be). In this sense, forms transcend the music itself, giving the music some familiarity from the start and anchoring the audience irrespective of the music’s style.

20 Form in Composition Form, therefore, can be a level of abstraction removed from the style of the music itself. Music can be reworked and rearranged with different styles. Style might be characterized by the melodic, rhythmic, and harmonic choices along with the instrument scoring, accompaniment patterns, and performance inflections. A traditional Christmas tune can be recorded in Cajun or Jazz styles far removed from their sacred or folk style originals. Modern pop songs may get a rework in the YouTube channel Bardcore, giving a new song an old medieval restyling. The instruments of today (electric guitars, synthesizers, and drum kits) are changed to the instruments of yesterday (recorders, lutes, and tabors). The style of the song is changed (instrumentation and accompaniment), but the form (verses and choruses) remains the same. Conversely, the song form of a piece of music may be altered without changing its style. Licensed music in advertising spots may be cut down from its previous form as a complete work of a couple of minutes in length into shorter snippets as little as 15-second long, incorporating the most memorable phrases of the song. The music is still recognizable, but the form is changed. In fact, we can recognize a song form just from the rhythm, or beats. We recognize it from somebody humming the notes − even badly. We know that they are humming badly because the form creates certain expectations for the listener. Our composing flow can be guided by the text (or libretto), or in purely instrumental music by instinctive and/or logical arrangement of phrases and sections. This relies on the conceptual framework for composition wherein the overall piece is divided into sections, or parts, or even divisions. Compositions based on text or ones that are purely instrumental can both benefit from a form-driven approach. It would therefore be good form on our part to describe these in more depth.

2.3 One-part Forms For a one-part, or singular, form, the overall approach to composing the materials is generally based on one simply stated idea that can be expanded upon, for example, using improvised passages. This most basic form for composition therefore might still incorporate varying degrees of complexity within its one-part structure. A good example of such a “simple” composition is Lavender’s Blue (Figure 2.1). The structure of Lavender’s Blue is called an “antecedent and consequent.” Here, the first phrase of melody, known as the antecedent (first four measures), is complemented by a second phrase, known as the consequent (last four measures), with the latter bringing about a satisfying conclusion to

2.3 One-part Forms

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Figure 2.1 Score to Lavender’s Blue.

the whole. Figure 2.2 indicates how Section A of this piece is broken into these two equal-length phrases.

Figure 2.2 Simple diagram with Section A shown to be composed of two equal-length (horizontal length is proportional to time) phrases, the antecedent and the consequent. This is a graphic representation of the Lavender’s Blue score shown earlier.

Lavender’s Blue may look rather short, musically. But, when combined with the libretto (singing) part of the composition, it readily extends to several minutes. Maybe even more if you add your own lyrics (note that some canonical forms of Lavender’s Blue include 30 verses of the song, or 60 repeats of the composition shown above since each verse is generally two repeats of the melody), as shown: Lavender’s blue, dilly dilly, and lavender’s cat When I see it, dilly dilly, well so does the rat Cat chases the rat, kitty kitty, and not as a friend A new start for the cat, kitty kitty, for the rat an end When the same melodic content is used for the different stanzas of lyrics, it is called strophic form. The obvious labeling for the one-part form would be indicated with the lettering of “A.” With the repeats of the structure, it would be realized as “AAAA. . . ,” for as many repeats are necessary for the song text (Figure 2.3). Fortunately, we have other options.

Figure 2.3 Simple diagram with Section A shown to be repeated four consecutive times. This corresponds to AAAA, or strophic, form, as discussed in the text.

For an example twice the length of Lavender’s Blue, consider the melody Das Neugeborne Kindelein, which was incorporated into one of Johann Sebastian Bach’s chorales (Figure 2.4). Here, there are two lines, each of

22 Form in Composition which can be considered an antecedent−consequent pair. Alternatively, you can consider it four sequential phrases, each with a similar rhythmic quality. Melodically, each of the four phrases has its own unique melodic path. So, even if you were to label this piece an AAAA structure, it is surely not overly repetitive. We mention this just to show you that the labeling is not set in stone: use whatever functionally works best for you.

Figure 2.4 Score to Das Neugeborne Kindelein.

There are certainly other song structures that could exist within a one-part form, which we see used by Chopin (specifically, the melody to the Prelude in A. Major, Op, 28, No. 7). The arrangement (Figure 2.5) here almost feels like Chopin is improvising on the antecedent and consequent form. That is, Chopin takes the idea of antecedent and consequent and expands upon it by moving through different harmonies as we might see in a classical prelude. The entire form unfolds without formal divisions like repeat signs.

Figure 2.5 Score to Chopin’s Prelude in A. Major, Op, 28, No. 7.

The general idea for singular forms is that the material within the onepart contains no material that contrasts significantly enough so as to have

2.3 One-part Forms

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a “weight” of its own and thus be considered another section unto itself. The amount of contrast you need to differentially label two sections is, generally, up to you. For example, we could re-label the Lavender’s Blue tune above based on a micro-level analysis. The labeling for the antecedent and consequent in Lavender’s Blue would be AA’, as the two phrases of melody start the same but have different endings. So, there is some leeway for interpretation here, and whether you use AA, AA’, or AB labeling, the music is still the same. It is safe to say when the Police keep “sending out an S.O.S.” it is AAAA. . . , but when they hope that someday someone finds a message in the bottle, it is AB. You can draw your own lines in between to make room for AA’. The next piece is Udite lagrimosi spirti d’Averno, udite by Lucia Quinciani. This might be considered the musical equivalent of an Anna Burns novel; that is, engaging stream of consciousness. Here, Quinciani’s libretto is based on the following single stanza of text: Udite lagrimosi spiriti d’Auverno udite nova sorte di pena e di tormento mirate crudo affetto insembiante pietoso La mia donna crudel piu dell’inferno This text guides her construction of melodic material and overall structure of the composition. There is no attempt by her to repeat the same melody as the composition unfolds, much as Anna Burns in her prize-winning novel The Milkman makes no attempt to revisit the same type of conversation twice. For Quinciani, the notes flow from the needs of the libretto [Quin17]. This approach is termed “through-composed,” because Quinciani is using the text to guide the melodic content and not the converse. This does not prevent Quinciani from using some additional partial repetition of phrases within each stanza in order to make the music flow. See for yourself in the score below (note that the brackets above the score correspond to each line (and repetition) of the text (Figure 2.6)). By analogy, imagine at the beginning of the day, with the dawn of a cloudless sky and the prospect of adventure before you, you say “What a great day this is!” At the end of the same day, after you have driven your car into the side of your garage, lost your wallet, and stepped on your cell phone trying to get out of the car in the garage, you say “What a great day this is!” Same words, but hardly demanding the same music.

24 Form in Composition

Figure 2.6

Score to Quinciani’s Udite lagrimosi spirti d’Averno, udite.

2.4 Binary Form Also known as two-part forms, binary forms are focused on the idea of incorporating two different musical elements, which are creatively called A and B, in sequence. These two parts do not necessarily need to be related. Traditional binary forms AB, however, have generally included material based on one or more motives throughout the composition (this is called rhythmic motive). The structure for a simple binary, representing often equal-length phrases A and B, is given in Figure 2.7.

Figure 2.7 Simple diagram with Section A and Section B of equal length. This corresponds to AB, or binary, form, as discussed in the text.

An example of simple binary form is given by the Scottish traditional song, “Catches and Glees,” here (Figure 2.8) showing the melody of the

2.4 Binary Form

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composition as represented in [Stra75], a tune popular during the American Revolution (the “75” in [Stra75] being “1775,” not “1975”).

Figure 2.8 Score to Catches and Glees.

In “Catches and Glees,” which come to think of it sounds like the dog that actually caught the proverbial car it is chasing, each section is repeated, which means that technically the structure is AABB (in performance). As a bit more in-depth analysis, here the A section begins and ends with the I chord, while the B section begins on the V chord, ending with the I chord. Often, for such composition, the material inside each structure will move away from the tonic harmony (I chord) by the end of the A section (e.g. reaching the V chord, or “A” chord, here), and usually by the end of the B section it will return back to the tonic harmony (I chord, or “D” chord here). Note that in “Catches and Glees,” the A and B sections are very similar in composition, with measures 2 and 4 literally identical. In such a case, the structure of this piece might be described as AA’ instead of AB. As mentioned above, technically “Catches and Glees” repeats each section in performance before moving to the next, and so the structure is AABB, as shown in Figure 2.9.

Figure 2.9

Simple diagram for “Catches and Glees” as performed. Please see text for details.

In a rounded binary form, for example, the Minuet by Johann Krieger shown below, the A section material is repeated within the B section (Figure 2.10). So, to sum up, do not be fooled, or be complacent, or even be a complacent fool, just because “Catches and Glees” uses equal-length A and B sections! In your composition, the A and B (or variants) sections of a binary form can be different in length. The B section could become longer and include phrases exploring closely related harmonies and/or keys. As an

26 Form in Composition

Figure 2.10

Score to Johann Krieger’s Minuet.

illustration, consider the melody from Gavotte II (Musette) from the English Suite BWV 808 by Bach, shown below (Figure 2.11).

Figure 2.11 Score to Bach’s English Suite BWV 808.

Here, Bach’s A section (first four measures, or uppermost line in the above) is a simple antecedent−consequent pair. The B section here is much longer than the A section, and you will note that the third line of the B section (i.e. the bottommost line in the music shown) includes a different consequent to the antecedent phrase with the “rounded” return of material from the A section. Overall, one could label this as three antecedent consequent phrase groups, with the repeats giving it a notation of (AA) ((BB’)A’) ((BB’)A’). This seems different – that is, more complicated – from the earlier description of the rounded binary. However, at the composition level, this is nothing more than the B section including a return of the A section.

2.5 Variation Form 27

Obviously, we are not the first to comment on variable-length A and B section. We turn for perspective on that to perhaps music’s prototypical Wunderkind. In a letter to his sister while traveling in Italy, a young Mozart noted the difference in scale of the binary form minuets: “But the Milanese or Italian minuets have many notes, and move slowly with many bars. For example, the first part contained 16, the second 20 and even 24 bars” ([Mers72], page 10). Do you have an Italian friend and an Austrian friend? It does seem sometimes in conversation that they might support Amadeus here in the length of their expressions, maybe just a bit? Well, so too can your music have different lengths of expression. The binary structure could expand even further (as seen in the keyboard sonatas of Scarlatti or keyboard suite movements of J.S. Bach) and include multiple phrase groups (or themes) while holding the idea of starting in a tonic key and moving away in the A section and returning back in the B section. Check out one of these compositions if you are so inclined, and try to diagram it along the lines of this chapter.

2.5 Variation Form In the discussion of the rondo below, we will show form that is determined by the sequencing of different musical sections. However, with variation form, we have form based on sequencing a musical idea in a manner that, instead of going over the material again in a series of exact repeats, the material is in turn manipulated, or varied. Variation form takes a musical idea, which may be a short bass line or other short compositional structure used as the basis for the variation. One such basis for variation is a binary form, as mentioned above. Another basis for variation is harmonic progression. Regardless, the variation form uses this base as a springboard for diving deeper into musical invention. After the first presentation, the material is modified in a variety of ways, with the number of variations left up to the composer. It may only be a few variations; however, some composers (Beethoven, for one, with his 33 Variations on a Waltz by Anton Diabelli) have written variation sets with 30 or more variations. The technique of variation is applied to one or more of the components making up the musical material. This can be the melodic, harmonic, or structural content of the composition, or even several of them simultaneously. The variation may also include changes to the textural and accompaniment features, which allows the composer additional leeway for creativity.

28 Form in Composition Theme and variation in composition is common, and typically incorporates a form shorthand of AA’A”A”’A””. . . , until you have run out of variants, scores, or a wrist unaffected by a repetitive-motion disorder. Many composers from the past have used original compositions or other popular tunes as a basis for sets of variations. Jazz music of today is an improvised version of theme and variation. Jazz musicians often use 32-bar song forms from popular music (see Section 2.9) to form the basis for improvisation. The performer or ensemble will play through the material of a chosen tune (known as the “head”) and, thereafter, improvise over repetitions (choruses) of the harmonic structure of the song. In composition, the variation of material is achieved in several ways, though there is always some aspect of the original that remains. Variation may be applied to any repetition of material as it returns in any formal structure of composition. The return of A sections in ternary or rondo forms (as we discuss below), for example, can be a place for variation (ABA’ or ABA’CA”). Variation can also be applied to alternating themes (ABA’B’A”B”). Two older variation forms are the Chaconne and the Passacaglia. Both are based on harmonic structures. For a good example of the Chaconne, try Bach’s Chaconne from the Sonata for solo violin in D minor (BWV 1004). For a good example of the Passacaglia, try Bach again in his Passacaglia in C Minor for organ (BWV 582).

2.6 Ternary Form In compositions of three parts, known as ternary form, the contrast between the A and B section takes on more importance. Ternary form (also known as song form) is realized as an A and B section that follows with a return to A as the third section. This return can be identical or varied (ABA or ABA’). The ABA’ structure is shown in Figure 2.12.

Figure 2.12

Diagram for ABA’ structure.

Whereas the departure and return from the tonic harmony occurred across the two sections in binary form, in the ternary form, this movement could happen inside the A section structure as a self-contained entity. The B section is now free to become independent of the A section and thus to offer more contrast with new themes and new tonal centers. The idea of a composition

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conceived in three independent parts ABC could exist. However, the idea of returning to the original presented material after contrast (ABA) in ternary form logically wins in competition with the alternative of a third independent section with no return to A (ABC). The structures within a section A or B can incorporate other form structures such as binary within the complete section. For example, you can find independent minuet compositions that have two binary forms (minuet I and minuet II or Minuet and Trio) that are combined to form one continuous movement. Thus, it is realized in ternary form as (A) minuet I (B) minuet II (or Trio) and (A) minuet I repeated. In each of these larger sections, the A or B expands into an A’B’ binary structure, so that the overall structure may be represented as ABA = (A’B’)1 (A’B’)2 (A’B’)1 . Here, interestingly, we can see the idea of structures within structures taking shape. Each minuet or trio unto itself is a binary structure, and therefore you have two binary forms coupled with a minuet da capo (repeat of the first minuet) to make the three parts. For examples of this minuet−trio structure, try Mozart’s third movement (minuet) of Symphony no. 40 in G minor (K. 550) or Haydn’s Sonata in B minor Hob. XVI:32, second movement. For an example of dual minuets creating a ternary structure (Minuet I−Minuet II), you might enjoy Mozart’s second movement of the Sonata in E flat major KV 282 (189g). The micro-structures of the three parts of the larger ternary structure do not, however, have to be binary. As examples, consider Albeniz’ Asturias from the Suite Española, Rachmaninov’s Prelude in G Minor, Opus 23, No. 5, or Chopin’s Nocturne in F Major, Opus 15, No. 1.

2.7 Rondo Form Expanding further, we have the rondo form, which is a composition with multiple sections characterized by the consistent return of the A section. Like an old friend, the A section works as the highlight of the composition, anchoring the listener. The material’s return is anticipated like a refrain or a chorus in a song. The intervening musical couplets or episodes (of at least two more distinct sections, B and C) act to contrast with, or counterpose, the A section. The typical realization is ABACA in structure, but other arrangements are possible. Rondos may expand further with additional contrasting sections (e.g. ABACADA) or work their way out and back as an arched form (ABACABA),

30 Form in Composition which you will note is a palindrome. These two structures are shown below (Figures 2.13 and 2.14).

Figure 2.13 Diagram for ABACADA rondo structure.

Figure 2.14

Diagram for ABACABA rondo structure.

Rondos may also skip over a return of the A section in a truncated form (ABACBA), in which case the composer can build the expectation for the culminating A section that much more. Examples of this form are found in many Classical genres from solo works to movements in sonatas, concertos, and symphonies. The always popular piano work, “Für Elise,” by Beethoven is a rondo (ABACA). The form is certainly still useful, as it is the basis for many familiar “modern” pieces of music. The form is found in popular music compositions such as Vince Guaraldi’s “Linus and Lucy” and Aaron Copland’s (and Emerson, Lake, and Palmer, come to that) “Hoedown.” Basically, the rondo is a way to highlight a particularly catchy section of music without hitting your listener over the head with it. Structurally, the A section (or any other B, C, D. . . ) may take on a form within a form, akin to the discussion on form variation above. It may comprise a binary structure or song form like A’A’B’A’ within the A section (see Section 2.9). This makes the structure recursive; that is, the A’ section functions within the A section just like the A section functions within the larger ABACA rondo.

2.8 Sonata Form With the sonata form, we have a compositional structure with its basis being the presentation of a theme or themes, followed by a section within the form devoted to developing the ideas of these themes. The sonata form, also known as Sonata-Allegro or First Movement form, has three distinct divisions. However, the Classical sonata evolves from the Baroque binary form, as there are usually two main sections usually, but not always ending with repeat signs. A generic description of the Classical sonata form structure

2.9 Song Forms 31

within each division is as follows. The A section, known as the exposition, introduces a principal theme group in the tonic key. It then moves to a related key in the secondary theme group and then a closing theme group. The term “group” refers to a collection of phrases or themes. The B section follows the repeat of the A section, and incorporates a Development section, which takes ideas introduced in the Exposition and elaborates on them, for example, by modulating more into remote keys. The B section then concludes with a recapitulation of the A section material. Repeat the B section, and there you have it. Figure 2.15 shows the structure of the sonata.

Figure 2.15

Diagram for sonata structure.

The recapitulation of section A in the B section is not simply a repeat of the A section material. For example, whereas the Exposition cadences on a related key, the Recapitulation will remain in the tonic key.

2.9 Song Forms Many an audiophile’s main musical diet may exclusively consist of song form. You may often hear someone say, “I love that song.” However, the term “song” or “tune” can describe music with several variations as to the overall structure of the composition. The term can refer to any form that has a vocal melody with or without accompaniment and include instrumental “songs” as well. That is pretty broad! In fact, perhaps the most diverse of the forms we consider herein is the song form. “Lavender’s Blue,” discussed above, is a song form. Songs can also be binary (the earlier mentioned “Catches and Glees”) or ternary (Da Capo Arias from the Baroque era) in form. Song structure can depend on how you want to bring the ideas together, and for that the words sung can have a significant impact on its shape. The structure of a song might be shaped by the need to highlight a particular performer, such as a guitarist, and include sections set aside to give them the spotlight. For today’s pop music, one can describe it with a simple “generic” song form, as shown in Figure 2.16. See if you can identify a song with this structure on your own music library!

32 Form in Composition

Figure 2.16

Diagram for a simple, “generic,” song form.

Even with this structure as a general template, you may find many variants in the shapes of songs, including other features such as a third verse after the bridge, intros, pre-choruses, and instrumental sections. Although a song may last several minutes in performance or in an audio recording, the amount of composed material may be surprisingly less than you may think. A verse or chorus section might comprise repetitions of phrases with 2−4 measure lengths, combining to create an 8 or 16 measure period (we shall dive into this more in depth with Chapter 3). Actual unique material in a song may be as little as 4−8 measures of music, with the entirety of the song being made of repetitions of a main hook. Even though this may be the case, it does not mean that it should be thought of as bad music. That catchy hook may be all you need for a successful “song.” A common form in songs is the “bar form” with a structure to its phrases as: AAB. A bar form tune may or may not be repeated in performance with a strophic form approach if there is more than one stanza of libretto. The different stanzas of lyrics are sung with repetitions of the same melodic material in bar form. Here we have Bach’s Chorale Nicht so Traurig (BWV 384), which might be described as a “song.” The labeling A and B are noted at the beginning of each phrase in the structure (Figure 2.17).

Figure 2.17 Score to Bach’s Chorale Nicht so Traurig.

Twelve bar blues is based on the bar form. The A is the first four measures, with the I chord forming the harmony. The second A section slightly varies

2.9 Song Forms 33

the harmony, with two measures of the IV chord followed by two more measures of the I chord. Then, the B section (last four measures) uses chords V, IV, I, and I for completion of the set of 12 measures. Keep in mind, a 12-bar blues song can go a lot longer than 12 bars, or measures. This 12-bar blues structure is itself an element of the larger, more complex structures in many Blues songs. Let us take a look at Texas Flood, originally composed and recorded (1958) by Larry Davis, diagrammed below (the song, not Larry, that is) in Figure 2.18. Here, a shorter four-bar instrumental intro is a modified form of the beginning of the “A” and the end of the “B” section. Then, two consecutive 12-bar blues sections are played, with the vocals following the melody over them. Another four-bar instrumental intro section is used next, featuring a solo instrument to differentiate from the earlier intro. The song finishes with a third 12-bar blues section (Figure 2.18). This is a total of 44 measures, which if played one beat per second would come to 2:56. This is just over the actual 2:44 length of the recording.

Figure 2.18 Diagram for Texas Flood by Larry Davis.

Stevie Ray Vaughan expanded this song out to 5:20 with the 76-bar structure below (Figure 2.19). The tempo is even slower, since at one beat per second, this would be 5:04, just under the actual length of the song. The intro is followed by an early 12-bar instrumental solo. The two 12-bar vocal sections follow, as with the original song. Then, two 12-bar instrumental solos are fit in before ending with the familiar third 12-bar vocal section. Overall, Stevie has added 32 measures of instrumental solo, as gleaned by comparing the two structure diagrams.

Figure 2.19 Diagram for Texas Flood by Stevie Ray Vaughan.

Worth noting is the difference in form factor for the release of these two recordings. Larry’s composition was released on a seven-inch, 45 RPM

34 Form in Composition record, whilst Stevie Ray’s was part of a long play album (LP), giving it more room for expansion to highlight his guitar playing. Another form for songs common in popular music of the first half of the 20th century was the 32-bar song form. The name describes the number of measures composed based on an AABA structure. Here, each section is an eight-bar phrase. “Santa Claus is Comin’ to Town” (Haven Gillespie and J. Fred Coots), for example, uses a 32-bar form. It only takes about a minute to play through 32 measures of music; so, once again, performance and recordings use repetitions of the material to make up the overall “song” structure we know from our favorite versions. Even so, there still may be variance. Bing Crosby’s version of “Santa Claus is Comin’ to Town” is shown here (M. and F. are the male and female vocal parts) in Figure 2.20.

Figure 2.20 Diagram for Santa Claus is Comin’ to Town as arranged by Bing Crosby.

The arrangement gives the opportunity for multiple vocalists to shine, as well as add contrast with instrumental breaks. The original sheet music (Figure 2.21), however, has a different structure, including a 16-bar verse section describing how the omniscient narrator actually met Santa and now knows he is “Comin’ to Town.” This section is not known to most of us, as we usually only hear the chorus section!

Figure 2.21 Diagram for Santa Claus is Comin’ to Town as original written by Haven Gillespie and J. Fred Coots.

Other arrangements of phrase structure are possible and, again, we shall explore this more in Chapter 3. With the song “Quiet Nights of Quiet Stars (Corcodovo),” by Antônio Carlos Jobim, a variance on the structure is employed. Instead of the common AABA form, an ABAC arrangement of the phrases is used. The “C” portion of the structure is also longer, using

2.10 Fantasia 35

12 measures instead of the more common eight. This is due to a repetition of a figure at the end of the material. In a recording by Stan Getz and João Gilberto, the structure of recorded “song” allows for the spotlight of four performers, including an opening that curtails the later ABAC vocal structure to a simpler ABC structure (Figure 2.22).

Figure 2.22 Diagram for “Quiet Nights of Quiet Stars (Corcodovo),” by Antônio Carlos Jobim, as performed by Stan Getz and João Gilberto.

When you are structuring your songs, considerations for the arrangement may depend on a range of options from a simple structure focused on presenting a lyric with melody to more complex structures allowing the spotlight to shine on particular performers.

2.10 Fantasia Composers finding the forms above too constricting might instead turn to the Fantasia. The Fantasia (or “Fantasy”) is a composition that generally gives the impression of being improvised and offers no formal confines as to the shape of the composition. Instead, it is constrained only by the composer’s limitless creativity. Fantasy may be characterized by the linking of multiple sections that stitch together many themes, motives, or figures, and so demonstrates a composer’s ability to move “through more keys than is customary in other pieces” [Bach49], either closely or remotely related. The composition may or may not repeat any material as it unfolds. Its structure (Figure 2.23) is therefore rather open-ended.

Figure 2.23

Diagram for the Fantasia.

Here as an example, we offer a general diagram of Wolfgang Mozart’s Fantasy in C minor K. 475. The composition contains six individually characteristic sections with a return to the A section (though not an exact

36 Form in Composition replica of the A section that began the Fantasy) at the closing of the work (Figure 2.24). There are changes of thematic material, key, tempo, and even a change of time signature (sections E and F) with each new section. The scale of each section varies, with a range from 17 to 37 measures.

Figure 2.24 Diagram for Wolfgang Mozart’s Fantasy in C minor K. 475.

Compositionally, the piece of music may have sprung forth from Mozart’s mind, beginning to end. Or, he may have gathered up fragments of ideas he had not worked out into sonatas, concertos, symphonies, etc., and combined them to create this composition. Both approaches might work for new composers. It may, however, be a good idea to have a plan or lay out a general map to give a start to your new composition. Pick the form, improvise your style.

2.11 Other Structural Elements There are ways to sculpt your compositions beyond the rather spelled-out structures described above. Form may be stretched, and sections may be joined with other structural elements, bringing more interest to your compositions. Introductions may be added to the beginning of a work, prefacing the main material of the composition. The introduction may or may not contain themes that occur within the main body of the work. Some overtures, for example, barely touch any of the main musical themes of the rest of the composition. The tempo may be different, as well, a good example being the Grave section of the first movement of Beethoven’s Sonata “Pathétique, Op. 13.” The Introduction section sets the stage for the composition, leading into the Allegro section of the movement. For any structure of music, codas are often added to bring a more grandiose ending, or extending or delaying the anticipated resolution. For example, in a rondo where we have heard the complete A section several times, a coda might be added, giving a heightened end to the final return of the A section, which we have heard concluded several times throughout the composition (Figure 2.25).

2.11 Other Structural Elements

37

Figure 2.25 Diagram for a rondo with a coda.

Sonata form often incorporates a coda to conclude the movement, as well. The B section may or may not have a repeat sign before entering the coda or include the coda all together (Figure 2.26).

Figure 2.26 Diagram for a sonata with a coda.

A coda can be added to any composition; for example, appending a ternary form as shown in Figure 2.27.

Figure 2.27

Diagram for a ternary form with a coda.

In general, there are no particular rules or restrictions on how to structure the coda itself. Codas, therefore, provide one final chance for compositional creativity, akin to an encore. Within a work, there are ways to shape the structure between sections of the overall form. Transitions, bridges, interludes, episodes, codettas, and retransitions are examples of these insertions that often more smoothly connect two larger structural elements. These passages may aid in modulating to the different key of the new section or to serve as entrances of themes or subjects. Examples of including them in your structure are shown in Figure 2.28.

Figure 2.28

Diagram for a form with multiple transitions.

Figure 2.29 shows an Exposition in a Sonata form showing a transition between two main musical themes.

38 Form in Composition

Figure 2.29

Diagram for an Exposition in a Sonata form with a transition.

When it comes to the choice of macro structure you want to employ in your music, a lot may depend on the type of music that inspired you to want to compose in the first place. Analyzing your favorite music and creating a diagram of its structure is a great way to give you a model for composing. Answering the questions of “What roles do the sections serve the structure?” and “What instrument is performing them?” can help lead the way in making choices for your composition. Old dusty forms from musical eras past might just create a spark of inspiration leading you to say to yourself, “I can do that.” Form (the arrangement of material) is just one component in an overall composition. Style is part of the individuality you bring to the table. What do Duke Ellington, a traditional Christmas song, and Mozart have in common? Stylistically, you may say, “absolutely nothing.” But in fact, Duke Ellington’s song Heaven, the traditional Christmas song Deck the Halls, and the main theme of the second movement of Wolfgang Mozart’s Piano Sonata in D Major, K. 576 are all composed using the same form. The material that makes up these tunes, which might get a labeling of “A” in their overall construction, are all arranged in an AABA micro analysis, across the same duration of 16 bars of music. So you may be able to fit a “new feeling of music” into a well-worn form.

2.12 Sidebar – Creative Sources for Musical Composition Any attempt to codify creativity is almost by definition doomed to failure. Once you explain to someone how to be creative, it is now passé, and therefore no longer creative. This concern set aside, however, creativity can be thought of like the river in Herman Hesse’s Siddhartha. The river flows past the same point, looking the same from day to day, but the water that flows past is always different. Providing sources for creativity is the river; the actual creativity is the flow. In this sidebar, the flow of creativity is considered from a wide, but certainly not comprehensive, set of sources. Our magical dartboard of topics for creativity was trimmed to just four for this sidebar, intended to be different enough in approach as to give a view into the overall realm

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of creativity. The four creative sources discussed here are pharmacopoeia, phenomena, philology, and forcing functions. Pharmacopoeia may be the least surprising source of creativity in the music industry. Insert your own joke here, as LSD became a touted source of musical creativity at least as far back as the 1960s. And LSD did not mean Lennon’s Special Diet – or did it? The public view of mind-altering substance intake changes from decade to decade, and we intend to pass no judgment there. We do, however, recommend using any mind- or moodaltering ingredient, whether it be as ubiquitous and seemingly innocuous as caffeine or as rare and dangerous as foxy methoxy, at the lowest possible dosage, preferably less than or equal to zero. We want to make that clear. That being said, recent studies have shown that psychedelic drugs may be at least helpful in the treatment of alcoholism, PTSD, DMS-5 depressive and anxiety disorders, and terminal illness. Never mind that being born is a terminal illness! Why does a mind-altering substance lead to creativity? It is essentially a tautology − creativity is an alteration in the status quo. A change in the status quo is, all other factors being equal, a platform for greater creativity. This lends the discussion a much broader voice − from the perspective of chemically enhanced creativity − to consider as “pharmacopoeia.” For example, let us consider exercise. You perform yoga, hike up a hill, or swim a few dozen laps, and wham-o, you have got yourself a spicy set of endorphins. Endorphins have multiple mind-altering effects as they wend their way around your vasculature: they act like analgesics, which means aches, pains, and irritations that may have prevented creative focus are minimized. They reduce agitation, too, since they can act like sedatives. Studies have been performed [Colz13] showing the link between regular exercise and creativity: exercising four times a week improves creativity over that of being sedentary, though the authors are careful to point out that this depends on “the nature and the consequences of this link depend on the particular task and the fitness of the individual” [Colz13]. What else can alter the status quo of your mind? Travel, conversation, reading a good book, or anything pleasant is likely to have some effect, which leads us to the point that everything is psychosomatic. Willing yourself to be in a good mood is a chemical process. A placebo can be just as potent as a pill. A second significant source of creativity is phenomena, particularly natural phenomena. Observation of the temporal nature of, well, nature is a powerful source of creativity. Found objects are particularly useful in adding percussion to music. Hitting a garbage bin with a baseball bat is an example of found music, the endorphin rush of which may allow you to double down

40 Form in Composition on your creativity. Sampling is a more intentional form of found music, but it also adds certain constraints, which as in poetry can form an excellent channel for creativity. Taking a set of “found constraints” is, in fact, a potent form of phenomenological music creation. Neil Peart of Rush, for example, used the Morse code of “YYZ,” which happens to be the airport code for his native Toronto, as the stimulus for the song of the same name. In Morse code, YYZ is “Dash dot dash dash, Dash dot dash dash, Dash dash dot dot,” which is the meter of the drum beat for the song. By the same approach, “Eine Kleine Nachtmusik” by Mozart is KAAA in meter. In other words, Mozart could have got the rhythm for this famous work from the Morse code of K, A, A, and A, in sequence. Take your own name and make a rhythm of it using Morse code. If your name is Ana, for example, then your signature knock should henceforth be “Dot dash, Dash dot, Dot dash.” Perfect for 3/4 time signature! Just sprinkle on the instrumentation. Other natural phenomena include birds on a wire, with the spacing between them indicating the timing of the notes. If the birds are mapped to 12 colors − for example, red, green, blue, cyan, yellow, magenta, white, light gray, mid-gray, and black − then these 12 colors can be mapped to each of the 12 notes; for example, red = A, green = A-sharp (i.e., B ), etc. Birdsong can be turned into written music in a number of ways, including directly sampling and using the principal frequencies for chords or single chords. Other natural phenomena used include compositions based on irrational numbers like π and e, and sampling the output of noisy signal generators for “random” notes. The third source of creativity in this section is philology, or the study of language. Language could in one sense be viewed as a “natural phenomena,” in which case the same rules as above could apply. One interesting means of mapping language to music is through parts of speech. Suppose that we are in a particular key. Then we could map parts of speech to the most common notes (say, the first, fifth, and forth notes) in the key. For example, noun = first, verb = fifth, adjective = fourth, adverb = second, pronoun = third, preposition = seventh, conjunction = sixth, interjection = accidental, and article = jump octave. In the latter two cases, the note following it determines which note to have an accidental and which note in the nearest octave to play, etc. A lot of different possibilities exist. In the key of C major, then, the sentence, “I went home at nine” would be “third, fifth, first, seventh, first” or E, G, C, B, C. But language does not end on the concept of found music. Music can also be constrained by convention, or rules, along the lines of poetry. Music is of course often sung with rhyming couplets. Rhyming octets especially work well with 4/4 time. Occasionally, you will find an accidental (pardoning the

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musical pun) crossover, such as when the Cars, in “Dangerous Type,” sing an iambic pentameter: “My curiosity’s got me tonight” Iamb implies unstressed−stressed pairs making up the (even number of) syllables. This can easily be accommodated using staccato for every other note. Other forms of poetry – from Haiku and Limerick to more sophisticated poetic meter such as in ballads − can readily be adapted to music. The hymn Amazing Grace uses the iambic tetrameter/trimester combination to good effect: Amazing Grace! how sweet the sound That saved a wretch like me; I once was lost, but now am found; Was blind, but now I see. Emily Dickinson is a great poet who uses the same balladic meter often. The following could easily be an additional verse in Amazing Grace: Because I could not stop for Death – He kindly stopped for me – The Carriage held but just Ourselves – And Immortality. The success of this meter stretches from the banal (Gilligan’s Island theme, which irritatingly serves as an excellent musical vehicle for Emily Dickinson’s wonderful poem) to the inspirational (America the Beautiful, Joy to the World) and shows the obvious connection between poetry and music. To add creativity, though, why not try a meter matching something personal; for example, your zip code or phone number? Or match the notes to your name, like BACH famously did with his B -A-C-B series of notes (H in German music Is B). If your name, like ours, does not fit into the range A−G (with the possible force-fitting of H), try its modulus and check out the notes. For example, if A−Z is labeled 1−26, then the letter “S,” which is the 19th letter, maps to 5, since 19 modulo 7 is 5. Thus, “Steve” becomes the note sequence 5-6-5-1-5, which in the key of C major is G-A-G-C-G (certainly not an unpleasant sequence). “Jeff,” meanwhile, is 3-5-6-6, which in C major is E-G-A-A (try this; for me, it naturally moved to quarter-quarter-eighth-eighth notes). The final stimuli for creativity discussed in this sidebar are forcing functions. A forcing function is a type of design constraint that “forces” attention

42 Form in Composition to be paid to it, thus redirecting the normal development cycle or performance of a task. I used to write meeting Haikus, with one that I was proud of being: The department of Redundancy department Brings you this meeting But Haikus are potentially even more interesting musically. For example, taking the traditional 5/7/5 Haiku, we could also enforce a pentatonic, heptatonic, pentatonic scale to be enforced over the appropriate elements of music (notes, measures, etc.). Feel free to mix and match these creative sources as you continue to compose!

2.13 Summary This chapter describes how to use style and form for music composition. The form is the structure behind the composition, and shorthand structures of note are introduced, including AA, AA’, AB, ABC, and more complicated structures leading to freeform and improvisational composition. Style is shown to be largely independent of form; in fact, you can use the form of an ancient piece of music such as a sonata as the basis for pop, hip hop, or other modern musical compositions. The style is your personality woven over the form, whether it is binary, variation, ternary, rondo, sonata, song, or fantasia. With these forms, you now have templates to begin composing, from the conceiving all the way to the producing of your own compositions. The chapter concluded with a sidebar highlighting some of the creative sources for aiding musical composition.

References [Bach49] Bach CPE, “Essay on the True Art of Playing Keyboard Instruments,” translated and edited by William J. Mitchell, W.W. Norton & Company, Inc., p. 430, 1949. [Box86] Box GEP, Meyer RD, “An Analysis for Unreplicated Fractional Factorials," Technometrics 28 (1): 11–18, 1986. [Colz13] Colzato LS, Szapora A, Pannekoek JN, Hommel B, “The Impact of Physical Exercise on Convergent and Divergent Thinking,” Front. Hum. Neurosci. 7:824, 2013.

2.13 Summary 43

[Copl53] Copland A, “What to Listen for in Music,” New York, Penguin Books Ltd., 1953. [Mers72] Mersmann H, ed., “Letters of Wolfgang Amadeus Mozart,” New York, Dover Publications, Inc., 1972. [Quin17] Quinciani L, “Udite lagrimosi spirti d’Averno, udite,” Creative Commons arrangement by Simon M, originally posted 13 November 2017, accessed from IMSLP.org at https://imslp.org/wiki/Udi te_lagrimosi_spirti_d’Averno%2C_udite_(Quinciani%2C_Lucia) on 30 June 2022. [Stra75] Straight and Skillern, “Two Hundred and Four Favourite Country Dances,” vol. 1, No. 74, p. 37, 1775.

3 Phrase, Period, and Expression

Beauty of expression is so akin to the voice of the sea – George Matthew Adams My music is the spiritual expression of what I am – my faith, my knowledge, my being – John Coltrane

Abstract The starting point for composition is the phrase. Related musical terms are melody, figure, subject, passage, and riff, each of which is discussed here. Next, an introduction in using rhythm, melody, and harmony together is provided. Mixing phrases into larger chunks of music, called periods, is then illustrated through techniques such as antecedent/consequent phrase pairing. Arrangements are shown to be specific sequences of periods. Mixing at different scales − including two, three, and four measures − is shown to provide nearly limitless possible arrangements, and even more means of musical expression. The sidebar for the chapter addresses sources of creativity (including poetry) and how these contribute to musical expression. Keywords: Antecedent, Consequent, Expression, Figure, Harmony, Hook, Measure, Melody, Motif, Passage, Period, Phrase, Rhythm, Riff, Subject.

3.1 Introduction We start this chapter with a simple premise: once you have a few musical phrases, you will have a large set of ways in which to use them together. As we build from smaller phrases to larger periods of music, though, we will find that our minds start to select phrase sequences based on prior experience.

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46 Phrase, Period, and Expression This is another way of saying that the more you compose, the better you get at composing. So, why wait? Start composing from the moment you start learning music! In this chapter, we will introduce some of the tradeoffs made in composition, which can hopefully keep you from ever feeling “stuck in place” when you try to compose. The key to composition is providing something of interest to your target audience − whether it be soothing and reassuring or provocative and dissonant. Your music, and your expression of it, will provide value to a given target audience. Maybe it is akin to the voice of the sea, per George Matthew Adams’ quote, if you want to relax and refresh your listener. Maybe it is a whole lot more (per Coltrane’s quote). Either way, having a goal in mind is a way to focus your creativity. Let us begin.

3.2 The Phrase The starting point for anyone wanting to compose music is the creation of a musical phrase. Phrases are then repeated or connected with other phrases to form larger segments called periods, then moving up to form larger sections and so on to complete pieces of music, or compositions. Though a composer may have decided a specific form to compose within, the beginning efforts will be with this smallest unit of the composition, the phrase. This is a way to reduce, or at least defer, the stress of initiating your composition. It also acknowledges the reality that complete pieces of music usually do not come out all at once. The composer starts with phrases and then combines them, building up to the complete structure of a finished piece. Any piece of music you look to as a model will have a structure to its phrases. And even though there is a different classification between “Art Music” and “Popular Music,” when you look at their construction you can find similarities even if their use or audience is not the same. The opening of a piece in classical sonata form, a single melody line of tune, or a catchy guitar riff all give great examples of this foundational element of music. Phrases of music can have a catchiness that brings out a listener’s desire to hear it repeated within the composition. Part of the catchiness comes from the composer’s ability to internalize structure into their composition. A good composer makes this happen such that you may not even notice it afterwards. Like a good invention (the patentable type, not a musical “invention”), it seems obvious afterward. Many composers (we, no doubt, included in this group on occasion) have a tendency to look down on pop music, for example, because it seems so simple and therefore, one presumes, easy to compose. Aha! Similarly, it is really easy to understand an iPhone after it is invented,

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but we never had it until 2007 (a good 50 years after transistors were readily available). Good music, like good inventions, seems “obvious” after it is composed precisely because the composer knows how to internalize the structure of the phrase into their composition. A riff, then, is long enough to move to the background or reappear in the foreground throughout the song. This structure then provides a canvas for the singer to put their own melody on top of. These riffs are catchy, in part, because they fulfill our expectations for the length and repeatability of the phrase. But, if used too often or in the wrong place, they can be monotonous, even dissonant. If used too little in a song, the listener might think, “Dang! That was the good part, why didn’t they repeat that a little more?” Balancing these considerations while also responding to the other constraints of harmony, melody, variation, and the like requires the mental dexterity of a chess player. That does not sound so easy now, does it? Having said that, let us make sure that the terminology sometimes employed here is not an impediment to your understanding moving forward. We will quickly make you comfortable with the terms “melody,” “figure,” “subject,” “theme,” “passage,” and “riff.” They are all related to the term “phrase” introduced above, and some might even say that they are synonyms; so we will make the distinction between these terms in the following few paragraphs primarily to highlight the richness of this set of terms. English, after all, is a language filled with redundancy (or should I say repetitiveness? Or superfluity? You get the point. . . ), but typically multiple terms for related concepts are there only because they are needed for the subtle differences in meaning of a rich topic. And, musical phrases are the Croesus of human experience. The “melody” is a sequential set of pitches that, in general, has meaning to its audience. It is perhaps the most important identifier of music. There are many elemental ways to differentiate a blues song from a classical minuet. One of these would be by recognizing the harmonic structure of the 12-bar blues of which a minuet would not use. But how do we differentiate between many different blues songs based on the same chord sequence? Even if the lyrical content is removed, we can identify each song because of the melodic fingerprint. The choice of pitches that form the melodies can come from many different scales, and from many different musical sources. Each can give a unique flavor to each composition. Thus, not surprisingly, melodies “make sense” to their target audience. An audience of blues music expects the signature sound of a blues scale just as someone seeking out a Halloween song expects something from a minor scale. This expectation fulfilled is

48 Phrase, Period, and Expression termed accessibility. The concept of accessibility is often used dismissively toward, for example, pop music. “That song is so accessible” is often another way for a music snob to say, “that song is so predictable.” But remember, predictability is often comforting, particularly when melody is the tapestry for other musical innovation or even other events (such as working on one’s writing or working in a production line). Within the context of a particular musical style, melody helps to reinforce the expectations. This provides the composer with a rich variety of tools to “go against expectations,” adding wonderful variety to the comfort of the expected. Think of P.D.Q. Bach “compositions” and their musical “satire” of the expected compositional flow of classical music. Melody, or the tune, is a way of calibrating the audience’s expectations. The concept of “figure” means a pattern used to ornament the rest of the musical piece. Some folks define it as “background” as opposed to a motif being “foreground.” However, it is a short set of notes that provides a pattern easily recognizable throughout a work. It might be used in audio−visual media (like, say, a Netflix series) to accompany a change in scene. Figures can be used to stitch together a piece of music that is otherwise disjointed in nature, possibly intentionally. The repeat of a figure gives the audience confidence that, yes, they are still listening to the same piece and the composer actually did intend it to be this confusing. In more common use, the figure is a small characteristic portion of a phrase that might be used elsewhere compositionally in the piece of music. Coming to the “subject,” here we have a phrase (or multiple phrases in sequence) with specialization. A subject is thus a phrase upon which a musical piece is rather highly dependent. For example, in a fugue, the subject is presented first by one voice; thereafter, the other voices pick up the subject. Later in the composition, the subject material is used as the basis for musical manipulations such as inversions, key changes, and augmentations/diminutions. The subject is therefore a “king” phrase with its own following of, ahem, subjects (if we may borrow obliquely one of the best lines in the movie Ridicule, “the king is not a subject”). Related to the subject is the theme. The concept of a leitmotif might be the best synonym for a theme. Darth Vader or Princess Leia appears, and a different musical phrase accompanies their entrance or the beginning of their scene. Classical (or Pavlovian) conditioning in action! If you, for example, horked down a mouthful of popcorn every time Vader entered a scene, due to stress or simply appreciation of his steam punk uniform, you are being conditioned. You go home, and your child plays the Darth Vader

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theme (or leitmotif, which is certainly synonymous here) on the piano, and you find yourself grabbing the butter dish and the Orville Redenbacher. You are Pavlov’s salivating dog in human form. The theme has worked its magic. Next is the passage. This is a phrase that is of indefinite length that typically relates to other phrases in the musical piece. As such, it is not necessarily self-contained (as opposed to a subject, theme, or even a riff, discussed next). In Rush’s “A Passage to Bangkok,” a passage to bring forth is the so-called “Oriental riff” that follows the opening guitar riff to transition the music from instrumental to choral sections. This passage, a somewhat stereotyped depiction of East Asian music (it was, after all, a “Western” creation), is used to tie the rest of the hard rock music to the theme of Thailand (and other parts of the world famous, at least in 1976, for their cannabis). The passage is not essential to the music, but it does connect the listener to the intent of other parts of the piece. A passage, if we use an analogy of a person, can be everything from an appendage to an apprentice − a helping hand of some sort but not the leader. That being said, a passage can also be used as a flourish to virtuosity, as an “appendage” to a jazz, rock, or even pop composition. We finish our tour of terms with the riff. As noted above, this is a generally melodic, or “catchy,” phrase that is repeated. Famous riffs abound in rock, including the openings of “Satisfaction,” “Seven Nation Army,” and “Day Tripper” (see below). But all musical forms have hooks and riffs. The riff might be the first few measures of guitar introducing Heart’s Barracuda. Riffs are often used to jog someone’s memory when you say “do you like that song?” and the answer is “what song?” Hum the riff, they will know which song. You may be wondering where “hook” fits in to all this. Hook combines some elements of expectation with creativity. An example of hook is AWOLNATION’s spoken text, “run,” in the middle of the eponymous song, which stands out melodically from the surrounding “alternative rock” portions of the song. The quietly spoken “run” is ironically placid against a background of horror and angst in the rest of the song. It would be completely unexpected, for example, in a Nirvana song, wherein the transition between the two sections likely occurs instantly, without the interposed “run” being spoken. A hook might be the part your confessor remembers about “Eine Kleine Nachtmusik” if you are a Salieri fatally envious of Mozart in the movie Amadeus. You might have a different sense for these terms than we do. And that is okay. The point of our explaining these terms was not to be didactic or

50 Phrase, Period, and Expression even exact-ic. We wanted to show the broad range of perspectives that one can have when thinking of a musical phrase. There are many ways in which a phrase can be used compositionally, whether it be for melody, harmony, counterpoint, development, variation, transition, or something you yourself define. Now, we will explore a few specific uses of phrase that will, hopefully, inspire you to tackle composing your own. The term “phrase” is used with some degree of flexibility. At the small level, in what Arnold Schoenberg describes as “what one could sing in a single breath” [Scho99], the phrase is typically notated in a space of 1−4 measures. The most common of these is the two-measure phrase that can be found in all styles of music from “Art” to “Popular.” Think of the familiar repeated opening guitar riffs in the Beatles’ song “Day Tripper” and the White Stripes’ song “Seven Nation Army.” Each of these riffs comes rounded out in a nice two-measure package. A similar two-measure length is used for the famous four opening notes of Beethoven’s fifth symphony. Good things do indeed come in small packages. Here we have a phrase example from the seasonal song Jingle Bells (Figure 3.1). The phrase, though not a long one (comprising only a short two-measure), demonstrates what a singer might sing before taking a breath. Although four eighth notes filling a measure might seem intact unto itself, this phrase gains a sense of completeness and balance by landing in the main beat of the second measure.

Figure 3.1 Beginning of the seasonal song, Jingle Bells.

The flexibility in the usage of the term “phrase” is now seen with the addition of the second phrase (Figure 3.2). Though it steals a half beat of time from the first phrase for the addition of a pick-up (corresponding with the lyric “In a”), the second phrase is a repetition of the first up until the last note where a change in the accompanying chord harmony leads to a different ending pitch. This difference also sets the composer up to go in a different direction musically, although she may just use it to add some variety and expectation to the piece. Combined, these two short phrases might also be

3.2 The Phrase 51

referred to as a single, longer “phrase” describing a more complex, yet more complete, idea.

Figure 3.2 First two phrases in Jingle Bells.

The terminology need not be too rigid lest it make for formulaic phrase construction. Just as in grammar and speech, some sentences may be longer than others, having their clauses (a clause is the grammatical equivalent of a phrase, including coordinate and subordinate clauses that might have an equivalent with parts of a composite phrase) divided with commas or having the attachments of prepositional phrases. As we look at phrases, they seem to exhibit two parts: the initial tension of existence and its relaxation. Generally, this might be likened to an inhalation and an exhalation. In our “Jingle Bells” example, for instance, the initial tension would be along the lyric “Dashing thro’,” and the relaxation along “the snow” where the phrase lands on a main beat of rhythmic stability in the second measure. No matter the length, phrases generally demonstrate some sort of weight and counterweight in terms of completeness. Here we have some notated examples of phrases from the common length of two measures. They all exhibit a sense of tension and relaxation and yet are all confined in the two-measured time span and have their own individual characteristics and time signatures. The first one is Amy Beach’s In Autumn Op. 15, No. 1 (Figure 3.3):

Figure 3.3 Phrase in Amy Beach’s In Autumn Op. 15, No. 1.

Here the upward motion without a corresponding downturn may seem to avoid a relaxation, but the doubling of the note values across the phrase brings about the sense of stability and completeness ready for repetition. Next, we have two examples with a definite sense of relaxation. The first is from Giuseppe Verdi’s La Donna e Mobile (Figure 3.4).

52 Phrase, Period, and Expression

Figure 3.4 Phrase in Giuseppe Verdi’s La Donna e Mobile, illustrating relaxation.

Ravel’s Pavane pour une Infante Défunte is the second example of relaxation (Figure 3.5).

Figure 3.5

Phrase in Ravel’s Pavane pour une Infante Défunte, illustrating relaxation.

The next example is the famous riff from the Beatles’ Day Tripper, which can be accessed from YouTube along with the musical score (https://youtu.be/O67LzW2XxCk, accessed 8 August 2021). Here, the riff provides relaxation by ending exactly one octave above where it started. Next, we move on to phrases across another common span of four measures. The same idea of tension and relaxation still applies. The first is from Haydn’s String Quartet in Eb Major, Op. 50, No. 3, III. Menuetto, Allegretto (Figure 3.6).

Figure 3.6 Phrase in Haydn’s String Quartet in Eb Major, Op. 50, No. 3, III. Menuetto, Allegretto, illustrating tension and relaxation.

The second (Figure 3.7) is from Isaac Albeniz’s Capricho Catalan from the suite Espana.

Figure 3.7 Phrase in Isaac Albeniz’s Capricho Catalan from the suite Espana, further illustrating tension and relaxation.

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The third (Figure 3.8) is from the composer Erik Satie’s First Gymnopedie.

Figure 3.8

Phrase in Erik Satie’s First Gymnopedie, again illustrating tension and relaxation.

The fourth example of a four-measure phrase is the keyboard riff in Van Halen’s Jump, also available on YouTube (https://youtu.be/ACtqCRWGq2k, accessed 8 August 2021). Though phrases based on the even numbers two and four are the most common, it is not hard to find examples of other lengths: phrases across odd number lengths exist with some frequency as well. Here we have some phrase examples of one measure. The first is Vivaldi’s Concerto in E Major: La Primavera, RV 269, I. Allegro, shown in Figure 3.9.

Figure 3.9 Phrase in Vivaldi’s Concerto in E Major: La Primavera, RV 269, I. Allegro, illustrating a phrase of one measure.

The second is Scarlatti’s Sonata in G Minor, K. 88 L. 36, shown in Figure 3.10.

Figure 3.10 Phrase of one measure in Scarlatti’s Sonata in G Minor, K. 88 L. 36.

The third example (Figure 3.11) is from Mozart’s Piano Sonata in C Major K. 309 (284b) II. Andante un poco adagio:

Figure 3.11 One-measure phrase in Mozart’s Piano Sonata in C Major K. 309 (284b) II. Andante un poco adagio.

54 Phrase, Period, and Expression Schoenberg’s Verklärte Nacht Op. 4 is the fourth example (Figure 3.12).

Figure 3.12 One-measure phrase in Schoenberg’s Verklärte Nacht Op. 4.

As another set of examples, some phrases comprising three measures, is provided. The first (Figure 3.13) is from the 15th century melody used in the Christmas hymn, O Come O Come Emmanuel.

Figure 3.13 Phrase of three measures in the Christmas hymn, O Come O Come Emmanuel.

The second (Figure 3.14) is from another 15th century chorale melody Allein zu dir, Herr Jesu Christ.

Figure 3.14 Three-measure phrase in the 15th century chorale melody Allein zu dir, Herr Jesu Christ.

And finally, a three-measure phrase from Joaquín Rodrigo’s Concierto de Aranjuez I. Allegro con spirito is available on YouTube (https://youtu.be/JCO 5LGGWvus, accessed 9 August 2021). What do we make of a phrase like the subject of Bach’s Invention in C Minor BWV 773 (Figure 3.15)? It is a phrase that exists in the common span of two measures but seems much more complex than any example we have seen above. Its many peaks and valleys give the impression of many phrases within the normal two-measure span. If we look at each grouping of beamed 16th notes, we see this phrase has more than one implied harmony with many smaller note values across them. If we dissect the phrase by stripping back some of notes, we find a

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Figure 3.15 Complicated phrase from Bach’s Invention in C Minor BWV 773.

Figure 3.16 BWV 773.

Stripping back of the complicated phrase from Bach’s Invention in C Minor

more skeletal version that resembles something closer to the phrases we have presented earlier (Figure 3.16). In this phrase, the non-harmonic tones (aka passing tones or neighbor tones) are removed, leaving behind the skeletal version of the phrase based on the principal notes of each grouping. The skeletal version is not just sampling the notes at every eighth beat. Instead, it represents a cohesive, self-contained, though simpler phrase. Both phrases “make sense” musically. Reverse engineering phrases like this can aid in finding ways to increase the complexity of your own creations. Examples outside of the normal one- to four-measure phrase duration are rarer, but, as we see below (Figure 3.17) with the Kyrie eleison from Palestrina’s Missa Brevis, a phrase across five measures is possible. It should be noted that this is a modern notation for this example. The original score document does not use bar lines.

Figure 3.17

The Kyrie eleison from Palestrina’s Missa Brevis.

Palestrina was likely not interested in the danceability of this music; so the regularity of a beat and a looping riff is not a consideration for this type of phrase. This phrase is a musical thread that weaves into a larger tapestry of polyphonic texture. Worth noting, we could re-engineer this example from

56 Phrase, Period, and Expression Palestrina into a four-measure duration by reducing parts of it to down the main melodic points (Figure 3.18).

Figure 3.18 Re-engineering of the Kyrie eleison from Palestrina’s Missa Brevis to be a fourmeasure phrase.

The general directional goal of the phrase is still achieved, though it is certainly not in as pleasing a manner as the original. Learning to manipulate phrases is the idea here. If you were to have started out with the four-measure example in your own composition and were not satisfied with it, you can see how adding some melodic play around certain notes (in this case the last three notes of our example) can enhance and create a much more flowing phrase. Thus, we can either take or leave the idea of staying within a certain duration of measures. In Figure 3.19, we have the opening phrase from Beethoven’s Piano Sonata, Opus 2, No. 1. It is a very focused two-measure phrase revolving around an ascending F Minor arpeggio. This also gives a great example of tension and relaxation.

Figure 3.19

Opening phrase from Beethoven’s Piano Sonata, Opus 2, No. 1.

Again, we can explore the idea of manipulating a phrase by expanding this example from two measures to three. It is only a question here, for purposes of this section, of whether it can be done, more so than whether the result is of any merit. When coming up with an idea for composition, it is an idea of identifying what you have to start with and how you can direct the material. For this phrase, we offer two realizations; the first (Figure 3.20) inserts material into the middle of the phrase, which interrupts the focused upward motion but gets back on track to reach the ascending goal of the high Ab.

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Figure 3.20 Manipulated opening phrase from Beethoven’s Piano Sonata, Opus 2, No. 1.

The second offering (Figure 3.21) reworks the arpeggio of the first full measure with repetitions that lengthen the duration of the ascending journey.

Figure 3.21 Reworked opening phrase from Beethoven’s Piano Sonata, Opus 2, No. 1.

In the end, even if we have distorted the focus of the original phrase, we achieved successful phrases that still work musically in a space of three measures. Just as a sculptor shapes stone, a composer can shape a phrase. Having an awareness of the space you are working within provides assistance in constructing the shaping of your compositional goals and in providing completeness for them. Once a complete phrase is decided upon, the general tendency may be to repeat it. The repetition of a phrase is usually observed starting from the same point of rhythmic placement in a measure. This tendency gives the listener a predictability as we have with a one-measure phrase from Alexander Scriabin’s Desir Op. 57 (Figure 3.22).

Figure 3.22 Repetition of a one-measure phrase from Alexander Scriabin’s Desir Op. 57.

The main body of the phrase exists on the first half of the measure, with the repetition in the same position of the second measure. However, Scriabin creatively inserts a chromatic lead-in ahead of the phrase repetition, which did not occur with the original presentation. Presumably without the leadin, the space would have otherwise only been occupied by rests. With the

58 Phrase, Period, and Expression addition, there is now more interest and emphasis placed into the phrase and the measure is filled. Any time you set a rule, you will certainly find examples of them being broken. The predictability of a phrase recurring in a reliable place for the listener can be pleasantly ignored to add interest to a piece. Next are two examples of phrases that break from the conventional norms. The initial phrase from the first movement of Ravel’s Sonatine, I. Modere (Figure 3.23) begins with a pick-up into beat 2 of the measure. The phrase is not typical as it has a duration of two and a half measures. Ravel gives a repetition of the phrase, and here it now has a pick-up into beat 1 of the measure. With this repetition, the extra half measure of the material is removed, and the phrase assumes a more expected duration of two measures.

Figure 3.23 The initial phrase from the first movement of Ravel’s Sonatine, I. Modere. Note the pick-up beat at the onset.

Our next example is from another Scarlatti keyboard sonata (Sonata in B Minor K.197, L. 147) and features an irregular phrase duration of one and a half measures (Figure 3.24). This is followed by a change in placement of the phrase upon repetition.

Figure 3.24 Phrase from Scarlatti Sonata in B Minor K.197, L. 147, featuring an irregular phrase duration of one and a half measures.

Could we rework this phrase into a complete two-measure? As an exercise, sure. But it would not have the interest provided by the original, irregular composition, would it? The point here is that phrases exist in small, easily manageable spans of time that should not be considered intimidating. Just as we can speak in sentences in a conversation about whatever is on our minds, so too when composing we should be able to come up with many phrases of music that provide candidates for the larger composition. What qualifies a phrase as

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a “good” one worth creating a composition out of? Who knows? But we certainly know one when we hear it. Different people will have different opinions on this. And they should, as it leads to variety. A phrase might just be some descending steps or an arpeggio. Maybe it is some rhythmic aspect or a particular interval in the melody that draws us in. The opening phrase of Beethoven’s fifth symphony is just three repeated notes that then descend a major third to a fourth note. There is nothing particularly extraordinary in this description, but this phrase immediately catches our attention when we hear it. In the end, composition comes down to what you do with the phrases in terms of ordering them, transitioning between them, and deciding how often to repeat them. Phrases are the building blocks of much larger compositions; so no matter what terminology you incorporate to describe the phrases in your music and no matter what style you compose in, they will still exist within the confines of a few measures. Once you find a phrase, riff, hook, or theme, what you do with it from there is the where the composing begins. Just as the step of a thousand miles begins with a single step, so too does the composition of a thousand seconds begin with a single measure. If each step gets you a few feet closer to the destination, you can already envision the entire journey in a single step. Each measure gets you closer to what you want to compose overall; so measure by measure, you can create whatever musical recipe you like. Let us now look at some of the ingredients in this recipe.

3.3 Ingredients: Rhythm–Melody–Harmony Just as bakers must bring ingredients together for their craft, so too must the composer bring ingredients together to form a phrase. The baker brings together water, flour, and yeast to make bread; a composer brings together the core ingredients of rhythm, harmony, and melody to create phrases of music. These ingredients create the characteristic DNA of each phrase. The consideration of an individual ingredient can quickly bring to life the other ingredients participating in the recipe. Ignoring an ingredient can result in a less memorable or incoherent phrase. There are certainly other ingredients to add to the recipe, such as the instrument or instruments that will play the phrases (timbre or tone color/instrumentation), how the notes will be dispersed among these instruments (orchestration), and performance considerations (dynamics/articulation). However, the core of compositional creation is the rhythm, harmony, and melody. Other teachers have shared similar experiences to those I have had when assigning composition to a student. Whether in a high school theory class or

60 Phrase, Period, and Expression in a private lesson, they are sent home with an assignment to compose something (anything!) and at the next session they present meandering measures of music filled with many small note values lacking in a sense of character or direction. The problem here is they began their “baking” without bringing all of the key ingredients from the pantry. They looked at the blank measures and felt that they had to fill them with as many notes as possible. Quantity over quality bias? Regardless, the rhythm and melody have no meaning because there is no sense of harmony to back them up. Not that having a lot of notes means that the composer has to meander like a river through Ephesus. The following (Figure 3.25) passage is extracted from J.S. Bach’s Prelude in Eb Major BWV 852 from “The Well-Tempered Clavier, Book One.” There are many small notes to fill the measure, yet all three ingredients are satisfied in this group of figures making up the phrase. The notes, even though many in this measure, do not meander but work together to create the desired “fullness” of the phrase.

Figure 3.25 Phrase from J.S. Bach’s Prelude in Eb Major BWV 852 from “The WellTempered Clavier, Book One,” illustrating a pleasing wholeness.

The figures work their way along key notes attached to the backdrop of two implied harmonies (Bb7 and Eb Major). The first figure starts on the third of the Bb harmony (D), making its way to the root (B flat) before dipping down to its leading tone (A natural). The second figure, after stepping back up, begins on the root (Bb) and follows the same melodic path down to the fifth of the Bb harmony (F). The figure passes through the pitch Ab, which turns the implied harmony from Bb Major into Bb7, setting up the new harmony of Eb Major. The cycle starts again with the same melodic figures across an Eb harmony. The third figure moves from the third of the harmony (G) down to the root (Eb) and its leading tone (D). And, finally, the fourth figure moves from the root (Eb) down to the fifth (Bb). Ending a phrase on the fifth of the chosen key satisfies the listener’s expectations, because that

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Figure 3.26 Phrase from Scott Joplin’s ragtime waltz, Pleasant Moments.

was set up at the beginning of the measure, and even with this “constraint,” the composer can choose from many possible paths to move from the first to the fifth. Any of the three ingredients (rhythm, melody, or harmony) can become the starting point for compositional invention. A specific rhythm or meter may lead the way. The rhythm of a particular style of composition might demand a specific meter. Specific rhythms or meter may be required for a characteristic style. Additionally, a particular scale may be employed for a particular sound. Harmony might only be made from simple primary triads or may demand the more sophisticated harmonic sound from complex chord structures. Here we examine some phrases with clear examples of the three ingredients. The first is from Scott Joplin’s ragtime waltz, Pleasant Moments (Figure 3.26). Ragtime, usually in duple meter, is noted for its syncopated rhythmic placement of melody. To compose a ragtime waltz, Joplin had to make the obvious meter change to triple meter. The rhythmic aspect of the upbeat syncopation characteristic of ragtime style is retained, creating a hybridization of two styles. Harmonically, the phrase is interesting due to the use of four different harmonic changes across the two-measure phrase. All three ingredients are clearly present.

3.4 Connecting Phrases Once a composer finds a phrase that they deem worthy of nourishing, the task moves to expanding or growing that seed into something larger. Generally, this is done by compounding the phrase based on even numbers. A twomeasure phrase pairs with another two and doubles to four, and those four measures double to eight (2 + 2) + (2 + 2). At this point, you have what is

62 Phrase, Period, and Expression called a period of music, an assembly of phrases that, under normal conditions, bring about some sense of completeness. Phrases can work together in what is known as antecedent and consequent groupings. The initial phrase (antecedent) is balanced with another phrase in succession (consequent). This terminology works at the 2 + 2 measure level as well as the 4 + 4 measure level. Figure 3.27 provides an example of a period of music from the third movement of Wolfgang Mozart’s Horn Concerto in Eb, K.417.

Figure 3.27 K.417.

Period from the third movement of Wolfgang Mozart’s Horn Concerto in Eb,

The period is eight measures in length and is constructed from four two-measure phrases. At the smallest level, the first two phrases form an antecedent and consequent grouping themselves and, in turn, the second two phrases form their own grouping. At the larger level, the first four measures create an antecedent, and the second four measures act as the consequent to form a complete period of music. If we were to label each two-measure phrase, the arrangement would be ABAB’ since the antecedent phrases are the same and the consequent phrases start similarly but have different endings. The period structure of eight measures is a very common duration in the construction of music. Though found in all styles of music, it is also the typical duration of measures for verses, choruses, and bridge sections in popular music. The so-called “bridge” section of a song, the part that gives contrast to the sequence of verse-chorus in the common song structure, is also known as the “middle eight.” Here, the name of the section is telling songwriters just how much material they need to come up with to create a break in the repetitive nature of the form. Fans of EDM (electronic dance music) know exactly when the “drop” will occur in the music because it will come at the start of a new cycle of eight measures. Even in a music style with

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a high frequency of repetition, the perception of time in regular groups of measures is predictable and thus something listeners can rely on. Though our examples have mainly displayed the melodic and rhythmic aspect of a phrase, the harmonic backdrop also displays coherence unto itself in terms of the structure of measures. A structural cycle of chords can lead the way for a melody to be “threaded through” across a duration of measures or be a secondary consequence of a clearly formed melody from a composer’s mind. If we look to the harmonies of these phrases, they have a sentence structure unto themselves even if you strip away the melody to have a glimpse at the background. If you were to play the succession of harmonies in the main pulses of the meter that each melody exists, you can still get a sense of the structure to the phrases and their one-, two-, three-, or fourmeasure durations. The harmonies can also be used as a sneak preview for what the accompaniment might be in the final arrangement. Thus, playing this succession of harmonies is not only a good way to prepare yourself for composition; it is also a great way to start your practice of a piece that is already finished. We see here, therefore, a tight connection between practicing and composing. The popular Christmas song “Have Yourself a Merry Little Christmas” (https://youtu.be/7D-hJq-U8-k, accessed 30 September 2021) uses the typical 32-bar AABA song form (Figure 3.28). Each section is a period of eight measures. The vocal melody of the “A” section period comprises three phrases in a 2 + 2 + 3 arrangement, which of course does not add up to eight. The last note of the melody falls on the first beat of the seventh measure in the period. This final note is sometimes notated as two whole notes tied across into the eighth measure, although singers usually drop off after beat 1 or 2 in the seventh measure. The phrase could end in seven measures and move on elsewhere, but the format for the typically expected eight measures prevails from the backing structure of the harmony. An interesting chord cycle creates its own phrase and fills the last two measures of time, delivering the expected eight-measure duration, while at the same time setting up the next eightmeasure period. The overall harmonic structure to the eight measures follows an AAAB pattern in a 2 + 2 + 2 + 2 arrangement, the chord progression of which is shown below. Note that the chords are grouped in two-measure groupings, which repeat for measures 1-2, 3-4, and 5-6. Measures 7-8 use a different set of chords but still ends on V7. The melodic phrase content is overlaid in the aforementioned 2 + 2 + 3 configuration. Different arrangers of this song treat the last two measures of the period in their own way (one option shown above), but any new

64 Phrase, Period, and Expression

Figure 3.28 Section diagram from “Have Yourself a Merry Little Christmas.”

melodic “filler” creates an elision (a point where one phrase ends, and another simultaneously begins) with the last note of the main melody. This creates a break from the primary lyrical melody, adding depth to the composition, though existing within the predictable eight-measure period. Here we see how the phrase examples from Section 3.2 are expanded to form complete periods. Let us consider Beethoven’s treatment of the piano sonata phrase from above. Beethoven rounds out the initial presentation of this phrase in a period of eight measures (Figure 3.29).

Figure 3.29 Period from Beethoven’s Piano Sonata, Opus 2, No. 1.

The opening phrase we explored above (in Section 3.2) is immediately used in repetition, though it is transposed over another harmony in a 2 + 2 arrangement. Beethoven then uses a fragment of the melodic phrase to

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sequence it upwards to a climax in the seventh measure; this then relaxes into a cadence in the eighth measure. The configuration of phrases in the second half of the period uses a (1 + 1) + 2 arrangement of phrase lengths. The next period, from Verdi’s La Donna e Mobile, also turns out in an eight-measure length (Figure 3.30). The rhythmic aspect of the phrase is used in repetition across all four phrases of the period. Verdi uses the tonic and dominant harmonies behind the melody, leading to different melodic note choices for each occurrence. The antecedent phrases use repeated notes, and the consequent phrases use descending notes to begin each figure. The arrangement is (2 + 2) + (2 + 2) in an AA’A”A”’ configuration.

Figure 3.30

Period from Verdi’s La Donna e Mobile.

The final example in eight measures is from the Amy Beach In Autumn Op. 15, No. 1 piano piece (Figure 3.31).

Figure 3.31

Period from Amy Beach’s In Autumn Op. 15, No. 1.

The initial two-measure phrase is repeated, though the final note is altered a third higher, thereby creating the high point to the phrase at the end of the antecedent. The start of the consequent is formed as a descent from the high note in a two-measure phrase. This phrase is also repeated, with just enough variation to make it interesting. The last phrase has the same descent to it; however, the notes in the first beat are displaced by an octave and the notes of the final measure are a third lower than its predecessor. These slight changes, in addition to the first note not being tied over from the previous measure, disguise its relationship. The structure is AA’BB’. The strategy of pairing phrases by compounding groups of two works with other phrase lengths is a good compositional technique, as well. If we revisit the examples from Section 3.2, we can see the same structural idea of

66 Phrase, Period, and Expression antecedent and consequent phrases even if the number of measures doubles in size from 8 to 16. The four-measure example from Albeniz’s Capricho Catalán (Figure 3.32) is also structured in paired groups with a (4 + 4) + (4 + 4) antecedent and consequent period.

Figure 3.32 Period from Albeniz’s Capricho Catalán.

The dotted quarter/eighth rhythm at the start of the third and fourth phrases owe their origins to the first phrase, though they unfold melodically in their own way under different harmonies. The structure is ABA’A” with a climax at the end of the second measure in the fourth phrase. The one-measure phrase from Scarlatti’s G Minor Sonata (Figure 3.33) demonstrates the same arrangement of paired groups, albeit with the period length being four measures in an AA’A”B structure (melodically).

Figure 3.33

Period from Scarlatti’s G Minor Sonata.

Though we may commonly find one-measure phrases group together in period lengths of four, Mozart finds a way to do it in eight measures (Figure 3.34). The second movement of the Piano Sonata K. 309 (284b) unfolds in a grouping of (1 + 1 + 2) + (1 + 1 + 2). The initial one-measure phrase ends with a rhythmic placement on beat 3 of the measure and is complemented with another similar measure. These two phrases are followed by a two-measure phrase with a similar dotted rhythm. This arrangement might be considered a period unto itself, as there is a cadence, but it lands with a rhythmic placement on beat 2 of the measure

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Figure 3.34 Period from Mozart’s Piano Sonata K. 309 (284b).

and the listener is given a sense of wanting to continue since our minds are expecting placement on beat 3. Mozart does continue and rounds out to eight measures with another group of 1 + 1 + 2 creating a complex assembly of phrases. Periods of phrases can of course come in other shapes and sizes. If we look back to Ravel’s Pavane (Figure 3.35), we see a phrase period of seven measures.

Figure 3.35

Period from Ravel’s Pavane.

After the opening two-measure phrase of the period, Ravel continues with what looks like an exact repetition at another scale degree. However, he sets into sequencing a figure from the phrase, which proceeds on landing in the sixth measure. The ending fragment of the figure is repeated to add reinforcement, completing the period in the seventh measure. Groupings of phrases can also come based on other numbers other than two. Looking to the Vivaldi La Primavera concerto (Figure 3.36), we see groupings based on three.

Figure 3.36 Period from Vivaldi’s La Primavera concerto.

68 Phrase, Period, and Expression The one-measure long phrase is grouped into an AAB arrangement. This structure is quite effective with the initial phrase presented, repeated, and then complimented with a corresponding phrase closing the idea. This whole phrase grouping is then repeated forming a period of six measures. Haydn’s Minuet from String Quartet Op. 50, No. 3 (Figure 3.37) also has a pairing of phrases based on the number three. The initial four-measure phrase pairs with two other phrases, totaling 12 measures (4 + 4 + 4) in an ABC arrangement.

Figure 3.37 Period from Haydn’s Minuet from String Quartet Op. 50, No. 3.

This pairing in three is satisfying even if some may wonder why the period did not come balanced out in a symmetrical duration of 16 measures. We could play out this idea and reimagine this period (Figure 3.38) into a 4 + 4 + 4 + 4 arrangement by inserting a repetition of the initial phrase, creating an ABAC arrangement. This idea of copy and pasting phrase components can be a useful tool to a composer. It does not mean the music loses sense of emotion even if there is some “nuts and bolts” tinkering during its inception. This arrangement is quite logical and would probably have never been questioned had the composition originally appeared in this form. As a composer, you get to make these decisions as to what is best for your creations, just as Haydn did in his choice for this piece. In some instances, periods may form a complete section of music; in others, they may be one of several components making up a larger section. The minuet example from Haydn’s string quartet is a period as well as a section of music with a repeat sign on the end, creating an overall listening effect of a paired group. The grouping of phrases makes up the A section to a binary form minuet, which is a sub-section to the larger overall ternary form “minuet and trio” ABA (Figure 3.39).

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Figure 3.38 Period from Haydn’s Minuet from String Quartet Op. 50, No. 3., reimagined into a 4 + 4 + 4 + 4 arrangement.

Figure 3.39 50, No. 3.

Section diagram of ternary form of Haydn’s Minuet from String Quartet Op.

Sections can be created with the same pairing strategy as periods, coming together to form larger ideas in antecedent/consequent groupings or other arrangements of grouped phrases and periods. The period from Mozart’s G Piano Sonata K. 309 (284b) (Figure 3.40) is paired with a repetition; however, the antecedent period cadences on the dominant harmony and the consequent cadences on the tonic harmony, creating a closed harmonic cycle for the section. The complete section from Isaac Albeniz’s Capricho Catalan from the suite Espana (Figure 3.41) again has a paired period grouping arrangement but does not close harmonically by returning to the tonic chord of Eb Major. The harmony is left open by cadencing on the dominant harmony; this sets up the start of the next section of this composition, which is taken up in dominant harmony of Bb Major. The overall structure for the piece is also ternary, but the scale of the piece is smaller than the form of Haydn’s minuet and trio. The section is not a subsection of a form within a form. The example above is the entire A section of the ABA ternary form, which also includes a codetta.

70 Phrase, Period, and Expression

Figure 3.40 Section of Mozart’s Piano Sonata K. 309 (284b).

Figure 3.41 Section from Isaac Albeniz’s Capricho Catalan from the suite Espana.

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The Amy Beach work, In Autumn Op. 15, No. 1 (Figure 3.42), also has a section made up from two paired periods of music. The first period cadences on the dominant chord of F# Minor. The material is repeated but moves toward the relative major of F# Minor: A Major. At this point, with the second period’s expected close in the eighth measure, Beach surprises the listener by keeping the music going. An added flourishing phrase begins out of the predicted ending of the period by use of an elision. The 19-measure section then ends back in the open harmony of the dominant setting up a repetition that returns in a more embellished version.

Figure 3.42

Section from Amy Beach’s In Autumn Op. 15, No. 1.

With Vivaldi’s La Primavera, we again see two periods paired to make up a section of the movement (Figure 3.43). However, the first six-measure period that we explored earlier is combined with another period made up of a new theme instead of repetition or variation. This consequent period is formed in a grouping of three like its antecedent; perhaps unexpectedly, it ends up being seven measures in length due to a rhythmic figure from the phrase that is repeated. This added figure adds a half measure to the first half, shifting the placement of the phrase from beat 1 to beat 3 in its repetition in the second half of the period. The added figure is again used in the repetition, adding another half beat totaling one added measure. Sections of compositions can include more phrases and periods beyond a pairing in twos. The Beethoven sonata example is a period within a larger

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Figure 3.43 Section from Vivaldi’s La Primavera.

exposition section of a sonata movement. Expositions in classical sonatas generally include a principal theme made up of periods or phrase groupings that then lead to a secondary theme and closing theme, all of them constructed of more phrase groupings or periods. If we revisit the example from the popular song, Jump, from the band Van Halen (Figure 3.44), we can consider the harmonic and melodic makeup of the verse section. Here, just as we have seen in examples from classical music, the four-measure phrases combine (4 + 4 + 4 + 4) to create a wellbalanced verse section. The main keyboard riff is played four times to produce the harmonic basis for the structure in an AAAA arrangement. The melodic makeup for the section, however, overlays in a slightly different structure. The four-measure lyric melody phrase, instead, has an AAAB structure. This pattern has a structure that presents an idea, repeats it, and then a final phrase rounds off the section, making the listener ready to enter the next section of the song. Melody Harmony

Phrase A Phrase A Phrase A Riff A Riff A Riff A Figure 3.44 Melody riff diagram for Van Halen’s Jump.

Phrase B Riff A

3.5 Emerging Patterns As we have seen in the examples of the previous section, the compounding of phrases based on pairings in even and odd numbers results in various

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arrangements for the incorporation of new or repeated material. The labeling applied to these antecedent and consequent phrases and periods might be expressed as arrangements of AAAB or ABAC, among others. There are many paths forward, but it is up to the composer to choose which way is best for their own composition (there will always be art in the final choice for composition). Considering other options in the arrangement can be a way of unlocking new ideas in the molding of your creation, particularly in the transitions between phrases. The notion that there is one ideal path for a composition and that it only comes from some divine spark of inspiration downloaded in its fully perfected form is not always the case in composing. Sure, there are anecdotes that promulgate the fable that a song drops out of the sky into the receptive frontal lobe of a musical genius. But this is insulting, both to the sky and to the musical genius. The sky, like the Houyhnhnms in Jonathan Swift’s Gulliver’s Travels, speaks its own language in thunderous fricatives, windblown consonants, and smoky vowels. Musicians do not speak that language (except for maybe Brian Eno), let alone have a perfect composition dropped into their head by it. Likewise, the musical genius rarely has the song formed fully in their dreams. There are exceptions that prove the rule: Mozart composed variations in his head and then dropped the score onto paper as fast as pen and hand could collude. And then there are the two Macs from Liverpool. One, Paul McCartney, claims Yesterday came to him in a dream. The other, Mac the Mouth (Ian McCulloch), claims The Killing Moon came to him in his repose under the same moon. I am not calling either of these rock idols a liar; I am just saying they are selling their own talents short. The only reason a dream could congeal a song like The Killing Moon in the head of Mac the Mouth is because Mac the Mouth already knew how to compose great songs. Note that The Killing Moon came after The Cutter, A Promise, and Clay had already suffused through Ian’s subconsciousness. Given this broader perspective, then, compositions take a long time to go from beginning to completion, even when a composer is not consciously aware of it. Some composers even revisit their creations later and revise them, reshaping it into something better that their younger selves could not attain. In order to benefit from your subconsciousness, then, it is never too early to start composing! Anyone familiar with Mozart’s Overture to his opera The Magic Flute eventually learns that the catchy theme in the allegro section was taken from Muzio Clementi’s Sonata in Bb Major, Op. 24, No. 2 (Figure 3.45). At first, one might think that Mozart took a well-formed, complete melody as a main theme for his Overture. But analysis of both compositions reveals two

74 Phrase, Period, and Expression completely different compositions that originate from identical seeds. The seed in question, which Clementi discovered, is a catchy one-measure phrase made of repeated notes with an ornamental figure on the end that propels into other repetitions of the phrase.

Figure 3.45 Theme from Muzio Clementi’s Sonata in Bb Major, Op. 24, No. 2.

Clementi treated the theme as the basis for a sonata movement for the keyboard. The original form of the phrase plays out in an AAAB arrangement. The initial phrase is repeated by the interval of a fifth higher, and then it is repeated again, another fourth higher. A final cadential exclamation forms the ending phrased of the overall theme (Figure 3.46).

Figure 3.46 Overall theme from Muzio Clementi’s Sonata in Bb Major, Op. 24, No. 2.

Clementi then sets off developing the theme with another material that allows the pianist to demonstrate their prestidigitation, playing out in a homophonic keyboard texture. Mozart recognized a different potential for this seed and created a completely different setting, restructuring the overall theme into an AABB arrangement (Figure 3.47). There is a minor (no pun intended) transposition of key from Bb to Eb and a change of meter from common time to alla breve for the setting of the phrase in question. But the significant alteration comes after the initial repetition with completely new material brought in for the “B” portion of the theme.

Figure 3.47 Mozart’s restructuring of the theme from Muzio Clementi’s Sonata in Bb Major, Op. 24, No. 2, used in the Overture to his opera The Magic Flute.

Mozart has his own treatment of the theme, playing out in a polyphonic texture for orchestra. Mozart’s version is certainly the more famous of the

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two, but Clementi’s original version is also a worthy composition in the Classical keyboard repertoire. Having shown how the sequence of phrases can affect the overall aural impact of a composition, you might be wondering, “Yes, I get that, but how much variation can there really be just from this?” Glad you asked. Let us take a look at the possibilities for phrase sequence patterns using the shorthand phrase descriptors such as AAAB and ABAC. Figure 3.48 illustrates the 2, 5, and 15 different phrase sequences a composer has at her avail when she has 2, 3, or 4 different phrases to bring together in the composition. Pretty compelling, actually: 22 different compositional choices for just 2, 3, or 4 phrases!

Figure 3.48

Phrase sequences available for compositions of two, three, or four phrases.

As an exercise, we will take the opening phrase of Vivaldi’s La Primavera concerto example from “The Four Seasons” and rearrange the structure utilizing all of the options from Figure 3.48. Certainly, Vivaldi chose the possibility he deemed best when he set out to compose this concerto (and we do not disagree!), but the point here is to show how the phrase could have taken many different structural paths forward as he began this concerto. AAB (Figure 3.49) Here, we have the opening phrase structure as it exists in the concerto. The structural arrangement for the phrase group is AAB with a slight difference in the pick-up for the second “A.”

Figure 3.49 Vivaldi’s opening phrase for La Primavera in its (actual) AAB structure.

76 Phrase, Period, and Expression But what if Vivaldi had taken a different path? There were other options to choose from. We shall now examine the structural possibilities for these phrases based on the original grouping of three and then move to groupings based on two and four. We are not trying to find “improvements” for this concerto theme with this exercise, but we will see that the other possibilities are still coherent. Thus, considering them might unlock new ideas for your own compositions. By analyzing your own composing tendencies, you may find you consistently use the same structures in your music. Evaluating this element of composition (varying the phrase sequencing that you started with to perhaps unlock other sequences that provide interest) is certainly one way to break out of well-worn pathways if you are looking to do so. AAA (Figure 3.50) Dropping the “B” figure from the phrase structure might seem as though we are losing an integral component, but the result is still usable. For example, using a subset of the phrases in the original sequence might prove valuable when transitioning from one period or section of the music to another. In fact, shortening the phrase can itself provide a signal that a transition is about to occur. Such compositional techniques will be discussed in more depth in other chapters of the book, but rest assured that varying the phrase sequence can be a useful part of an overall composition. Coming back to the specific example, the outcome of dropping the “B” figure is reasonable and could find its way into a composition before moving on to new material. Some contrast may be found by assigning the repetitions to different instruments or by using dynamic changes with each reiteration. Vivaldi uses the harmony of E Major across this figure in its original form, but a change of harmony to B Major on beat 3 of the third statement is also possible.

Figure 3.50 Vivaldi’s opening phrase for La Primavera in AAA structure.

The next two possibilities amount to a reordering and a different repetition pattern from the original. The suggestions for contrast from the previous example can still apply. ABA (Figure 3.51)

Figure 3.51 Vivaldi’s opening phrase for La Primavera in ABA structure.

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ABB (Figure 3.52)

Figure 3.52 Vivaldi’s opening phrase for La Primavera in ABB structure.

From here, we might add a third component “C” to the “A” and “B” grouping for increased three-phrase variability. The possibilities for this are vast, but we shall spare you from our own mediocre attempts and instead borrow directly from Vivaldi himself. The phrase material for “C” comes from the principal violin’s solo in the “Il canto degl’uccelli” section of the movement. We take just enough trilled notes to fill the phrase requirements of a one-measure phrase and leave room on beat 4 for the pick-up note as if we were to repeat the entire phrase again. ABC 1 (Figure 3.53)

Figure 3.53 Vivaldi’s opening phrase for La Primavera in ABC structure.

The next example considers the possibility that the “B” and “C” figures might have come to the composer’s mind in a different order and the labeling is swapped. ABC 2 (Figure 3.54)

Figure 3.54 Vivaldi’s opening phrase for La Primavera in an alternative ABC structure.

Incidentally, after the initial occurrence of any structure (let us say ABC), a composer could change the order of these phrase figures in a return to the material later on in a composition (ACB, BAC, BCA, CAB, and CBA). In our usual naming of a sequence, we will continue to alphabetize phrases in the order they first occur.

78 Phrase, Period, and Expression From here, we can easily regress to structures based on number 2 for a compositional basis. The possibilities here are smaller. Again, variables in harmony, dynamics, and instrumentation can aid in avoiding a sense of being too static with exact repetition. AA (Figure 3.55)

Figure 3.55 Vivaldi’s opening phrase for La Primavera in AA structure.

AB (Figure 3.56)

Figure 3.56 Vivaldi’s opening phrase for La Primavera in AB structure.

Finishing out this exercise, we augment the original structure based on “3” to one based on “4.” We jump from 5 to 15 structural possibilities as well as add a fourth phrase “D” into the mix on the last example. Here again, we will borrow material from Vivaldi to make up the “D” phrase and close out the period. AAAA (Figure 3.57)

Figure 3.57

Vivaldi’s opening phrase for La Primavera in AAAA structure.

AAAB (Figure 3.58)

Figure 3.58

Vivaldi’s opening phrase for La Primavera in AAAB structure.

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AABA (Figure 3.59)

Figure 3.59

Vivaldi’s opening phrase for La Primavera in AABA structure.

AABB (Figure 3.60)

Figure 3.60

Vivaldi’s opening phrase for La Primavera in AABB structure.

AABC (Figure 3.61)

Figure 3.61

Vivaldi’s opening phrase for La Primavera in AABC structure.

ABAA (Figure 3.62)

Figure 3.62

Vivaldi’s opening phrase for La Primavera in ABAA structure.

ABAB (Figure 3.63)

Figure 3.63

Vivaldi’s opening phrase for La Primavera in ABAB structure.

80 Phrase, Period, and Expression ABAC (Figure 3.64)

Figure 3.64

Vivaldi’s opening phrase for La Primavera in ABAC structure.

ABBA (Figure 3.65)

Figure 3.65 Vivaldi’s opening phrase for La Primavera in ABBA structure.

ABBB (Figure 3.66)

Figure 3.66 Vivaldi’s opening phrase for La Primavera in ABBB structure.

ABBC (Figure 3.67)

Figure 3.67 Vivaldi’s opening phrase for La Primavera in ABBC structure.

ABCA (Figure 3.68)

Figure 3.68

Vivaldi’s opening phrase for La Primavera in ABCA structure.

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ABCB (Figure 3.69)

Figure 3.69

Vivaldi’s opening phrase for La Primavera in ABCB structure.

ABCC (Figure 3.70)

Figure 3.70

Vivaldi’s opening phrase for La Primavera in ABCC structure.

ABCD (Figure 3.71)

Figure 3.71 Vivaldi’s opening phrase for La Primavera in ABCD structure.

From this point, all the phrases from this exercise could be paired with consequent phrases to form periods. And from there the periods paired to form sections. The possibilities from the table could then be applied to these arrangements in the larger view of the composition. A period or section may be made of groups of two, three, four, or more structural components, with all structural arrangements being considered from the above table. Perhaps this was a tedious exercise and after a few examples your mind tuned out and you glossed over the rest. However, each example may conjure different possibilities in harmonic backing, instrumentation, or orchestration, as well as dynamic considerations. A repetitious phrase like ABBB can be a great way to create dynamic contrast in a composition. Here you could have the instruments playing together reduced in the phrase marked piano (p) or have more added in the phrase marked forte (f) in the score, such as that shown in Figure 3.72. Same notes as in Figure 3.66, but a different “feel.” Variables like these need not occur in the initial presentation of a phrase. They may occur on repetitions later in the composition. Regardless, they are a source of further musical variability and elements of creativity.

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Figure 3.72 Vivaldi’s opening phrase for La Primavera in ABBB structure with dynamics (piano, p, and forte, f) indicated for a different “feel” than Figure 3.66.

3.6 Digitally Calculable Possibilities There is a trope about setting a nearly limitless number of monkeys in front of a nearly limitless number of keyboards. Enough monkeys, enough keyboards, and of course enough time, and these monkeys, with brains no bigger than a primate from the wrong side of the evolutionary tracks, and voila! You get Hamlet − at least in theory. Sure, mathematically, you do, but the near infinities involved might be precluded by relativity or some other principle of nature. Regardless, the odds of producing Hamlet are so astronomically low that no practical experiment will ever result in even “To be or not to be, that is the question,” let alone the hundred pages of angst-soaked obsessing that defines this masterpiece. Why do we dispel the notion of Shakespeare’s monkeys? Well, because we wish to show you that music, like monkeys at a keyboard, it offers limitless possibilities. Suppose we allow only the following options for music: one instrument; one or two measures of content; the choice of whole, half, quarter, or eighth notes; and a limit of only three octaves of notes. These are some rather restrictive constraints, right? Except they are not. We can choose to make our music any of 16 different lengths; that is, from one-eighth to 16 eighths of a measure long. Within the longest of these, we have the choice of two consecutive whole notes, four consecutive half notes, eight consecutive quarter notes, sixteen consecutive eighth notes, and any options in between. Even the simplest of these, that is, using only quarter and eighth notes, gives you these possibilities (Q = quarter; E = eighth) for sequential note selection, or “rhythmic construction”: QQQQQQQQ QQQQQQQEE (move the EE around for 8 variants) QQQQQQEEEE (move the EEs around for 28 variants) QQQQQEEEEEE (move the EEs around for 56 variants) QQQQEEEEEEEE (move the EEs around for 70 variants)

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QQQEEEEEEEEEE (move the Qs around for 56 variants) QQEEEEEEEEEEEE (move the Qs around for 28 variants) QEEEEEEEEEEEEEE (move the Q around for 8 variants) EEEEEEEEEEEEEEEE Note that this is 256 variations, even without including moving the Qs to start in eighth positions rather than only quarter positions, for example, like: EQEEQQQEEEQ Thus, there are hundreds of rhythmic constructions within two measures. Add in all the constructions for 15 eighths, 14 eighths, etc., and there are thousands of rhythmic constructions. Now, multiply this by 37 notes in three octaves (since you get 12 per octave and the extra note to complete the range, for example, C. . . .C. . . .C. . . .C). Add in staccato, legato, crescendo, diminuendo, and now we have millions of possibilities − for one instrument, playing only two measures (in 4/4 time) at most. Now add a bass, some drums, a flute, a synthesizer, maybe even a vocal and a rest or two! It is clearly going to take those monkeys, typing away at Sibelius or Finale (pick your favorite flavor for composition software here), a lot of bananas to replicate your latest catchy tune. In theory, all of the vast possibilities for phrase constructs in one, two, three, or more measures are digitally calculable by a supercomputer. Even if you could scour through some database of all the possibilities, you still do not have a composition. We can multiply the infinitely calculable possibilities for phrases by the infinite number of realizations for the compositions. Fortunately, even this extremely vast number can be readily grasped, making composition a lot less intimidating as a recipe than it is as a mathematical result. For creating your musical recipe, it is just a matter of identifying and selecting the best phrase candidates that suite your taste. As an example of the simultaneous complexity and simplicity of composition, it may be interesting to find that complete symphonies based on any famous composer’s style can now be produced by artificial intelligence (AI) algorithms. But, without a human to hear it, is it music? Music is meant to have a human element; it is meant to be experienced. Simply listening to a musical database of all the phrase possibilities will not give you a composition. The experience of listening to the performance is emergent, arising from the way the phrases sequence, repeat, and are varied across the

84 Phrase, Period, and Expression composition. A good hybrid approach is to use AI to select a manageable set of phrases and let the composer piece the phrases together with her own idiosyncratic skills and taste. AI, after all, is only as intelligent as it was programmed. With the wrong training set, or the wrong rules base for its preferences, it will produce a lot of music that almost sounds good but may not actually be good. AI can produce music that is erratic, foreign, or unfocused. The problem here is also in the time delay between training and evaluation. If AI is to create new music that is appealing, it by definition cannot have been trained on this same good music since, well, it is new. A composer, unlike AI, can compose and evaluate at the same time. There is no delay between training and evaluation. This alone argues for there to always be a meaningful and significant contribution of the human-in-the-loop for musical composition. Even AI must balk at the infinite, and hand off its output to the humans for which music is written to evaluate. This is a comforting thought, because the combination of composition and evaluation is creative, fun, and intellectually satisfying. So, with or without AI, you can go out there and clear your own path through the infinite possibilities!

3.7 Sidebar – How Being an Omnivore Aids in Musical Composition When it comes to sources of creativity, music is arguably the polymath, or at least the omnivore, of the arts. Music, using time as the signal carrier (where space is used in the visual arts), offers a significant difference and opportunity − it can incorporate virtually any message normally conveyed by the many visual arts in the same carrier medium of time. In this chapter’s sidebar, we look at how having an eclectic background aids in creating your music. One reason for this is because music, through phrasing, expression, and the concept of motif, allows us to incorporate the wide variety of spatial arts by association. In this section, we explore how musical phrasing can be used to explore several musical options at the same time (i.e. expression). For example, if music involves two or more styles (say jazz and hip hop), then we have created a tripling of our phrasing possibilities even if we allow the two styles to develop independently. That is, we can use jazz phrasing or hip hop phrasing alone or the two in combination. In general, if we allow N different styles to be used in the composition, we have 2N − 1 (e.g. 15 if

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we are interplaying four styles) different style combinations to use for our phrasing. More variation is possible when we hold one style relatively static and allow the other to vary off of the former. This may be said of either the rhythmic element of the phrasing or the harmonic aspects of the phrasing, or both. This is another 2N − 1 combinations, if we really want to go that route (i.e. the mathematical combinatorial route) here. More importantly, perhaps, in the present discussion, is that a properly phrased section involving two or more styles can attract enthusiasts of both styles. This is traded off against potentially offending the strict devotees of the individual styles; however, those folks are probably not the target of this book, anyway. A second positive benefit of being a musical omnivore is that it allows you an opportunity to broaden your musical spectrum, while still being able to bring the skills you have in a preferred genre. For example, suppose that you are an expert in Baroque composition, and you have recently heard some Cajun music that has a similar key progression, such that you feel you can merge the two into a single composition. Then, at the simplest level, you can provide a tradeoff between the Baroque melody and the Cajun melody, or use the two in some form of polyphony. In general, if you are using S different styles in a piece, then you have 2S − 1 different combinations of monophony and polyphony to choose from for each measure. If you pick an M-measure section, this gives you (2S − 1)M different possibilities for the sequence of measure-to-measure styles. Let us suppose that we are looking at an eight-measure section (or phrase) of music, and we have S = 2 styles (e.g. Cajun and Baroque) to choose from. Here, (2S − 1)M = (22 − 1)M = 38 = 6561. Thus, we have more than 6000 different possible ways to choose the eight measures. If we use the symbology C = Cajun, B = Baroque, and T = Together, then these 6561 possible measure sequences include, for example, {C,C,C,C,C,C,C,C}, which is just the Cajun piece eight measures in a row; {B,B,B,B,B,B,B,B}, which is just the Baroque piece eight measures in a row; and {C,B,T,T,C,B,T,T}, which is a common means of bringing the two sounds together, playing one measure each of the Cajun and Baroque followed by two measures of them together. Among these 6561 possibilities, of course, there will be some that are chosen far more frequently than the others. This can undoubtedly be described by a Pareto effect [Box86], although instead of the archetype 80/20 distribution, in this scenario it is more likely a 99/1 distribution (i.e. 99% of all selected music pieces are based on 1% of these 6561 possibilities). In addition, these types of variations can be used to diversify key portions of a musical passage; for example, the openings and endings of passages.

86 Phrase, Period, and Expression These may have a different progression of measures to intentionally introduce the set of musical thoughts in a piece in the opening, or to summarize them in an ending. The mathematics behind these is the same, although typically these may be arranged around phrases, which are often four measures. For these, 81 different sequences of measures are possible when choosing from the set of [C,B,T] in the above example. Some of the more likely phrase sequences to be chosen include {C,B,T,T}, {C,C,B,B}, {B,B,C,C,}, and {C,B,C,B}. A fourth area for the application of multiple musical styles is, not surprisingly, to create repeated dissonance and resolution episodes. These may simply be special cases of the possibilities already described but provide musical fulfillment through their sequencing. Among these are phrases or longer sequences of measures that create expectations for how they might be completed. Unresolved expectation is dissonance, and resolving it lets the listener know when the phrase is complete. In the context of our example, such sequences could include {C,C,B,B,B,B,C,C}, {C,B,C,B,C,B,B,C}, and the like. The combinations illustrated here are an underrepresentation of the possibilities in a sequence of measures. For example, suppose one musical theme were playing in 3/4 time and another in 4/4 time. Then, these two themes would start a measure together every four measures (for the measures in 3/4 time) and every three measures (for the measures in 4/4 time). If, however, the 4/4 time themes were in multiples of four measures, then the two pieces of music would “re-synchronize” every 16 measures (for the measures in 3/4 time) and every 12 measures (for the measures in 4/4 time). That is, the two themes would have 48 quarter notes to elaborate before re-synchronizing. If both themes used only Cajun and Baroque styles, and both alternated {C,C,B,B} in four measure phrases, then the 48 quarter notes would transpire as follows: 6 notes of {C} in 3/4 time and {C} in 4/4 time 2 notes of {B} in 3/4 time and {C} in 4/4 time 4 notes of {B} in 3/4 time and {B} in 4/4 time 4 notes of {C} in 3/4 time and {B} in 4/4 time 2 notes of {C} in 3/4 time and {C} in 4/4 time 6 notes of {B} in 3/4 time and {C} in 4/4 time 6 notes of {C} in 3/4 time and {B} in 4/4 time 2 notes of {B} in 3/4 time and {B} in 4/4 time

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4 notes of {B} in 3/4 time and {C} in 4/4 time 4 notes of {C} in 3/4 time and {C} in 4/4 time 2 notes of {C} in 3/4 time and {B} in 4/4 time 6 notes of {B} in 3/4 time and {B} in 4/4 time This simple example shows a particular meter arising from the combination of two meters. Here, we get a symmetric sequence of {6,2,4,4,2,6,6,2,4,4,2,6} quarter notes being played in one of four ways: {C,B}, {C,C}, {B,C}, or {B,B}. Overall, this sidebar shows that there are a wide number of ways of bringing two or more forms of musical style into a composition. These methods are an excellent means of bringing in a musical theme from a specialist into your broader composition; for example, using a hook that will complement your main musical theme. It is also a way to prevent the composer from making subtle, subconscious “blocking” of input from potentially rich, complementary sources. Importantly, the number of possibilities is both large and readily tested by using changes in meter or sequencing. Inspiration for variability in music can be garnered from a wide number of sources. In this section, we consider a simple form of poetry, the 5/7/5 syllable Haiku. In the following Haiku, we find a hopeful message of someone low on energy solving the problem by attaining nutrition: Running on empty Need food to replenish me Nutrition and taste However, taking the same 17 syllables as four phrases, we can say phrase A = “Running on empty,” phrase B = “Need food,” phrase C = “to replenish me,” and phrase D = “Nutrition and taste.” Originally ordered {A,B,C,D} in the above Haiku, we can also create a Haiku from the order {C,B,D,A}, shown below. Here, we instead find an ambiguous situation in which we are not confident that the writer is going to find nutrition. There may even be a hint of despair: To replenish me Need food, nutrition, and taste Running on empty Another 5/7/5 Haiku also shows a message of hope and overcoming a situation of difficulty:

88 Phrase, Period, and Expression Life in a war zone Running to escape and live Soon to be happy If we take apart this Haiku as five phrases, we can say phrase A = “Life in a war zone,” phrase B = “Running,” phrase C = “to escape and live,” phrase D = “Soon to be,” and phrase E = “happy.” The Haiku above sequences these phrases as {A,B,C,D,E}, but if rearranged as {D,B,E,C,A} as in the Haiku below, the sense of happiness that may be forthcoming certainly has a more tenuous, evanescent feel to it: Soon to be running Happy to escape and live Life in a war zone These examples, and this sidebar in general, only highlight the many possible ways to modify a phrase, period, or expression in music. We have not even touched on, for example, using the treble versus bass clef; the wide variation in the instruments available; the use of repetition at the more macroscopic level such as the use of the period (e.g. antecedent and consequent phrases); and adding unexpected elements within the phrases (e.g. variations, mordants, trills, seventh chords, etc.). These will be featured in other sidebars, and only add to the nearly limitless variability we have for expression, even when only a modest subset of the measure to measure sequences are used.

3.8 Summary This chapter described how to use phrase, period, and expression in your composition. Essentially, the phrase and the larger aggregate of phrases, the period, are the building blocks for composition. They are the “chunks” that musicians, in learning (and remembering) how to play a piece, think of as individual components. The sequence of phrases is complemented by the use of rhythm, melody, and harmony in parallel. This chapter also illustrates the nearly limitless ways in which just a few phrases and periods can be arranged. The sidebar for the chapter addresses sources of creativity and how this contributes to musical expression. In particular, poetry was shown as a rich source for musical inspiration.

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References [Box86] Box GEP, Meyer RD, "An Analysis for Unreplicated Fractional Factorials," Technometrics 28 (1): 11–18, 1986. [Scho99] Schoenberg A, Fundamentals of Musical Composition (Faber and Faber, 1999), Strang G and Stein L (eds.), ISBN 978 057119 6586, p. 3.

4 Rhythm/Motive

The best way to learn is through the powerful force of rhythm – Wolfgang Amadeus Mozart If the world were perfect, it wouldn’t be – Yogi Berra

Abstract In a perfect world, your musical score would spring from your head in perfect form, like Athena from the head of Zeus. But, as Yogi Berra noted, “If the world were perfect, it wouldn’t be.” Instead, you need to understand composition techniques in meter, rhythmic device, and motive to put together the beat, or rhythm, of your composition. In this chapter, we explore the use of rhythmic experimentation to hold together a composition and/or to provide variety in the face of a steady beat. Rhythmic variability can be provided by lead-in (anacrusis), emphasized notes (beats and pulses), and the duration of notes used in sequence. Keywords: Anacrusis, Beat, Compound Meter, Meter, Motive, Multimetric, Polyrhythm, Pulse, Rhythm, Subdivision, Time Signature, Tuplets

4.1 Introduction You are snapping your fingers, tapping your feet, or even strutting in place to a tune. Your fingers snap the same way each time, your feet tap with the same force and trajectory, or your steps are stereotyped, one foot in front of the other. There is no “note” to play – you are really just marking time. Is this music? Of course it is. What your snapping, tapping, and strutting all stems from is rhythm.

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92 Rhythm/Motive Rhythm is not a byproduct of the composition. It is a main ingredient. Just as it is difficult to build safety or security into an existing system, it might be difficult to “force” a rhythm on an existing harmony and melody. So, even if it is a hard mental gymnastic, you often want to simultaneously consider all three (rhythm, harmony, and melody). If you have selected a rhythm first, however, you may have a particular inspiration, or at worst constraint, for the rest of the composition. This does not mean that you must have the rhythm locked in place before composing, but often having that rhythm snap-snapsnapping or tap-tap-tapping in the back of your mind like some sort of cranial woodpecker is going to make the harmonic and melodic notes, or at least alternatives for them, flow much more quickly. You may decide to change the rhythm after they stimulate some notes, but you will generally find more options when rhythm is in mind during composition. Of course, you do not have to have a particular rhythm in mind when you are experimenting with the harmony and melody. If you put those in place first, then, you might try different rhythms to see if it stimulates a variant of the harmony and/or melody that was unexpected, and unexpectedly good. The point is, experimenting with rhythm is a good way to make sure you do not get complacent with the rest of your composition. All of this means that, in some cases, the rhythm may be more important than the notes. This is one of the reasons music teachers, including the authors, have students count aloud, use a metronome, or use some other method of staying in rhythm. When you miss a note, it is regrettable, but this is mainly because it is a temporary flaw in execution. When the rhythm is interrupted, that flaw is fatal. The piece is dead. In fact, this opinion is supported by how we identify missing notes in the first place. A note sounds “bad” if it does not provide the expected sound in the context of the rest of the composition. But, if rhythm is off, there may be no expectations whatsoever, and thus there are no “bad” notes but also there are no “good” measures. We just know the piece is badly executed, and even playing the right notes will not fix it. I think you would agree I would rather hear a bad note than a bad song. As an example, one of us uses Beethoven’s Ode to Joy as a means of showing the importance of rhythm. If you play the notes with written duration, it sounds like Ode to Joy alright. However, if you mess up the rhythm with the coin-flip experiment we are about to describe, it is more like Odious Joy. Here is the formula. For each note in sequence, flip a coin. Heads, leave the note as-is. Tails, flip the coin again, and a heads makes the note twice as long, and a tail makes the note half as long. So, if you have three consecutive quarter notes in the original score, and you flip a head, tail−head,

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and tail−tail for your coin tosses, you now have to play a quarter note, half note, and eighth note in sequence. Give this a try for your favorite piece and see what it sounds, and feels, like. Do you recognize the tune anymore? In short, rhythm is so important that, irrespective of the notes, the rhythmic characteristics of a song by themselves can indicate the style. For example, in swing, the distinct rhythmical characteristic is the syncopation location off of the main beats. This is true for other dance styles, as well, like the bossa nova and tango. The rhythm of the style will often be enough of a prod to drive the creativity of your composition. Akin to the rhythm of some forms of poetry, for example iambic poetry, syncopation can drive the way in which a person “clusters” the beats in their head. In this way, articulation and rhythm play hand in hand. For example, in iambic pentameter, every other syllable is accented. This is exemplified by the following from Act 1, Scene 1 of “Richard III” (with the accented syllables in bold): Now is the winter of our discontent Made glorious summer by this sun of York If you say this aloud (which, by the way, is the proper way to say things), you may notice that you might naturally give it a “short-long, shortlong” rhythm in addition to stressing every second syllable. In other words, the words (or more specifically, the syllables) Shakespeare chose just by themselves create a rhythm. But, we could just as easily (if incorrectly) say that the rhythm itself drove Shakespeare to choose these words. The rhythm helped persuade him to choose one word over another, but his creativity shines in spite of the seemingly restrictive constraints. The sun is shining, and Richard is the son of York. The meter did not stop him; in fact, it may have driven him to choose shorter, simpler words in order to provide more play on the same. After all, “to be or not to be” is hardly sesquipedalian, is it? The importance of rhythm for identifying a style is hard to overstate, whether you are sesquipedalian or brachysyllabic (by the way, why is the word brachysyllabic five syllables long?). If you want to compose modern EDM or pop music, you had better choose 4/4 time, or someone might mistake it for a more, shall we say, adventurous, genre. We generally advise making the rhythm of primary concern; that is, figure it out before you move on to the harmony and melody. With that in mind, let us start a more in-depth consideration of rhythm with a few “meters.” We have seen that rhythm is not a byproduct of the composition. It is a main ingredient. Again, the rhythm of a composition might come secondarily

94 Rhythm/Motive to the composer’s consideration of what the notes are; that is to say, what melodic notes or harmony is to be used. The rhythm is then just left to be felt naturally; in other words, the composer’s experiences, emotions, and other factors subconsciously drive the way the rhythm percolates into the composition. This is not an incorrect approach, but it may lead to a smaller field of view in scope of all of the possibilities out there. Rhythm should be a prime motivator for a composition coming along from the start of its creation. When we say “motivator,” it is worth considering that motivation includes logos (logic), ethos (ethics), and pathos (feeling); so any of those may play into the choice for rhythm. Chords and notes from a scale do not have much meaning until rhythm propels them forward into life. Choosing a particular meter or rhythmic characteristic might be the spark needed for a new compositional idea. Let us dive deeper. When setting a specific text to music, you may find it easier to come up with the particular rhythm in which words are to be delivered before even deciding on the actual pitch in which they are sung. When a composer is hired to write in a certain style for music in media, the rhythm is probably the first consideration for defining that style; be it straight or swing, marching or waltzing, disco or dubstep, etc. These choices will lead to the meter and individual rhythmic characteristics and figures that might define each style. Note that the choice becomes easier when the rhythmic skeleton is set in motion. Want to compose virtuosic music? You will probably need a lot of small note values at high speed in the piece. Are you looking to compose a pretty little ditty for walking through the gritty little city? You probably will not need as many notes rhythmically for that catchy melody. Beyond the specific rhythmic choice of the note values that make up a phrase or figure of melody, rhythm plays a role throughout the texture of a composition. Role is important overall in composition, of course: different voices or instruments within the composition may have different roles in conveying musical information to the listener. Melody, accompaniment, and bass may move in the same or different rhythmic values. Rhythmic placement for the different voices may depend on its role in the composition. Bass and accompaniment figures or patterns might center around or within main beats across a measure, thus creating movement and signaling changes in harmony. Percussion instruments may accentuate certain beats and/or frame the beginning and end of the phrase durations with cymbal crashes or fills. Whether the rhythm is simple or complex, it is an important ingredient as to when or how often changes of intent happen musically in your compositions.

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By “change of intent,” we mean a specific event in the composition that the musician places in order to add interest or a transition in the piece. In Figure 4.1, we show the melody to the first movement of Beethoven’s well-known Piano sonata Op. 27, No. 2, “Moonlight.” The melody is rhythmically rather simple, with some longer note values and dotted rhythms defining main beats in a measure. It has its own rhythmic fingerprint that makes it unique and identifiable.

Figure 4.1 The first movement of Beethoven’s Piano sonata Op. 27, No. 2, “Moonlight.”

Next, in the full realization of the piano score (Figure 4.2), we can see the other considerations defining what the piece represents rhythmically. An accompaniment of broken chords and bass notes add complexity to the texture interacting with and supporting the melody. The music is given forward momentum with the broken chords in triplets. The placement of the bass notes has rhythmic meaning as the basis of when and how often the harmony changes. These help to define and punctuate the stronger beats in the meter.

Figure 4.2 Full realization of the piano score of the first movement of Beethoven’s Piano sonata Op. 27, No. 2, “Moonlight.”

Movement of the music can be conveyed to the listener no matter what instruments are being used. You do not always need a drum or percussion instrument to convey the beat. Some listeners might find “classical” music

96 Rhythm/Motive boring because it lacks the drum beat we know so well in popular music. But other people might find the drum beat hits them over the head, making subtleties in the music too obvious, akin to a person who keeps explaining their jokes. For example, the left hand of a solo piano piece can provide the function of driving momentum or percussion when this hand is in the, ahem, hand of a master composer.

4.2 Meter Considering the rhythm to choose for a composition might naturally come after selecting the chords or scales for the piece. A lot of composers say they naturally come to “feel’ the rhythm in a piece after they have tweaked the harmony and melody a few times. There is nothing wrong with this method; however, you may find you use similar rhythmic trends across your compositions if you are not careful. Call it familiarity, call it practice, call it complacency, it does not really matter, because in the end it may narrow your field of view with regard to your musical horizons − the key word being “may.” As with all other suggestions in this book, the approach outlined here is one of several you can employ. Please do not employ it every time in the interest of adding variety. If every time you add variety is in the same way, it is rather self-defeating, isn’t it? A vast majority of popular music is written in the “common time” of 44 time. The bulk of composers’ or songwriters’ bodies of work might find this time signature as their hammer, with every piece being the proverbial nail. Although there is plenty of room for expression and creativity left out there for composing in the common time of 44 , there are also other choices of meter that can prove fruitful for the creation of successful music. The choice of rhythm, or time signature, may carry history with it. There was a time, maybe 150−200 years ago, when the waltz and its 34 time was the dominant music form for dancing and maybe even for playing. A popular music enthusiast of today may look back at the waltz, and its step-slide-step meter, with little interest, or even with nostalgia gilded with cringe. Anyone who has reached adulthood should be prepared to see the look of genuine disgust on the face of a child as the adult shows their preference for “old people music.” So, it is safe to say that a music enthusiast 100 or 200 years in the future will likely look back at today’s music, or at least the vast majority of it, with the same disinterest. Generally, meter is made up of equal rhythmic pulses, also called “beats,” along with equal subdivisions of those pulses (e.g. eighth note subdivisions of

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quarter note beats). In the simple meter of 44 , there are four beats per measure, where beats 1 and 3 are stronger than beats 2 and 4 (one being the strongest of all). Hence, in a basic “back beat” drum pattern used in popular music, the bass drum kicks on the strong beats of one and three while the snare drum hits on the weaker beats of two and four (hi-hat cymbal strikes might occur in the subdivision of the beats in eighth notes driving the momentum forward). Here we introduce a relatively simple graphic that focuses on rhythmic notation without the use of a traditional musical score. In Figure 4.3, we have the simple meters of 4, 3, and 2 depicted as quadrangular shapes. Simple meter refers to time signatures where the main pulses are divided into smaller even divisions (halves). The highlighted shapes represent the main pulse of the meter with some of the smaller subdivisions below, or longer overarching note values above. So, in the case of the 44 time signature (leftmost graphic in Figure 4.3), half notes and whole notes are represented one and two tiers, respectively, above the hatched “quarter” notes, while 8th, 16th, and 32nd notes are represented one, two, and three tiers, respectively, below the hatched quarter notes.

Figure 4.3 Graphic allowing one to focus on the rhythmic notation without the use of a traditional musical score. The simple meters of 4, 3, and 2 (left, center, and right, respectively) are depicted as quadrangular hatched shapes. Simple meter refers to time signatures where the main pulses are divided into smaller even divisions (halves). The highlighted (hatched) shapes represent the main pulse of the meter with some of the smaller subdivisions below, or longer overarching note values above. Please see the text for further details.

A rhythm may be made up exclusively from one division or subdivision of the meter (i.e. some combination of the hatched regions, or time divisions,

98 Rhythm/Motive in Figure 4.3) or from a mixture of larger and smaller values (including the unhatched time divisions in Figure 4.3). From this, we can imagine the vast numeric possibilities for different note value combinations that may make up a melody, accompaniment, bass, or rhythmic percussion parts. In addition to the equal half divisions of note values, dotted values and the tying together of notes values (e.g. a quarter note and eighth note tied together to effect a “three-eighths” note) also add to the vast possibilities for rhythmic variance. Also, don’t forget the rest! The rest where you do not play a note, that is. The silence between notes and phrases can add to the rhythmic character of the music. Like one of Shakespeare’s plays, it can be history, drama, or comedy. It can add history by providing a break between new and familiar music; it can add drama by the introduction of anticipation; or it can add comedy by upending the expected for a form of musical mini-mirth. Different meters will have different feels to them. If we had two compositions using only a perpetual run of eighth notes filling each measure for a melody, one that was 24 measures long in 34 time and the other 18 measures long in 44 time, both would have 144 eighth notes total across the compositions from beginning to end. Putting melody and harmony aside for a moment, the two pieces would rhythmically look the same. However, both pieces of music would “feel” different across the same amount of notes because of the sense of where the main pulse (beat 1) is in each composition. The phrasing across the two compositions would also feel different. A twomeasure phrase made up exclusively of eighth notes would have 12 notes in 3 4 4 time, and 16 notes in 4 time. In addition, the change of harmony, which commonly happens on the main beats in a measure, would occur at different points throughout each of the 144 note compositions. Next, we shall take a brief look at some time signatures and how different rhythmic values can be used across different voices for different roles.

Figure 4.4 Time signature of

4 4

with representation down to the 32nd notes.

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The time signature of 44 has four pulses represented as quarter notes. The measure can be occupied with the longer spanning values of half notes and a whole note, or with smaller subdivisions down to the 128th note (in Figure 4.4, we show representation down to the 32nd). With the following example (Figure 4.5) from the Bach Prelude in Bb minor, BWV 867, we can see the different note values across different voices in this keyboard texture. The lower voice pedal of the left hand in eighth notes provides steady movement forward while the middle voice (stems up, left hand) gives rhythmic emphasis around the strong beats of one and three where the harmony changes. The upper voice harmonized melody of the right hand moves above the left-hand structure with its own rhythmic character.

Figure 4.5

Phrase from the Bach Prelude in Bb minor, BWV 867.

With one less beat, the 34 time has a difference in its main pulses (Figure 4.6). Here beats 2 and 3 are the weaker beats in comparison to the strong beat 1.

Figure 4.6

Time signature of

3 4

with representation down to the 32nd notes.

Next, we look at an example of 34 time from the Adagio movement of Mozart’s Piano Sonata K. 576 (Figure 4.7). This piece has melody notes using note values ranging from half notes, including some with ties to other notes, all the way down to 64th notes. We take three phrase samplings from the composition to show how the left hand can provide both rhythm and

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harmony, keeping time using different note values. The first line of the score shows the left hand (lower notes of this first line) keeping the overall main pulse using quarter note values, with the lower lines of the score (lines 2 and 3) keeping the pulse of time using 8th and 16th notes, respectively.

Figure 4.7 An example of 576. 2 4

3 4

time from the Adagio movement of Mozart’s Piano Sonata K.

time (Figure 4.8) has a strong beat 1. Two measures of 24 could very well be written as one measure of 44 . However, there is an actual difference between these two meters. Both meters have a strong beat 1. Beat 1 in the second measure of 24 time has a stress equal to that of the first measure. Conversely, the third beat in a measure of 44 time, which you might think is the equivalent of a new first beat in 24 time, does not have an equal stress with beat 1 of that 44 measure. The half note, quarter note, 8th note, 16th note, and 32nd note divisions of 24 time are shown here.

4.2 Meter

Figure 4.8

Time signature of

2 4

101

with representation down to the 32nd notes.

Our next example of 24 time is from Mendelssohn’s Spring Song, Op. 62, No. 6 (Figure 4.9).The octaves of the left hand indicate a strong beat 1 and give signal to the harmony for each measure. Notes on the “and” of beat 1 and on beat 2 aid in keeping time, as the smaller ornamental notes ahead of them give more harmonic information to the listener without disrupting the rhythm. The melody moves about above the rhythmic structure.

Figure 4.9

An example of

2 4

time from Mendelssohn’s Spring Song, Op. 62, No. 6.

As stated above, the so-called simple meters of 24 , 34 , and 44 time have main pulses with uniform half divisions of the beat. In compound meter, we find meters where the initial division of the main pulse is in three and not uniform twos. Here, using our graphical representation (Figure 4.10), we can see two meters reflecting two pulses in the measure but with different initial

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subdivisions. The subdivision of three then resumes equal half divisions in the even smaller subdivisions.

Figure 4.10 Graphic allowing one to focus on the rhythmic notation without the use of a traditional musical score, applied to 68 time (left) and 24 time (right). Each graphic shows how we get two pulses in the meter, and that for 68 time the main pulse has a subdivision in three instead of the subdivision in two of 24 time. Note that further subdivisions for both meters are in twos.

In document notation, the numeric representation of meter is different. Compound meters are indicated with eighth notes as the bottom number in the time signature ( 68 , 98 , and 12 8 time, for example), though the main pulses in the measure are represented as dotted-quarter notes, as shown in Figure 4.11.

Figure 4.11 Time signature of

6 8

with representation down to the 32nd notes.

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Franz Liszt’s Les Cloches de Genève: Nocturne from Années de Pèlerinage, Première année: Suisse gives an example of 68 . The broken chord figure starting in the fifth measure clearly defines the main pulse and its subdivision (Figure 4.12). The melody incorporates regular divisions with some tied values, along with smaller divisions and ornamental notes. The introduction before the main melody sets the stage for the meter with the broken chord rhythm. The rests with fermatas across the second main pulse of the measure add to the rhythmic mood and character.

Figure 4.12 An example of 68 time from Franz Liszt’s Les Cloches de Genève: Nocturne from Années de Pèlerinage, Première année: Suisse.

An example of the related 98 time signature, with three main beats and their divisions in three, is given in Figure 4.13. Beethoven’s Andante movement from Piano Sonata Op. 79 is an example of a piece written using 98 time. Three phrase samplings are given in Figure 4.14. The initial phrase from the main theme shows typical division of the meter harmonized in sixths and thirds. The left hand is simply driving the basic pulses (nine even eighth notes per measure with the main pulses

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Figure 4.13 Time signature of

9 8

with representation down to the 32nd notes.

occurring on one, four, and seven). The accompaniment figure to the second theme (middle score in the example below) changes to 16th notes within the main pulses (and, yes, there are 18 16th notes per measure). The third fragment (lowest score below) shows the return of the main theme harmonized in reenforcing octaves with the original harmony adopting the broken chord rhythmic character from the second theme.

Figure 4.14 An example of Op. 79.

9 8

time from Beethoven’s Andante movement from Piano Sonata

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An example of music written in 12 8 time is shown in Figure 4.15. Note that each measure has four main pulses each with division in three.

Figure 4.15 Time signature of

12 8

with representation down to the 32nd notes.

Chopin’s Nocturne in Eb Op. 55, No. 2 is composed in 12 8 time (Figure 4.16). Here, the harmony generally changes every two beats, with the accompaniment figures largely ascending or descending in a manner not unlike stronger beats 1 and 3 corresponding to 44 time.

Figure 4.16 An example of

12 8

time from Chopin’s Nocturne in Eb Op. 55, No. 2.

In addition to the type of meters we have discussed so far, there are also the asymmetrical meters where the main pulses of the measure are made of

Figure 4.17 An example of asymmetrical meter, 58 time, where the pulses are felt in a 3 + 2 (first measure) and in a 2 + 3 (second measure) structure.

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unequal values. For example, a meter such as 58 time can have flexibility as to where the pulses are felt; for example, in a 3 + 2 or, alternatively, in a 2 + 3 structure to the measure. These two possibilities are shown in Figure 4.17. Scriabin’s Prelude Opus 67, No. 1, Figure 4.18, shows a structure to each measure based on a 3 + 2 arrangement with the longer dotted-quarter pulse ahead of the quarter note pulse.

Figure 4.18 An example of asymmetrical meter, structure: Scriabin’s Prelude Opus 67, No. 1.

5 8

time, where the pulses are felt in a 3 + 2

Next is a sample from the Allegro con grazia movement from Tchaikovsky’s Symphony No. 6 in B minor, Op. 74 using a 54 time signature (Figure 4.19). The principle for the structure of the uneven division of the

Figure 4.19 An example of asymmetrical meter, 54 time, in Tchaikovsky’s Symphony No. 6 in B minor, Op. 74. The first two antecedent phrases from the principle theme are shown, with Tchaikovsky dividing the measure in a 2 + 3 arrangement.

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measure is the same, though each measure may pass at a different tempo than the Scriabin example above. Here we see the first two antecedent phrases from the principle theme, where Tchaikovsky divides the measure in a 2 + 3 arrangement. The cello presents the main melody, while the other strings emphasize the main pulses with pizzicato punctuation on beat 1 and beat 3 in the measure. Another example of a 54 time signature comes from the popular Jazz tune “Take Five” written by Paul Desmond (https://youtu.be/8ZiN5awgUjY). The division of the measures in this tune is 3 + 2. Discussing the placement of the beat further, it is worth mentioning that often the first instinct with rhythm may be to start on beat 1 in any given meter. However, rhythm may begin on any beat or subdivision of a beat within a measure. Anacrusis is the name given to the use of pick-up or leadin note or group of notes before the first down beat in the musical phrase. A two-measure phrase with a pick-up beat might start on any beat or upbeat other than beat 1. This is shown below with anacrusis having zero (Figure 4.20), one (Figure 4.21), two (Figure 4.22), or three (Figure 4.23) pick-up beats. Visually each example looks similar, as there are eight quarter notes in each two-measure phrase, but the feel to the rhythms is different as to where the strong beat 1 occurs.

Figure 4.20 Two-measure phrase with a pick-up beat (anacrusis) having zero pick-up beats.

Figure 4.21 Two-measure phrase with a pick-up beat (anacrusis) having one pick-up beat.

Figure 4.22

Two-measure phrase with a pick-up beat (anacrusis) having two pick-up beats.

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Figure 4.23 Two-measure phrase with a pick-up beat (anacrusis) having three pick-up beats.

The next example is the Gavotte I of Bach’s English Suite in G Minor, BWV 808, which shows four two-measure phrases making up the section (Figure 4.24). Each phrase spans from beat 3 on through to beat 2 of the two consecutive measures. The character of this rhythm gives a strong beat one mid-phrase instead of occurring from the outset at beat 3. Effectively, the strongest beat is at the beginning of the measure (beat 1) while the beginning of each phrase leads in from beat 3.

Figure 4.24 Example of beat 1 pick-up in the Gavotte I of Bach’s English Suite in G Minor, BWV 808.

Next, we consider multimetric compositions. Composers do not have to stick to one meter for the whole composition. A change of pulses offers additional chances for creativity in composition. The seasonal holiday song “Here We Come A-Wassailing” has two different time signatures throughout the sections of melody. The song starts in 68 but changes to 24 in the refrain. Both meters have two pulses per bar but have different subdivisions of three and two. The 24 section begins with a pick-up in the second half of the eighth measure (shown with the dotted line division at the end of the second line of the score in Figure 4.25). Different performers might treat the change of meter idiosyncratically. You may find performances where there is a constant steady pulse of the two beats wherein a dotted-quarter in 68 equals the quarter in 24 . Alternatively, you may find performances where there is a sense of tempo change into the refrain with the main pulse becoming shorter and the eighth note divisions remaining equal. As the composer, you get to specify in these situations as to whether the quarter and dotted-quarter values equal one another.

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Figure 4.25 Example of multimetric composition, seasonal holiday song “Here We Come A-Wassailing.” Please see text for details.

Albéniz’s Rondena from Iberia Suite Book 2 (Figure 4.26) gives another example of a composition that changes meters. Both meters have six eighth notes filling the measure, but the location of the main pulse changes across the two meters, changing from two dotted-quarter note pulses in 68 time to three

Figure 4.26 Example of idiosyncratic change in meter from Albéniz’s Rondena from Iberia Suite Book 2. Here, the location of the main pulse changes across the two meters, from two dotted-quarter note pulses in 68 time to three quarter note pulses in 34 time.

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quarter note pulses in 34 time. The number of eighth notes in the two time signatures does not change, but the manner in which they are emphasized does.

4.3 Rhythmic Devices There are other creative ways to generate rhythmic interest in your composition beyond the considerations of meter presented in the previous section. For example, syncopation is another means of varying the rhythm. It is employed using the off-beat placement of rhythmic attacks, that is, attacks between the main pulses of a meter. Mozart uses syncopation in Piano Concerto in D Minor K. 466 in the opening strings section (Figure 4.27). After the first eighth note, the constant off-beat quarter-note durations of the material could deceive a listener in their perception of where beat 1 occurs. However, the cello and bass (the lowest bar, labeled “Violoncello e Basso”) parts keep the listener grounded as to where beat 1 is, reinforcing beat 1 each measure and adding a 16th-note triplet, 32nd notes, or even 16th notes, as leads into the next beat 1.

Figure 4.27 Example of syncopation in the opening strings section of Mozart’s Piano Concerto in D Minor K. 466.

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Scott Joplin’s Maple Leaf Rag uses, perhaps unsurprisingly, a characteristic ragtime syncopated off-beat melodic placement of 16th notes over a harmonic framework in regular eighth notes. The left hand is on beat and rhythmically steady. See the excerpt from the end of the first section of the score in Figure 4.28 and note how much less time it takes to master the rhythm of the left hand versus the right.

Figure 4.28 Example of ragtime syncopation in Scott Joplin’s Maple Leaf Rag.

Next up, we address the “tuplet.” Tuplets are a way of inserting other numerical divisions into a beat duration. Other divisions of the beat might include: duplet, triplet, quadruplet, quintuplet, sextuplet, septuplet, and beyond. A way to go Jack Kerouac on your composition, beat generation gone crazy, if you will. Tuplets allow you to add levels of complexity to your composition, including tuplets within tuplets. After all, tuplets in the general sense are any other division of a beat or measure other than the one posted by the key signature; for example, dividing a four-beat measure into five equallength notes. In the example in Figure 4.29, the tuplets are indicated with a

Figure 4.29 Example of tuplets in a 44 time signature, indicated with a numeral (“3,” “5,” “6,” and “7” below) above the beaming of notes. Quarter, eighth, 16th, and 32nd notes require no indication as they are on beat with the time signature.

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numeral (“3,” “5,” “6,” and “7” below) above the beaming of notes. Note that there is no number “1,” “2,” “4,” or “8” over those beamings, since those are on beat with the time signature as regular divisions. The next example (Figure 4.30) is for a compound meter, where the normal division of the beat is in three with their even divisions (6 and 12). The tuplets occur in other numerical divisions (“2,” “4,” “5,” “7,” “8,” etc.).

Figure 4.30 Example of tuplets in a compound ( 12 ) time signature, where the normal 8 division of the beat is in three with their even divisions (6 and 12), meaning that the tuplets occur in other numerical divisions (“2,” “4,” “5,” “7,” “8,” etc.).

As another example of tuplets, we consider Debussy’s Claire de Lune where a “duplet” rhythm is used in the main theme (Figure 4.31). Here, the duplet uses two notes across a regular division of three. We look to an excerpt of the main theme’s return deep within the composition (in case you are looking for it in the score) where the accompaniment helps to define the main pulses and also uses rhythmically shorter divisions of the beat that emphasize the duplet rhythm.

Figure 4.31 Example of tuplets in Debussy’s Claire de Lune where a “duplet” rhythm is used in the main theme.

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Continuing along this rhythmic vein, we turn to the Pastorale from Liszt’s Annes de Pelerinage, Premiere Annee: Suisse (Figure 4.32). This one involves a little more interpretation. Note the numeral “4” above several sets of four notes in the score. Then note that the section is composed in 68 time. These four notes (quadruplets), then, are played in the time of three beats. That is a hard one to count in your head, especially since the left hand is playing a dotted-quarter for the regular three (of six) beats for that part of the measure. When you are committing this one to muscle memory, counting is a difficult process, and you really need 12 sub-beats for these three eighth notes to set up the cadence. Some would find it easier to just try to get the four notes as close as possible to the cadence without having to divide a measure into 24 time units!

Figure 4.32 Example of tuplets in the Pastorale from Liszt’s Annes de Pelerinage, Premiere Annee: Suisse. Please see text for details.

In the Bach Toccata from Partita in E Minor BWV 830 (Figure 4.33), the phrase grouping is by seven notes for the tuplet − we can call this a septuplet, with the understanding that it is seven 16th notes played in the time of four 16th notes. This is shown in the third measure, and the first two measures are given to set the normal beat of the composition for you. Note that there are seven notes under each slur mark, with the stemming down (left) and up (right) indicating which hand to play the notes of the figure with on a keyboard instrument.

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Figure 4.33 Septuplet example from Bach’s Toccata from Partita in E Minor BWV 830.

Polyrhythm is the simultaneous use of different rhythmic divisions of a beat. Debussy’s Arabesque No. 1, shown in Figure 4.34, is a good example of this. Note the use of triplets over the regular set of two eighth notes in this section. A more contemporary example of this approach is given by Dawn by Dario Marianelli. This polyrhythm uses a two note duplet against the regular three notes division of the beat (https://youtu.be/nXPonfk6OmM), with the hand playing the two notes vs. three notes changing during the piece. Next, Rachmaninov’s Prelude in G Major, Opus 32, No. 5 is used to illustrate a 3 vs. 5 polyrhythm (Figure 4.35). The Andante from Scriabin’s Piano Concerto, Opus 20 (Figure 4.36), provides an example of a composition with three over seven over four polyrhythms (you do not need three hands − the top part is for the clarinet!). In swung rhythm, notes might be written in a uniform eighth note fashion; however, the performance realization of each set of two consecutive eighth

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Figure 4.34 Polyrhythm example from Debussy’s Arabesque No. 1.

Figure 4.35 Polyrhythm 3 vs. 5 example from Rachmaninov’s Prelude in G Major, Opus 32, No. 5.

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Figure 4.36 Polyrhythm 3 over 7 over 4 example from the Andante from Scriabin’s Piano Concerto, Opus 20.

notes is in long-short durations. This rhythm is commonly adopted in blues and jazz music. Here, in what might be an example of a left-hand piano score for a 12-bar blues composition (Figure 4.37), the swing of the rhythm is not visually indicated in the notation, which, if interpreted literally, would imply every note is maintained for the same amount of time.

Figure 4.37 Example of a left-hand piano score for a 12-bar blues composition in which the swung rhythm is implicit but not explicit.

The score of Figure 4.38 indicates how the first two measures of this 12bar composition might be realized in performance, and also might be notated to make the swung nature of its performance explicit.

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Figure 4.38 Score indicating how the first two measures of the 12-bar composition of Figure 4.37 might be realized in performance (notated to make the swung nature of its performance explicit).

This notation is more laborious to produce, and in the interest of efficiency, the even notation may be used with a performance note on its execution. And finally, we consider another rhythmic device, that of shifting the rhythmic accent. Within the course of a phrase or period, you may shift (i.e. change) where a perceived pulse or rhythmic accent occurs. Here, in an excerpt from the first movement of Mozart’s Piano Sonata in F Major, K.332 (330k), we can see that the emphasis on the perceived beat 1 is changed over the course of the phrase (Figure 4.39). A characteristic two eighth-note rhythm on beat 1 occurs every three beats, falling on beat one. However, in the fifth measure of the phrase, Mozart shortens the figure effectively changing the placement of the eighth notes. They change from occurring every three beats to hitting every two beats. This gives the effect of changing from 34 time to 24 time without an actual change in the meter. The rhythmic shift is

Figure 4.39 Excerpt from the first movement of Mozart’s Piano Sonata in F Major, K.332 (330k), where the emphasis on the perceived beat 1 is changed over the course of the phrase.

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brief; at the end of the material, the rhythmic pulse returns to beat 1. The mechanism for this shift is shown explicitly in the score below, where the rhythm aspects of the right hand of the score are annotated.

4.4 Motive For motive, we are concerned with the use of rhythmic character to drive a composition. Often we strive for rhythmic consistency, whether attained by natural instinct or with strategic compositional intent. For the first example, we consider Ernesto de Curtis’s Torna a Surriento. Here (Figure 4.40), there is a characteristic two-measure phrase creating the rhythmic motive for the tune. The first measure of the figure is composed of eighth notes, and the second measure is composed of longer notes (quarter and half).

Figure 4.40 Characteristic two-measure phrase creating the rhythmic motive for Ernesto de Curtis’s Torna a Surriento.

This rhythmic figure is used for almost the entirety of the song up until the ending coda (not provided in the example). The constant rhythm might otherwise be monotonous; however, de Curtis keeps it interesting by varying the melodic motion across different harmonies as seen in Figure 4.41.

Figure 4.41 Varying the melodic motion across different harmonies in Ernesto de Curtis’s Torna a Surriento.

According to [Rand99], motive is “a short rhythmic and/or melodic idea that is sufficiently well defined to retain its identity when elaborated or transformed and combined with other material and that thus lends itself to serving as the basic element from which a complex texture or even a whole

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composition is created.” This may or may not have an additional associative meaning along the lines of a leitmotif, discussed in the sidebar for this chapter (below). One of the more famous examples of the use of the rhythmic motive comes from Beethoven’s Symphony No. 5 in C Minor, Op. 67. This motive can rhythmically be described as “and-two-and one” and is used throughout the entirety of the first movement. The initial introduction of the motive in the opening hook of the movement is shown in Figure 4.42.

Figure 4.42 Rhythmic motive, “and-two-and one,” used throughout the entirety of the first movement Beethoven’s Symphony No. 5 in C Minor, Op. 67.

Next, in an excerpt of the string section from the symphony, we can see how Beethoven links repetitions of the motive together to create a longer period of phrases with the melodic material distributed across the different instruments (Figure 4.43). Here, the rhythmic character is kept while the melodic interval distances and directions are changed across different harmonies. Finally, in a reduction of the orchestra score on a grand staff (Figure 4.44), we see the rhythmic motive used later in the movement with an extension, creating a phrase that introduces the secondary theme. The motive is then used again in the bass to support the changing harmony. As shown in this chapter, rhythm is an important ingredient in composition. Using motives and meter consciously to start your composition is a nice alternative to waiting around for divine inspiration. After all, the divine one may be busy with more urgent matters, and you will end up waiting a long time. Plus, the motive need not be particularly complicated; for example, the motive for Beethoven’s symphony is rhythmically quite simple, but he took that starting seed and grew it into a masterpiece of music. With that, we turn in the sidebar to some creative sources for motives, as a starting point to your musical masterpiece.

4.5 Sidebar: Creative Sources for Musical Composition What else uses motive? Motive, or motif, is a short musical phrase or sequence of notes that has special meaning within a given context. Think

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Figure 4.43 Rhythmic character maintenance with change in melodic interval distances and across different harmonies in the first movement of Beethoven’s Symphony No. 5 in C Minor, Op. 67.

of it as the smallest tidbit of music that has a recognizable theme, like the music they always play when Darth Vader comes on screen, or the four notes that start off Beethoven’s 5th symphony (discussed in the previous section). Motifs are musical memes, bringing with them a lot more than simply the music. Like logos, motifs can represent brands. Like memes and “in” jokes, motifs can represent a lot more through association. A motif can be a musical avatar, standing in for a whole musical personality. Or a motif can simply be a jingle, a musical alarm clock that reminds you that your mind is a slave to correlation. A jingle played enough times – even an incredibly annoying one associated with, say, a high-tech company’s

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Figure 4.44 Rhythmic motive with an extension, creating a phrase that introduces the secondary theme, in the first movement of Beethoven’s Symphony No. 5 in C Minor, Op. 67.

adverts – insinuates itself into your brain through sheer repetition. This does not make this “good music,” and it is quite likely that most of us (ourselves included) do not find the simplistic jingles associated with popular brands and companies particularly compelling, musically. But they are memorable. In the actual musical world, simplistic music that wheedles itself into your subconsciousness – in spite of yourself – is termed “accessible.” We prefer to call it uncomplicated. There is nothing wrong with uncomplicated. The problem, instead, is that too much may be right about it. Uncomplicated lends itself to automation, to formulation, and if one is not careful, predictability. This is part of the issue with letting so-called machine intelligence write music. In allowing an automated music generator to create music, one must create an algorithm to generate potentially interesting sequences of notes or sounds. This requires a special type of algorithm, a predictive algorithm, which can score different possibilities based on a model of how acceptable the tunes generated might be to a human listener. In other words, it by definition will predict music that is predictable. One thing we have learned from the past six decades of music is that very little of its progress has been predictable. The predictive algorithms are based on what already exists; composers are always looking to create something new.

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This does not mean that humans cannot be as productive as machine learning algorithms. Think of, for example, the legendary stunt performed by that polymath of the previous century, Steve Allen. In a purported wager with singer-songwriter Frankie Laine, he claimed that he could compose 50 songs a day for an entire week. That’s 350 songs! Well, he did (or we would probably never have heard about this escapade), and did the compositions in full view of the public in the front window of Wallach’s Music City in Hollywood in 1953. Supposedly he won $1000 from Laine for writing these songs, but that comes to less than $3 a song. Of course, $1000 in those days would be how much today? If you said to yourself, “that would be $1,000,” you would be right, but of course the real question to ask would be how much is it worth in today’s money? About $10,000, which is actually quite a lot for a week’s worth, unless of course the songs were all rubbish. Anecdotally, one of the songs actually became a chart hit, tracking at #13 on the pop charts and #2 on the country charts. Maybe that made him even more than the $1000 he got from Laine. Steve Allen supposedly composed nearly 15,000 songs in his lifetime, though, so even if you are only 1% as productive as he was, there might be 150 songs in you. That is still a lot of songs. Also, if you can write 150 songs, you should be able to write 1500 or even 15,000 motifs. So, coming back to the topic of this sidebar, how is a motif conveyed? The easiest answer is “by association.” Pavlovian, or classical, conditioning leads to an association of an unconditioned stimulus such as taking a fright to a sudden, loud noise with a conditioned stimulus if the conditioned stimulus occurs with it several times in a row. If a loud noise occurs every time you open a bag of potato chips, you might get a scare every time you reach for a bag (maybe not the recommended way to diet!). If a jump scare occurs every time a character reaches the bottom of set of stairs in any movie or show you watch, you may end up buying a ranch house. All humor aside, it really does not take long for you to associate a motif with its context. As humans, we are pre-adapted to motifs, since we are so good at correlating events. Too good, in fact, as we often assign cause and effect to events when they are really simply correlated. For example, there is a high correlation between the use of methane and the drinking of eggnog. Notwithstanding the potential digestive effects of eggnog on the human body, in general eggnog drinking does not cause methane. Rather, both are correlated with (and more correctly caused by) a compounding factor; that is, lowered outside temperature which may make one chug a nog or turn on the furnace. In the case of a motif, then, the

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natural ability of humans to associate two events that co-occur can be used for a strong motif effect. That is how to establish a motif in someone’s head. Now, how do you “brand” the motif? Does it need to be “good” at all? Or does it just need to be novel? Or does it have to be so insidiously annoying that it bores into your head like an evil tree weevil? When it comes to motifs, then, there are several trade-offs. The first is length: too short a motif, and it does come off as one of those annoying, repeated-hundreds-of-times, tech company mnemonics. Or, worse still, like the “Ricola!” cry (it is three notes, Intel’s is five, TMobile’s is five), so short it is instantly a cliché. Too long, and it is no longer a motif but a song. The second trade-off is between accessibility and novelty. Make it accessible, and the classical conditioning is easier to create. Make it too inaccessible, and it quickly becomes associated with a particular time. Like the car names “Acura,” “Prius,” and “Supra” – which are close to the words accurate, prior, and super – making the motif positive but musically ambiguous is probably a good plan. In the end, a motif is a bit like a “kid’s show” that is really funnier for adults. The best example of that is, arguably, Spongebob Squarepants. Sure, the child laughs because rubbing two pickles together sounds funny. The adult laughs because Mr. Krabs, the former sailor, knowingly admits he knows the sound of two pickles rubbing together. Off-color enough to keep the parents interested long enough for their children to develop the need to purchase Spongebob paraphernalia. That is a successful approach. That is a creative and lucrative use of ambiguity. That is the heart of a successful motif: people can take different messages from it. Too short, there is no message. Too long, there is only one message. Keep your musical motifs in-between, so like Spongebob you can appeal to multiple groups. Of people, that is, not pickles.

4.6 Summary This chapter describes how to use lead-in (anacrusis), emphasized notes (beats and pulses), and the duration of notes used in sequence to provide rhythmic variability. Rhythmic experimentation is paramount in order to hold together a composition and/or to provide variety in the face of a steady rhythm. Yogi Berra sagely noted, “If the world were perfect, it wouldn’t be.” He could not be more right. A perfect beat, never incorporating meter, rhythmic devices, or motives, will become monotonous over the medium

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term, and torturous over the long term. Do not do that to your audience. Use some of the techniques in this chapter to keep your listeners guessing, if at least not snoozing. The chapter’s sidebar focused on motifs, and highlighted some of the creative sources for aiding musical composition.

Reference [Rand99] Randel DM, ed., “Motive,” New Harvard Dictionary of Music, 1st ed., 513, 1999.

5 Melody and Harmony

I’m in the mood for a melody – Robert Plant I like singing in harmony – I like not having to sing every song – Susanna Hoffs

Abstract In this chapter, we consider the interplay between melody and harmony. Among other approaches, the composer can hold the melody relatively constant and vary the harmonization. The concept of a chord progression for defining this varying harmonization is explored. Harmonic rate variability is shown as an additional means of adding variety to the composition. Melody and harmony are often textured, with variation in one being followed by variation in the other. The use of polyphony for generating rounds is illustrated as a means to add variance to simple compositions. Elaborating further, using harmonic tones for the melody is described. These provide a nice setting against which to set non-harmonic tones to break up longer pieces of the composition. The sidebar for the chapter covers some “patterns” to use for creating your own music: here, our muse is poetry in general and Emily Dickinson in specific. Keywords: Chord Progression, Chords, Harmonic Rhythm, Patterns, Pitch, Tones

5.1 Introduction: Melody and Harmony When beginning to compose, it is important to consider the relationship between melody and harmony. Perhaps when thinking about composing, you think the primary component you work toward is the melody. This is not

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necessarily incorrect, but the harmony behind the melody is just as important to the construction of the composition. The melody is perhaps the singer, and the harmony is the guitar strumming chord accompaniment underneath. A composer should be concerned with not only how the melody is progressing but also the harmony. These two components, along with rhythm, are what will propel your composition forward across phrases, periods, and sections toward the end goal of a complete piece. One component can lead the others, and vice versa. A melody might come to a composer easily, and if the piece is meant to be fully homophonic, the composer must go back over the piece and decide the harmony that supports it. From this angle of composing, there are several possibilities to add harmony over an already fixed melody. For instance, the melody may at minimum require only the primary chords from a key to support it; yet, in the hands of an experienced jazz arranger, the harmonic scheme will likely come out with a more complex series of chords supporting the melody. As the composer, you get to decide just how straightforward or complex the melody or harmony is crafted. Here, we have an example (Figure 5.1) of a single melody with two different harmonic structures. The nursery rhyme “London Bridge” traditionally uses a simple harmonic backing, which only requires the tonic and dominant chords of the key (I and V7) to support the melody. The harmonic rhythm changes every 1−2 measures.

Figure 5.1 London Bridge with a traditional harmonization.

Next, we have the same melody with another harmonic setting using a broader range of diatonic chords, with 7ths and some secondary chords to approach them (Figure 5.2). The harmonic rhythm changes more frequently with two harmonies per measure. Both of these harmonizations (Figures 5.1 and 5.2) are completely acceptable, and the melody is still recognizable with either setting. In fact, there are many other possibilities out there still. Several different arrangers

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Figure 5.2 London Bridge with a reharmonization.

would likely come up with several different realizations to harmonize the melody. Compositionally speaking, the other approach, of course, is to have a harmonic plan laid out ahead of time and then thread the melody across it. This is the approach used quite often in songwriting. For instance, a song writer may sit and find a succession of chords they like by strumming on a guitar or plunking away on the piano. After deciding on the chord progression, they then perhaps come up with a melody by humming along or noodling about on their instrument along with the chords. From here, lyrics might appear in a form of Gestalt moment from the character of what the music is suggesting or from an already existing text. The melody does not need lyrics either; it can be the same process for composing instrumental music. For example, we can clear out the “London Bridge” melody and retain the harmonic framework from both versions of the tune. This gives us a sort of blank canvas to work with; yet it gives us some direction moving forward with new compositions. The example below is the traditional harmonization without melody in the eight-measure layout. In this first, simple example, there is a single chord for each measure; namely {D, D, A7, D} repeated twice (Figure 5.3).

Figure 5.3 Harmonic scheme from the traditional harmonization of London Bridge in an eight-measure layout with single chord for each measure; namely, {D, D, A7, D} repeated twice.

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A more elaborate chord scheme is shown in the additional harmonic scheme with eight measure layout in Figure 5.4. Each measure here has two chords, with the implication of each chord being hit at the beginning and the middle of each measure.

Figure 5.4 Harmonic scheme from the reharmonization of London Bridge in an eightmeasure layout with two chords for each measure.

Next (Figures 5.5 and 5.6), we offer two new realizations for melodies across the harmonic schemes born out from the nursery rhyme. We certainly do not want to be influenced too much by the original melody; so we will be conscious to avoid any rhythmic or distinct melodic motion from that tune. This is probably straightforward enough when you consider that, in spite of its cheeriness and its adoption in a children’s game, the London Bridge song has a dark past. London Bridge actually did fall down − multiple times. The Viking invader Olaf Haraldsson turned it into a woodpile in 1014, and various fires and other calamities befell it over its next 800 years. Even worse, the lyrics “take the key and lock her up” may literally refer to the process of immurement, which was a rather strict form of punishment (or even a form of human sacrifice) in which a person was included inside a sealed chamber in the bridge’s structure and left to die. Coming back to the composition, we notice that London Bridge’s melody begins on the 5th (A) of the chord harmony D Major. Though we could start from this note and come up with something completely unique, for our new melodies, we chose the other tones of the tonic triad (D and F#) for starting points. We also took into mind rhythm as a primary ingredient in the search for a new melody. For the first realization, we used the “cakewalk” rhythm with its characteristic syncopation as a basis for the melody. For the second harmonic scheme (Figure 5.6), we found that changing from double meter to quadruple meter suits the succession of chords for a new setting. Go head, play the melody on any instrument of your choice (or play the melody and harmony together on a piano).

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Figure 5.5 New melody derived from the tradition harmonization of the London Bridge nursery rhyme using the “cakewalk” rhythm with its characteristic syncopation as a basis for the melody.

Figure 5.6 New melody derived from the reharmonization of the London Bridge nursery rhyme changing from double meter to quadruple meter.

The structure for the melodies naturally played out similarly to the original London Bridge, with the antecedent and consequent phrases made from the same material with different endings (ABAB’). However, you could also be mindful of this and try avoiding the repetition by searching out different possibilities. The table of structural possibilities in Chapter 3 could also be applied to the exercise to unlock new ideas.

5.2 Chord Progression Harmony occupies the same regularity in measures as we see in phrases, since it is essentially the background structure of the melody. Here it is commonly designated a chord progression, which is just a succession of chords existing in the same space as the melodic phrases. If we look at any lead sheet commonly used by jazz musicians, you typically see the melody of the tune on a staff with chord symbols printed above it. If, for example, you have access to or own “The Real Book,” you will see this notation. The performing musician takes this information and creates their own part; a pianist, bass

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player, and a trumpeter work from the same information and fulfill different roles in the ensemble. From this musical document, we can see the harmonic framework supporting the phrase structure. Generally, the trumpeter might take the melody, the pianist the harmony (chordal accompaniment), and the bassist takes the information to create a bass line. The performers then improvise over the harmonic structure of the tune. To a jazz performer, it is called the “changes.” To a composer, this is the harmonic framework for the composition. The succession of chords might be used in a looping fashion, repeating over and over as the tune progresses, or it may change constantly. It may follow the melodic needs of the tune or change and direct the melody toward a particular tonal center. As a composer, these are the individual choices you must make as you grow your composition. The choice for a succession of chords is an integral part of a composition. This can come from a predetermined formulaic arrangement or unfold naturally with a unique fingerprint. A group of chords can stay confined in one diatonic scale, defining a tonal center; include chords from outside a key; or progress chromatically. They may be chosen for having a close relationship with perhaps only one note difference between the chords, or a more remote relationship with every note being different and existing potentially in different keys. A cycle of chords can be based on an interval relationship, moving upwards or downwards by stepwise motion or larger intervals. A series of chords might fulfill a cadential task or just be a couple of chords toggling back and forth. A large vocabulary of chords and their usage is something every composer must work to build through the study of harmony and counterpoint, as well as from the analysis of other composers’ compositions. Here, we offer some examples of chord successions across phrase and period lengths. They are certainly not exhaustive of all of the possibilities, but they illustrate some approaches for new composers to consider. The 12-bar blues is a formulaic cycle of chords from popular music where the duration of the period is laid out with a predetermined chord structure (Figure 5.7). Even with this model as a starting point, many composers and songwriters have found ways to alter this basic chord layout with various substitutions throughout the structure. There is even a version of the structure in the minor mode. Next (Figure 5.8) we have an example of another period structure of chords that toggle back and forth between the tonic and dominant in an AABA phrase arrangement. The AABA phrase arrangement here is recursive, with an AABA arrangement on lines 1, 2, and 4 (as F F C7 F) as individual

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Figure 5.7 Harmonic scheme for a 12-bar blues.

Figure 5.8 Harmonic scheme for tonic dominant toggle.

lines, as well as for the entire set of four lines (A = lines 1, 2, and 4; B = line 3). Here, we have an example of the primary chords (I, IV, V7) that define a key in both major (Figure 5.9) and minor (Figure 5.10).

Figure 5.9 Primary chords in F Major.

Figure 5.10 Primary chords in E Minor.

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Of course, a progression may include other diatonic chords (ii, iii, vi, vii) from the key added along with the primary chords (I, IV, V), as in Figure 5.11.

Figure 5.11 Progression including other diatonic chords (ii, vi) from the key added along with the primary chords.

Next, a snapshot of chords taken from two phrases within Fredric Chopin’s Ballade in G Minor Op. 23 is shown (Figure 5.12). Here we have some of the same chords that define the minor mode (I, ii7, V7), with an additional secondary dominant (A7) that sets up the V chord in the second phrase.

Figure 5.12 Op. 23.

Chords taken from two phrases within Fredric Chopin’s Ballade in G Minor

An example from Lili Boulanger’s D’un Vieux Jardin shows a progression of chords with more remote relationships to one another (Figure 5.13). Each new chord defines its own tonal center instead of relating together in the same key with the others.

Figure 5.13 Lili Boulanger’s D’un Vieux Jardin showing a progression of chords where each new chord defines its own tonal center instead of relating together in the same key with the others.

The next few examples demonstrate a relationship based on intervallic distances. The first (Figure 5.14), as seen in Debussy’s La fille aux cheveux de lin, is based on a stepwise motion with diatonic chords straddling the keys of Gb and Cb Major.

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Figure 5.14 Debussy’s La fille aux cheveux de lin, based on a stepwise motion with diatonic chords straddling the keys of Gb and Cb Major.

The next (Figure 5.15) is a major chord cycle based on ascending movement in minor thirds.

Figure 5.15 Major chord cycle based on an ascending movement in minor thirds.

The next two examples are based on descending intervals of the fourth (Figure 5.16) and fifth (Figure 5.17), respectively.

Figure 5.16 Descending intervals of the fourth.

Figure 5.17

Descending intervals of the fifth.

Finally (Figure 5.18), we give an example of chords moving based on chromatic movement where the bass note in each successive chord descends a half step.

Figure 5.18 Chords moving based on chromatic movement where the bass note in each successive chord descends a half step.

A common occurrence in pop music is to have one chord per measure over a four-measure duration. Once repeated, this cycle of eight measures fulfills the typical length of a verse or chorus section in a song. An analysis of any song in popular music over the last few decades will show an individual cycle

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of chords for each of the verse, chorus, and bridge sections. However, it is not uncommon to see the same four-chord cycle used for each of those sections across the entire song. These four-chord “loop” progressions, based on the I, IV, V, and VI chords, appear in countless songs in many different genres of music. Here (Figure 5.19), we list the different arrangement possibilities for these chords (in C Major) in a four-measure loop progression, commonly seen in today’s music.

Figure 5.19 Different arrangement possibilities (24 in total) for the I, IV, V, and VI chords (in C Major) in a four-measure loop progression. A similar set of 24 could be presented for each major and minor key.

There are still many possibilities for individual melodic and rhythmic invention within each example even if people bemoan the same four chords appearing in song after song in today’s music. We can project more possibilities by reducing from four chords to three within the four-measure cycle, with one of the chords repeated somewhere in the cycle. Additionally, we can calculate even more possibilities by using the other diatonic chords (ii, iii, vii) from the key in these four-measure progressions. Even beyond the four measure chord cycle, progressions may be based on larger measure groupings of 8, 12, and 16 measures. The systematic approach of calculating chord progressions may seem uninspired, but this will lead a composer away from using the same four chords at the same one chord per measure harmonic rhythm over and over again, and introduce new harmonies in your vocabulary. Harmonic rhythm is the rate at which the harmony changes. This can be at regular intervals, or it can change whenever it suits the melody. It is quite

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common to see one harmony used per measure (as seen above), but the use of two or more chords in a measure is also frequent, as well as one chord for several measures. Here we have the first two phrases of Alexander Scriabin’s Etude in A Major, Op. 8, No. 6. This excerpt demonstrates a harmonic rhythm of one chord per measure seen clearly in the left-hand accompaniment; in addition, the upper note melody of the right hand is also harmonized with the interval of a sixth below in parallel, adding some more complexity to the texture.

Figure 5.20 The first two phrases of Alexander Scriabin’s Etude in A Major, Op. 8, No. 6, demonstrating a harmonic rhythm of one chord per measure (please see text for details).

The next example (Figure 5.21) from Robert Schumann’s “Of Foreign Lands and Peoples” from the Scenes of Childhood, Op. 15, No. 1 shows two chords per measure.

Figure 5.21 Robert Schumann’s “Of Foreign Lands and Peoples” from the Scenes of Childhood, Op. 15, No. 1 showing two chords per measure.

The Prelude in C Minor Op. 28, No. 20 by Chopin (Figure 5.22) gives an example of multiple harmonies per one measure of music.

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Figure 5.22 Chopin’s Prelude in C Minor Op. 28, No. 20 showing multiple harmonies per one measure of music.

As final example of harmonic rhythm (Figure 5.23), Mozart’s “alla turca” from the Sonata in A Major, K. 331 gives an example of one harmony over a four-measure run.

Figure 5.23 Mozart’s “alla turca” from the Sonata in A Major, K. 331, giving an example of one harmony over a four-measure run.

A composer need not stick to one established harmonic rhythm, either. They may change from, say, a harmonic rhythm of one chord per measure to a rhythm of two harmonies. This may happen wherever and whenever it suits the composition. Many admirable pieces of music have been constructed on a prescribed harmony and many different famous tunes might have the same chord progression. The number of different chord harmonies in a particular piece of music will not necessarily determine if a composition is successful and finds an audience. Sometimes, simpler is better; for example, if it is a slow piece or if the melody is particularly catchy, the chords might be few and yet the rhythmic and melodic aspect of the music may create something notable. Alternatively, the chords may be many, and it will still be an appealing piece; for example, a relatively simple saxophone melody played over a complex jazz piano chord progression. Different genres and audiences have

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different tastes. Punk Rock might use three chords throughout a piece, with the frantic melodic and rhythmic energy keeping you from ennui. A jazz piece might feature a few well-timed trumpet blasts in front of a complex chord progression that requires only an occasionally seventh or ninth from the brass to keep your feet tapping and the martinis coming. Some may prefer a more straightforward harmonic approach, and some more complex. Whatever the chord choice is for your composition, it comes down to how well you thread a melody through the “changes.”

5.3 Melody and Harmony in Texture In the general practice of composition, a melody finds its pathway in a symbiotic relationship with the harmony supporting it. From a triad alone, you have three choices for notes (the root, third, or fifth) as the melody starts or progresses through a given chord harmony. The more often the chord changes, the more melodic pitch variance you have as you progress through your phrases. The more static the chord being used for the harmony, the less pitch choices you have. There are many individual pathways to thread a melody through a chord or succession of chords. From one chord to the next, you may melodically leap directly to the note of choice or find a more elaborate pathway through other notes to arrive at a particular chord tone. Additionally, you may use more than one chord tone as you pass through any given harmony. As an example (Figure 5.24), we return to the first section of Robert Schumann’s “Of Foreign Lands and Peoples,” from the Scenes of Childhood, Op. 15, No. 1. The piece was composed in a homophonic texture for piano, and, in general, the melody notes fall rhythmically on the main beats of the meter signified by chord changes with these pulses. Next, we offer a diagram (Figure 5.25) of the composition to show the pathway of the melody through the note choices from each chord harmony. Though these may not be the chord voicings as they appear in the piano score, we diagram the general contour of the melody with the corresponding root position chord surrounding the melody. The chord analysis from the piano score is offered above the diagram. This melody uses mostly chord tones with the occasional passing tone (e.g. the “E” notes in the first line below). The melody exists at different points as the root, third, or fifth of a given chord. From this diagram, we can also see that there are many other paths a melody could take through this succession of chords.

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Figure 5.24 First section of Robert Schumann’s “Of Foreign Lands and Peoples,” from the Scenes of Childhood, Op. 15, No. 1, composed in a homophonic texture for piano (please see text for details).

Figure 5.25 Diagram of the composition showing the pathway of the melody through the note choices from each chord harmony. The chords are above the modified scores in Lighter text; for example, G/B is the G chord with the B in the bass.

Even in a monophonic setting where the composition may just be made up of a melody and there are no accompaniment instruments supporting it, a succession (or progression) of chord harmonies can still play a role in the

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Figure 5.26 The “A” section of the Allemande from the Partita for unaccompanied flute in A Minor BWV 1013 by J.S. Bach (please see text for details).

construction of the music. As an example, we have the “A” section of the Allemande from the Partita for unaccompanied flute in A Minor BWV 1013 by J.S. Bach (Figure 5.26). Here, with a general chord analysis, we can see how

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Bach projected a complex single note at a time monophonic texture through many different chord “changes.” Successful melodies in a monophonic setting can be constructed with even fewer changes to the background harmonic structure. There are many bugle call melodies that are composed for an instrument with a limited amount of notes available. The valveless bugle can only play notes from the harmonic series produced from a fundamental note and its overtones. The harmonic series forms the basis for tuning systems, the construction of scales, and the building of triads. The notes of the bugle are not fully chromatic like the valved trumpet. The notes from the second, third, fourth, fifth, and sixth harmonics form notes of a C Major triad with octave doublings (e.g. the notes are C, G, C, E, and G). The melodies we shall see below are constrained to just these three triadic notes. However, the melodies from these compositions do not come across as just broken chord arpeggios; instead, they are melodious and communicate a message musically and, at times, emotionally. Each of the following bugle call melodies (Figures 5.27, 5.28, 5.29, and 5.30) are made of the same constraint of notes, yet they are each completely individual to themselves. Composing within certain limitations can still result in a very appealing output. In fact, this chapter’s sidebar addresses the very issue of genre-specific imposition of constraints not preventing the creation of excellent poetry. Musically, constraints such as following a particular chord progression anchor a composition in a familiar genre, whilst allowing the composer to be creative with the melody or even contrapuntal melodies. With that in mind, let us consider several bugle call melodies. Play these on your instrument of choice, and you will note that they are not lacking in variety or in creativity.

Figure 5.27 Bugle Assembly score.

Even in a polyphonic setting, the combination of notes from more than one melodic voice can function harmoniously together. To get a general glance at how this works, we can look to another nursery rhyme that finds use in all the general musical textures. Frere Jacques is a tune that may be sung in a monophonic texture by, for example, a parent singing a cappella to their child. Here (Figure 5.31), we see the melody is made of four one-measure phrases where each figure is immediately repeated.

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Figure 5.28 Bugle First Call score.

Figure 5.29

Figure 5.30

Bugle Reveille score.

Bugle Taps score.

Figure 5.31 Frere Jacques, monophonic texture.

It might also be found in a homophonic setting for, say, piano with the melody supported by accompaniment (Figure 5.32). We can see the tune requires, at minimum, one chord harmony (C Major) to support the entire melody. The notes of each figure that have placement on the main beats of the meter form the notes of the C Major chord harmony (root-C, third-E, and fifth-G). Thus, in a polyphonic round setting, which this melody is known for, each figure will harmonize together with the others in any combination because the notes form consonant interval relationships with each other. The round is a form of canon that is an imitative compositional technique where

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Figure 5.32 Frere Jacques, homophonic setting with accompaniment.

the same melodic subject is presented in different voices. Each voice enters a short time (usually, every two measures) after the first voice and runs through the entire melody, repeating perpetually or a set number of times. If we take the figures and stack them on top of each other, we see that the starting notes of each figure form consonant interval relationships (in this case, thirds) with each other. The combination of any two or more figures works simultaneously (Figure 5.33).

Figure 5.33 Frere Jacques, stacked representation.

Here in a graphic diagram (Figure 5.34), we can see how each melodic figure overlays with the others forming the harmony of C Major on the

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main beats (1 and 2). The notes in the off-beat count (the “+” of beat one) themselves create a similar relationship based on the G7 harmony.

Figure 5.34 Diagram of melodic figures (four in total) overlaid with the others forming the harmony of C Major on the main beats (1 and 2). The notes in the off-beat count (the “+” of beat one) themselves create a similar relationship based on the G7 harmony. Multiple melodies cover all the notes of the harmony (chords) in this composition.

Next, we can see the melody realized in the polyphonic round setting (Figure 5.35) with each voice presenting the theme once and entering in turn after the first figure is completed. Imitative polyphonic texture can get even more complex than this example. However, creating a relatively straightforward compositional exercise where four melodic figures can combine together and work harmonically is a great way to start learning compositional polyphony for simple rounds.

5.4 Harmonic and Non-harmonic Tones Though it may seem a straightforward approach to composing, there are many successful melodies that are made up entirely of harmonic tones. That is to say, for each harmony in a succession of chords, the only notes used for that portion of the phrase or melody are notes that appear in the chord (see, for example, the four melodic figures in Figure 5.34). The chords may change frequently, in which case the melody has a lot of options for notes; or, the chords may change infrequently, in which case the melody will be generally more constrained for note selection.

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Figure 5.35

Frere Jacques, realized in the polyphonic round setting.

Our first example is the traditional Christmas tune Jolly Old Saint Nicholas (Figure 5.36). Generally, the harmony changes each measure with

Figure 5.36 Jolly Old Saint Nicholas.

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each chord tone used in repetition. The harmony changes more frequently in the 7th and 15th measure with each note change. These are the measures in which the melody is less constrained and, you might agree, more interesting. Examples of successful harmonic tone melodies need not be limited to children’s songs or folk tunes. Richard Wagner’s Ride of the Valkyries from the third act of the opera Die Walküre (remember this in Apocalypse Now?) is an example from dramatic operatic “art” music for orchestra (Figure 5.37). The melody progresses much like the bugle call melodies but allows for more notes as the harmony changes. Here we offer a lead sheet reduction, where the chord harmony is understood not only from the melody but also from the analysis of the other instruments in the orchestral score.

Figure 5.37 Walküre.

Richard Wagner’s Ride of the Valkyries from the third act of the opera Die

When a chord is extended (e.g. with the seventh or ninth of the chord), a harmonic tone melody based on this extended chord allows for a larger selection of tones without tension and resolution. Johann Strauss’ melody from the waltz “The Blue Danube” (Figure 5.38) has notes from extended chords contributing to its character and appeal. In some instances, the scale degrees of six and nine might function as passing tones or suspensions that cause tension and an expectation for immediate resolution by stepwise motion into a chord tone. Yet, in this melody, the tones from the extended chords exist equally with the notes of the basic triad.

Figure 5.38

The “Blue Danube Waltz” by Johann Strauss II.

Composers will naturally want to look for more options in creating phrases beyond the exclusive use of chord tones. The larger choices of melody

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notes from within (or outside of) a complete scale will sound with varying degrees of consonance and dissonance against a harmony. This brings up an occasion in a performance where some listeners may observe a “wrong note” in a melody. You may know a melody very well and a performer may just make a mistake. But mistake aside, the reason we may consider a pitch “wrong” is because it has a harsh or dissonant relationship against a particular harmony. Change the chord or find a more convincing context for the “wrong” note and it can become “correct.” A creative approach in constructing your melody is to find a way of using any of the 12 pitches against any harmony. Harmonic tones give a sense of rest or relaxation (consonance) within a harmony, while non-harmonic tones create tension against the harmony (dissonance) and can add more character to the phrase. In the analysis of a score of music, it becomes the task of a theorist or student to account for every note within a composition. The classification of harmonic and non-harmonic tones within a melody is a theorist way of accomplishing this. The understanding of these classifications can also be used to a composer’s advantage in constructing or improving melodies. We leave it to the student of composition to investigate each non-harmonic tone classification in their own study of theory. However, we offer some melodies with the non-harmonic tones labeled as examples. The melody of the tune “Lavender’s Blue” comprises mostly harmonic tones (Figure 5.39). The second measure, however, has two notes classified as accented passing tones (P.T.). The notes “C” and “A” react with some tension on the main beats (2 and 3) against the harmony of G Major (harmonic tones G, B, and D).

Figure 5.39 “Lavender’s Blue” with accented passing tones.

If we alter the rhythm and move the notes “C” and “A” forward to offbeat positions (Figure 5.40), notice that the tension is lessened, and they now function as unaccented passing tones. The traditional tune “Lonesome Road” is another melody composed mostly of harmonic tones (Figure 5.41). The penultimate note of the melody is classified as an escape tone (E.T.), which leaps to the final note of the phrase.

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Figure 5.40 “Lavender’s Blue” with altered rhythm and the notes “C” and “A” moved forward to off-beat positions.

Figure 5.41

“Lonesome Road.”

Another example comes from the first phrase of Robert Schumann’s melody to “Traumerie,” also from the Scenes of Childhood, Op. 15, No. 7 (Figure 5.42). Again, the melody has many harmonic tones from triads and extended chords, as well as the occasional neighbor tone (N.T.) and unaccented and accented passing tones. Also note how the harmony changes in places other than beat 1 of the measures; in this case, the second and fourth beats in the third measure.

Figure 5.42 The first phrase of Robert Schumann’s melody to “Traumerie,” from the Scenes of Childhood, Op. 15, No. 7.

Mozart’s Rondo K. 494 offers other non-harmonic tone varieties dispersed among the harmonic tones in this keyboard texture (Figure 5.43). Suspension (Sus.), appoggiatura (App.), retardation (Ret.), neighbor tone (N.T.), and passing tone (P.T.) react against the left-hand figures with the harmonic rhythm generally changing every two beats. Even in a polyphonic setting where harmony is formed from independent voices in combinations of consonant and dissonant intervals, non-harmonic tones can shape and add character to a theme. Here in the Bourree from the Lute Suite in E Minor WV 996 by J.S. Bach (Figure 5.44), we can see the twovoice texture play out generally in consonant intervals (third, sixths, fifths, and octaves). The classification of passing tones (unaccented and accented) occur often in the two-note against one combinations between the upper

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Figure 5.43 Mozart’s Rondo K. 494.

Figure 5.44 The Bourree from the Lute Suite in E Minor WV 996 by J.S. Bach.

and lower voices. Other non-harmonic tones used are escape tone (E.T.) and anticipation (Ant.) In the course of a creating a composition, there is always the question of where to go next. There is no one clear answer, but a path forward may come from considering any one ingredient of the composition. At times, focusing on the melody and using your ear to project the melody forward

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can be useful, aided by your knowledge of the note choice. Following your ear is an excellent approach, but you may find it helpful to also use some theoretical knowledge to try out, modify, or embellish a melody that needs a little more pizzazz. You can also use the harmony, projected forward, to drive the composition. In this case, your free-form composing may be with the chord progression, and the melody is more theoretically inspired. Hopefully, the balance between free-forming and using theory to guide your path will be right for your composition. Which side of the seesaw (free-form or theory) is heavier will depend on the context and goals of your specific piece of music.

5.5 Sidebar: Patterns for Creating Music In this sidebar, we consider some of the patterns for creating your own music. Patterns have a negative connotation for some creative types. If you are a top-notch tailor, you probably do not sew everything with a pattern. If you are a painter, you most likely do not use a paint-by-number system to create your landscapes and masterpieces. However, patterns for music are generally far less comprehensive than such patterns. Instead, patterns for music are more like poetic forms than music-by-numbers. Think of the broad range of constraints from a ballad to iambic pentamer to rhyming octets to a sestina to free verse: there is a widely variable level of constraints, and thus freedom, in the wide range of patterns for creating poetry. Yet, every poet is likely to tell you that working in the different patterns from time to time keeps them fresh, inviting them to relearn their command of English syllables and their flow of poetic ideals. Take the sonnet, for example. At first glance, it might seem to be a format that limits creativity − 14 lines of iambic pentameter with a number of “required” rhymes. The sonnet was introduced into English through Petrarch, and the rhyme scheme for the so-called Petrarchan sonnet was fixed at abba cde. So, there are 14 lines, with 5 different sounds to end the lines, including 4 of the same sound (a or b) twice. Probably it is easier to do in Italian than in English. Petrarch did use two other forms, abba abba cdc cdc and abba abba cde dce, but the same rules applied. Could one break the Petrarchan barrier without breaking the pattern? Spenser created abab bcbc cdcd ee, but this also had four endings of the same sound, twice. Shakespeare, who was perhaps to writing what Mozart was to music (an all-time wunderkind), broke from this limitation of the English language by introducing the rhyme scheme abab cdcd efef gg. Note, effectively, seven rhyming couplets. No more need to find four rhyming words

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in a language in which Germanic and Latin influences led to perhaps more word-ending sounds than in any other language. We see how the pattern remained (14 lines, rhyming couplets arranged in some format, etc.) but also how Shakespeare added opportunity for creativity within a pattern. This opened the door, albeit 200 years later, for further elaboration by Shelley (abab cdcd efef dd and abab cdcd ee fgfg) and Keats (abab cdcd bcefef and abca bdca bcdede). Keats also used the rhyme scheme aabb ccdd efgefg in at least one poem, and an example of this scheme is given here to show its implementation: Sonnet in Honor of Keats John Keats was an original poet Inventing new genre as we know it Meter and rhyme were the tools of his trade Many a novel poetic form made Sitting solemnly in a garden dim— We owe a debt of gratitude to him The greatest way to illustrate respect Is through writing an elegy direct Tuberculosis upon his short life Waited, weighing down on his timid frame Like Atlas, he shouldered this tragic curse Creating in spite of bodily strife Forever will live the Keatsian name Greatest of Romantic writers of verse It is clear to see from these examples that the pattern for the Sonnet is relatively broad − 14 lines, some type of rhyme scheme, and iambic pentameter. After that, the differences in rhyming can be suited to the language, to the taste of the poet, or even to the nature of the subject (I would personally hate to try to find three words rhyming with the most popular fruits – orange, banana, apple, and strawberry – for one example).

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As another example of pattern, consider the ballad form, as introduced in Chapter 2 with regard to Emily Dickinson. The stanzas are four lines, with the second and fourth lines rhyming, and alternating eight and six syllables per line. One of her ballads is: (Poem A) Emily Dickinson 479 Because I could not stop for Death – He kindly stopped for me – The Carriage held but just Ourselves – And Immortality. From that pattern, it is relatively easy to create an Emily Dickinson− inspired poem. Her constraints can be viewed analogously to the theoretical elements of composition, as described in the rest of this chapter. Suppose that we wished to write a poem about race relations in a way we think Emily might write if she were alive today. The following is one such attempt: (Poem B) Two halves make a whole I split a melon open wide – The two sides did not match It was not due to bruise or rot It came from a good patch The taste was fine – no preference – Each sweet and ripe and good Perhaps the color matters not – It’s lesson learned – as should The point has, hopefully, been made clear. This poem is nothing like the other poem (which actually is by Emily Dickinson), but the manner in which it is read (8-6-8-6, with similar stress) is the same. Why do we start with poetry in this sidebar? It is because poetry is another creative art in which composition is key. It could just as readily be argued that, in order to become a poet, one should be composing from day 1. While reading Emily Dickinson, in other words, one should write a “Two halves make a whole” of your own. Climb a mountain early one day, and use the

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inspiration to write a ballad inspired by your own version of a modern Emily Dickinson poem, like the one below: (Poem C) The breath of God below I climbed a mountain one bright morn – The fog I left behind A bright blue sky did I adorn A new coat for my mind My thoughts were clear—no prejudice— I thought that I could know The fog I rose through now was this— The breath of God below Is this a great poem? Hardly. But the point is, it is a poem inspired by the pattern Emily Dickinson used to create her much better poem. More importantly, if you read carefully, you will also note how much closer this poem is to the poem “Two halves make a whole” than to the stanza from Emily’s 479. The two poems I wrote are as similar as two 12-bar blues songs! In other words, we can apply the same type of analysis to two songs that use the same “composition scheme.” Patterns, whether used for poetry or for music composition, provide some similarity, even some substitutability, but also room for creativity. If we were to return to the poetry examples briefly, and compare the three poems for similarity (never mind by which method, but note the use of punctuation and the similarity of “no preference” and “no prejudice” in poems B and C, among other similarities these two poems share that neither shares with poem A), we might obtain Table 5.1. In Table 5.1, we call Emily Dickinson 479 poem “A,” and the two modeled after her “B” (Two halves make a whole) and “C” (The breath of God below). Based on the similarity scores, poems B and C are much more similar than either is to poem A. Table 5.1 Table of similarities between poems A (Emily Dickinson 479), B (Two halves make a whole), and C (The breath of God below). Based on the similarity scores, poems B and C are much more similar than either is to poem A. Poem A B C A 1.00 0.24 0.28 B 0.24 1.00 0.66 C 0.28 0.66 1.00

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This consideration of similarity brings us to a potentially even more interesting topic: when is a poem (or a song) a plagiarized version of another, and when is it a different enough variant on a pattern to constitute a new song? While poems B and C are clearly on different topics, they are also clearly related. But are they related enough to indicate plagiarism? Hardly! Plagiarism generally involves some level of identical elements being in two works of art. In music, this generally means the same notes. The notes should have the same beat, and occupy the same roles in a key. However, if one simply moved a tune to a different key and then played all of the same notes, relatively, in the new key (e.g. the root note, then the perfect fifth, and then the root again), it is not a new tune, right? Earlier, we made the argument that a new song could be considered sufficiently different from another, existing, song if an automatic song identification algorithm did not pick the existing song as the best match for the new song. However, what about a single phrase, measure, or section of a song? How much of a song has to be similar for it to be plagiarized? Is, for example, Led Zeppelin’s “In My Time of Dying” a plagiarized version of Blind Willie Johnson’s 1927 “Jesus Make Up My Dying Bed”? It sounds very, very different but includes some of the same phrases. Does this make it plagiarism? Well, this is actually a tricky question, since Led Zeppelin, Blind Willie Johnson, and others (Bob Dylan, for example) all made use of a traditional gospel song that has long been in the public domain. Public domain means no plagiarism, but it also means that you should give it credit as “traditional” or attribute it to the original composer if that is known. The concept of musical distance is important for capturing the style or even the “feel” of the music. The distance between two pieces of music is some function of the notes, the rhythm, the instruments used to create the notes, the sequence of phrases, and other factors. Table 5.2 gives the outcome for comparing the musical distances between six songs, A, B, C, D, E, and F. For this simple example, the distance based on notes, rhythm, instruments, and sequence are assigned scores of 0, 1, or 2. Thus, two identical songs have a distance of 0, and two songs completely unalike have a distance of 8. There are 15 different comparisons between songs in the matrix represented in Table 5.2. Note that the diagonals (values of 0) are for comparing a song with itself. The matrix is symmetrical, for example, the value for (row B, column E) is the same as for (row E, column B), or 3. Taking the 15 comparisons from Table 5.2, the distribution of song−song differences is collected in Table 5.3.

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Table 5.2 Table of distances between songs based on the objective function of notes, rhythm, instruments, sequence, etc. The range of distances is 0−8, with songs C and D being considered “nothing alike.” Song A B C D E F A 0 2 3 6 7 4 B 2 0 4 7 3 4 C 3 4 0 8 2 7 D 6 7 8 0 1 2 E 7 3 2 1 0 3 F 4 4 7 2 3 0 Table 5.3 Table of distances between songs from Table 5.1, arranged by distance. One cluster of more closely related songs has distance < 5, while a second cluster of less related songs has distance > 5. Distance 1 2 3 4 5 6 7 8 Number 1 3 3 3 0 1 3 1

The values in Table 5.3 show a cluster of songs that are somewhat related (distances of 1−4) and a group that are not related (distances of 6−8). Song A is related to Songs B, C, and F; Song B is related to Songs A, C, E, F, etc. What is more important to realize here is that there are not actually two groups of songs; rather, each song has its own set of relationships to the other songs in the set. For example, A and B are related, and generally related similarly to the other songs, except that B is like E while A is not. In Tables 5.2 and 5.3, what do the numbers mean, especially relatively? While open to interpretation, a few definitive statements can be made. A distance of “0” should correspond to an exact version, either the exact same song, a different version of the same song, or perhaps even a live version of the song (if the progression of phrases, etc., are similar enough, that is, as groups tend to take liberties with songs live). A distance of “1” or “2” or even “3” should have some rather obvious similarities. Distances of “4” or “5” or even “6” might have similar meter, chord progressions, or other shared compositional elements but really does not sound the same. A distance of “7” might only mean sharing the same key, while a distance of “8” might as well be comparing “Pumped Up Kicks” with “I Get a Kick Out of You.” So, where do patterns for musical composition fit in? Somewhere between “1” and “7,” using the scores of “0” to “8.” Can we use patterns without plagiarizing? Yes, we can, because the chords in every 12-bar blues songs are identical, but the songs are not plagiarized. Here are three songs all using

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12-bar blues patterns: “Cars Hiss by My Window” by the Doors, “Rock and Roll” by Led Zeppelin, and “Ball and Biscuit” by the White Stripes. Right, those might get a “7,” or at least a “6,” for distance. Not plagiarized, but definitely influenced by a confounding factor, maybe W.C. Handy, which makes this a handy time to end this sidebar.

5.6 Summary In this chapter, the interplay between melody and harmony was the focus. While many approaches are possible, it is often the case that the composer starts with a melody; in this case, the melody can be kept relatively unchanged while the harmonization is experimentally varied. Harmonization can be framed with chord progressions. These progressions can be viewed as the harmonic framework of the composition and are the basis for musical loops. Harmonic rhythm, or rate variability, was also employed as a source of variety for the composition. Texturing melody and harmony allow one to switch which of these varies at different times in the composition. Showing how rounds can be generated from polyphony was provided as a helpful approach to create catchy tunes. Finally, using harmonic tones for the melody was shown as a way to bring the harmony and melody closer together for part of a composition, allowing non-harmonic tones to be added to break up longer pieces of the composition. The chapter’s sidebar focused on patterns for creating music, including the ballad pattern and Emily Dickinson’s poetry.

6 Tonal Center

What has two legs and is dead as a doornail?...Your career – tone-deaf stand-up comedian We often refuse to accept an idea merely because the tone of voice in which it has been expressed is unsympathetic to us – Friedrich Nietzsche

Abstract Knowing your audience is a starting point for selecting the tone of your composition. The tone can be established using either the melody or the harmony (or both). Framing out a tonal center to a piece of music provides a set of expectations for the listener, as well as establishing rapport − they “trust” the composer to fulfill the expectations, and the composer can use creative pathways to delay this fulfillment that engage the listener even further. Further expectation and resolution is created by the use of chord progressions in the composition. The choice of chords can establish the genre of music; for example, popular and folk songs often employ the same set of chords {I, IV, V, vi} and use the melody to differentiate from other songs. Other approaches, such as the fermata, can be used to amplify tension in a composition. The different sounds to a composition achieved through choosing different modes (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian) in the modal system are illustrated. Atonality is shown to be the most comprehensive tone (or lack thereof) for musical creativity. In the sidebar, we address theory and experimentation through the broad set of possibilities afforded in synesthesia. Keywords: Accidentals, Aeolian, Chords, Dorian, Feeling, Fermata, Harmony, Ionian, Locrian, Lydian, Major, Melody, Minor, Mixolydian, Modal System, Mood, Phrygian, Scale, Tertian Harmony, Tonal Center, Tonality

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6.1 Introduction We introduce tonality with a funeral. A comedian shows up at Grandma’s funeral. Standing in front of the crowd of mourners, he says, “what has white hair, is stiff as a board, and will never say another word to you again?” Aghast, the audience thinks he means Grandma. Instead, he smiles and says, “Well, of course, an English Pointer.” OK, that is a definition of tone deaf. Do not be that guy. Know your audience. In music, as in funerals, missing out on the tone can result in some serious cringing, discomfort, and maybe even loss of audience. In this chapter, we focus on the gravity of tonal centeredness to anchor your piece with your (intended) audience. In doing so, we extend the tools picked up in previous chapters to allow you to paint mood, expectation, and a feeling of resolution over the canvas of your composition. This engages your audience more, calling on them to invest even further in your composition. We will start with a general introduction of tonality before diving deeper into its nuances.

6.2 Tonality Tonality is the filtered output of all the possibilities for musical input. Tonality is like your compositional paint palette. An artist’s palette gives her a set of primary colors to build the painting. We will talk a lot more about color in the sidebar later in the chapter, but for now please recognize that these are not necessarily the primary colors you learned about in school; for example, red, yellow, and blue. Primary colors do not have to be that far apart on the color spectrum. They are usually limited by the pigments that an artist has on hand. An Inuit artist, for example, might have 40 different shades of white, while a desert artist might have 40 different shades of brown. The pigments are the main tonal elements that you, as the musical artist, choose to use in your composing. In music, the equivalent of selecting a color pallet is selecting a scale for the basis of your composition. Your composition does not need to be limited to one scale, but that is a good starting point for composers, new and old. Each scale has its own character with its individual set of pitches made up by their distances from one another in tones and semitones. Sticking to one scale throughout a phrase, period, or entire composition is not required; however, the scale that you are currently using will largely define the notes you can use to construct your melody. In fact, some successful compositions are constructed using only notes of one particular scale; that is, there are no

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“accidentals” in the score. They do not bring in notes from outside the scale or move to another scale within the composition. This is not necessarily an onerous constraint: keep in mind, the notes of the scale already determine the harmonies (usually chords) that are used in the composition. If you are a pointillist, like Georges Seurat, you might just add these palette colors directly in the form of dots. That is not unheard of in music. An analogue to pointillism is using only the notes of the scale, with no “blending” of color by using accidentals. Of course, you could also argue that using staccato for articulation is analogous to pointillism, but it is OK to have multiple analogies, especially if you are trying to be creative (kind of the goal of this book, no?). Let us turn to a couple of examples of the former analogy for pointillism. The examples will be two compositions that, through the course of an entire period or entire composition, stick to notes of a single scale and use exactly zero accidentals, yet they do not come off as simplistic as a simple nursery rhyme or folk song. They sound like the eras in which they were written, yet they have an appeal to contemporary ears. Our examples here are indeed long in the tooth, one Baroque (and we did not fix it) and the other late Romantic. The Baroque one is François Couperin’s Les Baricades Misterieuses, in which the entire first period uses only notes and harmonies of the Bb Major scale (Figure 6.1).

Figure 6.1 Score for the first period of François Couperin’s Les Baricades Misterieuses (1717). Note the lack of accidentals.

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Figure 6.2 Score for Scriabin’s Prelude in Db Major, Opus 11, No. 15 (1895). Note the lack of accidentals (but the very common occurrence of black keys).

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Our second example is the work of Scriabin from 1895, Prelude in Db Major, Opus 11, No. 15. This relatively short score is shown in its entirety in Figure 6.2. Note again the lack of accidentals, even if the composition is howlin’ for you to play the black keys. As we have just seen, one form of tonality is to use only the notes that are part of the scale. This is hardly limiting, because it is worth keeping in mind that there are many different scales. There are Major, Minor, Dorian, Blues, Pentatonic, and many others, depending on musical tradition, instrument, context (e.g. Halloween versus a sixth birthday party), etc. Once a scale is chosen, the key can then be selected to enable further variability; for example, C Major, D Major, etc. Contextual considerations include selecting a key to match the vocal range of a singer. Of course, you may be thinking that the key you choose not only can match the vocal abilities of a would-be singer, but it can also set another sort of “tone” emotionally. Nigel Tufnel, for example, has made the claim that D Minor is the saddest of all keys. That may well be true, but is it true because people choose to write sad songs in D Minor, or that D Minor chooses people to write sad songs? Kind of feels like the first, but either way there is at least a cultural tendency for sad songs to be associated with minor scales, and in particular D Minor, while another tendency is for bright, happy songs to be written in G Major, among other keys. And you, as a composer, can tap (or is it spinal tap?) into this cultural tradition to instantly “paint” a mode onto whatever notes you select from that key. Let us start with the melody. Melodically speaking, the establishment of tonality in a listener’s ear can be accomplished by the basic principle of starting and ending a melody on the same tone. In any scale, the first tone has a gravity to it that provides a natural starting and stopping point in a melodic phrase or whole composition. This is not the only path forward in a composition, but it gives a solid foundation for tonal music composition. A tonal center is analogous to home plate in baseball. The batter starts there, which is the tonal center, and may visit other tones in the scale (like first, second, and third base), but always has the intent of returning to home plate (that is the only way to score). So, for your score, you may wish to return to the tonal center often enough to help your listener score. Visit the bases but with a mixture of single, doubles, and triples to keep it interesting. Returning to home is then seen as a desired state, and not something trite. Alouette, for example, a familiar children’s song about plucking a poor little lark bare, starts with the note of F and ends with the note of F (Figure 6.3). One might say this is a “normal” composition, since there is a certain

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expectation − especially for traditional, children’s, and other song forms − to bring a piece to completion with the same sound as it began.

Figure 6.3 The traditional French nursery composition, “Alouette,” showing the return of lines 1 and 3 to the starting note, F. The second line ends with the fifth note, C, of the F Major scale. Without any specified harmony, this tone leaves the listener wanting to continue on with more music, looking for a final resolution on F. Unintentionally, this song also incorporates no accidentals.

Another example of a tune with this basic compositional principle, and the basis for Mozart’s set of variations on the theme collectively known as “Twinkle, Twinkle, Little Star” in English, is the old French rhyming song “Ah! vous dirai-je, maman.” Its score is shown in Figure 6.4. This is a melody that also exemplifies starting on a first note of the major scale tone and then displaying the goal of returning to that same scale tone throughout the piece. In the first line, the opening phrase moves away from the tonal center (A) and its complementary phrase completes the return journey. In the second line, the phrase begins on the fifth tone of the scale (E) and makes a descending journey toward the key note, falling short of the goal, ending on the second tone of the scale (B). The tune has a “rounded” form with the opening section returning, completing the journey back to tonal center, A.

Figure 6.4 The traditional French nursery composition, “Ah! vous dirai-je, maman,” showing the gravity of the phrases aiming toward their starting note, A.

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In broader terms, one can think of the return to the original tone as a form of musical alliteration. If you “dynamically anchor” the piece with frequent returns to the initial sound, it anchors the music the way alliteration does in, for example, Skaldic poetry or Olde Englishe Poetrie (OK, we got crazy with the ending e’s, sorry); for example, the consistent use of alliteration in Sir Gawain. In fact, alliteration is often referred to as initial rhyming. So, you could also think of each return to the starting key or harmony as completing a rhyming line. Rather than several similar sounds in succession (alliteration), it may be a means of showing that you are in the knowing of how your tune is growing without the use of crowing (rhyme). This is not “challenging” music − it ends on the note it started on, and even Uncle Louie, who could not hold a tune if his hands were smothered in a Fred Biletnikoff/Lester Hayes level of stickum, “gets it.” This does not mean that you should not do this in your composition. For example, you can choose not to return to the same note (or a note on the same chord even) at the end, which may be more like a one-way ticket to a new destination instead of a round-trip ticket. This may or may not leave your listener waiting for the eventual element in your composition that does resolve this tension. Returning to the starting note after this tension is not a cliché, then, but rather a resolution of the tension − which your listener will appreciate. Having considered the melody, let us turn to the harmony. Harmonically speaking, the concept of a tonal center centers around a chord and functions in a manner similar to beginning and ending on the same note in the melody. Within a scale, chords can be derived from the tones to create the harmonies that define the key. In the western music tradition of tertian harmony, the chords are constructed in intervals of thirds (i.e. the first, third, and fifth notes of the scale for the I chord, the third, fifth, and seventh notes of the scale for the III chord, etc.). Figure 6.5 illustrates the C Major scale (starting with C and returning to C, upper staff of the score) and its corresponding chords (lower staff of the score) as triads of notes derived from the scale. It is worth noting that tertian harmony opens up to more chances for melodic variance. The tonal center chord (I chord, composed of notes C, E, and G in Figure 6.5) provides the “gravity” for the scale. This I chord does not have to comprise C-E-G in order, though. It can be included as E-G-C in order (the “E” being the lowest note in the triad) or G-C-E in order (the G being the lowest note in the triad). These are ways of harmonizing a start or end note on the third or fifth of the scale (E and G, respectively, for C Major). From the perspective of the melody, the tonal center note “C” (in the key of C Major) does not always need to be harmonized with a C triad. The tone (“C”)

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Figure 6.5 C Major scale and its corresponding chords as triads of notes derived from the scale − the basis of traditional tonal centeredness (the composer’s “palette”).

is also part of the A and F triads (A-C-E and F-A-C) within the same scale (IV and vi chords, respectively, in Figure 6.5). Continuing the discussion on melody, it is worth reiterating that an analogous approach can be used with the harmony (or chord progression). In composing, you may decide to bring a phrase to its expected conclusion by ending the harmony on the same chord that it started with, regardless of the melodic tone used. Using this harmony “cycle,” then, you should be able to start and end the melody on different notes without leaving the audience in expectation. In fact, this “twist” of the melody overlaying the expected conclusion of the harmony may be a simple way to “guide” the audience’s affect (emotions, feelings, etc.) at the end of the song. The harmony may provide closure and a feeling of completeness, for example, while the choice of the melody’s last note may convey happiness, longing, or even the craving to go buy the product whose jingle was surreptitiously hidden in the last notes of the melody. Having returned to the harmony, please note that the chords you use to harmonically complement the melody can be chosen carefully; alternatively, you can choose a minimum set that will cover all of the notes in the scale. So, if you are composing and you are writing something that only uses the seven unique notes in the scale, you only need three chords to cover all of the notes, irrespective of their order (melodic order). This is why the primary chords I, IV, and V are often used in simple chord progressions. Let us take a look, using C Major as our scale. The I chord (built off the first scale degree) is C-EG, the IV chord (built off of the fourth scale degree) is F-A-C, and the V chord (built off of the fifth scale degree) is G-B-D. Add them together and you get {C, E, G, F, A, C, G, B, D}. Alphabetize these and you get {A, B, C, C, D, E, F, G, G}. Ignore the repeats on the roots of the I and V chords and you have {A, B, C, D, E, F, G}. That is all of them. Painters use a similar approach

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with reduced palettes, in which choosing, for example, purple, brown, and chartreuse might cover a lot more ground (color ground, that is) than choosing just red, yellow, and blue (without mixing here). It should be noted that even two chords can cover the entire set of notes in a key. For example, in C Major, we can readily account for all seven notes of the scale in a variety of ways. Two examples are (1) using the I chord harmonized with the sixth note, A, or C-E-G-A, and (2) using the V7 chord extension as a ninth G-B-D-F-A. More commonly, all but the A are covered using the I and V7 chords. The I and V chords are a powerful pair because they can harmonize any note in the scale. We will illustrate this with a return to the Alouette song, now harmonization and two contrasting versions of the second line added (Figures 6.6 and 6.7). In the first harmonization (Figure 6.6), the C7 chord played with the whole note “C” at the end of the second line acts to intensify the need to continue on and to resolve the piece with F at the end of the third line (now would be a good time to play the score of Figure 6.6 on your instrument(s) of choice).

Figure 6.6 Alouette with harmonization (with C7) at the end of the second line that leaves you in expectation of resolution by harmonization with F at the end of the third line.

In the second harmonization (Figure 6.7, second line only shown since lines 1 and 3 are unchanged), we use an F chord to harmonize the “C” at the end of the second line. Effectively, this resolves the piece and you could end early musically (although the libretto may be unsatisfied). Regardless, the sense of urgency to continue after the second line of Figure 6.6 is missing with the alternative harmonization shown in Figure 6.7 (don’t take my word on it - get back to your instrument(s) of choice and see for yourself).

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Figure 6.7 Alouette with harmonization (with F) at the end of the second line that no longer leaves you in expectation of resolution with the additional third line of Figure 6.6 (because this line ended with F already, of course − thank you, Department of Redundancy Department).

As mentioned in Chapter 5, many modern popular songs use I, IV, V, vi as the set of chords for the tune. As we have seen, the {I, IV, V} cover all the notes of the scale and the vi chord functions as a substitution for the I chord while adding a minor harmony to the mix for additional color. Of course, you can use more chords than I and V, even if you have no accidental notes. For example, in François Couperin’s Les Baricades Misterieuses (Figure 6.1) and Scriabin’s Prelude in Db Major, Opus 11, No. 15 (Figure 6.2), there are no accidentals, but Couperin uses the {I, V, vi, ii} harmonies, while Scriabin uses the {Vi, V, ii, III, IV, I} harmonies. We will add a little more complexity to the analysis now. The first popular/folk song we will look into more in depth is Steven Foster’s Camptown Races (Figure 6.8). In this work, the melody starts on the fifth scale degree, which is another note of the I chord tonal center. The antecedent phrase of the verse melody generally works its way down, stopping on the second degree of the scale harmonized as the V7 chord. The consequent phrase completes the journey home to the first scale degree harmonized as the I chord. The chorus section displays a common starting and stopping point of the first scale degree and I chord harmony. The use of the “tonic/dominant” relationship is a common harmonic scheme for incorporating an antecedent followed by a consequent. In Camptown Races, this is accomplished by going away from the tonic at the end of the first line (to the fifth of the V chord) and then returning to the root of the I chord at the end of the second line. The harmony mirrors this, ending on the V chord for the first line and then returning to the I chord at the end of the second line. Note that Foster uses the occurrence of I, IV, V, and ii (not the I, IV, V, and vi) to harmonize in simple but “complete” fashion; that is, with a small set of chords that cover all seven notes of the key. Is Foster using the harmony or the melody to guide the composition? You can make this call for yourself: Foster has woven them together well enough that there is probably a little of both. It is worth noting, however, that the harmony covers all seven notes of the key, while the melody leaves one (C#) out.

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Figure 6.8 Steven Foster’s Camptown Races.

Turning next to the traditional Scots tune Auld Lang Syne, here the end of the antecedent phrase goes to the IV chord, and the consequent phrase returns to the I chord’s root (in the case of Figure 6.9, the note F). This choice bucks the common goal of going to V and back to I, and so has a different feel to it. With Auld Lang Syne, a less common phrase goal is employed: the first phrase is intended to get to the IV chord. The goal of the second phrase is a familiar return to the I chord.

Figure 6.9

Auld Lang Syne (traditional Scottish tune).

Next, this familiar tune is reimagined with the antecedent ending in the more common goal of reaching the V chord, and with the consequent phrase altered to further eliminate the IV chord from the piece (Figure 6.10). The general tune is still familiar even with the melodic and harmonic alteration. This different goal, however, may be perceived as removing some of the original tune’s character.

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Figure 6.10 Auld Lang Syne redirected toward the V chord (more commonly used), but here changing the feel of the familiar tune.

Whether you use harmony, melody, or both to establish your key, it is generally a good practice of tonal music to establish the key at the onset. This is true for music further afield than popular/folk music: it is also a good practice in art music such as Beethoven. In Beethoven’s Piano Sonata in G Major Op. 14, No. 2, Ludwig uses a similar set of chords to define the key (Figure 6.11). In this sonata, Beethoven uses I, ii, and V to define the tonality. Although not an accident, the character of the phrase is brought about by the use of lower neighbor tones a half step below to accentuate the harmonic tones of the figures. This illustrates the fact that harmonic tone can maintain a piece even with the occurrence of a substantial number of accidentals. Beethoven, as we see here, used these accidentals to simultaneously set the tone and to create interest for the listener.

Figure 6.11 Ludwig van Beethoven’s Piano Sonata Op. 14, No. 2.

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Defining tonality is not limited to major keys. Using a small (often “complete”) set of chords as a compositional approach also applies to minor modes such as C Minor (Figure 6.12).

Figure 6.12 C (Natural) Minor scale, also known as the Aeolian mode (more to come on this).

The harmonic scale alteration to the natural minor (Figure 6.13) has a raised seventh degree and its principal use is to alter the V chord from minor to major. This procedure creates a leading tone; that is, a note that provides an expectation of leading back to the tonal center (or first scale degree). This leading tone primarily affects the V chord, as noted, but also affects the III and the vii diminished chords.

Figure 6.13 The C harmonic minor scale. Note that it is spelled C, D, Eb, F, G, Ab, B, C, instead of C, D, Eb, F, G, Ab, Bb, C in the natural minor scale.

So, the harmonic minor, altered with the raised seventh, acts to introduce the leading tone. This is lacking in the natural minor. The use of this “introduction” capability is illustrated in Beethoven’s Piano Sonata in C Minor Op. 10, No. 1 (Figure 6.14). Beethoven primarily defines the tonality of the C harmonic minor scale using the harmonies i (C Minor), vii7 (B dim 7), and V7 (G7). The only “accidental” in the score example is the B-natural (the leading tone). The key is defined primarily with the i, the fully diminished seventh

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chord, and the V7 chord throughout the opening material. Sure the composition explores elsewhere throughout the course of the movement, but the motivic material and tonality are defined in the listener’s ear from the outset.

Figure 6.14 Beethoven Piano Sonata in C Minor Op. 10, No. 1.

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The V7 is often used but sevenths (and beyond) can be added above every chord within the key signature. Chord harmonies do not need to be confined to the basic triads of tonal harmony. Extended chords within a key can still define a tonal center, and they may incorporate a more contemporary (or more colorful, at least) harmonic sound beyond basic triads. Note that this capability is not limited to the octave you are within − in addition to adding the seventh chord (Figure 6.15), you can add the extended chords such as 9ths, 11ths, and 13ths above the root.

Figure 6.15

Seventh chords generated beyond the basic triads in the key of C Major.

To show how a composer might use harmonies beyond basic triads, we turn to Nikolai Medtner’s Six Tales Op. 51, No. 3 (1923), shown in Figure 6.16. Medtner includes seventh chord harmonies and suspended tones defining the key of A Major in this piece. Note that the main melody is harmonized using the cycle of chords based on the upward leap of the fourth starting on the vi chord (vi7, ii7, V7, I). Other chords used from the A Major scale include the ii chord harmonized with the seventh and the vii half diminished chord, as well as the iii7 chord. We have seen, then, that some predictability (and thence completeness, or resolution) in music composition can be provided by tonality. We will further consider predictability in tonality with specific elements of the works of Beethoven and Mozart (you might have heard of them). Beethoven uses tension and its delayed resolution in the opening portion of the “Ode to Joy” theme of his Ninth Symphony. The third to last note in Figure 6.17 (see figure legend for more specific details) is held for longer than expected, making the listener anticipate – and then be happy to have resolved − the completion of the phrase with the root note, D. We offer an altered version of the melody with the delay that causes the tension to be removed (Figure 6.18). Even though the melody is “watered down,” our expectation of the destination of each phrase is fulfilled.

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Figure 6.16 Nikolai Medtner’s Six Tales Op. 51, No. 3.

In the original Ode to Joy example (Figure 6.17) and our tension-free version of it (Figure 6.18), the score represents the single line melody as introduced in the basses of the symphony. The harmony, fulfilled by other instruments, is indicated by chord shorthand such as “I:D” and “V:A” in the scores of Figures 6.17 and 6.18. However, we do not really need the harmony to predict where the melody will land at the end of each phrase. The harmonic rhythm of one chord per measure is established across the phrase, providing a predictability that transcends the actual notes chosen. In the final measure of each line of Figure 6.17, the tension is increased with the delayed return to A (upper) or D (lower) with the addition of a note (the F# [upper line] or E [lower line] dotted quarter note) a second above the

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Figure 6.17 A section of the “Ode to Joy” theme from Beethoven’s Ninth Symphony. The melody for this composition uses an antecedent/consequent pairing as discussed in Chapters 2 and 3 as a way of providing tension (by the F# [upper line] or E [lower line] dotted quarter note at the beginning of the last measure of each line) followed by resolution of the tone. The eighth note (the E in the upper line or D in the lower line, last measure) is an anticipation note that foreshadows the harmony and melody coming together on the last half note.

Figure 6.18 The “Ode to Joy” section of Beethoven’s Ninth Symphony without the tension (delayed resolution) created by the F# [upper line] or E [lower line] dotted quarter note at the beginning of the last measure of each line as shown in Figure 6.17. Here, the harmony and melody track more predictably than in Figure 6.17, but perhaps musically this arrangement is “less interesting?” Undoubtedly, it was to Beethoven, as he chose Figure 6.17.

anticipated note, with the tension being resolved by the anticipated eighth note followed by the expected note as a half note. In Figure 6.18, there is no delayed return and thus no (perhaps much needed) tension. In either case, the music resolves as expected; however, most would agree that Beethoven’s delayed resolution (Figure 6.17) is more memorable than the “non-tensioned” version (Figure 6.18). Turning to Mozart, the Minuet in F K.2 is also worth exploring for the topic of predictability of tonal resolution. One “trick” of a musician good enough to write minuets at age five that are still played two and half centuries later is to deceive the listener temporarily, and then show them that the deception was simply a means of getting them to invest more fully in the music. This also has the possibility (almost a certainty in the case of

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Mozart’s combination of melodic magic and mirth) of making the listener feel smart when the resolution occurs. As a composer, just as you would being a lecturer or even a meme creator, a clever and fun way to make your audience appreciate your talent is to reward them for what they already know. Playing off the expected resolution with some tension is such an approach. In Figure 6.19, Mozart establishes the main theme of the minuet. At the end of the first line, the lower “suspension” note E holds off the expected note of resolution, F. The expectation did not simply drop out of the sky: Mozart established it with the main theme and motivic content of the first three measures. Note how the melody starts on the first tone of the scale (F) and works its way down to end exactly an octave lower.

Figure 6.19 Mozart Minuet in F Major K.2. Here, the lower “suspension” note E holds off the expected note of resolution, F.

When the phrase returns to conclude the composition (please see Figure 6.20), a deceptive cadence − that is, the vi chord − is substituted for the I chord harmony. The fermata over the F note (treble score) and D note (bass score) gives the listener a chance to really appreciate, both from a note and time perspective, that they have not yet arrived at where they predicted based on the key. This suspension of the resolution (the “tension” notes in the fourth measure) is brilliant: it allows the musicians to gauge the audience and hold the fermata just long enough to create the desired amount of tension

Figure 6.20 Mozart’s Minuet K. 2 with its deceptive cadence (fourth measure) upending and delaying the resolution. Please see text for details.

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and delay. The four-measure phrase is then repeated with the expected tonic resolution as established in the opening of the composition. This is really important here since in fact Figure 6.20 is the end of the minuet! There would be no later chance to resolve.

6.3 Modality We have talked about the major scale at length and introduced the natural minor scale (Figure 6.12) and the harmonic minor scale (Figure 6.13) above. There are other options for scales beyond the ubiquitous Major/Minor system. In this section, we consider the modal systems. With modal systems, the same set of pitches can be used and yet produce different centers of gravity. As one example, instead of using a key that moves from note C to C an octave higher with no accidentals (no sharps or flats), that is, C Major; you can use a key moving from notes D to D an octave higher (no sharps or flats). The latter mode has all of the same notes (same set of pitches), yet the tonal center or starting or stopping point becomes D Minor instead of C Major. An overview of these seven modes is given in Table 6.1. Table 6.1

The seven modes, from Ionian to Locrian mode.

The Greek names featured in Table 6.1, for us at least, evoke the feel of Homer’s Odyssey. While all of the places in the Odyssey are in a relatively smallish part of the world (the Eastern half of the Mediterranean), each of the locations has its own “vibe”. The notes are the same, but the tonal center is different for each. Picturing each of them as a different location in the Odyssey, including the largely alliterative association of them with seven key sites in the epic poem shown here, could be a good mnemonic for remembering their ordering, or just associating the “feel” of the mode with

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a place name (sort of a form of musical synesthesia, if this type of sensory association works for you). Ionian = Ithaca (Odyssey’s home and the destination of the Odyssey) Dorian = Troy (an extension of the earlier Dorian invasion of Greece?) Phrygian = Polyphemus’s Cave (Island of the Cyclopes) Lydian = Laestrygonia (or Telepylos, where giants pelted Odyssey’s boats with rocks) Mixolydian = Scylla and Charybdis (mix o’ rock and hard place) Aeolian = Aeolia (the island of Aeolus the wind god) Locrian = Lotus Land Regardless of your mnemonic, there are seven modes, and we will now briefly illustrate them. The first mode is the Ionian mode (Figure 6.21). Using C Major as our basis, the Ionian mode starts and ends in C. It is, therefore, more commonly understood as – wait for it – C Major.

Figure 6.21

Ionian mode.

The Dorian mode, in contrast, starts on the second note of the C Major scale and ends an octave higher on the same note, D (Figure 6.22).

Figure 6.22

Dorian mode.

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The Phrygian mode starts on the third note of the C Major scale and ends an octave higher on the same note, E (Figure 6.23).

Figure 6.23 Phrygian mode.

The Lydian mode starts on the fourth note of the C Major scale and ends an octave higher on the same note, F (Figure 6.24).

Figure 6.24 Lydian mode.

The Mixolydian mode starts on the fifth note of the C Major scale, and ends an octave higher on the same note, G (Figure 6.25).

Figure 6.25 Mixolydian mode.

The Aeolian mode starts on the sixth note of the C Major scale and ends an octave higher on the same note, A (Figure 6.26). Finally, the Locrian mode starts on the seventh note of the C Major scale and ends an octave higher on the same note, B (Figure 6.27).

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Figure 6.26 Aeolian mode.

Figure 6.27

Locrian mode.

Each of these modes has a different color to the tonal center, in spite of comprising the exact same set of seven notes. We illustrate this with the Christmas song Noel Nouvellete or Sing We Now of Christmas, which is given in Figure 6.28 (feel free to play it yourself). The melody is in the Dorian mode. One characteristic feature of the Dorian mode is the sixth tone of the scale, which is nine half steps above the first note of the scale, one more than the typical (Harmonic minor) mode, to be discussed shortly. In a technique of establishing a key using primary chords, the Dorian relationship between I and iv is different from the Ionian mode (or any of the other five modes in this section, overall). The chord built on the fourth degree is Major in the Dorian mode. In the harmonic minor mode, the E is flattened, but in the Dorian, it is natural giving the major chord spelling of C-E-G instead of the minor chord C-Eb-G. Next we can reimagine the composition if it had been conceived in the harmonic minor mode to employ the dominant 7 chord on the fifth scale degree (V7) directly. This is shown in Figure 6.29. Note that the Cm (C Minor) chord is used in the progression here, as opposed to the C Major chord in the Dorian mode (Figure 6.28).

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Figure 6.28 Noel Nouvellete in Dorian mode. A typical harmonization is given in which a D7 chord (which incorporates a note not in the Dorian scale) is used to create an authentic cadence (V7 to i).

Figure 6.29

Noel Nouvellete in harmonic minor mode.

The tonal center for both settings is G Minor harmony; however, the cast of characters is different in comparing the Dorian and harmonic minor scales (different numbers of “steps” on the chromatic scale between consecutive notes on the modes). This is shorthanded by “whole” and “half” steps, and is summarized for the seven modes in Table 6.2. Next we consider just the first line of Noel Nouvellete employing the Ionian mode (Figure 6.30), and the Dorian mode without any chord adjustments (Figure 6.31) introducing tones from outside the scale.

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Table 6.2 The seven modes, from Ionian to Locrian mode, showing the pattern of whole and half steps for consecutive notes. Each sequence is unique from the other six. The adjustment of the Aeolian mode, the harmonic minor mode, is added as an additional row here for comparison. Mode

Step 1

Step 2

Step 3

Step 4

Step 5

Step 6

Ionian

Whole

Whole

Half

Whole

Whole

Whole

Step 7 Half

Dorian

Whole

Half

Whole

Whole

Whole

Half

Whole

Phrygian

Half

Whole

Whole

Whole

Half

Whole

Whole

Lydian

Whole

Whole

Whole

Half

Whole

Whole

Half

Mixolydian

Whole

Whole

Half

Whole

Whole

Half

Whole

Aeolian

Whole

Half

Whole

Whole

Half

Whole

Whole

Locrian

Half

Whole

Whole

Half

Whole

Whole

Whole

Harmonic minor

Whole

Half

Whole

Whole

Half

Whole + Half

Half

Figure 6.30 The first line of Noel Nouvellete employing the Ionian mode. The root chord, G, is a major sound (as opposed to the minor sound, Gm, in Figures 6.28 and 6.29).

Figure 6.31 The first line of Noel Nouvellete employing the (unmodified) Dorian mode.

We finish our consideration of the first line of Noel Nouvellete employing the Phrygian mode (Figure 6.32), the Lydian mode (Figure 6.33), the Mixolydian mode (Figure 6.34), the Aeolian mode (Figure 6.35), and the Locrian mode (Figure 6.36).

Figure 6.32 The first line of Noel Nouvellete employing the Phrygian mode.

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Figure 6.33 The first line of Noel Nouvellete employing the Lydian mode.

Figure 6.34 The first line of Noel Nouvellete employing the Mixolydian mode.

Figure 6.35

The first line of Noel Nouvellete employing the Aeolian (natural minor) mode.

Figure 6.36 The first line of Noel Nouvellete employing the Locrian mode. The tonality of the root chord is based on a diminished G.

Successful songs have been written in each of these modes, even the Locrian mode (we are assuming you played each of the lines from Figures 6.30 to 6.36). The Locrian mode might fall flat for you depending on your compositional aims and, like our original example of the modified Dorian mode above, may motivate you to modification. Like the bad joke at Grandma’s funeral, you may feel one of these modes is a bit “tone deaf” for your composition. If so, a slightly different “punchline” can be attained through modification of one or more chords. Lots of room for experimentation, and really how hard is it to just change a chord to make the punchline more successful?

6.4 Atonality Returning to the Homeric analogy above, wherein the seven modes were associated, largely alliteratively, with seven locations in the Odyssey, for

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pantonality we will instead think of the Iliad. As the name implies (Ilium is another name for Troy), the Iliad is focused (barring a few minor skirmishes and the Greeks hiding while the Trojan Horse is rolled into the doomed city) on one location. In other words, everything all in one place, and all 12 notes (represented by A, Bb, B, C, Db, D, Eb, E, F, F#, G, Ab as one labeling option) freely used for the composition. There is no “tone” per se (thus the named “atonal”), because no notes are outside the scale. Thus, there is no clear tonal center, because such a composition incorporates all 12 notes, or pitches, of the chromatic scale into the composition without a sense of gravity toward one note or harmony (the latter being a main characterization of tonal music). Using atonality, then, you can use an effectively limitless number of ways to “surprise,” or “engage,” or even “enrage” your audience, depending on their expectations, sophistication, and systolic blood pressure. For example, musical dissonances can be created without preparation or even resolution. There is no need for starting or ending on the same note or harmony, which means when it ends, well, it just ends. Thus, if you choose, there is little or no predictability of what is coming. If so, the melodies may be less “catchy” than in tonal music. However, is any other approach more open to creativity than using any notes you want in any order? It is like free-form poetry. Just make sure you compose something better than this: Broccoli man digs the chartreuse cloud of penance That waves him on in his ocean of sorrow He digs the vibe, and vibes the dig Can you dig it, man? Alright, we will admit, it would be hard to not be better than this! Go do it! As an example of atonality, we consider Arnold Schoenberg’s Sechs Kleine Klavierstücke, Op. 19, No. 4 (1911), the entirety of which is shown in Figure 6.37 (as opposed to the last several figures, we are not asking you to play this, but if you can, kudos to you!). Note that all 12 notes of the chromatic scale are used within the first four measures of the song and the piece does not end on the note it began with. And so we conclude the compositional part of this chapter with yet another opus, in this case one by Schoenberg. Did you know that an opera cannot be an opus? And yet, Beethoven’s Fidelio is faithfully labeled Op. 72 (Opus 72). Opera is plural for opus! Get it together, opus committee! OK,

6.5 Sidebar

Figure 6.37

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Arnold Schoenberg’s Sechs Kleine Klavierstücke, Op. 19, No. 4 (1911).

thanks for letting us get that one out of our system. With that, we turn to this chapter’s sidebar.

6.5 Sidebar This chapter’s sidebar is on theory and experimentation, viewed through the eyes of synesthesia. We chose this chapter for the “synesthesia” sidebar because of the association of harmony and melody in the main body of this chapter. Synesthesia is all about association. Theory and experimentation are

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the triaging aspect of composition, and can be overwhelming. Relevant to the tonality focus of this chapter, for example, what chord progression will you use? How will you transition from one key to the next? Or will you choose to be chromatic, even atonal? From a composing standpoint, without some forms of rules, constraints, or formulas for limiting the possible experiments to perform, the act of composition may turn from one of creativity to one of frustration rather quickly. One means of providing constraint is by associating the act of composition with another act, in particular another sense. Many famous musicians have “admitted” to having synesthesia. Synesthesia is the situation in which sensing along one cognitive pathway (e.g. hearing music) simultaneously evokes experiences in an additional cognitive pathway (such as vision). It can be thought of as the co-activation of two senses at the same time. Do we believe that suddenly so many musicians (from Beyoncé to Billy Joel) have synesthesia? That is not a question worth answering. The one we can answer is that they all want people to think they have synesthesia. Just like modern architects who use such brain dead styles as “Brutalism,” “Deconstructivism,” and “High Modernism,” synesthesia is an unwelcome “in joke” that is used by some elite artists to try to intellectually separate themselves from the rabble that has the audacity to overvalue their creations. We will not be those people. In fact, we will be “deconstructing” their fallacies straightaway. It is a provable fact that we all have synesthesia. When you hear the word “green,” can you picture the color green (with apologies to the color-challenged women and [mostly] men out there)? Of course you can. So, you can associate the color green (visual) with the sound of green (auditory). In other words, if you see red when you hear “red,” then you have synesthesia. As Syndrome said in The Incredibles, “When everyone’s special. . . no one is.” Now that we have established that no one is special, we now find out why everyone is special. Sort of The Incredibles’ Syndrome in reverse, which is actually Emordnys, but I digress. Everyone is special because not only can everyone, upon closer inspection, recognize that they have synesthesia. Even more importantly, they can recognize that they can use their synesthesia to help explore a set of possibilities for their composing. Their innate, or natural, synesthesia must be incorporated, illuminated, or even induced for it to be a valuable tool in composition. Let us explore a couple of ways here. Suppose that your preferred mode of synesthesia is something called chromesthesia. With this, you associate sounds with colors. So, take 12 colors – maybe the six primary additive and subtractive colors {red, green, blue,

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185

yellow, cyan, magenta} all 60 degrees apart from the next one, along with the colors 30 degrees to each side of them (Figure 6.38). These 12 colors have the common names shown in Figure 6.39, which are {red, lime, blue, yellow, aqua, fuchsia} for {red, green, blue, yellow, cyan, magenta}, and the colors offset by 30 degrees are {orange, chartreuse, spring green, azure, violet, and rose}, as shown in Figure 6.39.

Figure 6.38 Color wheel with 12 colors, each 30 degrees apart from its neighbors. The entire wheel is 360 degrees in total, for 12 colors. Red, at top, is normally considered to be at 0 degrees.

How do we map from these colors to music compositions? Conveniently, the 12 colors correspond to the 12 notes in the scale, including the accidentals. Letting all the accidentals be sharps, we map as shown in Figure 6.40. We could just as easily have used flats; for example A# = B . Note that every neighboring note, even as we move up to a higher octave or down to a lower octave, is only 30 degrees away from the note closest to it in the chromatic scale (more on that fortuitous name shortly!). In our example, we have arbitrarily associated note A with Red. Once that occurs, we can either choose to have the notes ascend the octave clockwise or counterclockwise (we chose clockwise, because for one of us, A does associate with Red and B

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Figure 6.39 Color wheel with 12 colors, each 30 degrees apart from its neighbors. Here the colors are named with their common, rather than graphics/printing names (e.g. “Lime” instead of “Green,” “Aqua” instead of “Cyan,” “Azure” instead of “Blue-Cyan,” etc.).

with Yellow). The outcomes of this chromesthesia arrangement are shown in Figure 6.40. However, this is by no means the only possible arrangement. For example, Scriabin, who was an admitted synesthete, arranged colors based on the Circle of Fifths rather than consecutive notes [Gale01]. You can make any arrangement that aligns with your own synesthesia, or just one that matches the colors you would like to associate with each note with the notes themselves. Once we have an arrangement, though, the fun really begins. Now we can use a sequence of colors to define a composition. We will start with something simple, the American flag. Red, White, and Blue, that seems, easy, start with an A for Red and work to an F for Blue. But wait, what is between them? White, of course. And what is White other than all of the other colors combined? In other words, it is fully chromatic! So, we use white to create a chromatic transition from A to F, either playing A#, B,

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Figure 6.40 Color wheel with 12 colors, each 30 degrees apart from its neighbors. The 12 notes of the scale are written to the 12 colors, using sharps for all of the accidentals.

C, C#, D, D#, E, and F in fast sequence, or alternatively G#, G, F#, and F in fast sequence. The term chromatic comes from the chromatic scale, which is the 12 notes in Figure 6.40, the five sharps giving color to the seven notes of the octave (eight if you count the starting note in both pitches). This is an easy one. What if, instead, you decided to use a pointillistic painting to create music. By one account [Gold19], Seurat’s Un Dimanche Après-Midi à l’Île de la Grande Jatte contains 220,000 dots. With chromesthesia, that would be 220,000 notes. Even with an extreme tempo such as Bebop at 400 bpm (beats/minute), this is 550 minutes or more than nine hours of notes! We can then imagine “sampling” la Grande Jatte to obtain a different set of compositions! The mapping of dots to notes could also be tempered by sequences of colors in the dots; for example, two consecutive identical colors makes a single note with twice the length (e.g. a quarter note instead of a default eighth note). The set of possibilities is large. And we are just getting started.

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As one example, the color approach can be extended further using the concept of afterimage. This is when visual image is retained by the visual sensors (the retina’s photoreceptors) after the image has been removed (usually a very bright image or an image viewed for a relatively lengthy period of time). For color images, the afterimage is the color opposite (or color “opponency”) of the vivid image. So, the American flag, the afterimage of Red, White, and Blue, might be Aqua, Black, and Yellow, or the notes D#, rest, and B. The “rest” is the absence of notes, and the D# and B are from Figure 6.40. Following a musical image with its “afterimage” is a different means of progressing between phrases than, for example, using the Circle of Fifths. Any of the chromesthesia approaches mentioned can be used to create ambient music, in a way perhaps much simpler than some of those introduced by Brian Eno and other champions of that field of music. Instead of being like Dishwalla and Counting Blue Cars, you could note the color sequence of cars you drive by (or that drive by you) and convert that sequence into a musical composition. You could do this with any other set of color objects, as well. Synesthesia is more than chromesthesia, of course, and so the possibilities for “ambient” musical composition include any other sense-to-sense “transduction.” Music, an auditory medium, can create somatosensory feelings in several ways. Percussion leads to vibration, with the familiar sense of the ground moving underneath you. Tchaikovsky’s 1812 Overture is simply one well-known example of this. So is Rush’s YYZ. In addition, roughly half of people have frisson, which is a form of aesthetic “chills” or musical “chills” that one gets from certain sequences of music. Sure, this is due to emotional associations, but the chills are definitely a somatosensory output every bit as much as shivering. Because we can rehearse, reinforce, and even induce synesthesia, we can also use multiple forms of synesthesia in combination to create more complicated compositions. You might start with a sequence of random nature sounds to pick whether you are using only arpeggio notes or the full chromatic scale, varying this from measure to measure. Then, the melody could be selected by the sequence of colors belonging to the creators of the sounds, for example, a blue jay, a robin red, a yellow jacket, an orange cat, etc. The rhythm might be determined by the relative spacing of one or both of these sequences. Music is multi-media by definition − harmony and melody alone are two different

References

189

media. When you include instruments, possibly voices, and additional sounds (percussion, clapping, etc.), you can layer your composition with sensory input from visual to auditory to olfactory. Once you have decided on the source of your synesthetic-inspired composition, you need a way to optimize the output. This means a way to select among many candidates for the melody. It might take several books to even approach this issue, but the basic approach might be to determine which of your input sources provides the best “hook” for your audience. You can ask for feedback through simple survey mechanisms like Likert scales, or you can trust your own intuition. Do you wish to avoid a verse-chorus-verse structure, like Radiohead did with Paranoid Android? Then make sure that the sense you are sampling is not repetitive and causal. For example, sampling the output from a power generator probably is not for you (although it might work for the percussion). Basically, this is where the art comes in. Modify the synesthetic output to suit your taste. Synesthesia is usually just the start. Take some of the approaches in other sections of this chapter and book – not to mention other books and people you trust – and modify this already modified content. As always, have fun!

6.6 Summary In this chapter, we focused on the use of tone to engage your intended musical audience. Using some combination of harmony and/or melody, we showed how to use tone to create a center of gravity, or tonal center, for your musical piece. This establishes direct communication with your audience, and can provide various levels of musical expectation that you can fulfill, delay fulfillment of, or even ignore the fulfillment of, to make a statement. Chord progressions, from the traditional to those adding unexpected diversions to your music, are an important part of this “social contract” between the composer and the listener. We investigated the use of the seven modes (Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian) and some relevant modifications to show how tone changes even with the exact same melody and “steps” between consecutive notes. The last “tone” considered was atonality, with its lack of rules offset by its “infinite” creative possibilities. In the sidebar to conclude the chapter, synesthesia, or the tight association of two senses, was employed as a source of creative energy and possibilities.

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References [Gale01] Galeyev BM, Vanechkina IL, “Was Scriabin a Synesthete?” Leonardo 34(4), 2001, pp. 357-361. [Gold19] Goldstein JL, “Seurat’s Dots: A Shot Heard ‘Round the Art World—Fired by an Artist, Inspired by a Scientist,” Cell 179, 2019, pp. 46-50.

7 Mode Mixture and Modulation

There is no great genius without a mixture of madness – Aristotle I’m an icon that is made out of all the colors on the palette at every time – Lady Gaga

Abstract Nuance, or color, in composition, is added through mode mixing, modulation, and related techniques. Mode mixing includes borrowing chords from other keys (harmonization). Tonicization is a technique used to change the tonal center of a piece and can either be abrupt or (usually) involve a set of transition chords or notes. Modulation is the general technique for changing keys, while chromaticism is the general use of all notes, both within and outside of a key. In fact, chromaticism can be used to mask the key for some length of notes, akin to a musical metamerism, where one piece of music may sound like two different keys based on which key precedes and which key follows. This can be considered a musical metamerism, or form of “color ambiguity.” The chapter concludes with a discussion of color metamerisms as an analogy for this type of musical creativity. Keywords: Borrowed Chords, Chromaticism, Color, Metamerism, Mode Mixing, Modulation, Obscuring, Secondary Dominant, Tonicization

7.1 Introduction In this chapter, additional complexity and nuance for composition is explored by building on the techniques learned in Chapter 6 as a means for adding additional notes and harmonies into a piece of music, beyond the compositional

191

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idea of sticking to one scale. We begin with a description of mode-mixing, which includes such approaches as chord borrowing (harmonization) and parallel scale borrowing to introduce a new flavor to your composition, either temporarily or transitionally. Next, tonicization is described as a means of fine-tuning where the perceived tonal center is, temporarily, changed. For example, if C is the tonal center, then we can redirect our focus to another tone within that scale temporarily (like F, for example) to provide tonicization. This effect is temporary, and not an actual key change. Next, we describe the use of modulation, in which an established key is abandoned in order to use another key entirely. This is the familiar “key change” that is instantly recognizable to most listeners, even if they cannot differentiate the keys. Think of coming home to a door that will not open. You recognize immediately (you cannot get in!) that the key has changed, but you may need a locksmith to figure out the new key. In the next section, chromaticism is discussed. Usually, chromaticism involves introducing a lot more notes outside the key. You may end up abandoning keys altogether in the extreme of chromaticism where it is effectively atonality. However, chromaticism does not have to be that wacky and may only be used for a short phrase, even a riff. You may think of chromaticism as the musical equivalent of protists in biology; that is, a kind of “grab bag” that fits everything not described by mode mixture, tonicization, modulation, and the like. The sidebar addresses metamerism, which is a term more familiar to color scientists. This is when a color looks different under two or more different sources of light. You think you have found a great match to the paint on your house under the nauseating fluorescence of the hardware store lights, but once applied the bright sun of day reveals a much different color and potentially an ugly transition in your exterior décor. In music, one metamerism might be achieved by down-tuning guitars for aging rockers so that they can still hit the same “high note” (apparently) even though that high note has been tuned down a few Hertz in frequency. The song, generally, sounds familiar even though it does not match up side-by-side with the original recording. This could be a problem if you try to play along with the new performance using a standard tuned instrument.

7.2 Mode Mixture In Chapter 6, we described how tonality can be used to establish a flavor or a sense of personality to your composition. In this chapter, we extend the concept of tonality to that of modulation. In order to get there, however, we

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will start with the simpler construct of mode mixture. Mode mixture respects the current tonal center but allows variation in terms of the mode used to express the musical idea of that same tonal center. So, a composition could employ the note C as its tonal center but vary the mode (or set of scale notes) around the C with, for example, C Major, C Minor, or C Dorian modes. We will use an example from Mozart (Sonata for Keyboard Four-hands in D Major, K. 381/123a) in which he changes from the major mode to the minor mode, and in specific to the D melodic Minor from D Major. The period of phrases shown in Figure 7.1 comprise a secondary theme group of the sonata, as it appears in the recapitulation of the sonata form movement (an unexpected change in the material from the exposition, illustrating yet another example of Mozart’s compositional creativity). Within this period of phrases, there is an antecedent phrase of four measures in D Major. This phrase is, as we might expect, followed by a consequent phrase, also of four measures, yielding an antecedent−consequent pair of phrases. These we can denote AB, with B being this cadential consequent phrase, and they are the first two lines of the score shown in Figure 7.1. The next line (also four measures) is the antecedent phrase modified to D melodic Minor, constituting

Figure 7.1 Mode mixture Mozart on display. Mozart’s Sonata for Keyboard Four-hands in D Major, K. 381/123a.

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the mode mixture modification, and denoted A’. The final four measures of the period are a repeat of the consequent phrase, B, and so bring this period to a close (before entering the closing theme of the movement) with a notational shorthand of ABA’B, completely different from the first occurrence of this period in the sonata (where it was originally just AB). This “recapitulation,” then, is actually a new musical element in the piece, both longer (A’B added) and different (A’ not occurring in the earlier exposition) than its first occurrence. Hardly a recalcitrant recapitulation, it is a more endearing ending than simple repetition would have been. We see here that Mozart actually surprises the listener with a repetition of the theme in the minor mode (A’), adding variety and setting up the repeat of the cadential consequent phrase (B) as a way of bringing completeness to the period, fulfilling the expectations of the listener for the recapitulation but in a non-repetitious fashion.

7.3 Borrowed Chords Another means of meaningfully making mode mixture a part of your composition is the process of borrowing chords. Chords can be brought in from another scale without necessarily altering the melodic content of the current scale. For instance, if you are composing in the key of D Major, you normally have the basic choices of harmonizing the melodic note of D with the D Major, B Minor, or G Major triads from the scale. Within these chords, the note D appears as the root, third, and fifth, respectively [(D, F#, A), (B, D, F#), and (G, B, D)]. Additionally, we may borrow the Bb Major chord from the parallel minor mode since the note D is the third of the Bb chord (spelled Bb, D, and F). This borrowing can be used to add a new spice, or flavor, to your piece. You have always used oregano and basil, but maybe it will taste just as good (and refreshingly novel) with nutmeg and cinnamon. You can also think of “borrowed chords” as an analogy to “kit bashing.” During the Cold War, you may have had a model for a US F-14 and for a Soviet MiG. But, you decided to create a MiG-14 with the Soviet canopy steering the F-14 engines. Not only have you created a new plane, but you have also contributed to world peace with your chimeric bashed kit. Thanks to you, we can all sleep more securely tonight! We next show a chord progression that uses borrowing. In Figure 7.2, we are in D Major, and the chord progression is I (chord D), V (chord A), I again, IV (chord G), I again, V again, and then a temporary chord borrowing of the Bb and C (flat VI and flat VII) from the natural minor mode before a return to I (the last chord, D).

7.3 Borrowed Chords

Figure 7.2

195

Example chord progression borrowing in D Major. Please see text for details.

The diagram showing where the chords in Figure 7.2 exist in their scales, and how the borrowing occurs, is given in Figure 7.3.

Figure 7.3 Diagram illustrating the chord progression borrowing of Figure 7.2 within their respective scales (D Major borrowing from D natural minor).

Let us drop the hypothesis now and give an actual embodiment of this technique, with the score of the Andante un poco adagio from Mozart’s Sonata in F Major, K. 309/284b, Second Movement (Figure 7.4). The lower line of the score in Figure 7.4 is annotated with the chord progression and shows Mozart borrowing the Bb Minor chord from the minor mode and returning to the major mode with the C7 chord (second measure, lower line). Additionally, you may notice the Gsus harmony that resolves to G Major just ahead of the borrowed Bb Minor. This is also a harmony that is brought in from outside of the key called a secondary dominant. Collectively, these additional harmonies add some chromaticism to the phrase leading to the C7 harmony. We will discuss both of these topics in more detail later in the chapter. Overall, the introduction of both harmonies adds a new flavor to the phrase, which could have unfolded without their introduction using just the regular ii (Gm), IV (Bb), and V7 (C7) harmonies of the key. The diagram showing where the chords in Figure 7.4 exist in their scales, and how the borrowing occurs, is given in Figure 7.5. Maybe coincidentally, Mozart’s Sonata in F Major, K. 309/284b includes another example of temporary chord borrowing, this time in the Rondeau allegretto grazioso of the Third Movement (measure 157 in the score, if you

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Figure 7.4 Score of the Andante un poco adagio from Mozart’s Sonata in F Major, K. 309/284b, Second Movement. The lower line of the score is annotated with the chord progression and shows Mozart borrowing the Bb Minor chord from the minor mode and returning to the major mode with the C7 chord (second measure, lower line).

Figure 7.5 Diagram illustrating the chord progression borrowing of Figure 7.4 within their respective scales (F Major borrowing from F natural minor).

want to look it up explicitly). The score is shown in Figure 7.6, where the lower line of the score is annotated with the chord progression. Mozart here borrows the Bdim7 chord (see the first measure, upper line; note the use of the Ab, which is the indicator of the borrowing) from the harmonic minor mode, and then returns to the major mode with the C chord (second measure, lower line). The diagram showing where the chords in Figure 7.6 exist in their scales, and how the borrowing occurs, is given in Figure 7.7. Note the use of two different B diminished chords in the figure. The B diminished chord associated with C Major is shown as B◦7 , or B half-diminished, comprising

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Figure 7.6 Score of the Rondeau allegretto grazioso from Mozart’s Sonata in F Major, K. 309/284b, Third Movement. The upper line of the score is annotated with the chord progression and shows Mozart borrowing the Bdim7 chord (starting in the first measure, upper line; note the use of the Ab, which is the indicator of the borrowing) from the harmonic minor mode and returning to the major mode with the C chord (second measure, lower line).

the notes B, D, F, and A natural, is shown in the upper line of Figure 7.7. The fully diminished B chord, shown as B◦7 in the lower line of Figure 7.7, comprises the notes B, D, F, and Ab.

Figure 7.7 Diagram illustrating the chord progression borrowing of Figure 7.6 within their respective scales (C Major borrowing from C harmonic minor).

7.4 Tonicization Tonicization is the temporary treatment of a chord harmony within the current key that is not the tonal center as if it was the tonal center. For example, in the key of C Major we may tonicize any of the other major or minor harmonies, such as D Minor or F Major. It is accomplished by introducing the dominant triad or dominant 7th (V7 ) or diminished and diminished 7th (vii7 ) harmony,

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followed by the appropriate chord you are using to tonicize (e.g. in the key of C Major, tonicizing a G chord with D Major instead of the regular D Minor that defines the key). To understand tonicization a little more readily, the concept of a secondary dominant and secondary leading tone chords must be introduced. Secondary dominants are dominant chords of any specific major or minor chords that are included in the current key. A secondary dominant introduces a tone in that specific chord that would not ordinarily be in that key. An example will help. Turning to C Major (Figure 7.8), the set of chords derived from, and only from, the scale of (set of notes comprising) C are the following: C, Dm, Em, F, G, Am, Bdim, and back to C. To show what is meant by “derived from, and only from,” consider Bdim, which comprises the notes B, D, and F, all of which are in C Major (white keys on the piano). An example of a sequence of chords all derived from the current key are shown in Figure 7.8. Here, C, Am, and Dm are all composed of notes from the set of (C, D, E, F, G, A, B); in other words, the seven notes in the key of C Major.

Figure 7.8

Example of a sequence of chords all derived from C Major.

Figure 7.9, on the other hand, provides an example of a tonicization using a secondary dominant. Here, instead of using Am, the A7 chord (comprising A, C#, E, G) is incorporated, with the obvious use of a note not in C Major (the C#, which is the leading tone, a half step below D). In chord notation, A7 is the V7/ii of C Major (i.e. Dm is the ii chord of C Major and A7 is the V7 chord of Dm. The A7 would then be analyzed as the V7/ii (five-seven of two) in the key of C Major).

Figure 7.9 Example of secondary dominant in C Major, where A7 is the V7/ii of this scale, and Dm is the ii chord of C Major.

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The complete set of chords derived from the C Major scale is explicitly shown in Figure 7.10 (center row). Tonicization of any other major or minor harmony within the key could be accomplished with the approach of each chord’s dominant (V or V7), also shown in Figure 7.10 (top row). As we saw in Figure 7.9, the secondary dominant of the ii chord (Dm) was tonicized using the A7 chord with the introduction of the note C# as the third of the A7 harmony (A, C#, E, G). Additionally, the secondary dominant of the IV chord (F) can be tonicized with the introduction of the note Bb as the seventh creating its V7 (C7) harmony (C, E, G, Bb). This is an alteration to the normal Cmaj7 harmony with a B natural within the normal key (C, E, G, B).

Figure 7.10 Diagram illustrating the chords derived from the scale of C Major (center line). The line above indicates how to use secondary dominants derived from the V chord of the given chord (e.g. A7 is derived from the V chord of Dm), while the line below indicates how to use secondary leading tone chords derived from the vii chord of each given chord (e.g. C#◦7 is derived from the vii chord of Dm). Please see text for more details.

As another possibility, we could use the secondary leading tone chords tied to the vii chord of a would-be tonicized harmony rather than the dominant (V or V7) chord. The secondary leading tone chord is a triad or seventh chord (usually the fully diminished seventh) built off of the leading tone to whichever major or minor chord you want to tonicize. This approach of using secondary leading tone chords in the key of C Major is given in the lower line of Figure 7.10. The chord progression in Figure 7.11 shows the tonicization of Dm using its secondary leading tone chord (C#◦7 ). As an example of a commercially successful composition that uses the secondary dominant borrowing approach to tonicize, we consider Scott Joplin’s The Easy Winners (Figure 7.12). In this piece, the antecedent phrase establishes a harmony of Ab Major using its I and IV chords. Then, the consequent phrase employs a V7/V chord harmony (by the introduction of

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Figure 7.11 Example of a secondary leading tone chord in C Major, where C#◦7 is the vii◦7 /ii of this scale, and Dm is the ii chord of C Major.

Figure 7.12 Main theme of Scott Joplin’s The Easy Winners. This ragtime composition tonicizes Eb in measure 7 and returns to (re-tonicizes) Ab Major in measure 9.

Figure 7.13 Chords derived from the Ab major scale with the secondary dominant (Bb7) that is used to tonicize Eb major in Scott Joplin’s The Easy Winners.

its leading-tone, D natural, within a Bb7 harmony), using Bb7 to temporarily tonicize Eb Major within the key Ab Major (Figure 7.13) at the end of the phrase.

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A second example is given by Bach’s Prelude in D Major BWV 850 (Figure 7.14). This short example starts at the 25th measure of the composition, where the harmonies of G Major and A Major are tonicized with the dominant 7 of G (D7) and the fully diminished 7 of A (G#dim7). Figure 7.15 shows these harmonies in relation to the key of D major.

Figure 7.14 Bach’s Prelude in D Major BWV 850, showing two tonicizations of the IV and V chords (please see text for details).

Figure 7.15 Chords derived from the D Major scale with the secondary dominant and secondary leading tone chords (D7 and G#◦7 ) that are used to tonicize the IV and V (G and A) chords in Bach’s Prelude in D Major, BWV 850.

7.5 Chromaticism Chromaticism, as alluded to above, is music in which any of the other five pitches within an octave or chromatic scale can be used along with the regular seven pitches of the major and minor scales or modes. Chromaticism introduces half step motion in the forward movement of melody or harmonic content. As mentioned in the section on borrowed chords above, any borrowed chord can be viewed as a “temporary dance with chromaticity,” so

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that chromaticism itself is usually thought of as the continued borrowing of (usually multiple) chords or incorporating the notes of the chromatic scale into any current key. A borrowed or altered chord is, from this perspective, a temporary dance with chromaticity. With apologies to Sting, you can remember this from: With one chord, that’s altered You will know Chromaticity That is, one chord that does not belong to a given mode tells you the composer is (perhaps very) temporarily injecting notes from outside of the main scale or mode. Two examples will suffice here. The first is Julius Fuˇcík’s “Grande Marche Chromatique,” which is also commonly referred to as the “Entrance

Figure 7.16 Julius Fuˇcík’s “Grande Marche Chromatique,” introduction and first main phrase. The chromatic scale is used in context of the harmony, which is tonally C Major.

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of the Gladiators.” As shown in Figure 7.16, this composition’s first few lines employ the chromatic scale as part of the introduction (lines 1−3). The main theme (lines 4 and 5) uses many chromatic notes as non-harmonic tones in context of the harmony. The composition is tonally C Major, using the primary chord I and V7 as a basis for the melody to be constructed upon. There are many chromatic notes in comparison to harmonic tones of the given harmony and key. As a general note, in any scale, 7 of 12 notes in each octave are considered part of that scale. This is 7/12, or 58.3%, of all possible notes. So, if notes were “randomly” selected, you might expect 41.7% of the notes to be chromatic; that is, from the set of 5 notes out of 12 not part of the scale. From this perspective, when a composition moves from 0% to 41.7% chromatic notes, it spans the range from fully achromatic to fully chromatic. As a rule of thumb, if there are more than 41.7% chromatic notes, the composer has selected the wrong key signature either out of purpose,

Figure 7.17 Chopin Prelude in E Minor Op. 28, No. 4, where the harmony chromatically changes, one chromatic step at a time, with generally one note of the chord for each change.

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incompetence, irony, or a form of compositional temporary insanity. Not that temporary (musical) insanity can’t be fun! The second example of chromaticism is Chopin’s Prelude in E Minor Op. 28, No. 4. The first section of this prelude is shown in Figure 7.17, where one note out of the three notes of the left-hand chord harmony “melts” down the keyboard, in most cases one chromatic step at a time for each chord change. Compositionally, the harmony progresses chromatically while the melody uses mostly notes within the key.

7.6 Modulation In this section, we describe modulation as a musical event in which an established key is abandoned in order to use another key entirely. This “key change” may very quickly be recognized by most listeners, even if they cannot tell you what either key is. In a classical sonata, for example, one of the “key” (pun intended) structural characteristics of the exposition is the modulation from the key of the principle theme group (or “home key”) to a related key in the secondary theme group. An example of modulation to a “related key” is a tonic to dominant relation for a composition in a major key. This means from the key of the I chord harmony to the key of the V chord harmony. In C Major, this is a modulation to G Major. This modulation is considered “related” since six of the seven scale tones are the same, and four of the seven chord harmonies are shared. In a minor key, the common practice of prior musical eras was to modulate to the relative major; for example, from C Minor to Eb Major, that is, from the key of the i chord harmony to the key of the III chord harmony. Generally in this related minor, you use the harmonic minor alteration of the scale, which produces a major quality V chord. So, in C Minor, you would use the dominant harmony of G major. For minor key modulations to mimic the major mode in going from the I to V chord, this would produce a more remote relationship. You would end up going from C Minor with three flats to G Major with one sharp. There are a smaller number of shared scale tones (C, D, G, and the altered B natural) and even less shared harmonies (only G Major and the B diminished triad). If you are going to modulate to a major harmony (which gives good contrast to the minor), the relative major (here, of Eb) is much more closely related since it shares the same key signature. Modulations do not have to be related keys; for example, you can go from C Minor to G Major if you want to. Consider a composition in which the modulation might occur from the tonal center of C Major to F# Major. Here, only one scale tone is the same (B), and there are no shared

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chord harmonies. Of course, you can modulate anywhere you choose; it is your composition, after all. You should try out all possibilities for related and unrelated key modulation to evaluate the sounds they produce (guided by your own idiosyncratic choices for melody and accompaniment, etc.) and see which one best fits your compositional goals. From there, it becomes a question of where you want to go, and when and how you are going to go about getting there. Let us consider with some detail how modulation may occur within a composition. Phrase modulation, for example, is a specific type of modulation where a phrase, period, or section ends in a key and a new phrase, period, or section takes up in a new key without any harmonic transition. An example of phrase modulation is in Schumann’s Knecht Ruprecht Op. 68, No. 12 (Figure 7.18), where the ending phrase of the “A” section of this ternary composition uses its key (A Minor) primary chords iv, V, and I. Entering into the “B” section, the F Major key is established by incorporating its own primary I and V chord harmonies. Aside from the common tones between the two harmonies (the notes A and C), there is no “set up” or tonicization of F Major for this transition; instead, the modulation simply occurs. It feels musically analogous to walking from a wall-papered, wainscoted room into a minimally decorated Bauhaus room with an entirely different décor − unexpected, perhaps, but of course allowable.

Figure 7.18 Schumann’s Knecht Ruprecht Op. 68, No. 12, illustrating phrase modulation from A Minor (“A” section) to F Major (“B” section).

The choice of modulation is intimately related to the goal of the phrases and structural considerations for the composition. For instance, you may be modulating to set up a particular harmony at the end of a phrase; alternatively, you may wish to have a modulation across two larger structural elements of your composition, that is, the A and B sections. Modulation can move to related or remote keys, and structurally, it can occur within a period or section

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of music, or occur as part of a new section of the overall structure. After modulating, you can continue to use the same established theme or motives of the composition or move on to new material all together. You get to mix and match, and thus these choices for modulation are potentially powerful tools in your overall compositional workbox. Given that you have multiple pathways to move from one to key to another, you probably want a guideline of sorts to help you with these three aspects of the modulation: 1. Where are you now? (current key) 2. Where do you want to go? (key to modulate to) 3. How do you want to get there? (choice of modulation) This is another example of a common theme of this book: the composition does not just emerge from a conch shell in complete form like the birth of Aphrodite; rather, you need to make some choices along the way, and these choices are a great opportunity for you to put your personality and creativity into the composition. Modulation can aid in creating a wider pallet of colors, which can compositionally give the effect of starting in somewhere (establishing tonality) and then setting off on a journey elsewhere (modulation to new key) by foot, plane, train, automobile, or teleportation (how do you want to get there?). One example illustrating this three-part path to creative output is the composition of the melody familiar to Americans as that of O Little Town of Bethlehem. Overall, the melody is constructed with notes from the very comforting key of G Major, except for one lower neighbor chromatic note in the first and last phrases. As a straightforward approach, this melody could be harmonized exclusively with the primary chords that are derived from the same scale, in addition to, perhaps, one chromatic chord to go along with the chromatic note in the melody. Each phrase begins on the note “B,” and then ends with either the same note “B” or the note “G.” At minimum, each phrase could begin and end harmonized with the tonal center I chord (G Major). The composer (Lewis Redner) makes the choice of introducing some sort of tonal contrast for the tune, particularly the B phrase within the song’s AA’BA” structure. Redner identifies the opportunity to modulate from G Major to the relative E Minor as seen in Figure 7.19. Each of the “A” phrases − A, A’, and A” in lines 1, 2, and 4, respectively − starts and ends on the tonal center of G Major. Focusing on the (3.) above (i.e. choice of modulation), Redner makes use of a chromatic modulation to get to his new key over the course of the phrase. The chromatic alteration occurs on the fourth beat of the

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first measure of the phrase, going from the vii chord of F#dim to the A#dim7 chord. This A#dim7 acts as a secondary leading tone chord, temporarily tonicizing B Major on the first beat of the second measure of the phrase. However, this is B Major as it exists in the key of E harmonic minor as we see the rest of the phrase unfold. The “B” phrase ends on the V harmony of E Minor (B Major) with another modulation occurring to get back to G Major. A phrase modulation is used without any transition or tonicization of the G Major destination key, bringing the full body of the tune to a close.

Figure 7.19 Score of O Little Town of Bethlehem by Lewis Redner, showing modulation within the core melodic structure of AA’BA”. Please see text for details.

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Another example of modulation between two different sections of a composition is in Beethoven’s Piano Sonata Op. 79, 2nd movement (Figure 7.20). For this ternary movement, the “A” section is in G Minor, with some tonicization of other harmonies along the way but without any sustained key change. The “B” section of the composition introduces a new theme and modulates to Eb Major. Here we have a related key connection between the two tonal centers with G Minor having two flats and Eb Major having three flats. Using the three-step process from above, Beethoven wants to (1.) start with G Minor in the “A” section and wants to (2.) go to Eb Major in the “B” section. For (3.), Beethoven utilizes a common chord modulation with a couple of extra transition measures between the two sections to accomplish this. After ending on G Minor in the “A” section, Beethoven continues with the same harmony into the transition. Here the harmony of G Minor has a common chord relationship by being the i chord in G Minor and the iii chord in Eb Major. The harmony of Bb7 introduces the note Ab from the new key,

Figure 7.20 Beethoven’s Piano Sonata Op. 79 2nd movement, illustrating modulation from G Minor to Eb Major. Please see text for details.

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tonicizing the new tonal center of Eb Major. The modulation is complete, and Beethoven then introduces a new theme for the “B” section. The composition eventually modulates back to G Minor with the return of the “A” section and again with another common chord modulation (not shown in Figure 7.20). There are several choices of how to modulate, and you can grab a music theory book if you want to understand the specific mechanics and historical usage associated with each. However, you can still use creativity in how you roll out any one of these. As a short list, some of the modulation approaches are (1) common chord, (2) common tone, (3) enharmonic, (4) sequential, (5) chain modulation, (6) chromatic modulation, and (7) phrase modulation. Rather than being exhaustive here, we were able to highlight three of these (phrase modulation in Figure 7.18, chromatic and phrase modulation in Figure 7.19, and common chord modulation in Figure 7.20) to illustrate the process of modulation with respect to where it might be used in a composition.

7.7 Obscuring the Key Another compositional approach for a sense of mode mixture is that of not committing to or clearly defining a specific key, and understanding how to incorporate, perhaps, elements of two or more keys simultaneously. Two short examples are given, with the first (Figure 7.21) coming from the opening of Beethoven’s Symphony #1 in C Major, Op. 21. Here, the opening chord sequence of C7 to F obfuscates the actual key that Beethoven is presumably composing in (C Major, according to the title of the work and its key signature), giving it a feel of F Major (since this is a tonicization of F) from the very opening notes. This approach can be thought of as a form of musical metamerism, where it appears to be in C Major from one light, and F Major from another (nicely tying to the sidebar of this chapter in the following section). Within the opening four measures of the composition titled Symphony No. 1 in C Major, Op. 21, Beethoven tonicizes F Major, uses a deceptive cadence, and then tonicizes G Major. The harmony of C Major does show up within the opening Introduction of the movement, but Beethoven purposefully avoids committing full weight to the tonal center until entering into the main Allegro con brio section of the movement. We offer a general two-staff reduction of the score below. We conclude this short section with one additional example (Figure 7.22). In Brahms’ Intermezzo Op. 118, No. 1, the prolific use of accidentals leads

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Figure 7.21 Opening of Beethoven’s Symphony #1 in C Major, Op. 21. The opening chord sequence of C7 to F obfuscates the actual key that Beethoven is purportedly (according to the key signature) composing in, giving it a feel of F (since this is a tonicization of F). Given the contents of the sidebar for this chapter, it can also be thought of as a musical metamerism, where it appears to be in C Major from one light, and F Major from another.

us to conclude that they are not accidental. Are two cars smashing into each other at a demolition derby really having an accident? Brahms here has a demolition derby of sharps and flats, which work to obfuscate confirmation of a current key, akin to a chromatic composition. From the key signature, we get the impression of a composition that is either in C Major or A Minor. In the opening measure of the “A” section of the composition, there is a

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sense of C7 harmony (without the 5th, G). In the last beat of the measure, the note A shows up, producing an A Minor harmony although it is not in root position. The figure is repeated, however, this time over an Am7 harmony that turns to F Major. From there, the composition progresses with some chromaticism to D7b9. Brahms is certainly not defining C Major or A Minor with the regular harmonies that define these keys. Instead, the piece seems to be progressing downwards by the interval of the third (C down to A, down to F, and eventually down to D). The second half of the section eventually focuses in on C Major, with some back and forth with G7. The B section of the movement is rounded and brings back the A section material. This time, however, the section ends on A Minor, revealing the intended tonal center. Additionally, there is a Coda that mode mixes over to A Major at the end of the composition. With hindsight, we can see that the A section progresses with the idea of moving to a related key (A Minor to C Major) and

Figure 7.22 Brahms’ Intermezzo Op. 118, No. 1, illustrating obfuscation of key altogether. Please see text for details.

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the recapitulation of the material in the B section staying home (A Minor to A Minor). However, Brahms clearly (and creatively) avoids defining A Minor from the get-go in the traditional sense. There are many other possibilities for choosing scales and chords beyond the ones described in this chapter to help introduce more “chroma” into your compositions. We highly recommend analyzing your favorite compositions and composers in addition to thoroughly studying harmony to expand your musical vocabulary. We hope some of the ideas presented here, at least, give you a springboard to achieving this.

7.8 Sidebar In music, modulation is the change from one tonality to a different tonality. Often (but not always) this is accompanied by a key signature change. For the purposes of this sidebar, it will be a change in one “style” to another, using the broadest definition of style we can. To use alliteration, we will use modulation as a means to match music metamerically in this section. As we saw in the section above on tonicization, musical metamerism is a neologism we use to illustrate how a composer can deftly obscure which key they are committing to in a phrase of the composition. What is a metamerism? In color science, a metamerism is, quite simply, a mistake. More technically, it is a mistaken equivalence of colors under one illumination spectrum that is not observed in another. Thus, it is engendered by different illumination spectra in two or more environments. Two colors that are clearly different in sunlight then look the same under the fluorescent lights of indoors are a metamerism. Or worse, two colors that look alike in the store that are clearly different when you take them home and see them under natural light. Nobody appreciates this kind of metamerism, as it looks like half of your house, your fence, or your car faded faster than the other half. We can extend the concept of metamerism, with less apprehension, to other fields. Metamerisms help us to realize that sometimes two completely different things can look similar only because of what we choose to ignore. Shakespeare, for example, showed that he knew this in what he wrote in his famous Sonnet 130, “My mistress’ eyes are nothing like the sun; Coral is far more red than her lips’ red.” What a brilliant means to convey metamerism. “Nothing like the sun,” coincidentally, is a way of describing indoor lighting, which differs from the sun in its spectrum and thus can cause a metamerism for two colors that are clearly different in sunlight. More importantly, when Shakespeare looks at his love, he forgets the defects, and so his lover’s

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lips become for him the same color as coral, and his lover’s eyes the same spectrum as the sun. His lover’s appearance is a metamerism for visual perfection because of the intentional spectral reduction caused by his love. The expression “seeing one’s lover through rose-colored glasses,” is in fact an almost explicit calling out of this love-induced metamerism. Rose-colored glasses selectively filter out the non-red colors (or simply add red to all of the colors: either way, blue becomes purple, yellow becomes orange, etc.), changing the colors one sees. Part of the magic of being in love is, for those of us fortunate enough to be sighted, a metamerism or partial blindness. Metamerism can also be applied to music. Here, two tunes sound the same in a given context but not in another. Does this song sound like “We Three Kings” to you? [Douc15]. If it does, it is worth asking yourself why. If you came into the song at the 1:12 mark, the answer would probably be a resounding no. Then, starting again at 1:38, the answer would be yes, it certainly does. After 2:48, Michael Doucet carries out a musical piece really entirely different from any previous version of “We Three Kings” until the song ends at 3:41. So, in a 221-second song, 79 seconds are completely independent of the traditional aspects of “We Three Kings.” The other 142 seconds, however, use the melody and accompanying chord progressions we might expect of this Epiphany song. Filter out those 79 seconds, and you have a metamerism for a less feisty version of “We Three Kings.” Filter out those 142 seconds, and you have a metamerism for a Cajun/Bayou/Zydeco accordion jam session. It is all a matter of what you filter, and what you keep. We now turn to illustrating this diagrammatically. In the following four diagrams, we will plot two different factors across multiple musical styles. For simplicity, we illustrate three musical styles (labeled A, B, and C) along with songs differentially composed of elements of these styles. Additionally, musicians who have varying degrees of skills or familiarity with these musical styles are represented in these diagrams. The curves shown in these figures have higher values in the y-axis where the song or musician has more content or expertise. In Figure 7.23, the relative style content of two different songs (dashed curves) for three different Music Styles A, B, and C is indicated. To interpret this figure, we look at the area under the curves for the songs and the musician. Based on the areas under the curves, we can see that Song A is 50% Music Style A, 40% Music Style B, and 10% Music Style C. Song B is 25% Music Style A, 41.5% Music Style B, and 33.5% Music Style C (see Table 7.1). The musician, cleverly named Musician 1, has relative expertise of 10% for Music Style A, 85% for Music Style B, and 5% for Music Style

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C. Thus, the musician is much more familiar with Musical Style B, and so any elements of this musical style in the songs will be more highly noticed by the musician.

Figure 7.23 Musical metamerism illustrated by two songs (dashed curves) of greatly different content from Music Styles A, B, and C but the same relative overlap with the musician’s expertise (solid curve). Based on the areas under the curves, we can see that Song A is 50% Music Style A, 40% Music Style B, and 10% Music Style C. Song B is 25% Music Style A, 41.5% Music Style B, and 33.5% Music Style C (see Table 7.1). The musician, Musician 1, meanwhile, has relative expertise of 10% for Music Style A, 85% for Music Style B, and 5% for Music Style C. Please see text for details of how this results in musical metamerism.

Using these “area” values garnered from Figure 7.23, we tabulate them in Table 7.1. Now we show how to use them quantitatively. As noted, the area under the curve for each of Song A, Song B, and Musician 1 is normalized to 1.0. This means that the sum of Column 2, Column3, and Column 4 (from the left) in Table 7.1 is 1.0. The 1.0 sum comes from a different distribution for each curve, with the percentage of the curve’s area falling in each of the three music styles (A, B, C) computed and presented in Columns 2, 3, and 4 in Table 7.1. We represent the musician’s interpretation of the song as the product of the musician’s expertise with the song’s music style. This is Column 5 and Column 6 in Table 7.1. The product of Column 2 and Column 3 is given in Column 5, and the product of Column 2 and Column 4 is given in Column 6. Note that the sums of Column 5 and Column 6 are each 0.395. The impact of the song’s musical content and the musician’s relative expertise with the musical styles leads to the songs having the same net impression on the musician. That equality is the musical metamerism, with the musician thinking the two songs sound similar. This is the case in spite of greatly different overall style content of the songs!

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Table 7.1 Musical metamerism illustrated by two songs and musician 1 in Figure 7.21, with the percentage of each curve corresponding to each of the three music styles (A, B, and C) indicated in Columns 2, 3, and 4 from the left. The product of Column 2 and Column 3 is given in Column 5, and the product of Column 2 and Column 4 is given in Column 6. Note that the area under each curve (Musician 1, Song A, and Song B) is normalized to 1.0 (SUM at bottom), and that the SUMs of Column 5 and Column 6 are each 0.395. That equality is the musical metamerism. Music Style

Musician 1 Expertise

A B C SUM

0.100 0.850 0.050 1.0

Song A Relative Content 0.500 0.400 0.100 1.0

Song B Relative Content 0.250 0.415 0.335 1.0

(Musician 1) × (Song A)

(Musician 1) × (Song B)

0.050 0.340 0.005 0.395

0.025 0.353 0.017 0.395

The same “musical metameric” effect can be shown purely graphically, as illustrated by Figure 7.24. That area is the same, even though the two songs have greatly different overall musical content. Here, the elemental pieces of the areas under the curves are labeled from 1 to 7. The area under the musician’s curve is the sum of labeled parts 3, 4, 5, and 6. The songs, meanwhile, sum parts (1, 2, 4, 5) for Song A and (2, 5, 6, 7) for Song B. The impact of the songs on the musician is the parts in common, which are parts (4, 5) for Song A and parts (5, 6) for Song B. Since parts 4 and 6 are

Figure 7.24 Musical metamerism illustrated by two songs (dashed curves) of greatly different content from Music Styles A, B, and C but the same relative overlap with the musician’s expertise (solid curve). Here, the areas of the different sections under the curves are labeled 1−7. See text for details.

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equivalent in area, each song has the same net impact on the musician, who then may classify them as having the same style. The graphical approach to showing metamerism is shown in greater detail in Figure 7.25.

Figure 7.25 Musical metamerism illustrated by two songs (dashed curves) of greatly different content from Music Styles A, B, and C but the same relative overlap with the musician’s expertise (solid curve). Here, the areas of the different sections under the curves are labeled 1−7, and it is shown that the areas under the musician curve for Song A (1 + 2 + 4 + 5) and Song B (2 + 5 + 6 + 7); that is, (4 + 5) and (5 + 6), respectively, are equal. The musician thus classifies each song to have the same style.

As one final example of how musical metamerism may occur, two different songs, again labeled Song A and Song B, are shown with dashed curves in Figure 7.26. Two different musicians with greatly different expertise in the three Music Styles A, B, and C, are also plotted in Figure 7.26. Using the same sort of graphical interpretation as used for Figures 7.24 and 7.25, it is clear that the two songs have the same area of overlap for both musicians. Thus, both songs may be classified as similar by each of the two musicians but for different reasons. Musician 1 notices their similar content in the part of Music Style B that this musician is most skilled. Musician 2, meanwhile, notices their similar overall content in Music Style C. Thus, there are multiple musical metamerisms in the same two songs. What these examples show is a different variant of the famous infinite monkey theorem whose basic details were published in 1913 [Bore13]. That is, there are an effectively infinite number of ways to interpret a song based on multiplying the huge number of possible musical note progressions with the equally huge number of possible musical experiences a person may have

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Figure 7.26 Musical metamerism illustrated by two songs (dashed curves) of greatly different content from Music Styles A, B, and C but the same relative overlap with two different musician’s expertise (solid curves). Please see text for details.

been exposed to. Recall from Chapter 3 the quickly scaling number of musical note possibilities, even for a three octave range, one instrument, and only two measures in 4/4 time? The tens of millions of possibilities there might have meant several monkey-years at the keyboard would be required to replicate a particular two-measure selection of notes. So, this means that given enough time and monkey, you will get a musical monkey metamerism with two keyboards producing exactly the same tune. Given this monkey business, then, when does music plagiarize another piece of music? It seems that this is really a form of forensic science. And, for forensics, a typical probability brandished is “one in a billion.” That is, only once in one billion times will you accuse someone of plagiarism when they were not guilty of plagiarism. The problem is, how close does the music have to be, and how long does it have to be? The simpler the tune, the easier it is to unintentionally have similarity. The longer the tune, the easier it is to pick it apart and find some element of it not unlike some element of another song. There is no simple answer: it really depends on how many monkeys are typing, and in how many rooms. Plagiarism, in our opinion, is often just an accident of the simplicity of a song. Think of EDM (electronic dance music), which might only have four measures of actual content. Given that, how hard is it for a song to sound superficially the same? I guess we could ask Daniel Baron and David Guetta. The point is, composers like Deadmouse, Daft Punk, Kraftwerk, and New Order are not necessarily trying to write music that is different from anything else you have ever heard. The mix of familiarity

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and hook, hopefully, makes you want to dance. You might dance to different music than you eat dinner or fall asleep listening to, right? Coming back to a discussion on color science, perhaps the similarity between songs is more analogous to the differences between colors than we thought at first. The gamut of colors possible for a given scenario – for example, for a camera, a printer, a set of paints, an LED screen, etc. − is represented by what is called a color space. Some of these color spaces date back more than 90 years − for example, the International Commission on Illumination (CIE, not ICE, from the French spelling of this) created a color space in 1931, called XYZ. In this XYZ color space, larger changes in the green color areas are required for a “color normal” person to be able to consistently distinguish two similar colors. The concept of a “delta-E” was introduced (the E is the first letter of the German word, Empfindung, meaning sensation, which is just the starting point of a whole host of issues related to delta-E’s limitations) as a measurement supposed to correspond to how much one visible color can differ from another visible color before a person declares them as two different colors. A lower delta-E means two more similar colors, and for displays like computer screens or printed pages, a lower delta-E means better color accuracy. In 1976, the so-called L*a*b* color space was named and committeeapproved. The equally cleverly named delta-E 1976 (or dE76) was also approved at the same time (and presumably by the same overworked and under-inspired, at least for catchy names, committee). The delta-E is a distance in the world of color, where the world of color is three-dimensional (3D). Thus, it is a sphere surrounding any color point within which you think you are in a sphere of uniform color. At least that is what this hard-working committee wanted to have happen. However, dE76 does not really support a perfectly symmetrical-in-3D interpretation, because that color space, L*a*b*, is not as perceptually uniform as it was intended to be. Although far better than XYZ, in L*a*b* different distances between two compared colors (or color shift) have the same dE76 values, and vice versa. The eye is more sensitive to small differences in color where there is greater overlap of the eye’s photosensors; for example, between green and red (which includes all of the yellows and oranges, too). Overall, then, the delta-E, or minimum color difference that is perceptible, is dependent on the color space. L*a*b* provides a far better uniformity of delta-E across its gamut than does XYZ. In the same way, the minimum musical difference that is perceptible to a listener depends on the musical space. Some musical spaces might feel more uniform, perhaps when they are more mature, and benefit from a greater

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number of familiar patterns for expression. Swing, jazz, blues, rock, classical, punk and pop music might feel this way, because their limits have been explored and so their “volumes” can be more readily partitioned, with the delta-E replaced by some analogous relevant measurement (maybe deltaBlue, to use a color and a cringy play on words, for the blues?). Let us generically call it delta-Ear. Newer or more open-ended musical styles (hip hop, ambient, emo, country, dance, and world music, for some possible examples) may have less uniform differences in sound being noticeable across their gamut. For example, small differences in two Kizomba compositions might be more noticeable to two people from Angola than are small differences in two Isicathamiya compositions. Also, music with a reduced “palette” like some atonal music might have a more uniform delta-Ear distribution than does tonal music. There are, regardless of terminology, some music spaces that are more uniform than others! In those spaces, then, musical similarity – and perhaps musical plagiarism – is likely easier to assess.

7.9 Summary In this chapter, we consider some approaches to add “color” to your music, either with the use of harmonization (changing chords) or melody. Borrowing from the world of color science, we see that key changes and tonal centers can be perceived differently based on the key from which they started and the key to which they transition. Thus, keys can be obscured or obfuscated in the way that colors can be based on their light sources. This process, metamerism, is discussed in the sidebar, and applied specifically to chromaticism (the general use of all notes, both within and outside of a key), itself herein dubbed a “musical metamerism”. The earlier half of the chapter addresses more specific means of transitioning between keys to add color to the composition: mode mixing, chord borrowing, modulation, and tonicization being the primary methods.

References [Bore13] Borel E, “La mécanique statique et l’irréversibilité,” J. Phys. Theor. Appl. 3 (1), pp.189-196, 1913. [Douc15] Doucet M, “We Three Kings,” Christmas Bayou, January 1, 1986, posted to https://www.youtube.com/watch?v=4z5APGI8v4A, 27 September, 2015. Accessed 23 May, 2021.

8 Accompaniment/Instrumentation/ Orchestration

If you wish, gentle reader, you may augment your mental tableau with dramatic orchestral accompaniment – Marie Brennan Literature is the orchestration of platitudes – Thornton Wilder

Abstract A single voice can be beautiful, but often choosing multiple voices adds depth, mystery, and poignancy to the single voice. In this chapter, the techniques of accompaniment, instrumentation, and orchestration are explored as means of enriching your compositions. Texture is the combination of melodic, harmonic, and rhythmic elements in a composition. Adding voices to build from monophony to polyphony on one end of the spectrum, or homophony on the other, in which a subordinate accompaniment is used to complement a melody, gives three general possibilities for texture. Accompaniment is a more general term for adding support to the melody, often through chord arrangements. To achieve this, different chord voicing or spacing can be incorporated. One interesting choice is parallel harmony, in which the same structure (number of notes and interval distance) is used as you move chord to chord. Voice leading is a choice for chord-to-chord transition in which the common notes of the consecutive chords are considered to ease the playing. Orchestration, arrangement, and instrumentation are discussed as to the way textural features are assigned to an ensemble of instruments, as well as the means of using the different range, loudness, and harmonics (timbre) of each instrument to craft an overall sound for the composition. Here, each instrument and voice can be associated with a desired textural element in

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the piece. Range ordering (e.g. of strings, woodwinds, brass, and percussion) can be used to line up, or register, the choice of voice or implement of instrument with the desired texture(s). Additional choices include playing an instrument differently (e.g. using pizzicato on a stringed instrument) to produce inharmonicity (altered timbre). In the sidebar, color painting is used as an analogy for musical composition, with the self-expression possibilities of painting allowing the same gamut of expression and choice that a musician has when they choose to compose. Keywords: Accompaniment, Arrangement, Chord Spacing, Chord Voicing, Homophony, Instrumentation, Monophony, Orchestration, Parallel Harmony, Polyphony, Texture, Voice Leading

8.1 Introduction Accompaniment, instrumentation, and orchestration are compositional processes used to bring in additional “voices” to your music. Any time new sequences of sound are added, there is a potential trade-off between euphony and chaos. The right addition, you have achieved the successful sequencing of sound; the wrong addition, and you are creating cacophonic chaos cluelessly. Think of a derailed video conference, where people are entering the meeting muted, late, and/or unaware of what has already been said. The rest of the attendees are rightly put off by these interruptions. When joining a video meeting, you join quietly and listen before contributing, right? In other words, you accompany the meeting, and do not disrupt it. Not that disruption cannot be musical: think of the cannons in the 1812 Overture (best when outside, in my experience). This chapter, however, is not about disruption. Instead, it is about adding musical parts that enhance, enrich, and enliven an ongoing piece. In Chapter 5, we discussed the canon and the round, which are structured musical compositions in which similar voices are offset by the timing of their entrances (often two, three, or four measures), perhaps only differentiated by range and libretto. In this chapter, more comprehensive means of blending multiple musical threads are considered. We start with texture, which is used to describe the combination of musical elements within the composition. Next, the musical specifics of accompaniment are described. Then, putting all these threads together (orchestration or arrangement) wraps up the musical composition elements of this chapter. The sidebar uses painting as a source of creativity for musical multi-threading.

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8.2 Texture Texture describes the combination of rhythmic, melodic, and harmonic elements in your composition. It also is concerned with the choice of instruments for tone color (orchestration and instrumentation), the placement of notes across the range of available pitches (spacing), the degree of loudness in the sound (dynamics), and the indications for performance (articulation). From the onset of your composition, the considerations for what instruments are to be used and their roles in the output of the music will create the texture of sound in the finished work. There are three general types of texture: monophony, polyphony, and homophony. There are other degrees of texture, which may be a blending of two or more of these three “archetypes.” However, covering these three types will give you the compositional tools to create varying degrees of these three general types. We will cover these three in order, starting with monophony. Keep in mind, while composing, you can “switch” from one texture to another as it suits the overall feeling or needs of the current moment in your music. An example of monophony is Debussy’s Syrinx, L. 129 (Figure 8.1), which is played by a single instrument with only a single line of melody (not even an accompanying harmony). This means, in theory, a good whistler or good saxophone player could just as readily perform this piece as a pianist, guitarist, or flautist. The complexity and allure of monophony can be very high even though the texture is that of a single voice. Syrinx, for example, is highly chromatic and rhythmically complex.

Figure 8.1 Debussy’s Syrinx L. 129. The opening section of this composition offers an example of a solo instrument monophonic texture of a single melody.

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Maybe you, like us, instantly thought of the Temples of Syrinx, an important element in Rush’s magnum opus, 2112, when seeing the name of Debussy’s work. The libretto of 2112 is concerned with a “nice, contented world” in which only the high priests of the temple are allowed to decide what people do. In other words, monotony. However, monophony is not monotonous and is, in fact, the basis for polyphony, which can be viewed as the mellifluous combination of two or more monophonic elements. Polyphony, mentioned above, is music that simultaneously combines several lines, as distinct from monophony. The use of counterpoint is a signature of polyphony, which is simply the combination of multiple melodic lines, with a minimum of two, meaning mellifluous multiple melodic lines, that is, as the two (or more) melodies need to work together, simultaneously, to create harmony. A good example of polyphonic composition in which

Figure 8.2 Giovanni Pierluigi da Palestrina’s Kyrie Eleison from the Missa Brevis, an example of polyphonic music where each voice (text not shown) is its own independent line, yet all four voices work together to create harmony. From a compositional standpoint, Giovanni has given a meaningful melodic part to each voice, allowing each of them to contribute to the main musical texture.

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multiple voices (here four) are each independent from the other three voices yet also contributing to the main musical texture is Giovanni Pierluigi da Palestrina’s Kyrie Eleison from the Missa Brevis, as shown in Figure 8.2 (without text). Counterpoint is the combination of note against note in a polyphonic composition. It is a field of composition vast enough to be its own book; for example, the classic by Joseph et al. [Jose65]. Traditional compositions (including ones we have discussed in earlier chapters) include fugues, canons, and inventions. We have only scratched the surface here, but as you know scratching the surface allows you to see the actual metal through the rust. Homophony, as distinct from monophony and polyphony, is a composition in which the main melodic theme is largely concentrated in one voice or part, and the composer uses a subordinate accompaniment to complement this melody. This accompaniment might be a tom tom rhythm and a strummed harp harmony accompanying a singer. Edward MacDowell’s Woodland Sketches, Op. 51, No. 1 (Figure 8.3) is an example of homophonic composition along these lines for piano where the stems-up melody of the right hand is accompanied by sustained chord harmonies below.

Figure 8.3 Edward MacDowell’s To a Wild Rose from Woodland Sketches, Op. 51, No. 1, exemplifying homophonic texture with a single melody (upper staff, stems up) having harmonic support (upper and lower staff, stems down).

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8.3 Accompaniment Accompaniment is the support for a main part or melody. Depending on the capabilities of the instrument or instruments used to create the texture, accompaniment may have a wide range of contribution, from simply complementing the texture with a few notes to providing a voice with texture and nuance that occasionally approaches that of the main texture of the musical piece. A general description might be that of a melody with chord support. In one realization, this might be a singer providing the main melodic content while being accompanied with chords on a strummed guitar as the supportive accompaniment. The varying degrees of accompaniment can be realized as dense chords performed by many instruments across a wide range of available notes on one extreme, to sparse single note additions above or below the melody on the other extreme. Here, as an example, we have Johann Sebastian Bach’s Gavotte en Rondeau from the Violin Partita No. 3 in E Major BWV 1006 (Figure 8.4). The measures shown in Figure 8.4 feature a solo violin in a mostly monophonic texture with the occasional addition of accompanying “bass” notes on an adjacent string. These notes clarify the harmonic progression that the melody is threaded through without quite becoming its own fully formed independent line. For example, the first two melody notes in this short section of BWV 1006 are B and G#, but the accompanying note, E, establishes the tonal center of E Major.

Figure 8.4 Bach’s Gavotte en Rondeau from Violin Partita No. 3 in E Major BWV 1006 (please see text for details).

Accompaniment might also come in a more polyphonic, yet supportive role, with parallel melodic lines in intervals such as thirds, sixths, and octaves accompanying a melody that otherwise could stand alone. As an example, Mozart’s Andante amoroso, 2nd movement from Piano Sonata K. 281 (189f) (Figure 8.5) shows a main focal melody in the upper notes of the right hand

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being supported with additional lines in parallel and/or contrary motion that fill out the chord harmonies.

Figure 8.5 Mozart’s Andante amoroso, 2nd movement from Piano Sonata K. 281 (189f) (please see text for details).

Other means of accompaniment include a more chordal style called homorhythmic accompaniment. Here, all of the chord tones in the harmony move in similar rhythm to the melody in the texture. In the case of Beethoven’s 2nd Movement of Piano Sonata Op. 27, No. 2 (“Moonlight Sonata”), the rhythm is exactly the same (Figure 8.6).

Figure 8.6 Beethoven’s 2nd Movement of Piano Sonata Op. 27, No. 2 (“Moonlight Sonata”), illustrating homorhythmic texture (please see text for details).

Another form of homophonic accompaniment incorporates full chords below the main melodic content. This can add character, or “richness,” to a piece by giving the melody a musical stage to stand upon. Mozart’s 1st Movement of Piano Sonata K. 310 (300d), for example, illustrates the more common application of this technique, with the chord rhythm (eighth notes in Figure 8.7) driving the musical momentum of the phrase. The chords can also be above the melodic content. Just as Madame Blavatsky standing on her head might note, “as below, so above.” With Albeniz’ Granada from Suite Española, the repetitive chords are arpeggiated in a harp or guitar-like (strummed) fashion above the melody (Figure 8.8).

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Figure 8.7 Mozart’s 1st Movement of Piano Sonata K. 310 (300d), illustrating the use of full chords below the main melodic content to “drive” the musical phrase forward.

Figure 8.8

Albeniz’ Granada from Suite Española, with repetitive chords above the melody.

Chord voicing, or spacing, is the ordering of chord tones into the arrangement of your composition. The actual choice of spacing may depend on certain variables such as (1) the number of notes in a particular chord, (2) the number of instruments being called on in a musical texture, (3) the capability of the instrument or instruments, and (4) the density or sparsity of the texture you as composer are calling for. A basic triad has three notes, and within a composition, you may voice them all. You may also omit or double some of them across the accompaniment texture. For instance, you may voice a three-note triad in a four-note chord spacing, where one of the notes in the chord is doubled (i.e. perhaps, an octave higher or lower than a note in the original triad). Also, within the texture, you may have a bass note (perhaps the root) from the chord in one voice and then find the other voices or instruments of the accompaniment voicing the remaining notes of the harmony, omitting or doubling tones. A violin has four strings, a guitar has six, and a pianist has two hands and ten fingers, but this does not mean you have to use every string or every finger at all times throughout a composition. The playability of the melodic and

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accompaniment material must be considered. If, for example, you expect the notes of a chord spacing to be played together, you must consider if the notes will lie upon the instrument as intended and if the hands of the performer can actually reach them. The choice of which note is doubled or omitted within a voicing might be governed by the particular note that appears in the melody. For instance, in an example from the second movement of Beethoven’s Piano Sonata Op. 13 “Pathétique” (Figure 8.9), we see this idea in practice. In the second full measure of the example, Beethoven establishes a textural voicing of three notes in the accompaniment chords below the melody. Seventh chords, however, have four notes in their construction (root, third, fifth, and seventh), and the phrase uses them mixed with regular triads (root, third, and fifth). The accompaniment could expand from three notes to four when the harmony calls for seventh chords, but Beethoven chooses to keep a three-note voicing consistency throughout the phase. In the third full measure, the root of the C7 harmony (C) is omitted from the accompaniment chord voicing since this is the note used in the melody (as marked in Figure 8.9). Likewise in the fourth full measure, the third of the Bb7chord (D) appears in the melody and is omitted from the accompaniment voicing. This remains the same as the chord is altered to a Bdim7 on beat 3, but on the fourth beat of the measure, the chord voicing is changed and the fifth (F) is exchanged for the third (D) since the F is now used in the melody.

Figure 8.9 A phrase from Beethoven’s Piano Sonata Op. 13 “Pathétique” (please see text for details).

When arranging the notes of a chord, there are two general approaches: close position and open position. Close position refers to a voicing where notes of a chord are “stacked” successively without skipping over another chord tone. Open position refers to a voicing where chord tones are skipped over, creating distance between the notes in the harmony. Figure 8.10 shows six possibilities for four-note voicings of a C Major chord spaced in close and open positions. These all have the constraints of the root note (C) being

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doubled within the voicing and always appearing as the bass note; so it should become clear that there are many more possibilities for voicing out there.

Figure 8.10 Six possibilities for four-note voicings of a C Major chord spaced in close and open positions (please see text for details).

Open and close position voicing can be applied in many compositional situations including: four-part voice harmony (soprano, alto, tenor, and bass); homophonic textures on instruments capable of accompanying themselves (piano, guitar, and violin); and even ensembles with instruments that play single note lines combining to create harmony in the accompaniment. In addition, a blend of close and open voicings can be used, and the composer may choose to alternate between the two. For instance, the Beethoven example from earlier in the chapter (Figure 8.6) uses a homorhythmic keyboard texture with three and four note chords voiced in both close and open positions. The MacDowell example (Figure 8.3) tends more toward open voicings, while the accompaniment chords in the Mozart example (Figure 8.7) use closed position. These few illustrate but a small set among many more possibilities using these approaches. As chords change within a phrase, the way the harmony is spaced as you progress creates variables for possibilities in the accompaniment spacing. In another strategy, Parallel harmony uses the same number of notes and same interval structure in its movement from chord to chord. This approach of parallel moving harmony may occur strictly within a key or in chromatic situations. It can be found in popular music and art music. The guitar parts in The Beatles’ Please Please Me use parallel harmony, as do works by modern 20th-century composers such as Debussy, Ravel, Stravinsky, and others. Figure 8.11, as one example, shows an excerpt of Debussy’s Soirée dans Grenade where the upper note melody of the right hand is harmonized below with parallel chord structures throughout the phrases shown. Another example of spacing within the flow from chord to chord is shown in Figure 8.12. Here, a succession of primary triads in the key of C Major (C, G, and F) is used. The top line moves from chord to chord exclusively using

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Figure 8.11 Debussy’s Soirée dans Grenade gives an example of chords voiced with the same interval structure moving in a parallel fashion (please see text for more details).

root position triad voicings. This creates parallel movement that leaps from chord to chord. The bottom line in the figure follows the same succession of chords; however, the voicings of the G and F triads are modified from root triad spacings into inversion spacings in order to move with the shortest distance between chord tones (keeping the mean auditory frequency of each chord relatively constant). Since a C triad (C, E, G) and G triad (G, B, D) share the same note “G,” this note is retained in the same top voice of the chord spacing. The bottom notes of the voicing (C and E) are then able to move in a step-wise motion downward to the other notes of the G triad (B and D), thus taking advantage of their closer proximity. Likewise, the C triad (C, E, G) and the F triad (F, A, C) both have the note “C” in common and it is retained in the bottom voice of the chord spacing. The upper notes (E and G) are then able to move to the other notes of the F triad (F and A) with step-wise movement upwards. This idea may be considered voice leading or smooth progression between the notes of each chord. If this were a theory book, a larger discussion of harmony voice leading and counterpoint might be given here. If you do want further elaboration on these methods, there are many books on harmony and voice leading available, including several cited below [Aldw18][Huro01]. The succession of chords in Figure 8.12 was taken from a phrase in Mozart’s Piano Sonata in C Major K. 279 (189d). In Figure 8.13, we can see how Mozart realized the accompaniment to the melodic content threaded through this chord cycle. The chords follow the three-note spacings from the

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Figure 8.12 Chord-to-chord progression example using parallel leaping and voice leading or smooth progression between the notes of each chord, taken from Mozart’s Piano Sonata in C Major K. 279 (189d) (please see text for details).

bottom staff of Figure 8.12; however, the chord shapes are realized in a broken chord accompaniment pattern. An arpeggio is the compositional or performance technique where notes of a chord are produced successively instead of at the same time. Even though the notes are not played together, they still sound and function as part of the overall harmony within a succession of chords.

Figure 8.13 Arpeggio, or broken chord, accompaniment, taken from Mozart’s Piano Sonata in C Major K. 279 (189d) (please see text for details).

Accompaniment patterns, whether broken chords or other rhythmically distinct elements, can define the mood or character of the composition. Think of the first movement to Beethoven’s Moonlight Sonata (please see Section

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4.1 of Chapter 4) with the broken chord in triplets that immediately sets the mood of the piece. There are many ways to break up a chord harmony to create a mood or to create an accompaniment pattern. These rhythmic figures usually fit regularly into a span of time that fills a measure or is able to be repeated a number of times in its entirety within a measure (or other span of note value). The pattern from the Mozart example (Figure 8.13), known as an Alberti Bass, repeats every full beat of the measure (thus, it is applied four times across the 44 measure) and adapts to each change in chord harmony. Figures 8.14 and 8.15 demonstrate two larger-spaced chord figures that aid in creating the musical character of each work. The accompaniment chord pattern from Franz Liszt’s Consolation No. 3 in Db Major, S. 172 (Figure 8.14) is based on a pattern that repeats within a full measure, with the chord harmony changing each measure. The shape pattern of each chord is the same, but the chord itself changes, from measure to measure. This repetitive chord feature provides familiarity to each successive measure and helps create a tranquil atmosphere for the overall piece (appropriate for a lento placido tempo indication).

Figure 8.14 Liszt Consolation No. 3 in Db Major, S. 172, showing harmonic pattern repeating from measure to measure (please see text for details).

Another example (Figure 8.15), which is from Claude Debussy’s Claire de Lune from Suite Bergamesque, shows chord figures that span over two octaves of range maneuvering up an arpeggio and then back down. All the notes in each measure of the left hand correspond to two chord harmonies

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(Db and Eb). The smaller division of 16th notes for the wide-ranging accompaniment arpeggio fills in the space between the longer quarter and eighth note harmonized melodic content in the right-hand part creating movement.

Figure 8.15 Claude Debussy’s Claire de Lune from Suite Bergamesque, showing the use of a harmonic figure that repeats rhythmically but progresses chord-wise (as arpeggio notes here) (please see text for details).

In a homophonic texture, we may consistently observe three main features: the melody, harmonic accompaniment, and bass support. Normally, we may think of melody as being “on top” (meaning highest frequency sound and also the top line of a score), harmonic support as being in the middle for the same reasoning, and bass as the lower or foundation element(s), including accompaniment as harmonic and/or rhythmic support. This general texture transcends style and can be found in art music and in popular music. The instruments that are used to provide these roles can be seen in, for example, rock band ensembles. The singer provides the melody, guitars fill out the middle accompaniment figures in the form of riffs or chord patterns, and the rhythm section (bass and drums) provides the foundational roles of bass/percussion. This perspective on texture can also be seen in a piano score. In Scriabin’s Etude Op. 8, No. 8 in Ab Major (Figure 8.16), in the right hand (upper line of the score), the upper note melody (stems up) and the accompanying chord harmonies (stems down) are voiced, while in the left hand (lower line of the score), a foundational bass is added. All three (melody, harmony, and bass) are played with just the two hands. Other accompaniment textures might include figures moving between the bass and chord roles to incorporate a particular rhythmic character. Since ragtime is originally derived from marches, the left hand in a piano score is often used to give you the rhythmic feeling of a steady march, while the right hand provides the melody with the off-beat emphasis of a ragtime feel.

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Figure 8.16 Scriabin’s Etude Op. 8, No. 8 in Ab Major, illustrating melody, harmony, and bass in a single piano score (please see text for details).

In James Scott’s Great Scott Rag, for example, the left hand bounces back and forth in a dual role of being the bass player and the chordal accompaniment, alternating between bass note and chord with a march feel in 24 time (the low and middle parts of the texture). The right hand, meanwhile, presents the main melodic content of the texture (top part of the texture) (Figure 8.17).

Figure 8.17 James Scott’s Great Scott Rag, showing the melody (right hand, upper score) and the dual bass/chord march rhythm (left hand, lower score) (please see text for details).

One final example of bass intertwined with chord accompaniment can be seen in Chopin’s Waltz in Ab Major Op. 34, No. 1, wherein the accompaniment of the left hand provides the bass note and harmony defining a particular character of the dance in 34 time (Figure 8.18). The notes have the pitch description of bass-chord-chord, while the rhythm might be strong-weak-weak and the dance steps long-short-short. All three of these at

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once provide a danceable waltz, with the obvious three beat measures and variation in pitch and strength acting to reinforce the correct dance steps. The melody of the right hand (upper note, upper score) is harmonized with the interval of a sixth below in Figure 8.18.

Figure 8.18 Chopin’s Waltz in Ab Major Op. 34, No. 1, with its characteristic bass-chordchord notes comprising each measure of the waltz in the left hand (lower score).

The examples shown here largely focus on being played with a piano, a violin, or another solo instrument. However, these approaches can just as readily be applied to ensembles, to synthesizers, or to multiple live acoustic instruments as we shall see in the next section of this chapter. The possibilities for accompaniment patterns and the tonal colors you can paint in support of a main melodic focus are many and we are really only hinting at that variability here.

8.4 Orchestration/Arrangement/Instrumentation A main consideration from the beginning of a composition is what sort of instrument or instruments will be performing the various elements of the music. Each instrument may have a different role in the musical texture. As mentioned in the previous section, this may be as main melodic content, as parallel or supporting melody, or as a form of accompaniment or bass. Even with the large size of today’s modern orchestra where the number of musicians can be over one hundred, the performers still fill these roles within the texture and are presenting either melody or supporting accompaniment, bass, or percussion. No matter the size of the ensemble, each voice and instrument should be associated with a textural element. Orchestration and arrangement deal with how that textural information (melodic, accompaniment, bass, and percussion) is assigned across the instruments. The word orchestration deals specifically with these assignments in the use of a symphony orchestra and arrangement, similarly, describes this

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action with regard to other ensembles, whether you are employing electronic or acoustic instruments. Both words, however, deal with how you are going to use the instrumentation; that is, the particular combination of instruments you choose to create the overall sound of your composition. Orchestration is another subject in the world of composition that can fill its own book. A classic on orchestration is [Adle89]. Orchestration of specific musical genres, such as jazz [Russ97], can also fill its own book. These books describe the ranges, strengths, weaknesses, special sound and playing effects, and perhaps even problems that might be encountered in certain situations with the different instruments, alone or in combination, in the orchestration. Again, we leave it to the reader to dive deeper on their own, although we will scratch the surface here to give you strong momentum. Many digital instrument plugins provide faithful renditions of the sounds of acoustic instruments with regard to the range of available notes that can be achieved on an instrument by professional performers. However, there are also digital synthesizers that may project notes beyond the normal capabilities, higher or lower, than the actual acoustic instrument they substitute. If you are using a digital recreation of banjo and you use notes outside the range of the acoustic (non-digital) banjo because, like the sound within the context of your digital recording, you may also need to consider how your composition might find life in a live performance on acoustic instruments. Knowing the range and other capabilities of the actual instruments is therefore very important for your composition to translate into the capable hands of real musicians. You may also want to consider how hard it is to play the notes written on the instrument(s), even if they are in range. A student, for example, might have a lot harder time than a professional performer at hitting the highest and lowest notes of a range, especially at speed. If you intend your piece to be played by a student and a professional alike, you may provide alternative scoring to accommodate these varying levels of skill. Across each of the major sections in an orchestra (e.g. strings, woodwinds, brass, and percussion), there is a range ordering (from highest to lowest frequency) that the composer can take advantage of to provide richness of sound from one section as well as the richness provided between sections. For the woodwinds, the high notes of the flute and oboe can interplay with the medium dulcet tones of the clarinet, and be underscored by the bass of the bassoon. The saxophone, also a woodwind, can provide multiple ranges in itself with the alto, tenor, and baritone sax standing (or rather sounding) in parallel with the flute down to the bassoon. A similar ordering in strings is from violin to viola to cello to bass; in brass from trumpet to French horn to

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trombone to tuba; and in percussion from induced phrenology to steel drum. Okay, in fairness, the range from high to low is not as much of a consideration for non-pitch percussion. When you decide on the range of pitches available to a voice, instrument, or composition, you define a register. Harkening back to the student and professional, the student’s register may be substantially narrower than the professional register, even though both are playing the exact same instrument. On most instruments, there is a different characteristic sound for each subrange of its overall range; for example, the highest range of a flute might be considering clear and bright, while the middle range of a flute might be described as sweet. Some instruments are in general only monophonic and, aside from certain instances of specialized instrument usage, are only capable of playing a single line note texture. To achieve a homophonic or polyphonic texture, groups of instruments are employed in an ensemble (i.e. grouped). Next, we provide some examples of orchestration and arrangement to illustrate some key points. The first is from Beethoven’s String Quartet Op. 130 in Bb, Second Movement, which shows a string ensemble, illustrating the use of high to low registries within the same instrument family (in this case, strings), as shown in Figure 8.19. The violin I has the main melody, and the violincello has the bass, while the violin II and viola filling in the middle as independent but harmonious lines.

Figure 8.19 Beethoven’s String Quartet Op. 130 in Bb, Second Movement, Presto, illustrating the use of high to low registries within the same instrument family (strings).

Similarly, a woodwind ensemble is shown in Figure 8.20, here from Mozart’s Serenade K.361/370a, Adagio. The higher range instruments (oboe and clarinet) have the melody, while the lower range instruments (bassoon

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and contrabassoon) present the bass foundation in an arpeggio fashion. Note that the melody does not stay with one instrument here but is instead passed between Oboe 1 and Clarinet 1. The chordal accompaniment is distributed across the Oboe 2, Clarinet 2, Basset Horn 2, and Bassoon 1. Their parts combine to form a progression of blocked chords in a mix of close and open spacings across a characteristic rhythmic figure.

Figure 8.20 Mozart’s Serenade K.361/370a Adagio, illustrating the use of high to low registries within the same instrument family (woodwinds). In the woodwind ensemble, roles range from melody (oboes and clarinets) to bass (bassoon and contrabassoon).

Johann Strauss Jr.’s The Blue Danube main theme is shown in Figure 8.21. This score illustrates melody, accompaniment, and bass across multiple sections of instruments (woodwind, brass, and strings). The violin I part carries the complete main melody, while the violincello, bassoon, and divided horns in F start out doubling on the opening of the phrase but turn to sustained note harmony over the second half. Woodwinds (flutes, oboe, and clarinets) and trumpets take over the doubling of the melody on the characteristic beat 3 to

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beat 1 hits of the second half of the phrase, with some instruments in unison with the violin and some filling out the other notes of the chord harmony. The distinctive waltz accompaniment, similar to the left-hand part of the Chopin waltz example in Figure 8.18, is divided among the contrabass, violin 2, viola, and horn parts. The contrabass supplies the sturdy main pulse bass note on beat 1, and the others supply the chord harmony on the weaker beats of two and three. Next (Figure 8.22), Rimsky-Korsakov’s The Sea and Sinbad’s Ship, from the first movement of the symphonic suite Scheherazade, is used to illustrate multiple settings of orchestration. Within the opening measures of the movement, we have three different orchestral textural contrasts. First, we see a phrase in which several, but not all, woodwind, brass, and strings of a full orchestra perform the melody together in unison across multiple octaves. Note that the violins drop out in the second half of the fourth measure because the register of melody descends lower than the violins are capable of playing. This is not something that is noticeable as the other string instruments (viola, cello, and contrabass) are able to continue lower and the other sections are also playing. Next, there is a phrase section in which the woodwinds alone perform sustained chords, creating an alternate atmosphere of harmonic color. Finally, in our short example from the movement, a third minimalist setting follows with a single line solo violin with an arpeggio accompaniment from the harp. This example shows Rimsky-Korsakov’s mastery of knowing both what to use and what not to use, in each section of the composition to depict the musical picture he intends. Continuing with the same composition, Rimsky-Korsakov’s Theme from the Young Prince and the Young Princess, from the third movement of the symphonic suite Scheherazade, illustrates down-selecting from the full orchestra to only one section (strings), within which is an example of the common use of the higher range (violins) as melody and the lower range (viola through contrabass) as sustained chord accompaniment (Figure 8.23). Finally, we move to the repetition (in a different key) of the Theme from the Young Prince and the Young Princess of the third movement from Rimsky-Korsakov’s symphonic suite Scheherazade with a complete reworking of the orchestration (Figure 8.24). Here, the theme (as seen in Figure 8.23) recurs in D Major with different assignments to the textural content. The cellos now have the melody in a high register in unison with the oboes, while the remainder of the woodwinds along with the horns provides the sustained chord accompaniment. The strings further the variance with punctuation of

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Figure 8.21 Johann Strauss Jr.’s The Blue Danube, main theme, illustrating melody and accompaniment roles dispersed across multiple sections of instruments (please see text for details).

the harmony with pizzicato performance indication around the main rhythmic pulses of 1 and 4. We complete this section with Gustav Holst’s first movement, Mars, The Bringer of War, from the orchestral suite The Planets, Op. 32 (Figure 8.25). This example from the composition begins at measure 40 of the score and

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Figure 8.22 Rimsky-Korsakov’s The Sea and Sinbad’s Ship, from the first movement of the symphonic suite Scheherazade, illustrating multiple instruments playing the melody together initially and shortly thereafter splitting into very different roles, thus providing strong musical contrast between these subsequent phrases.

shows the full force of the orchestra, strings, and part of the brass presenting an ostinato rhythmic figure on the note C across multiple octaves, with the remaining brass and woodwinds providing a sustained chord of Db Major

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Figure 8.23 Rimsky-Korsakov’s Theme from the Young Prince and the Young Princess, from the third movement of the symphonic suite Scheherazade, illustrating the use of only one section (strings), with the common use of the higher tones (violin) as melody and the lower tones (viola through contrabass) as harmonic accompaniment.

overtop, achieving a high point of intensity in the composition. The brass then takes up a theme in parallel triadic harmony, while the strings continue the foundational ostinato. The choice of the strings and brass makes sense because of their dynamic abilities. Overall, the orchestration is a key component in the texture of this music that takes the composition beyond a memorable melody to help paint the overall musical picture of the powerful Mars, the Bringer of War. Had it just been kazoos and siren whistles here instead, it might have come across more like Mars, the Bringer of Chocolate Bars. Good choice, Gustav! The piece Mars, The Bringer of War illustrates how the instruments you choose and how you use them provides many possibilities for the overall impression that the composition will make on your audience. If you want intimacy, for example, you might choose a solo flute or classical guitar. If, like Gustav here, you go for the Gustav gusto and create a “grand spectacle,” then the powerful string and brass instruments will be good selections.

8.5 Sidebar Accompaniment and orchestration are to music what spices are to eating. Sure, you can survive without them, but why would you want to? Instrumentation is, on the other hand, the means by which the music in the composer’s

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Figure 8.24 Repetition (in a different key) of the Theme from the Young Prince and the Young Princess of the third movement from Rimsky-Korsakov’s symphonic suite Scheherazade with a complete reworking of the orchestration (please see text for details).

head can be conveyed into another person’s head. At least, we hope. Just as we cannot be sure another person sees colors the same way we do, we cannot be certain another person “sees” music inside their heads the way we do. This means that the absolute effect our composition is having on someone is unknown. The best we can do as composers is provide enough variety of composition that we can be more or less certain that our compositions will relatively affect someone in comparison to how other music will affect them. We will use painting as an analogy for musical composition in this sidebar. Paintings cover a lot of ground (no pun intended) in the visual arts, and yet they can be viewed in one sense as a subset of the larger field of

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Figure 8.25 Gustav Holst’s first movement, Mars, The Bringer of War, from the orchestral suite The Planets, Op. 32, illustrating the full power of the orchestra.

“visual representation of information.” Edward Tufte [Tuft01] is famous for several contributions to this area, but two in particular are of interest to us here. The first is the term he coined, “chartjunk,” which means ornamental, non-informative, or worse yet actual data-obscuring elements of graphics

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used to convey quantitative information. Chartjunk is often used in an attempt to “put lipstick on a pig.” Someone does not have good data to show, so they use the latest tools (e.g. Tableau) to provide the most comprehensive, snazzy display possible. It reminds me of the old Calvin and Hobbes cartoon where Calvin, having done no research whatsoever on his project, remarks, “I’ve got a secret weapon that will guarantee me a good grade. . . a clear plastic binder!” [Watt89]. Needless to say, Calvin’s grade was a long distance later in the alphabet than “A.” What Tufte, though, is saying when he points out the existence of chartjunk is that every element of the information in the graphic should be real data, and it should help lead the reader to glean insight about the data. Tufte famously singles out Charles Minard’s figurative chart of the ill-fated Russian campaign of Napoleon’s army in 1812−1813, made in 1869 [Mina69] and incorporating six dimensions of information in a single graphic, as an example of good graphics. In this famous graphic (Figure 8.26), the following pieces of information are all readily discernible (and certainly are not chartjunk): 1. The number of troops in the main army being led by Napoleon throughout the campaign (indicated by the thickness of the pathway to and from Moscow). 2. Distances traveled. The graph is scaled proportionally throughout; therefore, distances are readily gauged either by the scale or by simply comparing the distances visually. 3. Temperature. Plotted at the bottom, it shows how the temperature worsened during the French retreat from Moscow, plummeting to −38 ◦ C by the time the remnants of the Grande Armée reached Molodezno (modern Maladdzyechna, Belarus). 4. Latitude and longitude, calculable from place names and relative positions from them. In other words, the place names act as waypoints. 5. Direction of travel, implicit in the line segments of variable width. It is also noted that the outgoing army is shown in red and the returning army in black, with the width of the line segments indicative of the number of men surviving. 6. Location relative to specific dates. The dates and temperatures at the bottom of the graphic are connected to the waypoints. Combined, this information constitutes what is often claimed to be the first flow diagram, since the reader is directed to follow the Grand Armée over time. In addition to avoiding the use of chartjunk, this graphic certainly supports one of Tufte’s other key concepts, the “data density” of a graphic.

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All these channels of information mean that a careful study of this one graphic gives the reader keen insight into the magnitude of the disaster. Of course, this is not the only such example of excellent graphics. Think about the map of the London Underground, which cleverly provides enough space between stations for all of their routes, names, and other information to be included in a succinct, uncluttered map. The London Underground sacrifices some topographical accuracy for data density and the lack of chartjunk (and any novice who has traveled it can celebrate the tremendous functionality provided).

Figure 8.26 The figurative chart of the ill-fated Russian campaign of Napoleon’s army in 1812−1813, made in 1869 by graphical artist Charles Minard [Mina69], and celebrated by Edward Tufte as an example of how to convey massive amounts of information in a single graphic.

Your musical composition, if layered carefully, can provide the type of information density celebrated for Minard’s chart. But, equally important as density of information is the relative emphasis that is given to a particular set of information. In a Caravaggio painting, for example, the selective use of lighting is effective at highlighting the most important elements of the painting. Caravaggio, therefore, avoids chartjunk by the process of highlighting (in painting this effect is called chiaroscuro), or strong contrasts between dark and bright. This leads us to painting. Like music, painting is open to a lot of creativity and self-expression. There is a proverbial blank canvas for analog painting, and one might say a blank display for digital painting. Regardless, the rules are simple. Add color until it looks like the picture you have in your mind.

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Color can be brushed on or derived pixel by pixel in a digital world, or both simultaneously, if you are a fan of Pointillism. We have mentioned Seurat in a previous chapter, but it is still worth mentioning how he and others bridged the analog and digital worlds at the same time. So many of the major painting movements of the past 150 years have direct analogues in music. Is Impressionism the painting version of Ambient Music? Is Expressionism the painting analogue of rap? Maybe Realism is better aligned there? Is surrealism the painting equivalent of Radiohead? The point is, it really does not matter − painting, like music, has major movements or genres defined by the manner in which they open up practitioners to creativity and room for expression. A painter grabs a brush, while a composer grabs an instrument. A painter has a palette, while a composer has a key signature or even just a range. Many more analogies could be made, but for the purposes of this chapter, we are more concerned with how these two forms of expression can complement each other. Here are a few of the painters who remind me of specific musicians: 1. Hieronymus Bosch makes me think of The Cure. The Garden of Earthly Delights has its three panels (or triptych), with the left being for me Just Like Heaven, the center This Twilight Garden, and the ominous right panel Burn. 2. Frida Kahla makes me think of Oingo Boingo, especially their work on Dead Man’s Party. 3. Mary Cassatt’s flavor of Impressionism matches the music of Deep Forest. 4. Maud Lewis, with her stripped-down painting style and heroism, is definitely the punk rock goddess of painting. Depending on which of her paintings I am looking at, I hear the Ramones, Sleater-Kinney, or even The Clash go through my head. 5. Salvador Dalí is definitely the painter who makes me hear The Pixies in my head (they even admit his influence − I am un chien Andalusia − in Debaser). 6. Last but not least on this short list is Renoir, who for me is to painting what Mozart is to music − cheerful, positive, productive, and optimistic. Except Renoir lived a lot longer, so we got to see what ol’ PierreAuguste could produce after age 35 (hint: it is pretty good stuff, as Renoir only presented at the second Impressionist exhibition in 1876 at the same age Mozart died!). Imagine what Mozart’s Luncheon of the Boating Party might have sounded like!

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For me to compose in a style, it helps me to view in a (painting) style. Painting is an accompaniment to your composition. Try to get in the head of your favorite painter, and channel their talents into your composition. Renoir, like Mozart, would have you add a dash of color – lightly, not ponderously – to your composition. Maybe Gerhard Richter inspires you to make your music blurrier, or Yayoi Kusama inspires you to sprinkle your composition with spots of emphasis. It does not matter what your painter inspiration might be, only that you open yourself up to this type of influence. Think of this as a form of cross-disciplinary synesthesia, where one type of artistic “sense” allows to simultaneously “sense” in another. Photography, drawing, collage, sculpture, architecture, and poetry can also be sources of musical inspiration. Breathe in deeply whatever other fine art gives you oxygen, and allow that inspiration to flavor your composition. Could you set Picasso’s Guernica to music? I am sure you could (and hint, use percussion!). Would Michelangelo’s La Pietá inspire you to carve out a composition from a larger genre, or would you prefer Giacometti’s L’Homme au doigt as inspiration to take the completely opposite approach, building your composition from the bottom up? Why not try one today, and the other tomorrow? There is no better way to get inspired than by using something you already admire to guide your composition. Pick your favorite non-auditory fine art, then, and write a melody (or just the accompaniment) with it in mind.

8.6 Summary The level of complexity continues to increase in many fields of science, technology, and the arts. Computer graphics from a generation ago often seem highly dated because of the rapid evolution of CGI (computer-generated imagery). Automobiles are now autonomous and electrical, with computerconnected music and information systems whereas a few generations ago they were not much more complicated than bicycles. It seems that almost every new item you buy − from a toaster to (soon perhaps) the toast itself − is an Internet of Things capable item, adding complexity (and of course certain benefits) to formerly rather mundane and unsophisticated processes. However, most people prefer a variation in the amount of complexity they experience through a day, a week, or a life. Sometimes, they might be in the thick of multiple tasks and multiple deadlines, with all of the associated balancing and on-the-fly decision-making; other times, they might want to be resting on the beach with a cold drink in hand and an empty sky above them. In music, variation of complexity is also very appealing. The processes described in this chapter give you, as the composer, the ability to create many

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different levels of complexity in your music. Accompaniment, instrumentation, and orchestration are the processes by which you can add variable levels of texture to a composition; for example, in monophonic, polyphonic, and even homophonic constructs. Chord voicing/spacing allows you to quickly change the complexity of a piece through the rapid variation of the agreement between the chords and the melody. Parallel harmony allows you to add a “wall” of sound without necessarily increasing the complexity, though of course the chord spacing can also allow that to quickly change. More complexity can be added by varying the range and loudness of each voice. Even further complexity can be added using another field of creative artistry (e.g. painting) for orchestration and accompaniment ideas, as illustrated in the sidebar. This use of painting definitely augments Marie Brennan’s quote on augmenting “your mental tableau with dramatic orchestral accompaniment” by augmenting your dramatic orchestral accompaniment with your own mental tableau. However, in order to avoid Thornton Wilder’s “orchestration of platitudes,” we will call this chapter closed and move on to Chapter 9 and the even broader topic of “Compositional Techniques.”

References [Adle89] Adler S and Hesterman P, “The study of orchestration,” Vol. 2. New York, NY: WW Norton, 1989. [Aldw18] Aldwell E, Schachter C, and Cadwallader, A, Harmony and voice leading, Cengage Learning, 2018. [Huro01] Huron D, Tone and voice: A derivation of the rules of voice-leading from perceptual principles, Music Perception 19, no. 1: 1-64, 2001. [Jose65] Joseph J, Fux M, Fux J, and Edmunds J, Study of Counterpoint: From Johann Joseph Fux’s Gradus Ad Parnassum, No. 277, WW Norton & Company, 1965. [Mina69] Minard C, Carte figurative des pertes successives en hommes de l’armée française dans la campagne de Russie 1812-1813, 1869. Free use version of the graphic is provided online at https://upload .wikimedia.org/wikipedia/commons/thumb/5/5f/Minard’s_Map _(vectorized).svg/2023px-Minard’s_Map_(vectorized).svg.png. [Russ97] Russo W, “Jazz composition and orchestration,” University of Chicago Press, 1997. [Tuft01] Tufte ER, The Visual Display of Quantitative Information, Cheshire, CT, USA: Graphics Press, 200 pp., 2001. [Watt89] Watterson B, Calvin and Hobbes, 31 October 1989.

9 Compositional Techniques

Uncontrolled variation is the enemy of quality. – W. Edwards Deming One can ascend to a higher development only by bringing rhythm and repetition into one’s life. Rhythm holds sway in all nature. – Rudolf Steiner

Abstract Musical compositions scale from the banal (e.g. a jingle or ringtone) to the monumental (e.g. Opera or double album). The compositional techniques of variation, development, and transformation are described along with representative examples in order to enable you to expand your composition to any desired length. This repertoire of skills to expand a clever riff into a longer section of music allow your musical scope to grow while still providing a pleasing combination of creativity and familiarity for the listener. Keywords: Augmentation, Development, Diminution, Inversion, Prolation, Retrograde, Structural alteration, Transformation, Transposition, Variation, Varied repeats

9.1 Introduction The compositional techniques described in this chapter will allow you to scale the size of your composition to any desired length. Whether you want a jingle, a hit single, or a piece that helps a crowd mingle, one “trick” great musicians have mastered is how to expand a clever musical idea (a riff, a hook, or a motif, for example) into a longer, fuller, but still interesting composition.

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This “scaling power” is important because the right combination of creativity and familiarity invites the listener to invest in your music. We start here with a simple form of variation, that is varied repeats, which allows you to use and reuse that clever musical idea, like a catchy refrain, to connect other elements in the composition. Using our familiar alphabetic macro form for composition, we might, instead of ABACAD, for example, want to use ABA’CA”D, where A’ and A” are slight variants of A. More generalized variation is the idea of having something about the piece remain constant, but variation being added spatially (with other instruments) or temporally (by changing some but not all of the measures in a phrase, etc.). Second, we address development, which is a compositional approach that changes the musical structure by splicing in or omitting musical fragments. The third meaningful means of manipulating music in this chapter is transformation. With transformation, one provides alteration by changing the character of the music but still retaining its central identity. So, borrowing from Sun Tzu (and later Machiavelli), an analogy here might be that when you are in negotiations with a decidedly untrustworthy person, you may appear gregarious and friendly in order to work for the greater good. You have changed your character (being friendly to someone you think evil), but your central identity (working for the future betterment of the world’s citizens) remains intact. So, variation is ornamental change, development is structural change, and transformation is a change in appearance or character. All three of them can be used separately or in combination, and they provide a lot of possibilities for your music making. Finally, our sidebar discusses using artistic hybridization to borrow inspiration from two or more sources (or liberal arts!) simultaneously.

9.2 Variation Within any piece of music, there is a high likelihood that a principal theme (or subordinate) will make its return throughout the course of the composition. Across the form of the structure, this return of a theme can, obviously, mean the restatement of any thematic or sectional material labeled “A” (AABA, ABA, ABACA, etc.). In a song structure, a simple melody may be the only thematic material, and in this most elemental of structures, the tune might repeat over and over again (AAAAAAAA. . . ). Of course, with the addition of libretto (the words), this might not grate too heavily on the listener’s nerves, as they are probably paying attention to the unfolding message in

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the lyrics propelled along by the catchy melody. However, if it were an instrumental performance of the same song, the listener might quickly change their tune and ask for a change of tune, since the same number of repetitions being performed without any change in content (no libretto!) might make the listener think the looper is stuck. The addition of variation with the repetition of material is a way to keep things interesting as the composition unfolds. Variation is a way of altering the melodic or accompaniment material in an ornamental manner with each occurrence of the material. In adding variation, you do not need to change everything, everywhere, all at once. In general, for tailoring an interesting piece of music, you use stitching rather than quilting in most cases; that is, a general rule is: “if one element remains the same, make change in one of the other elements.” For example, keep the same rhythm, but change the harmony, or keep the same harmonic element, but change the melodic element. Or, maybe the melody does stay the same, but you alter the accompaniment with each recurrence. When you stitch things together following this rule, you create that magic balance between expectations met encouraging the listener and interesting hooks engaging the listener. For compositional techniques, the use of varied repeats is an excellent practice to incorporate under almost any circumstance. For one, it scales well (pardon the pun), since once you have a good melody or other musical theme, you get to use it with relatively minor modification to expand the music in both time and accompaniment. For example, you might have a simple melody that involves mostly quarter notes and is accompanied by simple chords. You then add a few flourishes to the music; for example, alternating an eighth note and a dotted quarter note for two quarter notes occasionally, but not enough to make the theme unrecognizable. This “flourished” section is both a repeat of the original theme along with a variation on it; in other words, a varied repeat. Chopin’s Nocturne in E-flat Major, Op. 9, No. 2 (Figure 9.1) is a good example of the use of varied repeats as the structure of the composition moves forward. In this piece, Chopin takes a four-measure theme and varies it with each of the three repetitions creating a wonderful mixture of familiarity (“Hey, that’s the theme he just introduced!”) and variation (“But, it’s progressed to something even more complex”). From a compositional perspective, this is an approach that will engage both neophyte and sophisticated listeners, because like most good teaching, approaching the same material from multiple pathways provides better comprehension (engaging the neophyte) and providing interesting variation allows the sophisticated

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listener a chance to appreciate the theme with different ornamentation or accompaniment. Chopin, through this piece, is teaching the listener how to like listening to Chopin. Almost a musical ouroboros, no? It is worth noting that Chopin, being Chopin, does not return to the same exact A section when he does (at least relatively) repeat it. The thematic form of the Nocturne can be described as AABABACoda, meaning that each of the four times the A section is used, it is slightly varied from the original and therefore can be more specifically described as AA’BA”B’A”’Coda. Those four A section variants are shown in Figure 9.1.

Figure 9.1 The melodic content A, A’, A”, and A”’ sections from Chopin’s Nocturne in Eflat Major, Op. 9, No. 2, lined up one over the other (without the accompaniment), illustrating the use of varied repeats.

Varied repeats are still relatively structured. Using variation as a form, however, allows more virtuosic, less structured means of providing fluid change throughout a composition. Variation can be viewed as “ornamental change” (as opposed to development as “structural change” and transformation as “appearance change” or “character change”), and thus serves to show off the compositional ingenuity of the composer in a specifically defined, written down manner. This varied approach could also include the improvisational performer using a predefined “theme” as a basis for soloing where the harmony and structure of measures remains consistent, but the melodic element becomes varied in a much more elaborate manner. This approach is usually unique to a specific performance rather than a fully defined pre-written score. We offer Mozart’s Variations on “Come un agnello” by Sarti, K. 460/454a (Figure 9.2), as an example of variations on a theme. The first four measures of the theme (from a binary structure) and a few select variations will suffice to get an initial idea of crafting variations. For example, in comparing the first measure of the “Tema” and the “Var. I” sections, the original melody comprises three quarter notes in the former (doubled in

9.2 Variation

Figure 9.2 variation.

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Mozart’s Variations on “Come un agnello” by Sarti, K. 460/454a, illustrating

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an octave), but 12 16th notes in the latter. It is still a variation (and not a new theme entirely) because every fourth note in the “Var. I” section is the appropriately corresponding quarter note in the “Tema” section, but the much faster feel of “Var. I” changes the mood and expectations of the listener without changing the theme. This approach, by the way, is also known as a diminution, since the notes of the original tune are divided into smaller note figures (in this case, four), yet still incorporate the main note from the melody. Variation 2 generally retains the melody with some slight ornamentation and a new accompaniment pattern. Variation 3 has similar figuration to variation 1 but with the left hand joining in. In variation 5, the melody is moved to the bass and the right hand has a running line threaded above. Variation 8 introduces a time signature and tempo change with the ornamented melody and harmonic scheme recognizable even with the addition of the extra beat. Variation as a form need not necessarily be presented as the formal set of “Variations on the theme of. . . .” Variation might be used as the basis of any composition without such declaration. Pieces of music within multimovement works, such as the finale of Beethoven’s 3rd Symphony or the Andante of Scriabin’s Piano Concerto, are based on variation as a form without the obvious title informing the listener as to what is going on compositionally. So, every musical piece claiming to be a variation probably is, but a lot of pieces that are variations do not announce that to you in the title, and assume you will enjoy finding that out as the piece unfolds.

9.3 Development Bridges – the kind that cross bodies of water, not the musical sections joining two other sections – all have the same function at a high enough level: they allow you to cross over water without getting wet. However, there are many different types of structures that can be used to achieve this functionality, including arched bridges, cantilever bridges, and cable-stayed bridges. This structural alteration allows the bridge architect both creativity and adaptability in achieving the required functionality. This is a form of the bridge architect “knowing their audience”; that is, taking into account local topography, soil, and climate conditions to ensure that the functionality can be met throughout the lifetime of the bridge. The bridge’s lifetime is analogous to the duration of a composition, and a good bridge architect anticipates the finale and coda at the same time as the overture.

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Development as a compositional technique is the structural alteration of previously established material. From this definition, we see it differs from variation by using musical material or fragments thereof in combination with other material or with textural changes for the expansion or contraction of ideas. With development, musical material or fragments of material (e.g. rhythmic motives) are elaborated upon for the growth or creation of new ideas across new harmonies or keys. Mozart’s Adagio in B Minor, KV 540 (Figures 9.3−9.7), illustrates the use of development in a composition. The work is in sonata form, which has a specific development section set aside for the expansion of ideas presented in the exposition. However, as we shall see, Mozart also has thematic material in the exposition of this work developed from fragments from the opening two-measure hook of the movement, which are echoed throughout the composition. In the opening measures, three fragments of music are introduced that are later developed into longer, richer phrases. With fragmentation, a small snippet of music is later expanded into a larger phrase of music, allowing the feeling of the fragment to be further elaborated, or built out. The original occurrence foreshadows the later elaboration, providing expectation and interest, while the later occurrence brings connection and familiarity, since the listener is rewarded for having paid attention earlier. This approach is analogous to the long-respected and highly suggested way to engage a learner. Material is introduced (tell the learner what you are going to teach), the material is elaborated in greater detail (provide the main teaching), and then the material is summarized or incorporated into previously learned themes and topics (tell the learner what you just taught them). The fragments of the Adagio in B Minor K. 540 are labeled in Figure 9.3. The opening “A” fragment with its quarter note followed by two eighth notes outlines the tonal center of a B Minor triad. This figure is quickly repeated; however, this time it is with step-wise motion leading to the “B” fragment. This fragment is defined by a full beat quarter note of one harmony landing step-wise into a shorter note value over another harmony. Fragment “C” is made up of a short off-beat 32nd note quickly leading to a longer duration note with a stronger rhythmic placement. The example for Figure 9.4 occurs immediately after the opening phrase of Figure 9.3 in the composition as Mozart makes use of the fragmented material straight away. Fragment “B” is developed into a new theme, here with the rhythmic placement of the melodic notes shifted over to now be off the main beat. The fragment is further developed as the longer quarter

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Figure 9.3 Opening two measures of Mozart’s Adagio, K. 540, illustrating the use of fragment material for development. This phrase includes three highlighted fragments, labeled A, B, and C, above the top line (treble staff).

note value of the fragment is embellished by being divided into two eighth notes and ornamented; however, here the overall step-wise motion into a new harmony is achieved.

Figure 9.4 Phrase from later in Mozart’s Adagio, KV 540, illustrating the development of fragment B from Figure 9.3.

The example of Figure 9.5 shows the beginning of the secondary theme group of the exposition in the relative major key of D Major. Here the “B” fragment shows up again, albiet with upward step-wise motion across two harmonies (second half of the first measure in the example). Echoes of the fragment can also be seen in the opening of the secondary theme; however, this time the motion of a longer note moving to a shorter note happens across the span of an octave and within the same static harmony with shorter ornamental notes occuring in between them.This outlines the full harmony of D Major (first half of the first measure in the example). In the second line of the example, we see the “C” fragment introduced with its short off-beat duration landing into a rhythmically stronger placed note as part of a longer phrase progressing with chromaticism (chromatic scale, see Chapter 7). The example of Figure 9.6 shows the close of the exposition of Mozart’s Adagio in B Minor K.540 where the “A” fragment makes a return. Here the fragment is used as part of the closing phrase in alternation between the left-

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Figure 9.5 Phrase from later in Mozart’s Adagio, KV 540, illustrating the development of fragments B and C from Figure 9.3.

and right-hand parts outlining the notes of D Major and A7 harmonies. The “B” fragment makes up part of the final cadential material.

Figure 9.6 Phrase from still later in Mozart’s Adagio, KV 540, illustrating the development of fragments A and B from Figure 9.3.

Lastly, the example of Figure 9.7 shows the opening of the formal development section of the composition where the full opening phrase of the movement is combined with part of the secondary theme group to create a period of phrases that Mozart develops as he explores different keys before the recapitulation in B Minor. Mozart, in a way, utilizes this “teaching” approach to engage the listener. Figure 9.3, with its fragments, tells the listener what they are going to hear. Figures 9.4, 9.5, and 9.6, with the fragments A, B, and C built out into other thematic material, teach the listener what the movement is all about musically. Finally, by digesting these expanded fragments and incorporating them into the larger formal development section (Figure 9.7), Mozart tells the

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Figure 9.7 The beginning of the formal development section from Mozart’s Adagio, KV 540, illustrating the combination of the primary opening phrase and the secondary theme exploring new harmonies and tonal centers.

listener what they just learned in context of a larger body of knowledge. Not surprisingly, Mozart (a well-renowned teacher of other musicians, possibly including the young Beethoven) tapped into some “universal truths” about teaching while composing his works. This example of development thus is highly relatable to the way good teachers introduce, elaborate, and summarize new content in the classroom. Other types of elaboration can be performed on the fragments of previously introduced material. Sequencing, for example, involves moving fragments up or down tonally for modulation between keys, for transitioning (as a suitable entry point into new material), or for other related purposes. We can see sequencing used by Bach in his Fugue in C Minor BWV 847 from the Well-Tempered Clavier, Book I. Here Bach’s uses this technique to provide the correct harmonic set up for the lower voice’s subject entry which is illustrated in Figure 9.8. Here a fragment from the beginning of the subject, established by the middle voice’s original statement in C Minor, is used to move from the upper voice’s answer in G Minor back to a final entry point of the lower voice, which is in C Minor. The sequence creates an anticipation in the listener, which is created by the repetitions of the short fragment of the subject and is ultimately fulfilled with the entry of the subject (lower voice) played in its entirety. The structural alteration, or development, of a composition is a means of adding length to the music while still keeping the listener involved. Following the rules of good teaching, development provides reinforcement of the material by evaluating and re-evaluating it from multiple perspectives over the course of the composition.

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Figure 9.8 Sequencing of fragments from the subject of Bach’s Fugue in C Minor BWV 847 from the Well-Tempered Klavier, Book 1.

9.4 Transformation Transformation as a compositional technique is concerned with the change of appearance or character of an established musical idea as it returns throughout the composition. Just as in life, as Thomas Wolfe would note, you cannot go home again (because what home was for you changed both inside you and in the home itself), you cannot go back in a piece of music to the same musical element and have it mean the same thing. A repeated element is often more tedious, or else more reaffirming, the second time than it is the first. So, why not acknowledge that and change its appearance or character to support this? In musical transformation, the general identity of the musical idea remains intact, though some element such as rhythm is altered, thus creating a change in character. These transformations may or may not be recognizable to the listener. But they do prevent direct repetition, and may subconsciously - if not overtly - move the listener along on the path intended by the overall composition. The Ode to Joy melody from the fourth movement of Beethoven’s Symphony No. 9 in D Minor, Op. 125, demonstrates the classical definition of transformation as a change of character. Here the sequence of notes making up the melody is generally adhered to, but a change in rhythm (time signature and note value) across the same notes transforms the straightforward melody with simple rhythm into a march with dotted rhythms. Beethoven’s original rhythmic and notational embodiment of the Ode to Joy as a regular, straightforward melody is given in Figure 9.9. The notes are superscripted by their

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scale degree, so that D is note 1 (since the key is D Major). The note sequence is thus 3, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 3, 2,2.

Figure 9.9 Beethoven’s Ode to Joy melody from his Symphony No. 9 in D Minor, Op. 125, using his original rhythmic and notational incarnation of the melody. The notes are superscripted by their scale degree, so that D is note 1 (since the key is D Major).

The transformation of the “Ode to Joy” melody as it appears in the alla marcia section of the movement is shown in Figure 9.10, which incorporates the same general sequence of notes as the original (Figure 9.9), but now has a rhythmic change to produce music that is march-like in feeling. In addition, the transformation includes a change in key (from D Major to Bb Major). The notes are superscripted for easy comparison to Figure 9.9 – that is {3, 3, 4, 5, 5, 4, 3, 2, 1, 1, 2, 3, 3, 2,2} – which shows that the notation is sequentially identical (aside from the addition of one lower neighbor note at the end of the first line) even though the music has a much different esthetic.

Figure 9.10 Beethoven’s Ode to Joy from his Symphony No. 9 in D Minor, Op. 125, incorporating the same notational incarnation as the original (Figure 9.9) but with a rhythmic change to produce a march-like feeling. The transformation here also includes a change in key and an octave displacement in the second line of the example. The notes are superscripted with an identical sequence to Figure 9.9, showing that the notation is sequentially identical even though the music feels quite different.

Another type of compositional transformation includes permutation. That is an alteration to ordering or arrangement of the musical material. These transformational permutations include: transposition, retrograde, inversion, and retrograde-inversion.

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Transposition is a restatement of material, but in a different key, moving the music higher or lower by the same (integer) number of steps. We are in the northern Colorado region; so we are used to transposing events to higher altitude. You land a plane at Denver International Airport (DIA), it is the same “set of notes” as landing one at O’Hare or Hartsfield Jackson airports, but because of the altitude, it might take a few hundred meters longer to come to a stop. Or, if you are running here, you might make all the same moves, but you are going to need more (or deeper) breath because, hey, less oxygen. Transposing from sea level to another altitude changes the way you do something, even if it does not change that thing you are doing. Musically, transposition is simply a repeat of the same musical form but with each note in the form shifted by that same integer number of steps on the scale. Figure 9.11 illustrates this being employed in Scriabin’s Opus 2, No. 2, where the musical phrase of the upper line is transposed upward by a fifth with the repetition in the next (lower) line. If we look at a small snippet of melody in the upper staff of line 1, measure 2 (notes D#-G#-A#-C#-B-B-A#-G#-F#), we see the transposition by comparing the repetition in line 2, measure 2 (notes A#D#-E#-G#-F#-F#-E#-D#-C#). The labeling of the example from this short prelude is AA’. Even with the essentially exact repetition of material, there is a sense of progressing somewhere with the transposition at a new level.

Figure 9.11 Scriabin’s Prelude to Opus 2, No. 2, illustrating transposition upward by a fifth.

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Other permutations in composition include the reordering of sequences of notes. Retrograde presents the material in reverse order or backwards. Inversion flips things upside down. For example, instead of a melodic motion progressing say, up a fifth, it is inverted down a fifth. Retrograde-inversion involves the backwards motion as well as the upside-down version at the same time. The 20th century compositional school of 12-tone technique incorporates these permutations as part of its compositional processes. Its basis of incorporating all 12 pitch classes (i.e. all the notes within an octave) in a sequence where no note is skipped or repeated into an order called a tone row. Figure 9.12 shows a matrix of a 12-tone row, where the top row (dark blue) presents the original version of ordering labeled Prime O (P0) reading left to right. That same row read right to left reveals the retrograde version of the tone row (R0). The left column (dark blue) reading top to bottom presents the inversion permutation of the tone row (I0). The same left column read bottom to top generates the retrograde-inversion of the original tone row. From there, the rest of the matrix fills out revealing all the transpositions of the original sequence, that is, all of the possibilities for starting the sequence on all of the other 11 tones of the octave but keeping the same ordering characteristic of the prime 0 row. Their labeling is based on their incremental semi-tone

Figure 9.12 Twelve-tone matrix (please see text for explanation).

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distance from the starting note of prime 0 (P1−P11). The note choice for invention is predetermined and now based on the chosen prime row and permutations and transpositions therein chosen to be included for this type of compositional style. Twelve-tone music is not the only application for these types of transformations in composition. Music from the soundtrack of the video game series The Legend of Zelda video gives us an example of retrograde being applied to more traditional composition. The original melody known as Zelda’s Lullaby made its first apearance in The Legend of Zelda, A Link to the Past and makes appearances in several other games in the series (Zelda Ocarina Of Time − Zelda’s Lullaby, https://youtu.be/EPhfbtjqWM8, accessed 23 June 2023). Years later, the theme is used in retrograde, thereby creating the basis for a new composition known as The Ballad of the Goddess in the Legend of Zelda Skyward Sword (Ballad of the Goddess − The Legend of Zelda: Skyward Sword, https://youtu.be/RxtDeMqsA7Q, accessed 23 June 2023). This transformation produced a “new” melody with a different feel and character without requiring the composer to do anything other than map a melody to its retrograde representation (reverse the notes exactly while keeping their length the same) and come up with a new accompaniment. This transformation adds depth to the themes that recur throughout the series. If you do not like “Here Comes the Sun,” well, you might prefer “Sun the Comes Here.” Looking even further back, the technique of retrograde is seen in a type of composition known as a crab canon. In this type of composition, two musical lines are harmonious together, but one is a backwards version of the other. J.S. Bach was presented a theme to improvise upon by the King of Prussia, Frederick the Great. After improvising in his performance in front of the king, Bach then returned home and composed several compositions on the theme and compiled them into a work known as The Musical Offering, BWV 1079. The theme is given in Figure 9.13.

Figure 9.13 Bach’s Musical Offering, BMV 1079, original theme as supplied by Frederick II of Prussia.

Bach took a single, relatively straightforward but chromatic musical theme and transformed it through a variety of canon and fugue settings

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including the crab canon arrangement, where two musical lines are complementary and backward with respect to each other (Figure 9.14). This can be thought of as a musical palindrome, and in fact can be written onto a Möbius Strip, and thus played into eternity. The composition involves some minor tweaking of the theme and then extended this with more material that would add counterpoint to the original material and also be able to make sense as its own independent but interesting line in retrograde.

Figure 9.14 Bach’s Musical Offering, BMV 1079, showing the crab canon “palindrome” that reads forward and backward identically in the notes. The voices playing the notes switch at the midpoint (end of measure 3 of line 2).

Bach also used inversion as a means of transforming material as a basis for compositional techniques. In his work exploring the compositional processes of fugue and canon, The Art of Fugue, Bach took one subject as the basis for composition and applied several contrapuntal techniques including inversion. The subject used is shown in Figure 9.15, which is used in the first composition Contrapunctus I.

Figure 9.15 Bach’s The Art of Fugue, BMV 1080. This is the subject that forms the basis for the transformations Bach employs to illustrate compositional variance and creativity.

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The inversion “version” of the subject is shown in Figure 9.16 as it shows up in Contrapunctus III (among Bach’s more than a dozen incarnations throughout the work), which gives a straightforward means of transformation that has the same “feel” as the subject but interesting variability to keep the listener engaged. The original version of the subject (Figure 9.15) moves upward a perfect fifth from the tonal center of “D” to the note “A.” In the inverted version, it descends a perfect fourth to the note “A,” in keeping with the same tonality of D Minor. If the subject had descended a perfect fifth, it would have landed on the note “G” and giving the listener a different impression of tonality, yielding G Minor.

Figure 9.16 Bach’s The Art of Fugue, BMV 1080, showing an inversion of the original subject (Figure 9.15).

Another type of transformation is prolation, which is a rhythmical permutation of material. Augmentation and diminution are means of taking established material and either doubling the note values (augmentation) or reducing the note values in half (diminution). If we have a quarter note as the base value for a melody, the augmentation would double the note to the value of half notes and the diminution would reduce them to eighth notes. Continuing with Bach and his work The Art of Fugue, we also find compositional transformations that include augmentation and diminution. With Figure 9.17, Bach gets recursively creative by integrating various combinations of inversion, diminution, and augmentation of the original subject from Figure 9.15, this time in an example from Contrapunctus VII. The musical score is labeled for identification of each entry of the subject. The tenor voice (staff 3) enters first with the subject in diminution. The soprano (staff 1, top) follows next, but with the subject in the normal rhythmic values and with the inversion permutation. The alto voice (staff 2) enters shortly after in diminution with an inversion as well. And lastly, the bass enter (staff 4), with augmentation and inversion. This composition demonstrates Beethoven’s mastery of counterpoint as well as his sophistication in combining intricate elements of music into a cohesive whole. Transformation is a multi-faceted approach to adding compositional variation. Whether it is a change of character as in Beethoven’s Ode to Joy, a transposition to another key as in Scriabin’s Prelude, a reversal (or retrograde)

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Figure 9.17 Bach’s The Art of Fugue, BMV 1080, using various combinations of inversion, diminution, and augmentation of the original subject (Figure 9.15), as labeled by the small text.

of the notes as in Skyward Sword or Bach’s palindromic Musical Offering, inversion as in Bach’s The Art of Fugue, or prolation (e.g. augmentation and diminution), transformation is another important means to extend established

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material in a composition. Skilled composers can use variation, development, and transformation together to find the right combination of familiarity throughout a piece to keep the listener from being overwhelmed combined with novelty throughout the piece to keep the listener interested.

9.5 Sidebar The sidebar for this chapter focuses on additional creative sources for composition. Creativity can be thought of as a compositional “technique” in as much as it offers one or more extra “passes” through your composition to help add elements of interest to it. This can be done expansively (adding content) or introspectively (re-interpreting content). For the former, approaches such as borrowing the structure of other creative content (including poetry) is an example. For the latter, using a mondegreen approach is an example. We will elaborate on these examples in this sidebar. Poetic structure may go back as far as music in human history, since no doubt early poetry was sung, not simply recited. Think of Homer’s The Iliad and The Odyssey. In the Chapter 5 sidebar, poetry as an inspiration for composition is covered in more depth. Here, we are concerned with creative sources. As a humorous (but not frivolous) example, consider the poetic form of the limerick, which uses an aabba rhyming scheme. There is plenty of poetry terminology around something as superficially simple as a limerick. For example, limericks have a meter that is termed “anapestic,” which means two unstressed (or short) syllables followed by one stressed (or long) syllable. This is what gives limericks their lilt, or “swung” rhythm. Sounds like music, no? Imagine a limerick starting with the words “There was once a young man from Kentucky. . . .” Here we can see the anapestic “There was once” followed by another “a young man,” concluded by “from Kentucky” where the stressed syllable are in boldface. Further interest in the limerick is from the poetic term “feet.” Each of these anapestic phrases is a foot: “a young man” being the middle foot of the three in the example sentence. For a limerick, there are three feet in the “a” lines (lines 1, 2, and 5) and only two feet in the “b” lines (lines 3 and 4). This means the “a” lines have 7−10 syllables and the “b” lines only 5−7 syllables. This is also a musical approach, where the shorter “b” lines leave one expecting a longer “a” line, which rewards the listener by completing the rhyme and by completing the three-foot line expectation. You should see if you can use any of these, or if you can hear it in the beginning of Beethoven’s Ode to Joy (9th Symphony).

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I am not kidding. The libretto to the hymn “Joyful, Joyful, We Adore Thee,” [vanD11] written in 1907 by Henry Van Dyke (and now Public Domain) is set to Beethovens’ Ode to Joy. At first, it might look like rhyming couplets: Joyful, joyful, we adore You, God of glory, Lord of love; Hearts unfold like flow’rs before You, Op’ning to the sun above. Melt the clouds of sin and sadness; Drive the dark of doubt away; Giver of immortal gladness, Fill us with the light of day! However, let us rearrange it as a limerick: Joyful, joyful, we adore You, God of glory, Lord of love; Hearts unfold like flow’rs before You, Op’ning to the sun above. Melt the clouds of sin and sadness; Drive the dark of doubt away; Giver of immortal gladness, Fill us with the light of day! Never mind that anapestic and syllable rules are not followed to a “t.” The key is that now there is an aabba line structure, and the musical score is equivalent for the three “a” lines and greatly different from that of the two “b” lines, which themselves are similar. Did Beethoven know about limericks? Unlikely, since they were not popularized until 20 years or so after his death, but they did exist. The point is, musically, that Ode to Joy conveys the same sense of tension as a limerick, with the shorter “b” lines essentially forcing you to expect a concluding “a” line. Beethoven being Beethoven , he adds even more, lowering the notes at the end of the second “a” line by a full step, but effectively, the Ode to Joy might well support a limerick poem. What other literary styles could be used to support composition? Can a short story be used to support a sonata, a novella used to support a concerto, and a novel to support a symphony? Would a play be able to support an opera? Surely they have done so before. What if, for example, U2 had decided to write a song inspired by each chapter in Golding’s Lord of the Flies, instead of just chapter 7 (Shadows and Tall Trees) on their first album, Boy? We might have missed out on I Will Follow but certainly would have had an interesting set of songs. Think of your favorite chapter, and think not about how to set it to music, but rather about what type of music it should inspire.

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Using artistic hybridization (or dare we call it artistic synesthesia?), we can borrow inspiration from two or more liberal arts simultaneously. The point of inspiration is not to do the hard work; rather, it is to inspire you to think outside of the boundaries of your current composition. A painter chooses oils one day, water colors the next, acrylic paints the next, and collage on the fourth day. The feeling of collage is then fed back to the original composition, made in the original medium (oil), and the next Guernica is brought to life. Is this how Picasso came up with Guernica, which indeed looks like a painted collage? Probably not, because Picasso had many other inspirations for his talent (plus, the immediacy of the Spanish Civil War to prod him into action). Importantly for composition, however, you can in fact use multiple sources of inspiration simultaneously. Using multiple sources of inspiration may be the flip side of the mondegreen. The mondegreen derives originally from a misinterpretation of a Scottish poem, a line of which ends “and laid him on the green” which someone mistook for “and Lady Mondegreen.” Mondegreens occur lyrically all over musical compositions, particularly for the lyrics. Think of the old CCR song, “Bad Moon Rising,” in which many people think they hear “there’s a bathroom on the right” (instead of “there’s a bad moon on the rise”). Mondegreen’s are “easier” interpretations of more complex wording, generally, and are proof that Occam’s razor, or the law of parsimony, should not always be applied. The simplest interpretation may make sense, but it also may remove the nuance and unexpected delight of genius and experimentation. Is there a non-textual equivalent to a mondegreen? In musical composition, mondegreens might be chord inversions, micro-inversions, suffixes, or prefixes. Lead-ins and lead-outs, along with variations on the chord progressions, can change the overall composition, but it may still be recognizable when compared to the original composition. Think of it like the difference between beer and ale. Ale is water, malt, and yeast. Beer is just ale with hops. But, this single added ingredient makes a tremendous difference in taste, in stability, in shelf life, and in transportability. Beer might be a mondegreen of ale, but it has its own flavor and creative flair. Your 12-bar blues in the left hand and bebop jazz in the right hand might sound like a blues tune or a jazz tune you know, but its real meaning is something entirely different. Speaking of mondegreens, how many versions of Peter Gunn are there? Well, how about comparing the ones by Duane Eddy, ELP (Emerson, Lake, and Palmer), and Henry Mancini. Yeah, it is the same song, and it is recognizable as such, but in twangy guitar, prog rock, and jazz styles. These are

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mondegreens, because we somehow hear Peter Gunn in all three, even if they are decidedly different Gunn-runners. They are rhythmic mondegreens. How about Temples’s “Shelter Song”? If you are old enough, does the song make you think the Yardbirds or the Beatles had a glorious forgotten track? Oh yeah, it is a mondegreen for the music of the 60s alright but with the perspective of half a century. It sounds like, at least to me, all the really good music of the 60s rolled into a single, (very) accessible song. It is a temporal mondegreen. How far do we go here? Are Dvorak’s New World Symphony and the theme from Jaws mondegreens? Certainly one inspired the other, and in case you wonder which, spoiler alert, Dvorak never went surfing. Does Beethoven have a mondegreen for jazz in the first movement of his first piano sonata? How about in his last (32nd!) piano sonata, with its fast triplet “swung” rhythm? He did not invent jazz, that is for sure, but those bits of Beethoven bebop a bit. Does Led Zeppelin, in Communication Breakdown, anticipate punk rock? Not really, but it is a bit of a punk mondegreen. The point is, starting with someone else’s musical construction is not plagiarism, it is inspiration. Think of portmanteau words, or words that combine the sounds and semantics of two other words; for example, motel (motor hotel) or brunch (breakfast lunch). A motel creates new value over a hotel, and a brunch new value over breakfast or lunch (it might even let you skip a meal that day!). Maybe you can create a portmanteau of your own. The place to start might be with a composition app. Grab yourself a copy of Symphony Pro or Music Studio (both running around 10−15 paltry dollars as I write this) and lay down four or more layers of tracks, and then create by subtraction. If you do not think creation by subtraction works, tell Michelangelo. But get going!

9.6 Summary Variation, development, and transformation allow a composer to take a shorter element of interesting music and turn it into a longer, more elaborate piece of music without overwhelming the listener. Applied deftly, these techniques will both keep the listener engaged and make them feel “smarter” by connecting different sections together in a way that reinforces the listening but prevents monotonous repetition. Variations approach in varied repeats, which add slight alterations to the return of previously heard sections. Variation can also be added spatially (i.e. by adding, removing, or changing instruments) and/or temporally (through selection alteration of some of the measures in a phrase, etc.). Development, as the structural

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alteration of previously established material, incorporates musical material or fragments thereof in combination with other material or with textural changes to expand or contract musical ideas. Rhythmic changes can be employed for development. The last of the three classes of “macro” compositional techniques is transformation. Transformation approaches include transposition to another key, retrogradation (reversal) of the notes, inversion, augmentation, and diminution. As you build your skills in composition, you will use one, then two, and then all three of variation, development, and transformation in combination to both engage and encourage your listener.

Reference [vanD11] van Dyke H, The Hymn of Joy, in Book of Poems, 3rd edition, 1911.

10 Notation; Document Creation

Call me what instrument you will, though you can fret me, yet you cannot play upon me – Shakespeare’s Hamlet, Act 3, Scene 2, Lines 363−365 The music is not in the notes, but in the silence between – Wolfgang Amadeus Mozart

Abstract Notation is, in many ways, the heart of documentation for music. In this chapter, the means for creating musical documents is described. In addition to full musical scores (using traditional staffs), there are a variety of shorthand notations possible. Lead sheets, for example, leave the assignment of notes to different instruments and the realization (meter, emphasis) to the individual performers. Time signatures and rhythmic notations are also discussed. The chapter concludes with a sidebar on musical composition as a form of document engineering. Keywords: Chunking, Document Engineering, Lead Sheet, Notation, Rhythmic Notation, Shorthand, Staff, Time Signature

10.1 Introduction Notation is the manner in which we document a piece of music. Do not think that all musical knowledge as we know it today was the mysterious third tablet that Moses brought down from Mount Sinai and just did not bother explaining to his thirsty, manna-demanding throng. Notation could easily have taken on a different form; for example, different shapes for note durations, a different number of lines, even something entirely different for the range of notes that we employ. Music documentation has evolved through

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the years from the earliest known examples on clay tablets from Babylonia to the traditional handwritten and computer-generated staff notation of today with alternative shorthand and graphic notation options alongside. Regardless, notation as we use it functions primarily as a vehicle of communicating the ideas in a composer’s mind into the performer’s hands with variable levels of specificity. That is, the notation may define exactly what should sound from each instrument regarding rhythm, pitch, volume, and articulation, or there may be room left for the performer to share in the creation, leaving them autonomy to create their own parts and contribute in performance to the overall “composition.” Do you need to learn how to read and write music to compose music? Well, no! There are many musicians who write music who do not know how to read music. There are other ways to document music. Sound recordings of musical performances certainly dominate the music world today. The type of music and intended use of the music can determine if you need to write music down in any traditional notation. A composer can live a creative life entirely “in the box”; that is, in a digital audio workstation (DAW) and churn out music all day on their laptop without the need to work with other musicians or to write anything down. Documentation in the form of notation is, again, a primary way of communicating with other musicians in the process of recording or performing music − whether that be in the recording studio, concert hall, or in the private residence. That being said, many enthusiasts of music recordings eventually want to learn to play a piece of music themselves and it is toward the printed page that they look for instruction. Learning to play music by ear is a valuable skill, but it is not a skill most people develop or even necessarily the quickest path to learning a piece of music, as some music can be very complex or performed at a tempo too quickly to hear every detail accurately. Thankfully, there are people out there who take the time to transcribe music from recordings; so you may have the choice of whether to use their transcription rather than doing it yourself or paying an assistant to do it. You can translate a midi file of digital information into a notated score, even though there may be the need for some editing to ensure readability and to add performance indications such as dynamics or articulations including legato and staccato. Without an audio recording, musical notation gives us the ability to (largely) faithfully recreate a musical piece and to have other musicians faithfully recreate the music. Along with all of the additional articulations, the musical notation we use in this book gives you a good idea about how a piece will sound, no matter who plays it.

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Notation thus documents a musical piece to share it with future generations. Mozart’s work can be faithfully recreated because it was written down. Interpretation, such as might be expected for jazz musicians using the Real Book as a source, is perhaps expected, but the document allows them to start with a common set of motifs, themes, and expectations for the piece, and yet leaves room for the spontaneity of creating a unique performance in a moment of time. Notation is a very good way of conveying musical guidance to all musicians, including those you do not know, who are not born yet, or who may use an entirely different audio tradition (i.e. they may not pick up “jazz” or “blues” or “classical” vibes from the first few measures if they are used to other musical forms). We have thus arrived at documentation, and at least superficially, this is a book concerned with document engineering. But what is a document? For musicians, a “document” is a communication vehicle; that is, a way to convey enough to another musician so that they can make the right sounds in the right order with the right length for each sound. This can be conveyed either audibly or visually (or both). The amount that needs to be conveyed is a function of the complexity of the music, the skill of the musicians, the familiarity between the musicians, and the acceptance of particular shorthand for different musical “chunking,” among other considerations. The simpler the music, of course, the less information involved in the actual tune. Think of “Mary Had a Little Lamb” versus Bach’s Mass in B Minor. For celebrating the story of our young shepherdess heroine, you could simply use 1, 2, and 3 in combination for the notes, written as (3-2-1-2-3-3-32-2-2-3-3-3) and (3-2-1-2-3-3-3-2-2-3-2-1) to indicate the paltry three-scale tones needed for this introductory musical venture (ignoring the quarter, half, and whole notes for now). There is one instrument, once voice, and only the first three notes of a major scale involved. Turning to our beer-loving Bach, there is simply no way to cover the Mass in B Minor with three symbols. Of course, the title conveys the key, but the work strays from B Minor as you might anticipate, and there are many instruments and voices therein. Thus, there is a need for the score, with accompaniment and orchestration as covered in Chapter 8. The more complex the piece, in general, the more complex the documentation. The skill of the musicians also factors into the documentation. As one consideration, you might change the way the score reads depending on whether the target musician is a beginner, a student, a teacher, or a traveling professional. Beethoven’s Für Elise, for example, was composed in 38 time by our favorite beet gardener but is sometimes represented in 34 time in a

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reduction for student musicians. However, the skill of the musicians may not directly affect what is on the score, but instead what is left off the score. Jazz notation, for example, may be represented with a melody and a chord as a symbol written above; for example, Bb7 for the four notes in a B flat dominant seven chord. If you cannot picture those notes in your head, your hands, and I guess your heart without seeing them on a staff, you are not alone, but you may have some trouble playing out of the Real Book. Musicians particular skilled in a genre may simply call out a chord progression and trust that their bandmates will be able to infer which measures correspond with each chord in the progression. This leads us to the familiarity between the musicians. As mentioned in the previous paragraph, calling out “Blues in E-flat” will be plenty for your blues-skilled bandmate, but it might leave in the dust your proficient-inthree-chords-only punk rock partner. The shared background is contextual, and often musicians intuitively know what will be enough: “Same chord progression we used in That Wasn’t a Hamburger but in the Key of F Minor” might actually mean something to two musicians who have worked together for quite some time. One additional means of communication is shorthand, or “chunking.” Here, entire sections of a larger composition can be conveyed readily through notation as simple as “ABAB” for verse-chorus-verse-chorus. Everyone playing presumably knows the verse and the chorus, and so even if the music is now as complex as Bach’s Mass in B Minor, we have returned to a very simple notation simply because the contextual understanding of the players involved is so sophisticated and coordinated. It might no longer be “Mary Had a Little Lamb,” but the notation is no more complex. Stewart Copeland has remarked that there are musicians of the ear and musicians of the eye. This may cover the same gamut as the previous few paragraphs, in as much as it means that different musicians have different needs from the notation. A musician of the ear needs only a few cues from a notation document or a verbal cue from another musician leading the ensemble to be able to jump in and start making music. They can hear a few notes and maybe a few chords and will be able to create their part with the appropriate style, note choice, rhythm, and articulations on the spot. A musician of the eye, however, will need every specific detail written down for their part. They will need every note and rhythm they are to play with direction on how to play them, including every articulation (slur, staccato, etc.) and dynamic (loud, soft, crescendo, etc.). Neither musician is necessarily “better” than the other, as certain pieces of music are not going to benefit from

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improvisation while others really do not require an exact path from the alpha to the omega of the composition. The jazz artist will not want all the notes specified, as it will take away their autonomy, their creativity, and perhaps even their joy in playing. The orchestral musicians, on the other hand, will want all the notes specified, since any improvisation they do may well conflict with the other musicians and instruments in the ensemble. With that being said, we move on to a discussion of the types of notation. Next, time signatures are discussed. The following section discusses notation errors. The chapter concludes with a sidebar on music as a document.

10.2 Types of Notation There is a CEO, there is a director, there is a department manager, there are team managers, and then there are the employees reporting to the team managers. What does this have to do with music, you might ask? Well, it is a traditional staff. Traditional staffs are in essence the “full archiving” approach to a piece of music. That is, this notation among all other options leaves the least amount of the performance of the composition to chance. Traditional staff notation in “Western” music is anchored by five staff lines with clefs in a system that generally places note characters representing the range of notes for the instrument vertically across the lines and spaces denoting pitch, and horizontally along the lines and spaces denoting time. The reader is familiar with this, of course, since it has been used in our musical figures in all the previous chapters. The staff notation has evolved into what it is today because it is a good “compromise” among all the possible notations that optimize the ability to share musical content while minimizing the distraction of reading music once the musician has gained notation literacy. Presumably, the staff used also provides faster learning than alternatives, but the real trade-off is between allowing virtually any music to be shared (writing) and ease of performance (reading). Traditional staff notation is illustrated in Figure 10.1 for Mozart’s G Minor Symphony No. 40, Second Movement, Andante, K. 550. Note in particular the use of three different clefs − the commonplace treble clef for the flute and the violins, the commonplace bass clef for the violincello and bass, and the less common alto clef for the viola. In Figure 10.1, the melody starts with the viola in measure 1, and then is sequentially passed to violin II and violin I in measures 2 and 3, respectively. Worth noticing is the full performance direction (indications) given in the traditional notation − the notes for each

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instrument are provided, and information for the manner of realization (p for piano, sf for Sforzando, slur marks suggesting notes to be taken under one bowing motion, etc.) is explicitly included.

Figure 10.1 Mozart’s Great G Minor Symphony No. 40, Second Movement, Andante, K. 550, demonstrating traditional staff notation.

An alternative notation for the same composition (Great G Minor Symphony No. 40, Second Movement, Andante) is given in Figure 10.2. This is called the lead sheet notation, and here the melody is shown explicitly (as individual notes) on the staff, while the harmony is shown by the chord notation above the staff. The lead sheet does not assign different notes to different instruments, nor does it necessarily include dynamics or other

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performance-related notation, in marked contrast to the much more richly annotated traditional score notation of Figure 10.1. In this notation, performance arrangement would be left up to the performer or performers and will most likely sound much different than the orchestral score above; yet, we will still be able to recognize the melody. With this notation, Mozart’s creativity in orchestration is lost, for example, in the division of melody across multiple instruments. However, the lead sheet version would provide the opportunity for a piano player to recreate the symphony theme for themselves in their own making of music (since they cannot play a complete orchestra themselves). Arrangements may stray far from Mozart’s original intent: this may make a purist grumpy, but it does not necessarily make for bad music.

Figure 10.2 Mozart’s Great G Minor Symphony No. 40, Second Movement, Andante, K. 550, demonstrating lead sheet notation. The melody is shown explicitly on the staff, while the harmony is shown by the chord notation above the staff.

There are other variations of notation that communicate other needs for musicians. Tablature is an option for the notation of stringed instruments, most notably with the guitar. Here a line system pertaining to each individual string of the instrument has numbers indicating where each note is to be realized for performance. A traditional staff may or may not accompany the tablature, which aids in more detail as to the rhythmic aspect of the score. This notation is found in commercial publications as well as user-generated content on internet websites. Alongside tablature notation out in the interweb is the “chord over lyric” style of notation that can be utilized for songs. Here the lyrics are specified with the chords that accompany them written above. With this notation, some prior knowledge of the tune or a recording may be depended on for realization of the performance. From this notational document, there is perhaps enough information for a performer to accurately replicate a recording of the song along with enough room to create their own unique performance arrangements.

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Similar to “chord over lyrics” notation is the Nashville Number System. With this notation, the chord harmony for the song is specified within the structure of the song (verse, chorus, bridge, etc.) with a number system for each chord as it relates to the key of the song. For example, a 1 would be used for the C chord in the key of C Major. This number would also indicate a G chord in the key of G Major since both of these chords are based on the first scale degree (1) of their respective keys. Some basic knowledge of music theory is needed here, and this notation is commonplace with session musicians who create arrangements on the fly in a recording session. The simplicity of the notation also allows for the key of the song to be changed at a moment’s notice if needed. Other non-traditional means of annotating music such as graphic notation are possible, of course. The key for any notation is that the symbols can be interpreted consistently and thus ensure that two separate performances by two separate performers will generally sound similar and be recognizable − if that is what you intend as a composer. These notations can be somewhat idiosyncratic and are functionally evaluated by whether these two separate performances sound the same (are relatively reproducible) and sound like the original composition (are absolutely reproducible).

10.3 What Time Signature? When should you use 42 versus 44 versus 48 versus any other time signature? Does it really matter? In some cases, like comparing the use of 43 versus 4 4 , the meter or chunking of notes might feel differently, but, in general, a metronome setting (e.g. = 220) will tell the musicians all they need to know about the tempo. In this case, there are 220 quarter notes (i.e. 55 measures in 4 N time) per minute. The need for notation of time signature in 3s or 4s is still important, but is there a guideline for when to use 83 versus 43 versus 23 time signature? These distinctions may not be as subtle anymore with the use of metronomes. That is, with metronomes, you can specify that any note equals an exact period of time. This type of metronomic notation therefore lessens the need for a diverse range of time signatures, since an eighth note, a quarter note, or a half note, as three examples, can be assigned specific beats/minute, with the choice of which note to associate with the tempo being chosen based on the distribution of such notes in the composition. Summing that up, because the metronome exactly specifies the frequency (beats per minute) of the chosen

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note (eighth, quarter, etc.), the need for a wide variety of time signatures becomes lessened in terms of dictating the meter. As an example, Beethoven’s Sonata Pathétique was composed in alla breve or cut time (Figure 10.3). From this, Beethoven’s choice of notation here is meant to convey the manner in which his composition is to be recreated. Included are the specific notes and rhythms for the sonata, but the choice of meter for the notation is, for Beethoven, key to the intended pulse and tempo for performance.

Figure 10.3 Ludwig van Beethoven’s Piano Sonata No. 8 in C Minor, Op. 13, (Sonata Pathétique) in traditional score notation. Note the “shorthand” notation for the lower staff, which simplifies the notation of eight eighth notes in each measure.

Most recordings and performances of this work are consistent regarding interpretations of this composition. That is, when you listen to Beethoven’s Sonata Pathétique, you expect a particular sound in performance, and most performers deliver to that expectation. But, had you never seen the score and were asked to transcribe a performance of this music (and have the ability to do so), would your score look like Beethoven’s? Would you use alla breva? Maybe, maybe not. In Figure 10.4, we offer an alternative rhythmic notation. Would it lead to the same performance expectations? Probably. But Beethoven’s choice for alla breve was a relevant choice for him to convey with clarity his metrical and tempo expectations of the piece. This choice might no longer be required if, for example, a metronome frequency is indicated. That is, we can specify that the 16th notes of Figure 10.4 are equivalent to Beethoven’s eighth notes of Figure 10.3, but perhaps something is lost from his score.

10.4 Other Notational Concerns Just because you use notation does not always mean you are helping the future performer of your composition. The difference between a neophyte and a skilled professional may be as simple as how readily their notation can be read by another musician. One form of notation for a particular rhythm is

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Figure 10.4

Beethoven’s Piano Sonata No. 8 in C minor, Op. 13, (Sonata Pathétique).

shown in Figure 10.5. An improved rhythmic notation for the same music is given in Figure 10.6. Clarity in the notation for ease of reading is important, and this includes denoting the main beats of the time signature within the measure. Figure 10.6 aids in the readability by having these beats visible on the page and thus outlines whether the attack of a note occurs on them or not. With regard to the beaming of notes, this helps the reader keep their bearing and not get lost in a jumble of notes.

Figure 10.5 Rhythmic notation with accuracy to the sounding of notes but in notation that is difficult to read due to the beaming and choice in note duration.

Figure 10.6 Corrected rhythmic notation of the music from Figure 10.5, making the location of the main beats clearer with corrected beaming and note duration.

Another mistake in musical notation arises when the composer wishes to use a shorthand specifically to guide a particular instrument. One such example is in a “chord over lyrics” chart, such as that shown for the Christmas Carol, “Silent Night,” here:

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F C7 F Silent night, holy night! All is calm, all is bright. A# F A# F Round yon virgin mother and child. Holy infant so tender and mild. C7 F F/C C7 F Sleep in heavenly peace, Sleep in heavenly peace. The use of A# for the first chord on the second line in this notation will guide you to the correct keys or frets for the chords on the instrument of your choice, but it is grammatically incorrect. However, Bb is the correct name for the chord in the particular key of F Major. This may seem like splitting a hair, but it is always a good idea to view yourself as a master of your craft. Anticipate your music needs to be as “perfectly” annotated as possible for posterity, because you never know when your musical inspiration from a peaceful winter’s walk will end up getting played around the world for 200 years. For a deeper analysis of musical notation, along with a justification for both human and computer expertise to work together on notation, an in-depth source is [Goul16]. This section merely scratches the surface of potential annotation errors but should motivate you to find your own in your musical experience.

10.5 Sidebar: Music as a Document This book is part of the River Publishers’ series on document engineering. The impetus for this series of books comes from the home page for the ACM annual symposium, https://doceng.org/, which provides the definition “Document engineering is the computer science discipline that investigates systems for documents in any form and in all media. As with the relationship between software engineering and software, document engineering is concerned with principles, tools and processes that improve our ability to create, manage, and maintain documents.” As applied to music, we can adjust this quote to be “music engineering is the discipline that investigates systems for musical creation in any form and in all media. Musical engineering is concerned with principles, tools and processes that improve our ability to create, manage, and maintain music.” In this sidebar, we will diagnose this quote in some detail. The first part of this definition of music as a document states that “music engineering is the discipline. . . ,” which deserves some exploration here. The

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definition of discipline that we allude to here is “a branch of knowledge, typically one studied in higher education.” Playing music may be an art, but composing music is certainly a branch of knowledge, the tenets of which have been largely explored in the 10 chapters you may already have read. More interesting, perhaps, is the allusion to higher education. As a discipline, it speaks to augustness, sophistication, and comprehensiveness. While this is certainly true for some professional composers and some musical genres, it does not have to be the case. We argue throughout this book that composition can - and should - be integrated into the learning process, as it can enable creative, engaged, self-actualized learning. So, from this perspective, we consider the “other” definition of discipline; that is, “orderly or prescribed conduct or pattern of behavior.” Composing while you are learning a piece for example, creating variations on the piece even as you commit the piece to memory - takes discipline. But, it will reward you with a higher, deeper education level. The next phrase in this definition is: “that investigates systems for musical creation in any form and in all media.” Systems are aggregates of multiple useful elements, mechanisms, or processes that effectively give a musician a “tool box” of capabilities from which to choose. For the purposes of providing simultaneous music learning, practicing, and composing, then, these systems include software that contains libraries of musical ideas from which to select. Other systems include specific musical composition “packages” that bring together theories on different aspects of music creation, including counterpoint, form, harmony, melody, rhythm, and semantics. One such system is the Schillinger System of Musical Composition, which was created by Joseph Schillinger (1895-1943) to tie music creation to mathematical processes. In addition, there are increasing numbers of artificial intelligence (AI) systems for creating music; for example, MuseNet, AIVA, and Amper, to name just three. There is the possibility that such music creation AI will do to music what the camera did to painting; that is, drive musicians away from familiar territory. When the camera came out, landscape painting and portrait painting had significant competition. What happened? Impressionism, Expressionism, and Surrealism, which might never have had the impetus to evolve without the uncaring “push” of the camera. These AI-based composition systems are likely to push musicians to new areas of creativity - they are not a threat to the composer. “Musical engineering is concerned with principles” is the next part of the definition, and it is a little bit pompous in tone compared to the normal demeanor of this book. A principle is a central truth serving as the foundation

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for an entire system of approaches; in our case, a system of approaches to composition. Fortunately, we can readily deflate the gassiness of this expression by noting that our principle is simple and open to all: compose while you are learning a piece of music. Music may, at times, be sacred, but the sequences of notes that define the music are certainly profane. A principle of profanity, and of daring, is really all that is needed. The definition continues mentioning the “tools” of composition. At the simplest level, the tools are the notes of the scale. However, that is like saying that your ABCs are the tools for writing. Accurate, maybe, but not useful. The real set of tools we have for composition are “chunks” of notes, including both simultaneous notes (e.g. chords) and sequential notes (melodies, harmonies, etc.) and both together (e.g. chord progressions). These tools allow us to readily differentiate classical, jazz, and blues. From this perspective, different music styles are differentiated by their toolbox. Sort of makes sense: an electrician, a plumber, and an HVAC technician are readily differentiated by their toolboxes! The “processes” of composition is the next stage in our consideration of music creation as a document engineering task. Composition has changed considerably over the years, in no small part because the technology enabling greater breadth, depth, and creativity in composition has changed. Advancements in technology are correlated with advancements in triaging music that is, creating a large set of candidate compositions, and “down-selecting” to the chosen finished product. For most people, experimentation leads to innovation. Therefore, advances in the ability to more efficiently experiment increase the likelihood of finding that perfect musical composition that you know you have inside of you. In Classical times (say 1650-1800), music was often - perhaps typically - composed for a specific event. Mozart composed for the masses and for the mass, for the buffo and for the buffoons, for carnivals and for carnivores, and so on. If he had access to digital technology, he may have composed a lot less, and reused a lot more, because it is certainly easier to hit the “play” button than it is to write another symphony. Imagine what the Kendrick Lamars, Beastie Boys, and Nine Inch Nails of Mozart’s day might have done with the Eine Kleine Nachtmusik, 25th Symphony, and 29th Symphony to sample! Handel, as another Classical composer example, would corral a choral for almost any occasion, but would he not occasionally wish to simply ouroboros an oratorio? Mozart and Handel left many a squid empty with their inked instrumentazioni and quilled quarti. If they had recording equipment, there is no doubt that they would have used it. Instead, they used motifs for their compositions, which effectively gave them structure against which to innovate. That is, they sampled themselves!

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In more modern times, whenever musicians are required to produce music at a rate that is non-conducive to relaxed creativity (think of the Beach Boys and other bands and their 3-4 album/year requirements in the early 1960s), they will generally have to resort to one or more means of reusing existing music: covering previous songs, the every song sounds the same approach (“Hey, we really liked that chord progression, let’s use it for all of the songs on Side B”), or the massive sampling approach of composers mentioned in the previous paragraph. Nowadays, though, with the distribution network for music almost entirely digital, there is a new emphasis on the individual piece of music. When you need not bundle all of your music into the constraints of an album, you can create a single song at any time, for any occasion. Taking a shower after a sweaty workout? Time for your water music. I am sure you can Handel that! This naturally leads us to the next part of the definition: “improve our ability to create.” This is potentially contentious: “improve” might imply to some that music keeps getting better. We know how tenaciously the music that you listen to from the age of 18-22, for example, stays with you. So, it is natural for us all to think that the music we listened to when we were emerging from the chrysalis of childhood was the music for all time. It does not matter whether this is true or not, however, because this part of the definition does not pass any value judgment on the music quality. It simply says that our ability to create music continues to improve. The greatest music of all time is subjective, but even if everyone could agree on the best song ever (e.g. “Imagine” by John Lennon on a quick web search), there is no way to predict when, where, and by whom this perfect song would be discovered. We say discovered, because if there really is one best song ever, then it is discovered more than created. But, this is all just prevaricating about the bush, as our favorite man of clay might say. Because, what technology does is increase the throughput of high-quality music triaging. It maximizes, in other words, the product of these two factors: (1) The number of different pieces of music that can be evaluated in a given time (2) The mean quality of different pieces of music that can be evaluated in a given time When you both increase the throughput (1) and the mean quality (2), you statistically increase the likelihood that you will create better music in a shorter amount of time. Of course, sometimes when you have more choices, it can be overwhelming. Think of the dad in the old Calvin and Hobbes comic

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strip, screaming in the store about all the different options for peanut butter. Unlike that fussy fellow, we believe in peanut-free peanut butter (for those with allergies), not to mention smooth, chunky, sort of chunky, and definitely twinned with chocolate. More choice is better, since you always have the right to just listen to your own playlist! There is an interesting, potentially nefarious, role that all this technology can play in the creation of new music. Let us suppose without laughing out loud that copyright protection was still a thing. That means automated software could be used to determine whether one song was close enough to another to warrant a payment to the first composer. What is close enough? Led Zeppelin’s version of “You Shook Me” should raise a flag for an earlier version of this cover song. Would Van Halen’s “You Really Got Me” put a kink in this software? Speaking of the Kinks, does “Hello, I Love You” by the Doors really borrow from “All Day, and All of the Night” sufficient to warrant plagiarism? Is there an MGMT song close enough to one of John Lennon’s songs (not “Imagine,” of course) to fail this test? It gets murky pretty quickly here. But, murkiness or not, the more nefarious part might be what composers do once they recognize the characteristics, and especially the limitations, of the plagiarism-detection system. Would a composer simply change their recording just enough to not trip the “plagiarism” flag, like a student might do with their term paper and whatever software their instructor is using to check for plagiarism? If we can think of it, then it is happening that is a fundamental rule of criminal behavior. On to a happier topic; that is, the managing of music, our second-to-last part of the consideration of music as a document. There are two meanings of “manage” of interest here. If you manage to do something, you barely do it: one example being that you barely manage to grab the cliff before plummeting. This can be thought of as a bottom-up version of managing, where everything you do is just enough to meet some threshold or criterion. In contrast, the top-down version of managing is to manipulate or handle something, as in providing a guiding hand. This top-down version relates to the multiple words derived from the Germanic “hand” or the Latin “mano” (which also means “hand”); that is, hand, handle, manipulate, manage, etc. When you manage something, you are handling it - you are giving it a hand (yours). It is this top-down version that we think of when we consider music composition. In olden times, musicians literally handled their music - they carried around their sheet music from place to place. Whether a palimpsest or a revision of an earlier work, these physical copies of music have the advantage of showing the process of the artist bringing a piece to completion.

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Physical music remained in the mind or the music book of the artist well after the ability to mass distribute music improved. Distribution of music could be done by hand-copying these manuscripts, with simple industrial processes such as polygraphs, letter copying presses, and mimeographs eventually complimenting this time-consuming and tedious process. Transduction from sound directly to a recording surface came in the late nineteenth century, eventually introducing the phonautograph and phonograph (or gramophone record). Once this process was created, a reliable means of making as many copies of music as possible had been achieved. Rotation speeds changed until the 33 1/3 rpm LP took over the “record” vertical. Cassette tapes, eight-track tapes, and compact discs (CDs) followed as the 20th century progressed, providing greater portability, not to mention resilience to dancing! Each of these was a physical reproduction of another copy of the content, performed through mechanical means. Somewhere in this mechanical process, the information moved from an analog representation of the data into digital form. Once the digital representation of music was possible, a device that could stream the bit depth times the sampling frequency of the content no longer needed a physical copy. The most needed is the upper frequency of human hearing (say 22 kHz) multiplied by the maximum bit depth needed to reproduce the range of human loudness detection (say 3 bytes or 24 bit), which comes to only 0.5 Mbps (megabits/second), readily handled by even weak internet connections. Once 0.5 Mbps (actually, far less due to the high compressibility of sound) was reliably available for portable devices, the portable media player and the streaming service arose in short order. Who can say what is next? One thing is certain, it will have to be very convenient, because the gulf between having someone trained on the instruments playing your instrument to streaming it while you are riding your bike (not that we recommend this!) is more like an ocean than a gulf when it comes to convenience and range of musical choice. We complete the consideration of musical composition as a form of document engineering with the maintenance of music. Maintenance is the process by which something (e.g. a condition or capability) is caused, empowered, or otherwise enabled to continue, preferably indefinitely. For music, this is integrally related to recording and archiving the music; in other words, music preservation. Once we have reached the digital representation of music (and that was essentially fully reached with the advent of the CD in the 1980s), music preservation is simply piggybacked to digital preservation. Preservation is then in the hands of the digital archivists. Seems simple enough, right? However, there is a problem, and one that (without getting too expansive

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here) looms over human culture, history, education, and other topics of crucial importance. Once all of music is digitized, if the digitization code is no longer understood, then the information is no longer understood. The Rosetta stone was decipherable after 1995 years of life because it was concrete, tangible, and durable. Most media used to store digitized information is not. Does this mean you should not be using digital means of musical engineering? Absolutely not. But, if it is really important, you might want to print a copy.

10.6 Summary This chapter considers how notation is used to provide musical documentation. In addition to full musical scores (using traditional staffs), a variety of shorthand notations (lead sheets, rhythmic notation, and chord over lyrics charts) were described. The changing importance of time signatures is discussed. The sidebar provides insights into how document engineering applies to musical composition. In the era of generative artificial intelligence (GAI), it is really important for the composer to consider how their music will best be permanently recorded. Recording is more than just a means of archiving your work; it may also be a means of protecting you from the predatory nature of GAI bots that try to be a wall of musical creation. Audio recording, of course, is perhaps the least arbitrary way to record your composition. But, even without an audio recording, musical notation gives us the ability to (largely) faithfully recreate a musical piece. Along with all of the additional articulations, the musical notation we use in this book gives you a good idea about how a piece will sound, no matter who plays it.

Reference [Goul16] Gould E, “Behind bars: the definitive guide to music notation,” Faber Music Ltd, 2016.

11 Application (Democratization of Creation)

Democracy is the government of the people, by the people, for the people. - Abraham Lincoln It’s a relief to hear the rain. It’s the sound of billions of drops, all equal, all equally committed to falling, like a sudden outbreak of democracy. – Alice Oswald

Abstract In this chapter, the variety of compositional techniques explored previously is simultaneously brought to bear on the analysis of works by five different composers: Bach, Mozart, Tárrega, Paganini, and Debussy. The ability to vary harmony, melody, and rhythm - separately, together, or in any order are shown to underpin creative means of mixing (such as transposing) and matching (such as transforming) a composition to add both length and depth to it. This chapter’s sidebar is on the democratization of creation, which is what the compositional tools illustrated in this chapter help to create. Keywords: Development, Form, Harmony, Interlude, Melody, Modulation, Rhythm, Structure, Theme, Transformation, Transposition, Variation

11.1 Introduction In this chapter, we will give an overview of a small set of compositions to provide a model for how you might be inspired to create your own music. By explaining how a piece “works,” you will see how the elements of a composition come together to create something “emergent” and perhaps even complex. From this chapter, the last chapter specifically dedicated to introducing compositional techniques (Chapter 12, as you will see, is a creative

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adjacency to the other chapters), we hope to instill the confidence in you to take on any type of composition that you may be interested in. There are a limitless number of compositions that we could have chosen here. The ones that we have chosen are meant to highlight a sense of how planning a composition from the start, in its use of form or modification of form, can provide a blueprint for the rest of the composition. This is like the tarmac worker who pulls out the chocks, holds up the orange batons, and directs the airplane to its runway. Sure, the pilot gets all the credit, but we all know that tenacious tarmac Terry is the person responsible for making sure that $250 million Boeing 787 does not back into a fire hydrant or get sideswiped by a tricked-out A318 with a meathead pilot trying to impress the viewers peering from the terminal windows. This chapter, then, is a tribute to tenacious tarmac Terry and we hope your compositional career takes off after this chapter has run its course.

11.2 Bach’s Prelude in C Major BWV 846 When you consider any composition, its incorporation of elemental ingredients such as tonality, rhythm, texture, structure, and arrangement are highly repurposable to your own composition, even if you are composing in an entirely different musical style. In other words, you can glean musical compositional insights from those relics of the European Enlightenment (Bach, Mozart, Beethoven, Haydn, and more) even if you never intend to compose anything other than Hip Hop. Bach’s Prelude from the Prelude and Fugue in C Major BWV 846 from the Well-Tempered Clavier Book I is the first illustrative composition considered in this chapter, and yes he is a long-dead relic of the Enlightenment, having spent far longer decomposing than he ever did composing. But we digress. This piece is chosen because it provides an excellent example of how having a harmonic plan in place can facilitate a composition. In the Prelude, shown in Figures 11.1 and 11.2, one might ask if this is composed as a succession of chords randomly unfolding at the composer’s fancy, or if there is a thoughtful plan in its creation. Chunking the composition into four measure groups, you can see that there is a definite intelligent plan in the prelude’s construction. Here, the harmonic strategy gives rise to form. Of the three main elements (rhythm, melody, and harmony) of a composition, harmony - in this case, chords - takes the forefront of this composition. With any composition you analyze, looking to the way each element is used can aid you in your own compositions. Rhythmically speaking, the prelude is

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made up of a broken chord figuration in a constant stream of 16th notes, as seen in Figure 11.1.

Figure 11.1 Bach’s Prelude in C Major BWV 846, first four measures, with all of the notes in the (broken) chords indicated explicitly.

Since the same broken chord figure is used for each chord, and the rests on the upper staff align with the notes on the lower staff, there is a note initiated on every 16th beat of the score. Even though the rhythm is consistent measure by measure (not Measure for Measure, sorry Duke Vincentio), a constantly changing broken-chord harmony prevents the feeling of repetition. In fact, this repeated figure, which played alone with a pencil tapping on a tabletop would be annoying to your company, is countered by the ever-changing chords used as the basis of these notes. We can see the general guideline, as mentioned in Chapter 9, put to practice; that is, “if one element remains the same, make change in one of the other elements.” Melodically speaking, there is no “melody.” Instead the composition’s appeal is the constant unfolding of chords in a consistent arpeggiated figure. The listener’s ears follow the construction of each chord, generally following the highest and lowest note of each voicing as they smoothly progress from one to the other. Digging into the harmonic structure of the composition, the entire 35measure Prelude is given using block chords (Figure 11.2), as a shorthand for the sequential (broken) chords that (as in Figure 11.1) are used in performance. We can see that Bach clearly establishes the tonal center of C Major in the first four measures (Figure 11.2), with use of the I, ii7, and V7 chords in a closed succession (C-Dm7-G7-C). All the notes of the C Major scale are contained within these three chords, giving the listener a clear sense of the tonality for the composition. Continuing with the second line of Figure 11.2, we see two four-measure groups of chords that are based on the opening four measures, albeit with some chord substitutions. The opening chords of the Prelude, C and Dm7/C are substituted with Am/C and D7/C. The Am7 is the relative minor of C and the D7 is a secondary dominant for the G7/B in measure 7. The lower notes of each voicing (lower staff) in measures 5−8 are similar to the opening

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Figure 11.2 Bach’s Prelude in C Major BWV 846, illustrating a harmonic plan realized. Here, block chords are used to facilitate the viewing of the harmonic structure, but the actual notes comprising the chord are played sequentially, as in Figure 11.1, as “broken chords” in performance.

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measures 1−4 with the upper structures changed. The last chord of the group is altered to a CMaj7/B chord instead of C Major. Measures 9−12 are a repetition of measures 5−8; however, the Am, D7, and G7 are now voiced with their roots in the bass. Additionally, the final chord of this group is changed from the CMaj7/B of measure 8 to a C#dim7/G chord, which sets up the next run of eight measures. In Figure 11.2, measures 13−20 are an almost exact transposition of measures 5−12. This new run of two four-measure groups begins on the ii chord of Dm/F, which was set up with the C#dim7 chord in measure 12. Bach anchors the listener in the piece by having the chord voicing structures the same for both of these two lines (measures 5−12 and 13−20). However, there are some subtle but intentional differences. If the same chord relationship were used comparing measure 14 to measure 6, then measure 14 would use a G7 chord. Bach substitutes the G7 chord with a Bdim7, which creates a borrowed chord variant, adding a different “color palette” for the piece; that is, by using a chord from a different scale. But, either G7 or Bdim7 is a good choice for a chord to set up the chord of measure 15, C Major; so the temporary break with direct transposition keeps the listener invested without abandoning expectations completely. In measure 20, we find a C7 chord used at the end of the eight-measure run. If the same corresponding chord was used transposed from measure 12 into measure 20, we would see an F#dim7/C that could set up another run of similar measures starting on G/B. Bach, however, has other plans and changes the chord to C7, which leads toward a FMaj7 chord. This starts off another group of four measures (21−24) with a new musical goal in mind. The chord harmonies in measures 21−24 unfold with a goal of reaching a pedal point based on the fifth scale degree of C Major (G). A pedal point is simply a sustained tone that incorporates at least one dissonant harmony contrasted against the repeated (or “pedaled”) tone. In this case, a bass note remains the same while the chords above it change, creating consonances and dissonances for a period of measures. Following the bass notes of the chords in the fourth line of Figure 11.2, we see the intent of centering in on the note G by chromatically rising from F to F#, then skipping over the target to Ab, and finally descending by a half step down to the G; goal achieved. Interestingly, Bach could have established a pedal point on the note G out of the 20th measure if he had used the F#dim7 transposed from the corresponding measure 12 since this chord could function as a set-up in that manner. However, this detour through the measures 21−24 starting on FMaj7 creates an architectural symmetry in the composition. In Chapter 6, we

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discussed the tonal center as being analogous to home plate in baseball. In this composition, home plate is C Major, but Bach visits other bases throughout the course of the composition before the eventual return home to C Major. If we look at measures 1, 5, 13, and 21, we find C Major, A Minor, D Minor, and F Major (Maj7) chords. These measures are starting points for chord runs on harmonies built from the C Major scale (I, vi, ii, IV), as Bach seems to make an effort to visit various scale degrees along the way. In addition, the choice of these chords as starting points creates an interesting symmetry. C Major and A Minor are relatives the same as D Minor and F Major are, too. This is an excellent combination of using familiarity (repeating the use of relatives) with variance (different relatives). Just because something is familiar does not mean that it cannot be creative! Continuing in the composition, we enter the pedal point based on the note G in the fifth line of Figure 11.2 (measures 25−31). There are two more four-measure chord runs based on a cycle of chords (C/G, G7sus4, G7, and F#dim7/G). Following the top note of each chord across these measures, we see an ascent that reaches a high point in measure 29. From here, the chord cycle starts again (C/G, G7sus4, and G7), and the upper note of each chord descends back down. In measure 32, we find a C7 chord substituted for the F#dim7/G in measure 28, which puts an end to the pedal point on G and sets up the ending of the Prelude. With the new bass note of the C7 chord, Bach establishes a new pedal tone on the tonic note of the scale (C). In measure 33 (Figure 11.2), the well-established broken-chord pattern from the main body of the prelude is abandoned for a new arpeggio pattern that aids in bringing the composition to a close. With the final three measures, the harmony returns to home plate once more with movement from the IV chord of F Major, briefly changing into a Dm7/C chord at the end of the figuration. The harmony then moves to G7 based on the new figuration before sliding safely into home plate with C Major.

11.3 Selected Mozart Sonata Movements No matter what form you structure your composition on, and no matter what your style, you will have room for flexibility, and creativity applied here will increase your listeners’ engagement in the piece. While we often use Classical music pieces due to copyright considerations, rest assured that the same rules apply to Tame Impala as they do to wild Liszt. With the Bach piece just described, the harmonic plan was of interest. In this section, we illustrate the plasticity of form that is possible even when the same general

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form is used across multiple pieces. For our example, we consider five pieces written by the same composer more or less co-temporally: one movement each from Mozart’s K. 304 (300C), K. 330 (300H), and K. 315a (315g); and two movements from K. 331 (300I). Each of these five movements have the same general form, but Mozart uses some creative means to make each rather distinct in its overall shape and sound. All of these pieces use ternary form (ABA), which you may recall (from Chapter 2) is realized as an A section, followed by a B section, with a return to A as the third section. The structure for phrases and periods of music within each section of the ternary form is up to the composer. Mozart, however, in these examples, uses binary form. Each section of the macro ternary form (ABA) is made up of a binary (AB) structure (Figure 11.3).

Figure 11.3 General diagram of an overall ternary form ABA, with a sub-structure within each division of binary form.

Of the five Mozart realizations, we start with the first of eight minuets from Mozart’s K. 315a (315g). This is shown in Figure 11.4, where only the melody is annotated for ease of reading. When performing, the keyboardist usually plays the minuet (A) with repeats, followed by the trio (B) with repeats, and finally the minuet (A) without repeats, which builds the overall ternary structure of ABA (minuet-trio-minuet). This structure can be labeled: (A1 A1 B1 B1 )(A2 A2 B2 B2 )(A1 B1 ). The “A” for the minuet is represented in Figure 11.4 as A (first line) and B (second line) to indicate its internal binary form. Similarly, the “B” for the trio is represented in Figure 11.4 as A (first line) and B (second line) to indicate its own, distinct internal binary form. Structurally, the minuet and trio are constructed similarly with eight measure sections made up of antecedent and consequent phrases (4 + 4). The minuet is in the key of C Major and moves harmonically from the tonic I chord to the V chord at the end of the A section. The B section then moves from the V chord back to the I chord. The antecedent and consequent pairing of phrases (4 + 4) here has a “rounded” character. The consequent is reprised from the “A” section, however, with an ending in the tonic of C Major. The trio is structured like the minuet, although it is set in the key of F Major and its A section ends on the I chord instead of the V chord, while the B

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section follows the minuet’s scheme and moves from the V chord back to the I. Overall, this minuet and trio is of simple construction on a small scale. You might therefore think that it was among the first that Mozart composed among the examples we consider here, but chronologically it was the last.

Figure 11.4 The melody from the first of eight minuets from Mozart’s K. 315a (315g), where each section of the macro ternary form (ABA) is made up of binary (AB) structure. Realization in performance consists of playing the minuet (A) with repeats, followed by the trio (B) with repeats, and finally the minuet (A) without repeats.

Next, we address (Figure 11.5) the Second Movement, Menuetto (Minuet and Trio), of composition K. 331 (300I). Bear with us here, because you will note that Figure 11.5 also uses the ABA ternary form assignment for the minuet, trio, and return to minuet (top row of Figure 11.5), but just as in Figure 11.4, both of these elements (minuet and trio) have their own internal form, indicated by (separate) A and B form shorthands, AA|BA’BA’ or A|BA’, in the third row of Figure 11.5. This is the binary form for the expression of the minuet and trio sections, and keep in mind that all of the “A” of the minuet in the upper left of Figure 11.5 is elaborated musically as the binary form AA|BA’BA’, as described in the leftmost field of the third row of Figure 11.5. Thus, even longer, more complicated works such as K. 331 (300I) can be “chunked” as ternary (ABA) at the highest level and binary within each section of the ternary form. In comparison with K. 315a (315g), we observe a much larger scale to each section of the micro binary structures in the Menuetto of K.

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331 (300I). Whereas the A section of K. 315a (315g) uses a concise antecedent/consequent structure of eight measures (4 + 4) based on one musical idea, K. 331 (300I) is enlarged to 18 measures and based on three musical ideas.

Figure 11.5 Mozart’s Menuetto, the second movement of his Piano Sonata in A Major K. 331 (300i).

Next, in Mozart’s Andante Cantabile, which is the second movement of the Piano Sonata in C Major K.330 (300h) (Figure 11.6), Mozart has further elaborated a top-level ternary form ABA by inserting a bridge after the B section and a closing after the return of the A section. This allows Mozart to emphasize specific phrases, alter specific phrases, or even add short additional musical ideas to round out the piece and give it its own personality even though it is using a familiar ternary form.

Figure 11.6 Mozart’s Andante Cantabile, the second movement of the Piano Sonata in C Major K.330 (300h).

Next, Mozart’s Alla turca, the third movement from the Piano Sonata K. 331 (300i), adds further elaboration to the ternary form, here using a bridge section at the end of each of the sections (A, B, and then A again) of the ternary form (Figure 11.7). The key of each bridge section is A Major,

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which was perfectly chosen to “bridge” between two remote keys, A Minor to F# Minor or the converse. A Major gets along with both of these keys, since A Minor is its parallel minor and F# Minor is its relative minor. So, the bridge is actually a friendship bridge, allowing A Minor and F# Minor to work together even though they are remote keys. Mozart adds further creativity by having the bridge provide its own established theme instead of modulatory material with the aim of creating space and transitioning between two points. Were the bridge a little longer, one might be tempted to write the overall movement as ACBCAC in form (this might explain the sometimes misnomer of this movement as rondo alla turca, but we prefer the overall ternary form with a coda expressed as: A-bridge-B-bridge-A-bridge-coda, as shown in Figure 11.7.

Figure 11.7 Mozart’s Alla turca, the third movement from the Piano Sonata K. 331 (300i).

We finish this section with a fifth use of ternary forms by Mozart, the Tempo di Menuetto, which is the second movement from the Violin Sonata K. 304 (300c). This piece (Figure 11.8) shows even greater freedom of composition in spite of following the ternary form. Here, two instruments (violin and piano) are used to alternatively carry the melody, and to make this happen, Mozart adopts a more complicated binary design, especially in the first A section. Interestingly, the overall ternary A and B sections are already in compatible keys (E Minor and E Major, respectively), but Mozart adds a transition (in E Minor) anyway, which mainly serves to give the listener a chance to breathe between the two larger sections. These five variants on a theme are characteristic of Mozart’s compositions throughout his life. How else could he have composed hundreds of major works in such a short life? He innately understood how the flexibility of structural design allows you to create new and interesting pieces from the decomposed “rubble” of previously interesting forms.

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Figure 11.8 Mozart’s Tempo di Menuetto, the second movement from the Violin Sonata K. 304 (300c).

11.4 Tárrega Capricho Árabe As our Mozart examples show, form need not be maintained rigidly throughout a piece. Often, in fact, it is the variation from expectation that makes a piece sing, or dance, or whatever other metaphor you prefer. As jazz great Miles Davis said, “if you hit a wrong note, it’s the next note that you play that determines if it’s good or bad.” So, leading your listener into a temporary predicament − is this tune suddenly off the rails? − and then competently showing them that you intentionally left them on the edge in order to satisfactorily resolve the musical cliffhanger is a top tier musical creativity ploy. Do you ever feel better than right after something painful has gone away (like that minute after stubbing your toe when you feel no pain in the toe)? Are we saying that you might want to cause temporary “pain” for your listener and then alleviate it? Well, yes, yes we are. Even though many of our examples start on dusty old forms that you may not be technically “interested” in, they provide an excellent basis for showing how to provide engaging variation in your composition. In this section, we consider how Francisco Tárrega, in his Capricho Árabe, Serenata para Guitarra, transforms a theme across form. That is, he provides a modification on a strophic song form of AAAAAA, with settings of the main theme in different keys transforming the mood of the melody. Consider a Christmas song like Good King Wenceslas or Silent Night, where the same melody is used throughout the carol. The only change is the lyrics with each repetition of the melody (strophic form). Tárrega uses this general approach to form for Capricho Árabe; however, he modifies the repetitions to avoid monotony (no lyrics!) even though the composition is based on one theme. Overall, the structure of Capricho Árabe is repetitions of the theme, which are prefaced with short introductory interludes along with an improvisational sounding introduction that opens the piece (Figure 11.9).

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Figure 11.9

Form diagram of Tárrega’s Capricho Árabe.

With these short introductory interludes, Tárrega accomplishes three things: (1) breaking up repetitions of the melody, thus preventing monotonous anticipation by the listener; (2) introducing the overall rhythmic character to the accompaniment of the melody with a bass-chord-bass-chord feel; and (3) establishing the tonality for the settings of the theme. With introductory interlude 1 (Figure 11.10), we see the establishment of D Minor with use of the i and V7 chords (Dm and A7). Interlude 2 introduces a variation to number 1 with the addition of the VI chord (Bb) and the flat-II Neapolitan chord in root position (Eb), creating a new color pallet to reintroduce D Minor. Introductory interlude number 3 is based on number 2; however, the goal by the end is to set up F Major with movement through G Minor and C7 (ii and V7 of F Major.) The final interlude incarnation moves from the theme in D Major, transitioning back to D Minor (similar to interlude 2) for the final presentation of the theme in the home key of the composition. The main theme for Capricho Árabe is, as mentioned, set in D Minor (Figure 11.11) and consists of a 4 + 4 measure antecedent, consequent structure. The melody starts on fifth of the tonic harmony D Minor (A). A one-measure phrase is repeated three times with the third repetition deviating from its normal course to conclude the idea in the fourth measure, where Tárrega lands on a V7 harmony. This sets up a repeat with a consequent run based on the same idea with a new trajectory, but then pulling the listener back into familiar territory though ending the theme again on the V7 chord. The complete period of music is set up again for repetition by starting on the tonic harmony (Dm). At this point, the theme is reintroduced with introductory interlude no. 2 (Figure 11.10) and repeated unchanged. After two repetitions of the theme in D Minor, Tárrega then transposes to F Major, thus transforming the character of the theme. The melody starts on the same scale tone, in this case the fifth of the tonic harmony of F Major (C). There is a slightly different melodic content here, with the 16th notes at the end of the first measure taking a slightly different path (Figure 11.12). The end of this section, instead of ending on the V chord (C7) of F Major, works its way back to the A7 harmony where the listener may predict the return of the initial theme in D Minor. Instead of an introductory interlude, the next section is set up through an ascending chromatic scale adding two measures

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Figure 11.10 Tárrega’s introductory interludes for Capricho Árabe. These interludes break up repetitions of the melody and their placement within the composition can be seen in the form diagram of Figure 11.9.

Figure 11.11

Main theme of Tárrega’s Capricho Árabe.

to the period of music and where we land on the theme now set in the key of D Major.

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Figure 11.12 Theme of Tárrega’s Capricho Árabe in F Major, similar to its appearance in D Minor. Note, however, the chromatic scale ascending at the end of the phrase.

Figure 11.13 Two successive occurrences of the theme from Tárrega’s Capricho Árabe set in the key D Major without an interlude to break up the repetition. These are the fourth and fifth repeats of the theme as seen in Figure 11.9.

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The theme is next presented with two repetitions in the key of D Major (Figure 11.13) and follows the same general scheme as the F Major (Figure 11.12), though back in the eight-measure confines of the original of D Minor. With the chromatic approach at the end of the F Major and no interlude in the middle of the D Major repeats, Tárrega gives us a break from the predictability of the interludes prefacing each presentation of the theme. We do see two more interludes as we transition back to D Minor for a final run of the theme back in the home key along with a final interlude acting as the close of the composition (Figure 11.9). The sheet music and a performance of this work are available online [Tárr92].

11.5 Paganini Caprice Op. 1, No. 1 Another important form of compositional creativity is composition that is tailored toward the particular technical capabilities of an instrument. Virtuosity on an instrument can include more than simply which notes are played: how they are made is also often a sign of instrumental mastery. For example, there is a bowing technique of the violin called ricochet wherein detached notes are produced by the continual bouncing of the bow off of the string. In Caprice no. 1 (Figure 11.14), Paganini applies the technique by asking the performer to produce the ricochet in a back-and-forth motion across all four strings of the violin. On the violin, this also produces an arpeggio or broken chord effect, so it is indeed quite musical, and not just a form of dissonance. One note of the chord is voiced on each string, in both closed (first three up and down sets of eight notes) and open (fourth set of eight notes) positions. Closed voicings include only consecutive chord notes, while open voicings will jump over at least one chord tone to the next in the arpeggio.

Figure 11.14 Paganini’s Caprice no. 1, illustrating ricochet technique for the violinist (please see text for details).

Compositionally, the broken chord pattern of Figure 11.14 could produce a similar listening experience to those of the Bach’s Prelude in C Major BWV 846 (Figure 11.1); however, Paganini finds ways to break away from

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Figure 11.15 Paganini’s Caprice no. 1, showing additional variation by continuing upward arpeggiation with 16th notes followed by a cadenced closure of the idea with three of the four “ricochet” notes played simultaneously instead of sequentially (end of upper line and start of lower line). Mode mixture (switching from E Major to E Minor) then follows, with the key change indicated near the beginning of the lower line.

the established figure throughout the composition by creating contrast to the established ricochet figure. Paganini’s additional variation (Figure 11.15) includes (1) continuing upward arpeggiation with sixteenth notes; (2) a cadence closure of the idea of the phrase by using three of the four “ricochet” notes played simultaneously (triple stops) instead of sequentially (see the end of the upper line and the start of the lower line in Figure 11.15); and (3) mode mixture (here switching from E Major to E Minor), with the key change indicated near the beginning of the lower line of Figure 11.15. Paganini’s Caprice no. 1 continues with further creativity, next incorporating contrasting scale figures in triplet rhythm (Figure 11.16) and an adventurous harmony, which sequences from G to Ab to A to Bb in just a short 10-measure section. This is a developmental approach to composition familiar to you from the earlier Chapter 9. The sheet music and a performance of this work are available online [Paga20].

11.6 Debussy Prelude “Voiles” The final example is taken from Claude Debussy’s Prelude “Voiles,” a composition that is melodically based largely on the whole-tone scale. This choice gives a different pallet of notes from the normal major/minor aspect of typical “Western” music. Instead, it is music composed to evoke an image or feeling that matches its descriptive title. The composition is constructed using three main figures that recur throughout the piece, sometimes alone and sometimes with the other figures

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Figure 11.16 Paganini’s Caprice no. 1, here illustrating developmental material incorporating contrasting scale figures in triplet rhythm and the continual changing of keys.

Figure 11.17 Opening theme to Debussy’s prelude Voiles, illustrating the use of the whole tone scale.

or accompaniment elements. The first (Figure 11.17) establishes the atmosphere of the composition, utilizing every note of the whole tone scale in a circular nature. The phrase is harmonized in parallel major thirds (and the enharmonic re-spelling in diminished fourths). A secondary theme is also established, which is characterized by three notes in ascending steps and a second longer, more complete, phrase that expands beyond the opening three notes (Figure 11.18). With use of the whole tone scale, there is no sense of tonality so that the traditional rules of counterpoint can go by the wayside as all the tones are equidistant from each other. This allows for a layering effect in the

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Figure 11.18

Second phrase in Debussy’s prelude Voiles, “B.”

construction of the piece as Debussy continues to provide variation and the introduction of new thematic elements overlaying the existing themes. For example, after the initial opening with the theme of Figure 11.17, the theme is repeated with a layering of the themes along with an ever-present foundational (low) Bb pedal tone that remains constant throughout the composition despite a variety of rhythms (Figure 11.19). Is Bb the tonal center of the piece? Probably not, since the composition does not begin or end on it. Throughout the composition, Debussy brings back the established themes combining them or stating them along with variance in the accompaniment as we see two occurrences of the “B” theme as shown in Figure 11.20. A natural tendency when analyzing a piece is to find familiar patterns for the overall structure of a composition. A composition does not, however, need to have a clear structure and may unfold in its own way. The structure for Voiles is certainly not clear. Is it ternary (ABA), binary (AA|BABA), or just free form? One thing for certain is that there is a “layering” to the multiple themes that make up the composition. We will let you decide for yourself based on what you have read so far, hopefully with some insights in this and the previous 10 chapters. The sheet music and a performance of this work are available online [Debu09]. With that, our next section is our final sidebar, and we go in a different direction, creativity-wise, in the last chapter (Chapter 12). Thus, our discussion of Debussy’s Voiles more or less completes our analysis of specific musical scores. Keep in mind, we chose a lot of our music based on the public domain associated with the music, and your choice of music is likely to differ (as is ours in our own listening, composing, and teaching time). So, whether you do your composition with a pencil in hand or a Midi editor open in front of you, you will likely end up creating music in a much different genre than the majority of the music we used in this book. That is okay, because all of the approaches you will take will benefit from the design, transition, and juxtaposition skills we have tried to explain in this book. We have also tried to overlay these skills with the stimulus for creativity that can come from almost any digital source − imaging, sensing, signal processing, word processing, text analytics, and many more both in the text and in the sidebars. We hope

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Figure 11.19 A later section of Debussy’s prelude Voiles, illustrating incorporation of both the “A” and “B” of Figures 11.17 and 11.18.

you find this combination of musical skills and musical creativity motivating and energizing to you in your musical experiences moving forward. Whether music is a hobby that anchors you in life or a job that helps you anchor others − or more likely a combination thereof − we hope this book helps make music more meaningful to you.

11.7 Sidebar The sidebar for this chapter focuses on how much smaller (and yet bigger) the world of music has got in the age of technology. The Internet, of course, has led to a massive change in how people remember content. No longer does

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Figure 11.20 Two recurrences of the secondary theme (Figure 11.18) from prelude Voiles, illustrating how it can continue to be used throughout the piece without stifling further creativity.

all of the content need to reside in your head; instead, the means to access the content is what you remember, if even that (you might just remember that Google.com is a search engine, for example). Does that really mean we are all getting more stupid? Hardly! It means we get to fill our minds with other things. More room for creativity, perhaps, if the mind is less saturated with facts? Do not misunderstand us here. As far as intelligence goes, the Internet makes us both smarter and less smart. For every Alex Pentland, there is a Nick Carr. Yes, the Internet may lead many of us to be less contemplative, and less patient. But isn’t being able to access information faster a better world? If one was to make a case against the Internet, I would argue that the most harmful side effect of the Internet is, at least obliquely, an actual argument for the Internet. This is the echo chamber effect, wherein no matter how outlandish your idea is, you can find a community online justifying your interests. Here is one I would have thought might come up a bit blank on the old search engine: “Men who like dressing up like Napoleon Bonaparte.” Far from it: 4,730,000 results. Really? The guy’s been dead 200 years. The point is, the echo chamber effect means you might not be tempted to get actual feedback on your fantasy, fetish, or festering fiction.

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As Lincoln noted, though, democracy is government of, by, and for the people, and so in that not-so-narrow sense, the Internet is a democracy. You vote with your page openings. Some would say that not everyone should be allowed to vote, especially those who spend their time searching for “vegetables that look like Abraham Lincoln” (123,000,000 results!). I say, well, at least Lincoln-like leeks are 25 times as popular as coarse Corsican conquerors. Pages, like rain, are the billions of downloads, all equally committed to loading on your browser; in other words, a sudden outbreak of democracy, to paraphrase Alice Oswald. Sure, you can choose your own echo chamber, but this also means you can find like-minded people to hone your understanding with! You should not stay in the echo chamber necessarily, but you can use it to refine your message so that you emerge from the echo chamber with a resonant message for the world outside of the chamber. Speaking of echo chambers, isn’t that what musical creation software and digital tools are? Well, at least with a bad headset on, that is. One of us (Steve) uses Audacity, because I like singing and overlaying someone else’s much more skilled instrumental play (along with samples of noise, nature, and nuance) rather than trying to play instruments my meaty hands are best left banned from. The editing interface on Audacity is intuitive and rather easy to edit. Some of you might be thinking, yes, but can it handle 12 or even 16 tracks at a time? It can, but for that level of complexity with Audacity, you probably need a lot larger screen than the 17” laptop-as-work station screen I use. Maybe you prefer ProTools, which makes the processes, at least, of producing music a lot easier (it will not necessarily make your timing or your volume mixing better; you still need to make the calls there, as with all music software). It is designed to handle 16 tracks even for the “First” version (which is free). The “Ultimate” version (which is not free) handles up to 2048 tracks! Because of tools like Audacity, ProTools, Logic, Reason, and Ableton (among others − sorry for the product placement and lack thereof here), collaborating on music creation is so much easier in the digital era. Whatever your DAW (digital audio workstation), you have the ability to overlay many different tracks at a time. Why work together at the same time, trying to balance distance, daylight savings, and disposition differences, when you can just tape and share? That is a 24/7 “echo chamber” if you are a trio in Sidney, Ohio; Sydney, Australia; and Sidney, British Columbia. So, pick your favorite software, and find someone to work with − so please do it, using the previous chapter sidebars for inspiration as needed! Democratization of musical creation, of course, extends well beyond the software used to create it. In addition to software to create music, we have

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software to search it, find it, and stream it. If Pandora and Spotify do not have a song, then you can certainly find it online. As one example, the Shellyan Orphan song “Burst” is not (as of 1 October 2021, anyway) available on Spotify. I had no trouble finding it, along with its perplexing and somehow charming video, on YouTube [Shel92]. Ditto the (also 1992) Deep Forest album, though Spotify did contain the greatest hits of sorts for them. It was not that long ago − just a generation − when you had to borrow a CD or even a tape or LP to get the music you wanted when you wanted it. Not anymore. A limitless supply, and a near-limitless demand. A democracy, or at least an economic form of democracy, is built on supply and demand. Both of these are at an all-time high for music. If you can hear any music, then you can incorporate its feel (if not its outright sampling) into your own music. Democratic markets give power to the consumer. Consumers of notes have never had more power. Democratization of music extends to its patronage. While consumers have a lot of power (and privilege) in being able to find music off of the Internet, there still needs to be an incentive for musicians to compose. With records and even CDs, there was a controllable market, because the music was tied to something tangible; that is, something you could hold in your hand. Now, however, a single MP3 can be replicated as many times as wanted, and so the sales model has to change. Enter online funding: from Patreon to SoundCloud to Twitch, and even to Etsy and YouTube and GoFundMe, there are a plethora of ways to monetize your musical talent. These online incentives have various degrees of overhead, to be sure, but we are used to that as a society. We tolerate far more overhead in healthcare now than before the rise of the HMOs in the 1980s and nearly four times what we had in the 1960s [Yang21]. Is it worth it? Are the advantages in 24/7 healthcare and access to modern diagnostics, surgery, and testing worth nearly a fifth of the USA’s expenditures? You decide for yourself, but remember that any time there is a “value add” there is a “price add,” as well. Spotify and Pandora are likely doing a lot better financially than most of the musicians posting to their platforms, judging from their market capitalizations. Democracy has always been a way not only to provide supply to demand but also to concentrate earnings in the hands of the few. You cannot put the genie back in the bottle, and in the balance we probably do not want to. There has never been a time when so many had access to so much music at such little cost. Plus, no impulse control required. You get it when you want it. So, where do these democratizations of music creation, supply, demand, and patronage leave us? In a very creative space, to be sure. Not only can

References

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you create (or pitch-shift!) virtually whatever music you like, but you can find music that was virtually inaccessible just a generation ago. Trust me, as a record store junky in the 1980s and even 1990s when CDs were also ubiquitous: I miss a lot of the wild, and wildly fun, people in those stores, but I do not miss not being able to find the music I liked. Celebrate the accessibility and searchability of today’s music, and while you are at it, contribute to tomorrow’s. You now have the tools. You definitely have the creativity. And, if you have read this far, you definitely have the tenacity. So, get out there and vote with your creation, with your supply, with your demand, and with your patronage. That is, ultimately, what the democratization of music means. And, it is a vote you do not even have to register for.

11.8 Summary In this chapter, compositional techniques for using harmony, melody, and rhythm – together and in any order − are illustrated to be key components of adding variation to the composition’s form, or structure. Means of mixing and matching − including interlude, modulation, transformation, and transposition − are illustrated through the analysis of works by Bach, Mozart, Tárrega, Paganini, and Debussy. The last sidebar, appropriately, focuses on the democratization of creation.

Reference [Debu09] DeBussy C, “Debussy. Preludios. Libro I. Preludio no. 2 Voiles,” https://youtu.be/t_lsFxsAJEU?si=kU767WMaWORUtoVY, first published 1909, accessed 7 September 2023. [Paga20] Paganini N, ”Caprice for Solo Violin, Op. 1 No. 1,” https://yout u.be/tUKPPRN-Y00?si=651HfXuaAR7vqhyY, first published in 1820, accessed 7 September 2023. [Shel92] Shellyan Orphan, “Burst,” 1992, https://www.youtube.com/watc h?v=FHE7pS8S9oQ, accessed 1 October 2021. [Tárr92] Tárrega F, “Capricho Árabe,” https://www.youtube.com/watch?v =w8JfyQuWzFs, first published in 1892, accessed 21 September 2023. [Yang21] Jenny Yang, “U.S. health expenditure as percent of GDP 19602020,” 8 September 2021, https://www.statista.com/statistics/ 184968/us-health-expenditure-as-percent-of-gdp-since-1960/, accessed 2 November 2021.

12 WWWD?

All that we see or seem is but a dream within a dream – Edgar Allan Poe I got a callback – Kirk Kirkendall the Woodsman The future’s uncertain but the end is always near – Jim Morrison

Abstract In this concluding chapter, we consider WWWD; that is, What Would Wolfgang Do? In a nod to the absolute wunderkind of music, Wolfgang Amadeus Mozart, we consider what he might do if alive today and still gifted with his limitless talent, timing, and tenacity. This is done through the mechanism of telling several fables, then summing up what it means to be a modern Mozart. In order to emphasize the creative flow, a modified genre of tale is introduced, the science-based fable. Five novel tales are told, each revealing a source of musical inspiration with an anchor in science. Only the last tale in this chapter is truly suitable for the little ones, just a warning. Keywords: Ambient Music, EEG, Fable, Inspiration, Little Red Riding Hood, Mozart, Odyssey, Pitch Shifting, Sirens, Whalesong

12.1 Sky Echo the Blue Whale Sky Echo was a busy little whale, if one could call a blue whale, even a toddler version, little. The little part was Sky Echo’s 10-meter length, well less than the 30 meters owned by the adults in the pod, although to you or me that hardly constitutes “little.” The busy part was easy to see, as Sky Echo was always swimming in strange little patterns that the matriarch proudly told the rest of the pod had to have some sort of mathematical basis.

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Blue whales are not known for having particularly large pods, but this pod was large in two ways. The matriarch, Baleen Queen, and the pod’s top krill tracker, Kriller Queen, were the two leaders, if such a collaborative group could be considered to have leaders. The matriarch was responsible for navigating the pod to its feeding grounds with the changes in season. Kriller Queen provided the hunting plan once the pod reached a feeding site. The big male, Plankton’s Bane, over 30 meters in length, was responsible for defending the pod from the occasional great white shark or orca pod. He was still trying to live down the most recent pugilistic episode, in which he successfully defended the pod from a particularly menacing abandoned raft. The splinters were not the only injury he had taken that day, with his pride being first in line. Altogether, a dozen blue whales formed this pod, which used the Indian Ocean and the Southern Ocean as its neighborhood. It was the biggest pod in number – and size – in the entire Indian Ocean. Sky Echo admired her mother, the matriarch, immensely, always marveling at her understanding of the currents, the seasons, and the seasonal location of krill and copepods. These small animals were consumed in masses of up to 50 tons a day by the pod, and without Baleen Queen’s direction, the pod would be hard-pressed. Sky Echo knew this, and hoped to someday provide support for the pod as valuable as her mother. After a few years, the pod noticed how musical Sky Echo was. Sky Echo had augmented her strange patterns of swimming with a musical score to accompany it. Plankton’s Bane noted, “perhaps she has found her calling as a musician.” Kriller Queen admitted that she had no idea how Sky Echo was composing her songs. “I don’t know her source of inspiration,” she said, “but I do appreciate how catchy it is!” Each year that passed, Sky Echo added more nuance to her songs as the pod made their 10,000 kilometer migrations north to south to north again. As Sky Echo grew into her last few years of adolescence, her songs seemed complete, and she seemed settled into the pod as the musician and one of the protégés of the matriarch. The future was bright for her and for the growing pod. Nothing stays the same, though. Seasons change, and conditions both improve and worsen. Whales, like some indigenous populations, have a tradition of a “winter count,” where the defining event or events of the year are memorialized (and since whales do not have surfaces to write them on, memorized) by the pod. This particular year, Sky Echo’s ninth, was destined to be a year in which several pictographs would be needed. The pod was swimming along, led by Baleen Queen, to their southern feeding grounds. A dire setback came in an unexpected form when one cloudy night, Baleen

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Queen attempted to surface to get fresh air in her lungs but could not. Something very long − as long as 10 whales − was between her and the air her mammalian lungs needed. Baleen Queen hit this obstacle with full surfacing momentum, and afterwards forgot who she was. It was a cetacean concussion, and it would have been of little solace to Baleen Queen to know that the much smaller mammals aboard this moving obstacle temporarily were afraid that they would run aground some unknown, phantom Indian Ocean island, like Juan de Lisboa, or bump into some newly calved ice sheet from Antarctica much further south. They had not done either of these things, though, and eventually their precious shipment reached safe harbor, making their story of far less interest than ours about Baleen Queen’s pod. As to the pod, the matriarch for days thereafter swam in circles, turning to the side opposite her concussion, and the pod became concerned that they would never find their cozy summer feeding ground. Amidst this anguish, Sky Echo continued singing her song and following close behind her mother for both protection and out of habit. Plankton’s Bane commented, “Wouldn’t it be nice if somehow we could encode the path to the feeding grounds into something the entire pod could memorize?” In answer, Kriller Queen opened her mouth in astonishment. That is a lot of astonishment − 10 meters of it. “Say that again!” she cried, and after Plankton’s Bane repeated it, she turned to Sky Echo, and said, “Sky Echo, how did you come up with your song?” Now, as we all know, great composers sometimes are not aware of how a particularly marvelous song has come into their head. But Sky Echo did know that the inspiration came to her from her mother’s navigational skills and from the extra time to think she had during their migrations. “I would have to say that our trips together were the inspiration,” she said. “I thought you’d say that!” Kriller Queen blurted. “I’ve got it! Sky Echo’s song is about the stars!” “The stars?” asked Plankton’s Bane, “what does that mean? And why are you so happy about this? We’ve got a couple of big problems to take care of right now.” “Well, we’ll just have to wait for Baleen Queen to get back her memories,” said Kriller Queen, “but at least we have one of hers – and the one we need to survive – right in front of us.” She beamed at Sky Echo. “Why are you looking at me?” Sky Echo asked, fidgeting with her flipper. “Because your song is about the stars!” Kriller Queen said, “Can you please teach us all your song? I have the beginning memorized, and it got us to where we are now.”

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So, Sky Echo taught the entire pod her song, and it indeed was a code for the stars to follow to the feeding ground. The space between the notes was related to the space between stars, and the order of them gave the pod each new direction during the migration. It is hard to explain this to humans, because of course it was in whale code. But it worked, and soon the pod had safely reached their summer feeding grounds. There, three wondrous things happened. First, the pod ate better than ever before, proof enough that Sky Echo’s song had led the way. Second, the matriarch got her memory back, except for the few seconds before her head hit the hull of the container ship. That was a blessing, who would want to remember that? The third event was the most amazing: when Baleen Queen got back her memory, she immediately noticed that Sky Echo’s mottling pattern on her back was a map of the stars in the night sky, with the path between the feeding grounds of summer and winter right along her spine. And these miracles explain the science behind blue whales being identified in the Indian Ocean by their newly found song (https://happymag.tv/bluewhales-new-song/). Inspiration for music can come from anywhere and for anyone, even Sky Echo. And good music saves us in many different ways.

12.2 Dances with Traffic Neobrain liked noise, but only when he made it. When he went to Madrid, the beauty of the Prado was ruined by the buzz of traffic in the roundabout. When he went to New York City, the breathtaking esthetics of the Guggenheim were drowned in the noise of cantankerous, confrontative cabbies, and arguing Aussies and Austrians. Neobrain listened to the noises around him, and wished the white noise machine he used to fall asleep with could be with him in the city. Sure, he had noise-canceling headphones, but he did not like wearing them, feeling he was not really there if his ears were covered. He knew that he had to find a way to accept, and even enjoy, the noise around him. Walking through the cities, he picked up sounds in the chaos that he liked. If he could take those sounds and filter out the rest, he would be happy. But he did not want to wear headphones; so he did not have a way to filter. Neobrain figured that if he could selectively add to the noise, the combination might be more pleasant. He remembered the concept of phrenology, in which bumps or relative distances on a person’s head were associated with particular personality attributes, like cautiousness or secretiveness, or even “tune,” which means musical adeptness. He also remembered the concept of induced

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phrenology, in which a hammer was used in a decidedly non-Laputan way to create the desired bumps on someone’s head to induce those specific mental traits. Could Neobrain perform induced auditory phrenology on the traits of the city? Neobrain set to the task, programming a large “boom box” like device to sense the sounds of the city, to compute what sounds to add to create the desired output, and to create the sounds. He used artificial intelligence (another form of neobrain?) to help. Adding sounds to sounds, his goal was harmony. Not just harmony of music but harmony of life. Neobrain realized that, sometimes, adding sound to sound actually created something less noisy. His program focused on interference; in effect, adding noise 180 degrees out of phase with the noise around him. When Neobrain’s program heard this noise (Figure 12.1):

Figure 12.1 Noise.

His program spit out this countering anti-noise (Figure 12.2):

Figure 12.2

Anti-noise.

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And the sum of it was this (Figure 12.3):

Figure 12.3

Sum of noise and anti-noise.

Peace, calm, relaxing, and soothing. Noise canceled by noise collision, somehow poetically like matter and anti-matter meeting and leaving behind perfect stillness. Neobrain realized that two signals, if complementary, allowed his noise to make the world safer for ears. Neobrain liked the peaceful vibes that he could impose on his surroundings, but he knew that there could be more. The idea of induced phrenology kept, as it were, rearing its head, and then it all became clear to him. If he added his anti-noise to the noise around him, he effectively created a blank slate, a fresh page, an unpainted canvas for sound. Onto this canvas, he could render his desired phrenology of phonology. If he added the desired ambient music to the anti-noise signal, the noise was canceled, and the ambient music was all that remained. But could he also induce better behavior in those around him with his sound? Neobrain knew how upsetting certain sounds were to certain people in certain circumstances. What if he could change the sound around them so that he induced happiness, or equanimity, or even the need for specific physical activities such as dancing or certain behaviors such as being courteous to others? This was powerful, this little sound-controlling box, wasn’t it? So, ask yourself, is Neobrain’s magical music box playing in your environs? Are you happy? Do you notice any noise? Are you inspired to make music by the story of Neobrain? If so, you are not alone. Word has it that Neobrain has been taking advantage of ambient music for decades to make people’s environment more peaceful (https://www.youtube.com/watch?v=X RiBrWY3NB4).

12.3 Siri-ously? That’s All It Takes? Odysseus was set to leave Circe for the final time. In spite of her pangs at losing him, she provided him with a roadmap of his trip home, and all of the pitfalls to avoid along the way. Circe had warned him that, on his way to splitting the distance between Scylla and Charybdis, he and his men

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would encounter the Sirens, legendary women whose sounds would charm Odysseus and his men to their deaths. Circe told him, in words more Greek sounding than these, about the dangers of the Sirens: “The Sirens mesmerize any and all who approach them. There is no return to Ithaca and Penelope for the sailor who comes upon them unprepared...With their high, clear song the Sirens beguile him, though they sit there in a lea piled deep with the crumbling skeletons of sailors, withered skin still hanging upon their bones” (paraphrased from the Odyssey, 12:39−47). Odysseus, being Odysseus, was more curious than cautioned. Odysseus had never seen a Siren. He could say “Siren” but imagine only the noise of a siren when he called for a Siren. But, surely, their legendarily beautiful songs would not sound like this toxic tocsin, this noxious noise, that was all that his own cacophonic consciousness could conjure. He would have to hear it for himself. Gently pouring wax in to stop up the ears of his men (except for Marcion − he already had enough ear wax to be deaf to any sounds), Odysseus wanted to hear their sounds as their ships steered past. His men were forewarned − under no circumstances were they to free Odysseus from his self-imposed bonds lest the Sirens add him to their ossuary collection. This was an odyssey, not an ossuary, after all. Time passes, as it always does, and Odysseus and his intentionally deafened men soon sailed through the sound side-by-side with the shore of the Siren’s island. Only Odysseus could both enjoy and tremble from the beauty and the dread of the Sirens’ songs. Calling him to them, they meant to guide him into the rocks and unswimmable swells of their shoreline. Drawn both by love and by horror, Odysseus needed to get closer, closer, and closer. Odysseus ordered his men to steer to the shore, only to be stared at blankly by his unhearing henchmen. Yearning for more, tearing at his bonds, crying out in misery, Odysseus eventually fell into a fitful sleep as the sounds of the Sirens faded. When his sleep ended, Odysseus barely noticed the Mediterranean sun shining in his brown eyes. All he could think about were the sounds of their singing. Did they sing words? Were there lyrics, a libretto, or even a melody? He could not remember. All of the music had turned into emotion, into memory, into a longing for its return. His men could get the beeswax out of their ears, but he could not get the echo of the Sirens out of his. Odysseus dreamt that night of a device capable of responding to his commands to produce any sound. He envisioned an electronic device that, like a Siren, could respond to his desires. He returned back to Circe a third time, because any Bronze Age Greek sailor worth his salt knew that Circe was

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the best maestra of microelectronics in the Mycenaean Mediterranean. With the help of Circe and her magical tools – including the pencil of Hephaestus to bring two metals together and the Zeus-juice-cylinder to bring the device to life – he crafted a device to provide any sound that you asked. He named the device after both the Sirens and Circe: he called it Siri. That night, alone in his quarters, he turned to this new device. “Siri,” he said, “please play the sound of the Sirens.” Whirring awake, Siri aimed to comply. Immediately, the sound of waves, that combination of white noise and structured sound. White noise with crescendo, diminuendo, crescendo, diminuendo. Slowly at first, a different sound could be heard. Then, crescendo after crescendo, with the cyclical sound of the waves ever more overcome by the sounds of the Sirens singing in synchrony. Odysseus felt the sounds pass through him, and recalled the approach to the rocky shore of the reallife Sirens. Sound after sound, closer and closer. He could feel the emotions arising within him. Welling up, and with no way to be collared. He had forgotten to tell Siri to stop. He had forgotten to tell Siri to let his men steer him to safety. He had forgotten to tell Siri that he, being mortal, might have a physical limit. Sorrow mixed with joy, longing mixed with fulfillment, rapture mixed with horror. It was not that the singing of the Siri as Sirens was something terrifying. It was that it was everything terrifying, and everything not terrifying, all at the same time. Music with the depth of Mozart, Shostakovich, and Miles Davis, all in one. Every emotion in full development, every possible mental state combined in a single instant. Everything. Nothing left in reserve, nothing more to bring. And then, nothing. He was fully reset. When that happens to a living brain, it becomes something else. All of what he had learned, all of what he had ever done, ever undone, ever felt, ever feared, ever loved, ever lived, ever thought, and ever fought. All of it at once. And then it all flipped. Odysseus, in his mind, had joined his men in the shades of Hades. They had died differently: Laogonus at the hands of the Laestrygonians; Pelonus in the gaping maw of Polyphemus; Scyllias in the claws of Scylla; and Charidemos in the spiral of Charybdis. But died they had, and were humbled and hungry in Hades, like him, and there to remain. Odysseus, his mind regained, regretted what he had done with Siri. “Never again,” he said, but of course that had to be the case if he too were in Hades.

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12.4 Headband Harmony Edgar was the earl of the EEG. He knew that the electroencephalogram, called the EEG because nobody really wants to keep saying “electroencephalogram,” was a way of measuring, in some form, the overall electrical patterns in the brain. It had been around for a long time before Edgar, but no one had ever made electrodes, not to mention figured out how best to arrange them on the surface of the scalp, the way Edgar had. Edgar incorporated new alloys, new patterns, and new electromagnetics in order to achieve what had before been thought impossible − a way to map the entire brain with high resolution just from using electrodes on the surface. Edgar knew that his technology would open up a world of possibilities. But he gravitated toward his own personal hobby, which was composing. How Edgar hated having to use composition software. It was not that the software wasn’t good: it was just that sometimes Edgar fell into the flow and did not want the software getting in the way of him writing down his music as fast as he possibly could. With his invention, he could go directly from EEG to the musical score. Edgar wanted to be as fast as Mozart, whose notes flowed (with some spilling) from the pen almost as quickly as they entered his mind. With his new “EEG to score” software, Edgar felt that he could, at last, write music as quickly as his great idol. Edgar set to work, and within a month had composed 15 major works, including two symphonies. This was on pace with Mozart in even those crazy years of 1772−1773. Emboldened by the device, Edgar let his mind wander, and new genres of music leapt from his mind to the page. Some of these were very interesting, and others filled a much-needed void. Regardless, Edgar was spitting out scores at a rate, well, scores of times faster than he ever had before. Seeing the advantages of his invention, Edgar, as many inventors do, became emboldened. The invention became more than a tool for composition − it became an end in itself. Edgar did not realize that he was starting to set aside his own critical judgment, which is the very attribute needed by composers like Mozart to continue creating new, fresh music over their entire career. Instead, Edgar fell in love with the process itself, with the automation of his formerly manual process, and with the quantity instead of the quality. Worse yet, Edgar, like a four-year-old discovering videos for the first time, stopped doing anything else. Edgar stopped listening to new music. He stopped seeking feedback from his fellow composers. He even stopped showering (turns out, Edgar was never really fond of hygiene in the first place). This monomania, or obsession if you prefer to call it that, resulted

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in so much musical output – combined with increased insular behavior – that Edgar was essentially producing music that no one ever heard. If a score falls in the forest, and no one hears it, does the music actually exist? The answer in this case is yes and no. It exists because Edgar’s technology created the files saving the music. It exists because it passed through Edgar’s consciousness, if just temporarily in most cases. But, at the same time, it does not exist, because it was never actually heard, or indeed audible, outside of Edgar’s head or his computer’s hard drive. Existing and yet not existing, all at the same time. Edgar himself stopped existing for some people in his acquaintance. He did not show up at the café for his usual double ristretto. He did not need to go into work − his infrastructure traveled with him. He became less real than before his invention. All of which makes us wonder what really is real. Which is more real, what goes on inside your head, or what you share with others? Edgar created music at a rate even Mozart could not match, faster even than Schumann in his hypomanic years (1840 and 1849). Edgar figured that he could produce even more music if he wore the headgear to bed. A few twists of the screwdriver, an adjustment on a potentiometer or two, and a couple of extra self-adhesive bumpers, and voila! Edgar had his own version of a sleep mask. Edgar gave it a few nights, waiting to see if he produced music during his sleep. Not a lot, on most nights. When he did produce music, it was pretty much “background music,” music you might hear in a waiting room (assuming your office professional is not one of those who think that “creativity” in music ended with Journey, Foreigner, and Bad Company). This actually helped him get over the obsession with his headgear. He had already “maxed out,” and so why worry about it? Nevertheless, he did continue to wear the headgear to bed. Shortly thereafter, he returned to some semblance of normalcy in his life. He started listening to new music. He started taking input and feedback from other composers. He started a new semester of teaching. He even showered once in a while. Life was life again, and he was looking for a way to integrate his new-found compositional approach into his classroom. He decided the best starting point was to integrate the equipment into the lab for the class. Never mind the woodwinds, never mind the brass, time to wear the electrodes, time to join the student and the system. The students enjoyed the lab, although their proficiencies did not match that of Edgar. Some of the music was banal, some of it was decidedly derivative, but all of it poured from the students’ heads like grammatical errors during an in-class essay exam. When the music scores were converted

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to audio files, however, they underwhelmed. Edgar liked what he saw but not what he heard. The students needed an inspiration, and he was worried that the experiment in the class lab would discredit his whole invention. What if his invention was a fraud, an idiosyncratic idiocy ideal only idiopathically to Edgar? A fitful sleep followed that night, with Edgar frankly forgetting to forego the headgear. The morning came and the music from his nightmarish repose was interesting, to say the least. Fascinating, haunting, and flowing, he of course found it compelling, because he had birthed it. Then, he decided to birth it on his students. “Class,” he said, “I have a surprise for you today. You will be the first group of students, and people for that matter, to get to hear the dreams of another person, rendered in musical form.” The students, intrigued, placed the headsets on, clamped them in place, and started the feed. It was like turning off a light switch. Instantly their surroundings were forgotten, in fact disappeared into an imaginary world suddenly more real than the classroom. Then, dizziness, spinning, a feeling of free fall, no control over one’s limbs, consciousness separated from sensorimotor input and output, then completely liberated consciousness, free of all checks and bounds. Knowing the music was shaping, reshaping, controlling, rewriting their brains, the students, like of course people asleep, could not move their hands to take off the headset. Somewhere inside they knew it was necessary, desperately necessary, to take off the headset but being somehow functionally asleep from the sounds of the headset they also knew it was a dream, just a dream, nothing really that serious. Settling in, then, the nightscape of their instructor, Edgar’s unrestrained consciousness, merged with theirs. Seconds became minutes, minutes became meaningless, time lost its thread, and the dreams and the students became one. Someone was shouting, they thought, but in another place, another world, another reality. All they were, was the music of the dreams. The nightmare became their nature. “Wake up! Wake up!” Edgar was screaming, when he finally took the headsets off himself, seeing as the students could not. The room was quiet, deathly quiet, and forever changed. Instead of eight students in the lab, there were eight new, different beings. Fused with the dreams of another, they could never recover what they had been. Now the eight students had become three zombies, three automatons, one golem, and one raving mad person. Unsurprisingly, there were repercussions. And though Edgar to this day resides in a state penitentiary, he is still making music. Sometimes while awake, sometimes while asleep. There is a demand for his work among certain circles, as it is said that his “good stuff” is better than any illegal

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substance some might wish to use to forget the misery, the tedium, or the penury of their existence. Smuggling his output as bootleg recordings, Edgar continues to avenge himself on a society that neither appreciates nor fully understands his genius. The invention of the bidirectional EEG, which could both go directly from thought to score, and as it turned out score to thought, is Edgar’s legacy. The bootleg albums give Edgar continued influence on society. Ask yourself, reader, if you would, “Have I ever met a soulless person? A person in whom there seemed to be no inside, no center, but simply a walking, talking shell without substance?” If your answer is yes, then perhaps you have met one of those intrepid individuals who have dared to listen to one of Edgar’s bootleg recordings. Whatever you do, do not swap Spotify lists, okay?

12.5 My What Big Hands You Have The axman saw it coming. He was going to get the ax. His voice was not good enough, and he was clearly going to be the next contestant cut from The Sawmill Soloist, the latest in a long and somewhat tired line of shows devoted to finding the hidden voice talent latent in the woods. Maybe it was for the best. The axman thought about all those long afternoons in the woods, cutting down trees to make houses, furniture, stables, and gazebos. That somehow seemed so much more productive, fulfilling, and just flat out useful than being a singer in a sawmill. Hard work, heavy work, honest work. Back to the woods he went, ready to sweat and saw. Besides, with the experience on The Sawmill Soloist, he could sing along with the birds as he forced them to find a new apartment building with his raspier noise-making device. Still, it was honest work, and because the woods were dense and the demand for furniture reasonable, the axman could leave behind a dozen trees for every one that he actually did chop down. The woods would always be dense, so long as the axman, known to his friends as Kirk, was in charge. Happily singing and simultaneously slinging one day, Kirk saw something flitting through the forest just far enough away for him to observe it without himself being discovered. It was the wolf. Kirk knew the wolf, and not just by reputation. The wolf and his gang – known as Wolfgang – had virtually depopulated the forest of rabbits, raccoons, and even rangers. Biodiversity was suffering, and a mammalian migration was yet to be mitigated.

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The axman, seeing the forest depopulate, had joined a group of concerned forest denizens who reported the whereabouts of the Wolfgang to the remaining rangers and their renegade cadre of volunteers. “What would Wolfgang do?” became the mantra of this forest-felony fighting faction. Soon, the Wolfgang was reduced to simple the lone wolf. Their ranks diminished, only one was left, but the last was certainly not the least − the least loathsome, the least lethal, and the least loquacious, that is. The wolf was still able to use his powers of paw, jaw, and persuasion to eliminate the remaining forest dwellers, who he blamed for the loss of the rest of the Wolfgang. Indeed, when it came to payback, the lone wolf was very calm, collected, capable, and culpable. His goal was to turn the forest into a desert, at least as far as fauna was concerned. Driven by animosity, aiming for extinction, the wolf figured revenge was best served when there was no longer any need for it; that is, when no one was left in the forest but him. All of this flashed through the axman’s mind as he saw the wolf. Another thought occurred to him simultaneously: he knew where the wolf was going! Oh yeah, the wolf was going over the river and through the woods. So, to grandmother’s house he would go! In the blink of an eye, the wolf was banging on the door of grandma’s house. Slowly, with the various clicks in her joints foreshadowing her subsequent arrival at the other side of the door, grandma worked her way through her rustic but expansive cabin. “Who’s there?” she asked, her voice weak. The tremor in her voice triggered salivation on the lupine Lucifer’s lips. “it is me, the Ranger,” the wolf said, cheerily, “here to make an inspection to make sure that your cabin is safe from the wolf.” “I will unlock the door for you, my dear ranger,” grandma said, “but please out of modesty allow me to return to my bed before you come in the door.” The wolf, hardly able to restrain himself, felt his appetite for revenge and flesh forcing his heart to pound, his breath to deepen, and his forehead to sweat. “Keep it together,” he told himself, “keep it together.” When the word was given, the wolf-as-ranger entered the cabin. “I’ll join you in a moment,” he said, “after I check your doors and windows.” Quickly, the wolf firmly locked, and where possible dead-bolted, the doors, windows, and weirdly enough the toilet. With the house firmly secured, the wolf felt that no one – not even the real remaining ranger or that horrible handy and handsome axman – would save grandma from her impending demise.

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Walking up to the bed, the wolf-as-ranger said, “There you go, grandma, the house is secure, and it has passed my inspection.” “My, what terrible teeth you have, my dear,” Grandma said. “The better to chase off wolves and werewolves,” he said, noting that the smell of garlic, which is what he blamed his halitosis on, was a repellant for the lupine threats of the woods. “My, what big teeth you have,” Grandma said. “The better to bite into all those wonderful nuts and berries in the woods, to live off of the forest just like the animals that I protect do,” said the rangerwolf. “My, what big claws you have,” said Grandma, “and to that I really have to wonder what your reply will be.” “The better to scratch the trees to use as path markers and to trim back the bushes and weeds,” said the ranger-wolf, “it’s amazing what you can do with those modern nail trimmers, isn’t it?” Grandma did not reply at once. She seemed thoughtful, as if a dawning awareness was coming over her. “My, what a big neck you have,” she said, finally. “The better to. . . wait, what?” asked the wolf, confused. That confusion was the last thought the wolf ever had. Down came the ax, homing in on that big, thick neck, that easy target for an axman skilled enough to trim his beard, let alone bushes and trees, with the ax. The ranger, it turns out, was not the only one in the cabin wearing a disguise. The real grandma was actually hiding under the bed with Little Red Riding Hood. The person, who the wolf thought was his dinner for the night, was Kirk. “Too bad,” said Grandma, brushing herself off as she stood up, “that we’ll never be able to tell the wolf about your talents, Red.” Red, it turns out, was the proud owner of some amazing pitch-shifting software skills, and it was she, under the bed, carefully replacing the hardy woodsman’s baritone with the supposedly weak soprano of Grandma. The same pitch-shifting software that allowed singers of modest talent to sing like nightingales on their latest hit singles. Pitch-shifting software, the lipstick of sound, cleaning up the cacophony, nullifying the noise, dismissing the dissonance. It would come as no comfort to the wolf, of course, that the woods came back to life. Word passes quickly between the forest fauna, and the rabbits, raccoons, and rangers – not to mention the moose, mice, and men – quickly filled in the void, and all lived much more happily ever after. And, as for our heroes, Kirk and Red? They are friends to this day, and have even formed a band. Red has a beautiful voice (or does she?) and Kirk of course wails on his ax guitar.

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12.6 Modern Mozart and Musical Meaning “What would Wolfgang do?” (WWWD, for short) is something we ask for reasons other than fairy tale forests. Since much of the music that we can reproduce in this book without copyright violation must come from over a hundred years ago, you have seen a lot of Mozart and other composers from the classical music era. This is not to say that we somehow think this music “better” or somehow more “sophisticated” than the music of today. In fact, when it comes to answering WWWD, we feel it is quite the opposite. WWWD if he appeared in our times, armed with our instruments and tools for composition? As Yogi Berra (definitely one of our favorite sources of quotes) said, “It’s tough to make predictions, especially about the future.” But we will perform some alternative history here, and provide one in which Mozart – instead of dying of uremia, trichinosis, or Salieri (pick your favorite explanation for his tragically early passing) – was transported into our era at the very height of his powers; that is, at age 35 when he supposedly died but actually traveled forward over two centuries into our time. To put some context around this, one needs to see just how creative Mozart could be. The story of Adriana Ferrarese del Bene and Mozart’s opera, Cosi Fan Tutti, is a good way to illustrate that. According to [Oper17], “Mozart had an extreme dislike for the soprano Adriana Ferrarese del Bene, for whom the role of Fiordiligi was first created. She had a strange tendency to drop her chin and throw back her head while singing low and high notes respectively, and knowing this, Mozart chose to fill her showpiece aria (“Come scoglio”) with constant harmonic leaps. Presumably he took great pleasure in watching her bob her head ‘like a chicken’.” Check out the score if you get a chance, and in particular sections like the “contra i venti” section below (Figure 12.4).

Figure 12.4 Section of Mozart’s Cosi Fan Tutti, contra I venti.

The point is, if someone has enough talent to compose music to intentionally mock someone while still holding together an opera (a well-regarded one at that), then they could probably make good things happen with a synthesizer and a digital audio workstation. Let us simply apply the Law of Parsimony here. What are the odds, really, that the world’s all-time wunderkind of

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music, when transported into the 21st century, would require music to be all Classical, all the time? Isn’t Mozart (along with the prodigiously talented Haydn) the reason for the break with Baroque? Mozart, the template, the mold, the archetype, the very model of musical creativity, was in fact the original hit single artist. If he were alive and composing today, he would be cranking out hit songs. A lot of them, in fact. Recent research, in fact, supports our view that Mozart would be successful today. Justin Berg [Berg22] has shown that composers with a greater variety of musical tools in their tool belt are more likely than other composers to be “serial hitters.” That is, more than one-hit wonders. Berg’s work also shows that the musical attribution of these serially successful songwriters changes over time, naturally if they are indeed, like Mozart, overflowing with talent. For long-term success, composers have their breakthrough hit sound similar to other recent hits; thereafter, to sustain success, they need to pull in from different genres. Think of Radiohead − their breakthrough song, “Creep,” is indeed similar to a lot of the rock/grunge sound of the early 1990s. They have sustained themselves, starting with “OK, Computer,” with a much different sound. Would Mozart be as creative as, say, the Beatles, who arguably changed their sound at a rate unmatched by any other popular band? After all, they went from covering “Twist and Shout” to composing “A Day in the Life” in just four short years. There is no way to test this, because sadly we cannot bring Mozart himself into our present day. But I think we can all agree that Mozart, armed with today’s technology, would be like a kid in a candy store! And you too, armed with the musical and inspirational approaches outlined in these dozen chapters, can be as creative as Amadeus himself. We will leave you to it.

Reference [Berg22] Berg JM, "One-Hit Wonders versus Hit Makers: Sustaining Success in Creative Industries," Administrative Science Quarterly: 00018392221083650, 2022. [Oper17] Opera Omaha website, “Did You Know...Così Fan Tutte Edition,“ https://www.operaomaha.org/blog/did-you-know-cosi-fantutte-edition, 25 January 2017, accessed 20 January 2022.

Index

Document Engineering 2 Dorian 157, 161, 176, 179, 189, 193

A

Accompaniment 221, 226, 232, 243 Aeolian 169, 176, 177, 180, 189 Ambient Music 248, 317 Anacrusis 107 Arrangement 236 Augmentation 267

E

EEG 325, 328 Expression 45 F

Fable 317 Fantasia 35 Feeling 157 Fermata 157 Form 17, 18, 24, 27, 38, 304

B

Beat 100 Binary Form 24 Borrowed Chords 194 C

Chord Progression 129 Chord Spacing 222 Chord Voicing 222 Chords 132, 133, 194, 200 Chromaticism 201 Chunking 294 Color 185, 186, 187, 248 Composition 17, 38, 84, 119, 286, 287 Compound Meter 91 Consequent 45 Creator 1

H

Harmonic Rhythm 125 Harmony 59, 61, 72, 125, 129, 137, 325 Homophony 225 Hook 49 I

Inspiration 87, 320 Instrumentation 221, 236, 243 Interlude 37, 303, 304, 305, 306 Inversion 48, 231, 262, 264, 268 Ionian 157, 176, 180

D

Democratization 2, 3, 293, 314 Development 31, 256, 272 Diminution 251

L

Lead Sheet 129, 145, 275, 280 Little Red Riding Hood 330

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Index

Locrian 175, 176, 177, 178, 180 Lydian 157, 176, 177 M

Major 53, 117, 142, 200, 301 Maker 1, 7, 11, 332 Measure 53, 105, 127, 135, 197, 200 Melody 21, 48, 101, 137, 219, 221, 304, 323 Metamerism 191, 212, 213, 215, 217, 219 Meter 40, 96, 150 Minor 58, 113, 139, 204, 278, 302, 308 Mixolydian 157, 176, 177, 184 Modal System 157 Mode Mixing 191 Modulation 191, 204, 206 Monophony 222 Mood 157 Motif 120 Motive 91, 118 Mozart 8, 66, 74, 149, 193, 227, 239, 300, 317 Multimetric 91 Music 1, 7, 38, 84, 214, 215, 275, 324 N

Notation 9, 275, 279, 283 O

Obscuring 209 Odyssey 175, 176, 181, 317 Orchestration 221, 236

Period 32, 45, 130, 205, 304 Phrase 11, 45, 107, 205, 310 Phrygian 157, 176, 180 Pitch Shifting 8, 330 Pitch 4, 47, 137, 175, 235, 330 Polyphony 85, 125, 143, 221, 225 Polyrhythm 114, 115, 116 Prolation 267, 268 Pulse 96, 99, 100, 108, 241 R

Retrograde 262 Rhythm 20, 51, 93, 103, 227, 309 Rhythmic Notation 102, 275, 283, 284 Riff 45, 72, 234, 251 Rondo 27, 29, 30, 148, 302 S

Scale 45, 47, 61, 140, 157, 203, 309 Secondary Dominant 132, 195, 198, 199, 200 Shorthand 12, 42, 172, 275, 277, 283, 300 Sirens 323, 324 Sonata 27, 58, 74, 170, 208, 272, 302 Song 18, 31, 101, 133, 153, 162, 214, 318 Staff 275 Structural alteration 251 Structure 293 Style 42, 213, 214, 215, 216 Subdivision 91 Subject 45

P

Parallel Harmony 221, 230, 250 Passage 20, 45, 85 Patterns 10, 94, 236, 325

T

Templates 17 Ternary Form 28

Index

Tertian Harmony 157 Texture 137, 221, 223 Theme 2, 28, 74, 240, 243, 306 Time Signature 282 Tonal Center 157 Tonality 158 Tones 143 Tonicization 191, 197, 199 Transformation 261, 267, 273 Transposition 263, 293

Tuplets 91, 111 V

Variation 27, 252, 254, 256 Variation Form 27 Varied repeats 254 Voice Leading 222 W

Whalesong 317

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About the Authors

Jeff Ewing received the BA degree in music theory and composition from Otterbein University (1998), following an Associate in Specialized Technology Degree in industrial design technology from The Art Institute of Pittsburgh (1993). Being a lifetime composer and private teacher, Jeff’s work has been used for education, including student recitals, film, theatre, and other public events since 1995. Steve Simske is a professor with the Systems Engineering Department at Colorado State University (CSU), where he leads research on analytics, cybersecurity, sensing, imaging, and robotics. Before joining CSU, Steve was a Fellow in HP Labs. Before that, he was a life sciences researcher at a NASA Center for the Commercial Development of Space. Steve is a Fellow of IEEE, IS&T, NAI, and CSU’s Faculty Institute of Inclusive Excellence. Steve received a 2022 Best Teacher Award from Colorado State University Alumni Association.

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