Music Numinous and Mathematics. Form and Analysis Through Fourier Space 4048197053, 9784048197052

Table of contents :
Cover
Computational Music Science
Music: Numinous and Mathematics. Form Analysis Through Fourier Space
©
Contents
Part I. Music and the Numinous
Contents
Preface
Introduction
1 The Transcendental and Rational Discourse
2 Music as Sublime Organism
3 Process Philosophy
4 Music and Process
5 A Whiteheadian Aesthetic and a Musical Paradigm
6 Music, the Other Arts and Process
Conclusion
Selected Bibliography
Index of Names
Part II. Music and Mathematics: From Pythagoras to Fractals
Preface
CONTENTS
Music and mathematics: an overview
I Music and mathematics through history
1 Tuning and temperament: closing the spiral
2 Musical cosmology: Kepler and his readers
II The mathematics of musical sound
3 The science of musical sound
4 Faggofs fretful fiasco
5 Helmholtz: combinational tones and consonance
III Mathematical structure in music
6 The geometry of music
7 Ringing the changes: bells and mathematics
8 Composing with numbers: sets, rows and magic squares
IV The composer speaks
9 Microtones and projective planes
10 Composing with fractals
NOTES ON CONTRIBUTORS
NOTES, REFERENCES, AND FURTHER READING
ACKNOWLEDGEMENTS
INDEX
Part III. Musical Form and Analysis: Time, Pattern, Proportion
CONTENTS
PREFACE
PRELUDE: Why Analysis?
I - TIME: The Motivating Forces
CHAPTER 1: Basic Factors in Form
I. Rhythm
II. Melody
III. Harmony and Tonality
IV. Tension and Relaxation
V. Articulation of Structural Units
CHAPTER 2: The Phrase
I. General Characteristics
II. The Additive Process
III. Phrase Length
IV. The Semiphrase
V. The Rhythmic Structure of the Phrase
VI. The Harmonic Cadence
VII. The Harmonic Structure of the Phrase
VIII. Phrase Extension
IX. Motivic Structure of the Phrase
CHAPTER 3: Phrase Groupings
I. The Two-Phrase Period
II. Symmetrical and Asymmetrical Periods
III. Three- and Four-Phrase Periods
IV. The Repeated Period
V. The Independent Phrase
VI. The Repeated Phrase
VII. The Phrase Group
VIII. The Connection of Phrases
IX. Disguised Phrase Endings
X. Duple Measure Groupings
XI. Description of the Period
II - PATTERN: The Shaping Factors
CHAPTER 4: The Simple Part Forms
I. One-Part Form
II. Two-Part Form
III. Macrorhythm and Macrotonal Plan
IV. Three-Part Form
V. Four- and Five-Part Forms
VI. Simple Part Forms as Internal Units
VII. Simple Part Forms in Vocal Music
VIII. The Connection of Parts
INTERLUDE: Auxiliary Members
I. Beginnings
II. Connections
III. Conclusions
CHAPTER 5: Composite Part Forms
I. Composite Three-Part Form
II. Composite Five-Part Form
III. Composite Part Forms in Vocal Music
IV. Other Composite Part Forms
CHAPTER 6: The Rondo
I. Historical Background
II. The Classical Rondo: General Characteristics
III. Treatment of the Principal Theme
IV. The Episodes
V. The Transition
VI. The Coda
VII. The Five-Part Rondo
VIII. The Seven-Part Rondo
IX. Rondo and Part Forms: Similarities and Differences
CHAPTER 7: Variation Forms
I. Theme and Variations
II. Ostinato Variations
CHAPTER 8: Fugue
I. The Exposition
II. The Episode
III. The Middle Entries
IV. The Conclusion
V. The "Form" of the Fugue
VI. Fugues with Multiple Subjects
VII. Related Types
CHAPTER 9: Sonata Form
I. General Characteristics; Historical Background
II. The Introduction
III. The Exposition
IV. The Development
V. The Recapitulation
VI. The Coda
VII. Sonata Form in the Concerto
VIII. Related Forms
III - PROPORTION: The Distinguishing Features
CHAPTER 10: Multimovement Form
I. Classical Models
II. The Concerto: Special Considerations
III. Cyclical Design
IV. Away from the Classical Model
CHAPTER 11: Broader Horizons
I. Rhythmic Delineation
II. Parametric Change and Expansion of the Phrase Concept
POSTLUDE: METAFORM: Beyond Formal Analysis
I. The Musical Idea
II. Musical Character
III. Proportional Aspects
IV. Under the Magnifying Glass: The Copyist
ANTHOLOGY: MUSIC FOR ANALYSIS
SELECTED BIBLIOGRAPHY
CREDITS
INDEX
Part IV. Music Through Fourier Space: Discrete Fourier Transform in Music Theory
Introduction
Historical Survey and Contents
A Couple of Examples
Public
Acknowledgements
Notations
Contents
1
Discrete Fourier Transform of Distributions
1.1 Mathematical definitions and preliminary results
1.1.1 From pc-sets to an algebra of distributions
1.1.2 Introducing the Fourier transform
1.1.3 Basic notions
1.2 DFT of subsets
1.2.1 What stems from the general definition
1.2.2 Application to intervallic structure
1.2.3 Circulant matrixes
1.2.4 Polynomials
Exercises
2
Homometry and the Phase Retrieval Problem
2.1 Spectral units
2.1.1 Moving between two homometric distributions
2.1.2 Chosen spectral units
2.1.3 Rational spectral units with finite order
2.1.4 Orbits for homometric sets
2.2 Extensions and generalisations
2.2.1 Hexachordal theorems
2.2.2 Phase retrieval even for some singular cases
2.2.3 Higher order homometry
Exercises
3
Nil Fourier Coefficients and Tilings
Cyclotomic polynomials
3.1 The Fourier nil set of a subset of
3.1.1 The original caveat
3.1.2 Singular circulating matrixes
3.1.3 Structure of the zero set of the DFT of a pc-set
3.2 Tilings of Zn by translation
3.2.1 Rhythmic canons in general
3.2.2 Characterisation of tiling sets
3.2.3 The Coven-Meyerowitz conditions
3.2.4 Inner periodicities
3.2.5 Transformations
3.2.6 Some conjectures and routes to solve them
3.3 Algorithms
3.3.1 Computing a DFT
3.3.2 Phase retrieval
3.3.3 Linear programming
3.3.4 Searching for Vuza canons
Exercises
4
Saliency
4.1 Generated scales
4.1.1 Saturation in one interval
4.1.2 DFT of a generated scale
4.1.3 Alternative generators
4.2 Maximal evenness
4.2.1 Some regularity features
4.2.2 Three types of ME sets
4.2.3 DFT definition of ME sets
4.3 Pc-sets with large Fourier coefficients
4.3.1 Maximal values
4.3.2 Musical meaning
4.3.3 Flat distributions
Exercises
5
Continuous Spaces, Continuous FT
5.1 Getting continuous
5.2 A DFT for ordered collections of pcs on the continuous circle
5.3 ‘Diatonicity’ of temperaments in archeo-musicology
5.4 Fourier vs. voice leading distances
5.5 Playing in Fourier space
5.5.1 Fourier scratching
5.5.2 Creation in Fourier space
5.5.3 Psycho-acoustic experimentation
Exercises
6
Phases of Fourier Coefficients
6.1 Moving one Fourier coefficient
6.2 Focusing on phases
6.2.1 Defining the torus of phases
6.2.2 Phases between tonal or atonal music
6.3 Central symmetry in the torus of phases
6.3.1 Linear embedding of the T/I group
6.3.2 Topological implications
6.3.3 Explanation of the quasi-alignment of major and minor triads
Exercises
7
Conclusion
8
Annexes and Tables
8.1 Solutions to some exercises
8.2 Lewin’s ‘special cases’
8.3 Some pc-sets profiles
8.4 Phases of major/minor triads
8.5 Very symmetrically decomposable hexachords
8.6 Major Scales Similarity
References
Index

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Computational Music Science Series editor Eva Li

Music Numinous and Mathematics Form and Analysis Through Fourier Space Edited by Eva Li

"Music: Numinous and Mathematics. Form and Analysis Through Fourier Space" Edited by Eva Li

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Contents Part I. Music and the Numinous Introduction The Transcendental and Rational Discourse Music 1 as Sublime Organism 2 Process Philosophy 3 Music and Process 4 A Whiteheadian Aesthetic and a Musical Paradigm 5 Music, the Other Arts and Process 6 Part II. From Pythagoras to Fractals Music and mathematics: an overview 1 Music and mathematics through history The mathematics of musical sound 2 Mathematical structure in music 3 The composer speaks 4 Part III. Form and Analysis: Time, Pattern, Proportion PRELUDE: Why Analysis? 1 TIME: The Motivating Forces PATTERN: The Shaping Factors PROPORTION: The 2 Distinguishing Features 3 POSTLUDE: METAFORM: Beyond Formal Analysis ANTHOLOGY: MUSIC FOR ANALYSIS Part IV. Discrete Fourier Transform in Music Theory 1 Discrete Fourier Transform of Distributions Homometry and the Phase Retrieval Problem 2 Nil Fourier Coefficients and Tilings Saliency 3 Continuous Spaces, Continuous FT 4 Phases of Fourier Coefficients 5 Conclusion 6 Annexes and Tables 7 8

Music and the Numinous by Richard Elfyn Jones

Contents Preface

5

Introduction

11

Chapter 1: The Transcendental and Rational Discourse

21

Chapter 2: Music as Sublime Organism

43

Chapter 3: Process Philosophy

63

Chapter 4: Music and Process

73

Chapter 5: A Whiteheadian Aesthetic and a Musical Paradigm

85

Chapter 6: Music, the Other Arts and Process

95

Conclusion

107

Selected Bibliography

117

Index

119

Preface The lines of thought that joined my interest in music and the arts with my enquiries into metaphysics began to emerge some twelve years ago. However, since childhood I have been aware that, as a keyboard player, making music was for me essentially a form of philosophising (carried out, I hope, spontaneously and instinctively rather than in any over-ambitious manner). Early memories of recorded performances by Schnabel, Solomon, Arrau and Brendel served to instil a restless curiosity about what comprises the real essence of the musical art. This book therefore aims to explore music, and to a lesser degree the other arts, in a somewhat unusual way by relating it directly to its ontological roots. For many years I have been a proponent of Process philosophy. Process philosophy is derived from and inspired by the writings, grand in scope and bold in application, of Alfred North Whitehead (18611947). In works like Religion in the Making, Adventures of Ideas, Science and the Modern World and especially Process and Reality he formulated a metaphysics applicable to all aspects of life. His system is intrinsically interdisciplinary and interrelational. All individual beings, from God to the most insignificant thing, are explained through Whitehead’s set of metaphysical concepts. The philosophy’s influence has been wide-ranging, especially in the USA. From the middle of last century many American theologians embraced Process as a tool for developing a new Christian natural theology whereby ideas of God as an absolute predestinator, or as a “beingitself”, was rejected in favour of a more world-affirming theism. The concept of the numinous is obviously central to theology as well as to other contemporary expressions of Christian faith. But this book has little to say about theological perspectives. The numinous is defined by me as pertaining to the numen or the supernatural. Although this

6

Preface

essentially Kantian idea of the numinous as a category for understanding religion was developed forcefully and somewhat mystically by the theologian Rudolf Otto, this book avoids theological arguments. On the contrary it adheres to the basic tenets of Whitehead’s metaphysics as expounded in Process and Reality. In choosing not to examine any Biblical and confessional gloss on Process that appeared after Whitehead’s time I accept the general character of Whitehead’s teaching and apply that to a specific example of reality which we value, namely music. Naturally, such is the generality of Whiteheadian Process that other aspects of reality could just as easily have been chosen. It is inevitable therefore that our discussion should be as broad based as possible. The reason Whitehead is not discussed until Chapter 3 and afterwards is because the Introduction and the first Chapter provide a historical preview recalling the pervasiveness of ideas of process in Western thought since the time of the Greeks. In providing these two introductory chapters we are also reminded that it was Whitehead himself who proclaimed that famous judgement on Western philosophy, namely, that it is all merely footnotes to Plato. The Introduction presents an oblique approach to the subject through links between art and mystical and esoteric theories. Joscelyn Godwin’s Harmonies of Heaven and Earth is a rich compendium of ancient beliefs about music’s magical powers and the connections between its mathematical substructures and the architecture of the universe. I am indebted to this source for many intriguing facts that are discussed in this chapter. The Introduction provides a critical potpourri of what Godwin terms “speculative music” preparatory to the more important approaches which will be discussed later. In Chapter 1 “The Transcendental and Rational Discourse”, there is an inevitably succinct review of Process’s indebtedness to Plato, Plotinus, St. Augustine, St. Thomas Aquinas and some later writers before focussing on Schopenhauer’s important hypotheses on music’s capacity to lead to a transcendental reality. It was Mendelssohn who, in a famous letter, pointed out that, far from being an abstract art music is the most particular. Our examination of the materials of Western music must therefore be technical, but without analysing pieces of music in a conventional manner. Chapter 2, “Music as Sublime Organism”, provides a detailed examination of theories by the Austrian musicologist Victor

Preface

7

Zuckerkandl (1896-1965) starting with his systematic derivation of music’s implications from the harmonic series. Clearly this could not be discussed without scrutinizing music’s raw materials, the pitches and their ordering in space and time. Chapter 3, “Process Philosophy”, is an introduction to Process thought. Here, the most important Process terms are defined, but with particular reference to the idea of God playing a role in the birth of every aspect of reality, whether that be physical, biological, psychological, sociological, educational, theological, aesthetic, or any other. What will become clear is the value of Whitehead’s ideas as a cauldron from which others can draw in a manner suitable for their own phenomenological enquiry. At this point the book becomes technical in a philosophical rather than musical way. Although Whitehead did not write extensively about God it is clear that for him God offers a “subjective aim” to every being in the universe. As we shall see, God in his primordial nature is the ground of all possibilities, but, as both creator and component in the universe, always persuasive never coercive. Fundamental to Whitehead’s concept of God in the image of an ultimate philosophical principle is the idea of divine creativity, indeed creativity is the “ultimate inexplicable stuff” of the universe, and it is as crucial a concept for the philosophy of Process as “being” is in Aristotelian or Thomistic philosophy. Firstly God is viewed as primordial: “He is the unlimited conceptual realization of the absolute wealth of potentiality. In this aspect he is not before all creation, but with all creation.1 But in this abstraction he is “deficiently actual”, and in two ways: “His feelings are only conceptual and so lack the fullness of actuality.”2 Whitehead maintained that conceptual feelings, when existing apart from complex integration with physical feelings, “are devoid of consciousness in their subjective forms.”3 It follows therefore that there must be a further aspect of God, for as well as being primordial he is also consequent. He is the presupposed actuality of conceptual operation, in unison of becoming with every other creative act. Thus, by reason of the relativity of all things, there is a reaction of the world in God. The completion of God’s nature into a fullness of physical feeling is derived from the objectification of the world in God. He shares with every new creation its actual world; and the concrescent creature is objectified in God as a novel element in God’s objectification of that actual world ... God’s conceptual nature is unchanged, by reason of its final completeness. But his derivative nature is consequent upon the creative advance of the world. 4

8

Preface

While endeavouring to assimilate the characteristics of God to those of every other actual entity, perhaps the denial of God’s omnipotence is an attempt to absolve him of responsibility for evil. Whatever was the case, in Process and Reality Whitehead produced an elaborately systematised philosophy in which the concept of God and other philosophical conceptions are made to cohere with the reality of the world. When referring to this consequent God, Whitehead often maintained that when we speak of the world we are saying something about God. It will soon become clear that throughout this book I define God according to Whitehead’s concept of him. Chapter 4 is devoted to “Music and Process”. In this Chapter the universal nature of Whiteheadian concepts are extrapolated vis-à-vis music. We explore critically where might the ontical (defined in a special sense as representing the world and material things) end and the ontological (again defined in a special sense meaning the sacred) begin. This is done in the light of assertions by F. David Martin and others. With reference to these two terms (in Chapter 4 and elsewhere) I follow the distinctions of Heidegger, especially as modified after Being and Time (1927), in calling the world of beings and things “ontical” reality, and Being, defined as a primordial power which reveals itself as a presence in our experience, “ontological” reality. Chapter 5, “A Whiteheadian Aesthetic and a Musical Paradigm” offers a case-study based on the first Prelude of Bach’s WellTempered Clavier, used as a means of teasing out the numinous from what is no more than a musical excerpt. Later in the chapter we proceed at a more abstract metaphysical level to relate the aesthetic and artistic implications of the analysis to ultimate considerations involving God. But music cannot be considered in isolation from the other arts, and Chapter 6, “Music, the Other Arts and Process”, aims to compare music with other arts in the context mainly of observations about literature by George Steiner, J.A.W. Heffernan and others. Here, in the references to literature I aim to understand the relationship between rational discourse and the approach to the numinous. It will by now be apparent that the book is wide-ranging. Such a bold aim could not easily have been achieved without help and encouragement from two very perceptive friends, the philosopher Dr. Meredydd Evans, and the musicologist and aesthetician, Emeritus

Preface

9

Professor Peter Williams, both of whom read early and late drafts, respectively, and gave valuable advice. Notes 1. Process and Reality (1929). Revised edn., ed. Griffin and Sherburne (New York1978), p. 343. 2. ibid. 3. ibid. 4. ibid, p.345.

Introduction A friend persuaded me to go to Ely Cathedral to hear a performance of Bach’s B Minor Mass. I had heard the work, indeed I knew Bach’s choral works pretty well. I was sitting towards the back of the nave. The Cathedral seemed to be very cold. The music thrilled me ... until we got to the great Sanctus. I find this experience difficult to define. It was primarily a warning. I was frightened. I was trembling from head to foot, and wanted to cry. Actually I think I did. I heard no “voice” except the music; I saw nothing; but the warning was very definite. I was not able to interpret this experience satisfactorily until I read - some months later - Rudolf Otto’s Das Heilige Here I found it - the “Numinous”. I was before the Judgement Seat. I was being “weighed in the balance and found wanting”. This is an experience I have never forgotten.

This testimony to the numinous power of music comes from Sir Alister Hardy’s book The Spiritual Nature of Man.1 In it is reflected Hardy’s abiding curiosity for that reality which is concealed behind the appearance of things. As a distinguished zoologist and founder of the Religious Experience Research Unit at Manchester College, Oxford, his approach was a scientific one insofar as this was compatible with exploring the continuum between temporality and eternity, between matter and spirit, between man and what Rudolf Otto called the “wholly other.” The quotation raises a number of issues, is psychologically redolent, and has very problematic implications. Suppose that what music does is transport us to a world of imagination in which we experience a range of feelings, depending on the context. Then we might realise that the human imagination carries us to another, perhaps transcendent, reality. But as I shall note in my Conclusion, defining this reality is inevitably bound up with our personal psychological state. Consequently, to sense the presence of unearthly powers may be no more than a projection of personal

12

Introduction

desires. With this in mind, many readers will find the quotation sentimental, but at least it will serve as a trigger for the large question that is to be raised in this book, namely, to what extent art, and specifically music, is underwritten by the religious and the metaphysical. What statements can be made which can validate a reexamination of the aesthetic and religious experiences in relation to each other? To do so we must elevate aesthetics to a position it has not enjoyed for centuries. At the same time, we need to capitalise on the highly original work in metaphysics in the form of Process philosophy, as exemplified by its founder, Alfred North Whitehead. Also, there has been a combination of developments in science, in psychology, and in philosophy in general which warrant a fresh approach to the spiritual dimension. In a scientific-secular world this is fraught with hazard. Scornful comments like Dickens’s about the American Transcendentalists (“I was given to understand that whatever was unintelligible would certainly be transcendental”) are familiar to us. But even among the most rational scientists and logicians there are plenty who will draw inspiration from Whitehead’s rueful observation that when the topics of aesthetics have been sufficiently explored it is doubtful whether there will be anything left over for discussion. There is surprisingly little reference to art or aesthetics in Whitehead’s work, but he infuses his writings with statements defining aesthetic order as derivative from the immanence of the divine in the world. If we follow him in relating the aesthetic consistency of the world to a non-temporal purpose, then we are of course defining “aesthetic” in its very broadest sense. In so doing we embark on a historical journey back to the very roots of philosophical speculation. In the specific area of metaphysical aesthetics, and in particular with reference to music as a divine art, (if “divine” is not too loaded a term at this early juncture), we must remember that the theological-metaphysical approach was the normal one up to at least the baroque era. But afterwards, rational philosophy tended to deflate any claim of music’s transcendental powers, and with the exception of some romantics (most notably Schopenhauer) this has been the case until the present. In Greek the very name of music, the art of the muses, points to its divine origin. So the Greek thinkers will be integral to our discussion not least in the contradictions between them. We will not discuss in detail technical aspects of Greek music since

Introduction

13

their nature and significance cannot now be fully recaptured. We do not know Greek music, we know only its theory and that imperfectly and many of its complex speculative aspects are quite foreign to modern thinking. But certain aspects need our attention. For instance, we need to recall that although the Greek heritage dates as far back as the fourth century B.C., we must go further back into the past than this for the famous ancient quarrel of poetry and philosophy which Plato refers to and which is relevant to us. It was the ancient myths which fuelled philosophy with an outlook on life and an interpretation of the nature of things - with poetry and art increasingly uneasy subjects for the ensuing logical discourse of philosophy to feed upon. The quarrel which followed between the aesthetic and the rational was one of the most striking features of ancient thought. It was a quarrel which existed before Plato’s time but was eloquently reasserted by Socrates in the Republic (607b 5-6) where he argued for the banishment of the “honeyed music” in lyric and epic from his ideal city in favour of more rational values. In the present context, we too will have to understand the relationship between rational discourse and other forms of understanding. As soon as one starts to speculate about the world of the psyche one is inevitably drawn into something whose separateness from the real world hinders coherent discussion. If we speculate about the relationship of art and music to the transcendental then we know that, despite the mechanics of its articulation, music is widely regarded as being closer to the world of the psyche than to the external world. Since its essence has no tangible reality, no body, no place, it might be well described as a psychological process. (And this is despite the fact that the organising and performance of it involves self-evidently physical processes). If that which is of real interest in music has none of the qualities of the external world we might indeed assume that music is a totally psychic phenomenon. One view of music is that it mediates between the external world and whatever other world there might be in a manner which can have a profound emotional effect on us. Our own personalities are affected by it, and few would dispute Hegel’s description of it as echoing the motions of the inner self. Similarly, Susanne Langer’s memorable encapsulation of music’s essence as an “unconsummated symbol” and as a “myth of our inner life”2 reflects the inherent mystery in music which we, in this book, will attempt to address.

14

Introduction

But our experience of music often takes us beyond a personal psychology. It often gives us signs of a deeper reality. Whether we in the twentieth century are in a better position to validate this than our forefathers may be questionable, living as we do in an age where the overriding role of music is as a commodity whose commercial exploitation blunts any awareness we may have of an elevated function. Even a casual review of the extraordinary range of musics available to us cannot but remind us yet again that this apparently limitless wealth of expression emanates (usually) from only twelve notes. This elementary fact should in itself prompt us to explore deeper the metaphysics which underlies this extraordinary manifestation of multum in parvo. Sadly, phenomenological enquiry has restricted itself to analysis of techniques. Musical analysts have never been so single-mindedly persistent; whether the procedure be Schenker’s, La Rue’s, Forte’s or Lerdahl/Jackendoff’s the current trend is to assiduously pursue an explanation for music in terms of the music itself. This is usually beyond reproach and often of a dazzling competence. On the other hand we may, as Wordsworth put it, “murder to dissect”, for at times much of the intellectual energy expended in brilliant analysis seems counter-productive. It was Mahler who reminded us that the most important thing about music is not in the notes - the thing that is really worth bothering about is the ineffable. What technical analysis can do is to deepen our awareness of musical processes and identify what unifying power underlies a work’s individual expression, and, of course this must be done in a technical way. It is a purely musical exercise, but it has very little to do with the metaphysical import of art. In contrast, the other, more literary approach to explaining music has perhaps not enjoyed much credibility in academic circles in recent years. But metaphysical aesthetics must hinge on this rather more discursive (albeit still analytical) procedure allied with as logical a philosophical approach as possible. Clearly, courage is required in discussing the transcendental elements in those objects which clearly are transcendental. And music is by common acceptance such an object. Through it we can hope to transcend ourselves by knowing ourselves to be transcended. And if the musical analysts have concerned themselves with structure and expression, I with my metaphysical bias would rather concern myself with exploration and discovery of a kind which can be called “metaphysical aesthetics”.

Introduction

15

One starting point is the following simple fact, which will have a striking confirmation when we come to discuss Whitehead later. Unless we decide that man is unrelated to the cosmos in which he lives, what happens to him (whether musical or otherwise) must bear some relationship to what is happening to the whole of which he is a part. One reason why this approach to the cosmic problem has been studiously avoided by many philosophers lies in the notion of philosophy itself as knowledge. Since knowledge must be true to exist then philosophical problems are usually related to the truth of certain propositions. (Truth, in Etienne Gilson’s difficult phrase, “is the conformity of intellection with its object”.) If there is no object, there is no truth. So in this respect philosophers behave like scientists. But the intangible nature of the very act by which works of art are produced have often reduced philosophers to silence because, for them, what remains to be known is only to be found if homogeneous with what they already know from nature. One of the great misunderstandings of aesthetics is the belief that art conforms to nature and life. Indeed, there may be more validity in the opposite view, illustrated by Oscar Wilde’s shopworn epigram about life imitating art. At least art tells us of the dramatic patterns of human life, defines its sense, and it is clearly the experience of many that they discover in life what the artist through his work tells us is there. First, we look to the distant past, and even beyond the earliest Greek philosophers to the mythical background against which much of Greek thought must be viewed if we are to appreciate and understand it properly. Here, music played a role that identified it as intermediary between man and the gods. A reverence for antiquity inclines even the most rational to give credence to the myths, which tended to magnify the physical power of music to irrational extremes. To take a realistic if not everyday occurrence, we are all aware of the capacity of a voice to shatter glass, and we understand that this is the result of the normal behaviour of matter under the influence of air waves and amplitude. How this disproportionate result is brought about is easily explained by gauging the accumulation of energy over a period of time. The ancient myths, however, constantly involved a disparity between the physical energy expended by singing or playing and the ensuing physical result, so that nature is ultimately answerable not to commonsense laws of cause and effect but to a transcendent principle, dependent on a cosmic consciousness, and evidenced by musical or

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Introduction

harmonic laws. The ancient synthesis which gave to music such a crucial role is explicit in many stories, which are by no means confined to antiquity and the Greek tradition. Awareness of the existence of unheard music is not a philosophical matter, as the group who investigated the Rollright Stone Circle in Oxfordshire was well aware. In a BBC science programme dating from 1983 it was revealed that these megalithic stones actually gave off ultrasonic vibrations of a remarkable strength. These varied in their patterns from hour to hour, and according to the phase of the moon and the season. Modern scientists were able to trace this energy to the way the geometry of the stones’ placement ingested a microwave energy from the sun. This ultrasonic energy was so high that it damaged the scientific instruments. These effects must have been known in ancient times and they certainly formed the basis for stories that were widely known. Later there were many attempts to find psychological or symbolic explanations for apparently incredible feats, as we note from the writings of Joscelyn Godwin and others who have explored those mysterious mythological and historical bye-ways unfamiliar to most musicians and aestheticians. Fantastic myths have no credibility for the majority of us, yet the fairly new science of cymatics reminds us that the physical world still holds many secrets which even today would seem to repair its broken relationship with the spiritual and the supra-sensible. For instance, the Swiss physician and natural scientist Hans Jenny brought to cymatics a rational approach enriched by his artistic and medical skills.3 He photographed the effects that sound produced on substances like smoke, fluids and lycopodium powder and revealed beautiful new shapes with wonderfully mysterious symmetries bearing a close relationship to the patterns found in nature, organic and inorganic. His new science was dedicated to the study of vibrations at every level of existence, from the molecule to the galaxy, and he discovered that one of the most fascinating activating agents is sound. Jenny’s research served as a rational link with the improbable phantasmagoria of many an ancient myth. And while they might not lend plausibility to theosophic self-indulgencies they do provide a proper scientific basis for probing areas virtually ignored by scientists. Similarly, a direct link between music and the vegetable kingdom has been a recurring element since those mythical times when Orpheus’s musical powers were said to move stones and trees and

Introduction

17

charm the beasts. In due course a semi-scientific correspondence was found in such writers as the fifth century poet Martianus Capella, whose description of Apollo’s Grove at Cirrha near Delphi described the harmony of the wind coursing through the trees and producing the octave, fifth, fourth, and whole-tone, according to how high the branches were.4 This effect was accepted over a millennium later by the Jesuit polymath Athanasius Kircher (1602-80), who said that the height of pine trees and their relative proportions set up a similarly relative harmonic proportion in whispering breezes. He went further in observing the harmonious proportions of plants, which in themselves were seen to have nodes spaced exactly as the division of the monochord in the proportions 1.2.3.4,5 a fact which, in the light of what we will discuss in Chapter 2, may be significant for us. We are indebted to Joscelyn Godwin for cataloguing so much about music’s connection with esotericism, occultism and myth. His book is disarmingly open-minded, indeed to the point that it is sometimes hard to discern what are his criteria of truth. Among the many fascinating facts which he uncovers is that describing how the power of music over nature extended to medicine. Certainly, music’s healing properties have been well-documented and in various forms. Even the materials from which the instruments are made have had a curative role. Giovanni Battista Porta writing in 1588, for instance, advised the use of instruments made from particular stalks or wood in the healing of particular illnesses. Thus, lymphatics might be relieved by music played on the stalk of the hellebore, and so on.6 Although we are not particularly concerned with these medical implications the general point here is that some explanation of the power of music by way of sympathetic vibration of some intangible substance is typical of all pre-modern accounts. Such is the significance of music generally in antiquity that Marius Schneider, the Alsatian ethnologist, has written in many places that in cultures where music was used as a magical force, a total absorption in sound brings to being in man the primordial condition of the universe. According to Godwin, Schneider’s research confirmed universal beliefs that the universe was musical and temporal in nature, not visual nor spatial, indeed, to the extent that the “ego-bound consciousness is supplanted by the state of music.”7

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Different theories about the essentially therapeutic effect of intervals proliferated during the seventeenth century. By the eighteenth century the whole understanding of perception was re-examined but with very little advance in either new theories or discoveries. Leibniz addressed the question, how do notes get from the ear to the perceiving soul? His position was put as follows: Nature must always be explained mathematically and mechanically, provided it be kept in mind that the principles of the laws of mechanics and of force do not depend upon mathematical extension alone, but have certain metaphysical causes.8

On the one side, the mechanical explanation carries one to the mathematical basis of music; on the other, the revelatory spiritual impact carries one to an intuition of the harmony of God’s universe, a dipolar function happily synthesised in Leibniz’s famous definition of music as “an occult numeration of the soul.” The well-being of the soul through a sympathetic correspondence in music is the aim of all music therapy, as can be seen today in the work of Paul Nordoff and Clive Robbins, whose dramatically successful work with autistic, psychotic and subnormal children, including deaf ones, has been one of the musical and medical revelations of our time. Both Nordoff and Robins were independently influenced by the anthroposophist Rudolf Steiner who had previously shown what a potent force music could be. Steiner’s work received an effective educational manifestation in the Waldorf Schools, where music therapy was used to great effect with mentally retarded and congenitally handicapped children. The tale of the Trappist monks in an American abbey who, following the prohibition of the Second Vatican Council (1962) obediently discontinued the singing of their daily offices in Latin, shows the deleterious effect this had on their mental well-being. No longer able to survive with only four or five hours’ sleep a night, sickness and psychological problems ensued. They tried all sorts of remedies until they deduced that their ills were the direct result of losing those hours previously devoted to singing the liturgy in Gregorian Chant. Godwin interprets this story as evidence for the deep-seated therapeutic effect of singing (particularly so in a silent order). The lesson of this anecdote is that singing was instituted in the contemplative orders not only for the glory of God but also as a practical means of harmonising the personality, and the community, in

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a situation of great psychological stress. The use of the voice is a human need no less compelling than sexual desire. The Trappists, forswearing conversation, exercised their voices in song, and it was the removal of this sublimation that brought disharmony to their lives.9 The modernist trend since Vatican 2 would seem to throw into relief the deep-seated psychological, even quasi-supernatural, powers of one of the Church’s most ancient musical forms - Gregorian chant, which in its impersonal monophony is above the assertive individuality of a composer. As Olivier Messiaen put it, “Plainchant alone possesses all at once the purity, the joy and the lightness necessary for the soul’s flight towards Truth.”10 We shall discuss this issue later in the book. In our present discussion we must venture beyond the therapeutic and purely psychological response to inhabit rather more difficult territories. In so doing we will have to use the term “supernatural.” Unfortunately this is a word that has been justly disparaged on a number of grounds. Biblical scholars have criticised it as failing to convey the concreteness and historical character of the Israelite religious experience; Christian theologians have attacked it as potentially offending the world-affirming doctrine of the incarnation; historians and cultural anthropologists have pointed out that the term suggests a division of reality into a closed system of rationally comprehensible “nature” and a mysterious world somewhere beyond it. Nevertheless the term is in everyday usage denoting a fundamental category of religion, the assertion of a belief in another reality that is of ultimate significance for man and which transcends the reality within which our everyday experience unfolds. Rudolf Otto, in The Idea of the Holy, attempted what may still be regarded as a definitive description of this “otherness” of religious experience. He emphasised that the sacred (that is, the reality man believes he encounters in religious experience) is “wholly other” than ordinary, human phenomena, and in this “otherness” the sacred impresses man as an overwhelming, awesome, and fascinating power. Most of this book will be concerned with a wide-ranging discussion of the nature of that psychical relation which is found in art between the so-called artistic experience (of creator, performer or audience) and the “wholly other”.

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Notes 1. (Oxford 1979), p.85. The book relates several similar experiences by a wide range of interviewees. 2. Philosophy in a New Key (Cambridge USA 1942), pp.240 and 245 respectively. 3. See Hans Jenny, Kymatik (Basel 1967). 4. Martianus, The Marriage of Mercury with Philosophy, tr. W.H.Stahl and R.Johnson with E.L.Burge, as Vol. 2 of Martianus Capella and the Seven Liberal Arts (New York 1977), sect.2., quoted in Joscelyn Godwin, Harmonies of Heaven and Earth (Rochester, Vermont 1995), p.16. 5. Athanasius Kircher, Musurgia Universalis, facsimile of Rome 1650 edn. (Olms 1970), Vol.2 pp.411 ff., quoted in Godwin, op. cit. p.16. 6. See Godwin, p.17 ff. for a detailed historical survey of various bizarre practices. 7. ibid., p.94. 8. G.W. Leibniz, Discourse on Metaphysics, Correspondence with Arnauld, and Monadology, tr. Montgomery (Chicago 1927), pp.135-6. 9. Godwin, op.cit., p.54. 10. Recherches et expériences spirituelle (Paris 1977), p.3.

Chapter One The Transcendental and Rational Discourse As we formulate arguments which show music’s ontological status we must use language, and do so inside a closed speech system, thus laying ourselves open to the scorn of the logical positivists, who would see our predications as no more than nonsense. For talk can often neither be verified nor falsified; its essential axiom, as George Steiner has suggested, is that the root of all talk is talk! In his book Real Presences, Steiner reminds us that one of the messages in Schoenberg’s great opera Moses und Aron is contained in Moses’s cry of abstention, “O Word, thou Word, which I lack”. It is precisely because the golden-tongued Aron can discourse so eloquently on God and on man’s fate that the ensuing symbolic lie of the Golden Calf is presented as a falsehood. To the inarticulate Moses, the stutterer, the only true statement is the music. The meaning of words and the meaning of music are set in opposition. For Steiner, to perform music and respond to it are themselves metaphysical experiences. Furthermore, to ask “what is music” may well be our way of asking “what is man?” But using words and expounding on this is difficult. The mass of critical verbiage about works of art in the form of discursive interpretation (as well as formal analysis) reflects the dominance of the “secondary” and the parasitic over the “primary”, as Steiner has argued. No music criticism or musicology can tell us as much about the meaning of a piece of music as the performance of it, the great bulk of writings on music, in Steiner’s opinion, being “benign illusions of significance.”1 The story about Schumann being questioned as to what was the meaning of a piece he had just played is a happy confirmation of this point - the composer said nothing and simply played the piece again. If we are to discourse with any confidence we should at least have an overview of previous writings, so the remainder of this chapter will seek to provide a historical survey of the vast literature of rational discourse which should give us a selective frame for our own

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speculations later. In Harmonies of Heaven and Earth,2 Joscelyn Godwin attempts to categorise the main levels of artistic endeavour. He describes the highest level as the “avataric” level, which is like that of a divine manifestation in the minds of those who respond to it. The avataric creator is an inspiration for followers to re-interpret and imitate according to the model. “For instance, the painting of Jesus and his mother originally attributed to St. Luke became the model for every subsequent ‘Virgin and Child.’ ”3 Among composers are those central to various traditions, most notably for our purposes figures like St. Gregory the Great, to whom all of Gregorian chant was at one time attributed, or Pérotin of Notre Dame, often said to be the creator of the first polyphony in four parts. Gregory’s contribution became iconic for others, notably for those monks who composed “Gregorian” chants to re-create after the revealed pattern. This is inspiration of the “second level”. Godwin explains that in Antiquity and Eastern cultures the task of the creative artist at this second level was to work strictly within the traditional forms bequeathed by the avataric masters, who often, as in the case of Orpheus or Sarasvati or the Chinese emperor Fo-Hi were regarded as divine or semi-divine revealers of wisdom. At this level the “maker of songs” was no different from, say, the lute maker. “The arts and the crafts, in short, are synonymous.”4 A third level of inspiration exists, but according to Godwin this is the creativity proceeding from the creator’s own ego, from his subconscious mind. It is regarded as inferior “because it no longer has a connection with Memory” which, at the second level, the copying of canonical works of art or craft supplied.5 Although our artistic heritage during recent centuries is largely the history of this third type of inspiration, we shall see below in the arguments put by F. David Martin how the concept of an avataric master has been perpetuated, not surprisingly, in sacred and other works by J.S.Bach. Godwin continues his descent “through the creative hierarchy without a break to the position of the artist’s audience”,6 who, ideally, should aspire to achieve an awareness of the Intelligible Beauty that is the source of the contemplated object, rather as Plato taught us in the Symposium, (210 d-e). In the traditional crafts this is reached by means of symbols, geometrical patterns, or, in fine art, animal emblems. In the traditional arts, the symbols are also overt but their meanings are often not understood except by the cognoscenti. Godwin goes on:

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It is up to the beholder to follow the symbol as far as his capacity allows, but his effort is sanctified by the fact that the object is true to its source. The only such musical art in the West is plainchant.7

Clearly there is in plainchant an inner continuity with the religious dimension, for its conventional signs over many centuries have come to be widely accepted as avataric and expressing the religious. As an icon its configuration or gestalt is immediately recognisable since it contains an embodied reference to its source which creates feelings of ultimate concern or reverence in the listener. Psychologically this creates the conditions for a greater awareness of a numinous reality. In our reaction to such music, as Rudolf Otto points out, musical feeling is rather (like numinous feeling) something “wholly other”, which, while it affords analogies, and here and there will run parallel to the ordinary emotions of life, cannot be made to coincide with them by a detailed point-to-point correspondence.8

All music that is art (and all other arts) reveal something about higher presences, but certain genres must reveal these more directly because this has been their historical role. This is the case with plainchant or indeed with any religious music. In one sense at least, Bach’s St. Matthew Passion is ontologically different from Beethoven’s Sixth Symphony, because Bach’s masterpiece sets words which directly invoke religious feelings. Plainchant might be compared with Bach’s oratorio in some respects, but has a more direct connection with religious feeling or liturgical activity. In his book Art and the Religious Experience: The Language of the Sacred9 F. David Martin offers one interpretation the different degrees of ontological meaning of widely differing pieces of music, religious and secular, and points out that whatever all musics have in common there are obviously some types of works which have a greater claim to sublimity. Martin’s arguments are striking and idiosyncratic and will be discussed in greater detail in Chapter 4. He examines an early and rather weak composition by Lennon and McCartney, All My Loving, to show that while it may indeed evoke emotion it fails “to inform about these emotions or anything else.” What is lacking here is what Martin describes as “translucent iconicity.”10 In contrast, this is what Gregorian chant and much other religious music has. The “region” revealed by plainchant is symbolic of Being as a preserving agency that enables the past to be immanent in the present, and Martin attempts to show how the past is preserved in a particular way in the

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present. The past is brought into ecstatic unity with the present and, indeed, the future. Underlying this is our sense of history being inextricably bound with our knowledge of time’s passing, which is so central a feature of all metaphysical thought and which is a fundamental structural feature of music. Both life and music are transient, and our oneness in some mysterious sense with God is the proper solution to the problem of the transitoriness of life. It is relevant that by disclosing the main musical archetype of religious feeling the symbolic power of plainchant makes possible the immanence of any past in the present. If we allow all art to aspire towards being an immanent representation of a divine of a force, some would argue that there is a danger in “corrupting” the notion of transcendence. They might argue that a value judgement on individual examples should surely be made, as is already implied in Martin’s reference to Lennon and McCartney. But a contrary argument could also be levelled, namely that we cannot deny a transcendent character to raw, familiar reality in art even if there is no suggestion of ultimate concern or reverence. For, logically we might not be able to disqualify even the most trivial pieces, since they also inevitably employ structures which are common to all instances of that particular art form and therefore are potentially as mysterious and transcendental as more overtly “religious” examples. For an attempt at rationalizing this we turn to Kant. The beauty we find in plainchant, for instance, and the specific connection it has with man’s religious quest would tend to classify it as one of Kant’s adherent beauties. For Kant, such objects as houses, palaces, arsenals, churches, summer-houses, and anything which is functional, in which appreciation of design (involving a pure sense of form) mingles with awareness of the end to be served (the practical), is called adherent.11 Then the two satisfactions, that of our pure sense of form, and that which is practical, can coalesce in a single experience. Kant warns that in this dipolarity there is loss in purity, but with an attendant gain in richness, and he admits a greater importance to those experiences where we are aware at once of the form and the content, the form as a harmonious design, and the content as an apt instrument for some recognised good. Plainchant therefore ingresses into our daily existence as a thoroughly plausible manifestation of an adherent beauty, its liturgical function providing the strong practical function which is also overtly religious. But,

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depending on your approach to what might be revelatory, the same might be true of music very different from plainchant. As we have noted, we need to go back further than the music of the early church if we are to examine the philosophical sources of a revelatory theory of art. Firstly, we need to consider Plato’s Doctrine of Ideas to see if we can apply it to art. In it are contained the distinctions made by Plato between reality and appearance, between universals and particulars, knowledge and opinion. Plato thought that the objects of sensory experience and of scientific knowledge are only imperfectly and derivatively real in so far as they imperfectly approximate to, or are “imitations” of, the “ideas” which are the divine maker’s prototypical “forms” of real things - animals, plants, earth, air, fire and so on. Though there are many beds there is only one “idea” or “form” of a bed. Just as a reflection of a bed in a mirror is only apparent and not real, so the various particular beds are unreal, mere copies of the one real bed made by the divine imager. A philosopher is a man who understands this, who knows of this vision of truth, of the ideal, of the absolute and eternal and immutable. In other words he has knowledge. Merely having a love of “beautiful things” is not real wisdom since this is to do with the particulars, the mere reflections of ideal entities. In any case they are full of contradictions and always partake of opposite characters so that, according to Plato, we cannot have knowledge (which is infallible) about these, only opinions. In the last book of the Republic there is a clear exposition of the doctrine of ideas or forms, which precedes Plato’s condemnation of painters,(for his doctrine of divine enthusiasm had room for poets and musicians but not for artists). The following is a famous quotation (from elsewhere in Plato, the dialogue Ion), where he accords a special status to the poet as a vessel for divine musing: That’s why the god relieves them of their reason, and uses them as his ministers, just as he uses soothsayers and divine prophets – so that we who listen to them may realize that it is not they who say such supremely valuable things as they do ... but that it is the god himself who speaks, and addresses us through them. 12

Similarly, human music is seen as an imitation of the divine melody which can tune the soul to that eternal harmony which it is the musician’s task to bring from heaven to earth. It is the function of

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music to imprint upon the soul the hallmark of its divine origin. The hypothesis here is that there is a cosmic source for music contained in the concept of “the music of the spheres” from which human music is derived. This divine music box is imitated by musicians. And this evidence of an aesthetic element in the cosmos was further refined by the Pythagoreans into a form of primitive psychology by the introduction of the soul in the form of a harmony, or at least a musical attunement based on numerical proportion and illustrated by sweet concords on the strings of the lyre. As the lyre goes out of tune when touched by an unskilled performer, so the harmonious disposition of the soul will be sensitive to mishandling. The mechanics of all this attains a high degree of speculation and may strike us as unpromisingly theoretical in character. (This is cryptically summed up by Iris Murdoch in The Fire and the Sun, where she refers ironically to Plato’s high regard for music – “the fine art preferred by God is music - but inaudible, of course!”13) Clearly for Plato there is an inspired artistic activity which imitates the ultimate reality of the Ideas themselves. The works of painters and sculptors did not belong to this higher activity because they were reproductions, “imitations of imitations”, and twice removed from reality, but those most intangible of expressive phenomena, human song or chords (which at that time were deemed sweetly plucked concords on the lyre), seemed to form a bridge between the visible and the invisible. And ever since, man has explained the mystical qualities of song by reference to this Platonic justification. This profound implication of the transcendental ulteriority of music needs to be considered in relation to metaphysical concerns by Plato which have been central to Western philosophy since his time. For instance, one fundamental question which has been asked many times over the centuries is whether the Form of the Good (to use a Platonic/Aristotelian gloss on the Deity) is overwhelmingly the universal object of desire, that which draws all souls towards itself. For Plato, the chief good of man is the contemplation of this absolute Good, and once one experiences this vision then one will not willingly busy oneself with worldly matters, but will apply oneself to the study of eternal verities. Music-lovers may not fathom how or why God as self-sufficient and “wholly other” can be included in any metaphysical discussion of music. The answer lies in the conception of God as immanent. While the idea of a self-sufficient God is clearly

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expounded by Plato we should also remember his presentation of the opposite conception, one of God as manifestly of this world too, and therefore inextricably bound to what we value in life and nature. Thus, having formulated the doctrine of a transcendental God, Plato develops a metaphysical notion of an immanent God, to the extent that a logical ground for the existence of this world is deduced. Faced with the nonsense of a world full of things which are supererogatory additions to the Eternal, we can therefore accept that mundane artefacts and utilities can indeed derive from the Idea of the Good. God as transcendental or God as immanent? is the question posed. Scholars have suggested that it seems to have caused confusion even for a thinker of Aristotle’s stature. In the Endemian Ethics Aristotle contradicts Plato by asserting that One who is self-sufficient can surely have no need of the service of others, nor of their affection, nor of social life, since He is capable of living alone and He cannot have need of friends. Plato had already struggled with the contradiction which arises from the idea of an immanent God in Republic 509b, where even bad things are derived logically from the eternal source. For our purposes the main question which this raises is the nature of the relationship between the transcendental and the immanent. Why does God as Being manifest himself also as a God of Becoming, and what is the nature of this process? A satisfactory answer to this question will present us with an imaginative means of evaluating worldly things including art. In particular, we are bound to become more aware of the significance of works of art, and of music in particular, for it is precisely in this area that the artist presses most persuasively his claim to be “another god” (to use a Renaissance commonplace). The question posed has been of perennial fascination ever since Plato’s time, and we cannot overestimate its influence on Western thought. Yet, in Timaeus 33d Plato argues that it is better for the world to be self-sufficient. Thus we may logically ask why should mundane entities exist, or have to exist at all? What possible purpose have they for a God whose perfection is already realised and who surely cannot be enhanced by anything else? But Plato assumes paradoxically that the absolute Perfection cannot be fully perfect if it is in supreme isolation. He asks, is it then less perfect if existing alone? Thus was instituted the notion of a God immanent in the world, a fecundity who

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brought temporal and material things into existence in a richly pluralistic and variegated universe. If the temporal and the material exist, and if time and multiplicity are so fundamental to our existence, perhaps we can deduce that they have to be attributes of a God even if he be separate from us, out of time and wholly unitary. The answer may lie in the saying, Omne bonum est diffusivum sui (everything should be as far as possible like Himself). This is how the Middle Ages saw it, and this concept of two Gods in one has underpinned a great deal of philosophical conflict over the centuries. The notion of the immanent God had logically spawned a divine craftsman, the demiurge who filled the world with all kinds of creatures and things. For confirmation that a connection exists between the Ideal world and ours it is logically necessary therefore for all eternal essences to have temporal counterparts (see Plato’s Timaeus 39e, 42e, 51a and 92c). Thus comes into existence the principle of plenitude. History has learned from Plato’s famous simile of the Cave in the RepublicVII that the sensible world is seen as an idle flickering of insubstantial shadow-shapes, at two removes from God. This allegory of human enlightenment tells of those who are destitute of philosophy likened to naïve prisoners in a cave, who have a fire behind them and a wall in front. All that they see are shadows of themselves and of objects behind them cast on the wall by the light of the fire. Inevitably they regard these shadows as real, as the “whole truth”, for they have no notion of the objects to which they are due. This story illustrates the difference between the sensory faculties and the intellectual, together with the corresponding difference between their proper objects. If we can accept that not all the cognitions we have are of sense-transmitted objects, this will allow us to suppose that some things can never be seen and touched, yet may still exist. Thus, having no real stability our thoughts are not the direct basis for any knowledge of real things. Plato teaches us that at least they can be subdivided into belief and conjecture. Conjecture is simply our awareness of false visible things, mirror reflections and so on. No doubt the objects and even the shadows do have some reality, but this reality is incomplete and raises paradoxes. Here is where the intellect must step in to make a distinction and give us the stability for which we seek through the lower of its two subdivisions, namely hypothesis, which is the reasoning from set assumptions. But this method also

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falls short of the whole truth. Plato formulates an all-embracing truth by tracing all hypotheses and beliefs and conjectures to a final unity, a single idea in which all the partial existences and arbitrarily grounded fragments of truth could take their places and thereby show all their interrelations one with another. Words by Dante spring to mind, those describing his own ultimate vision of God “wherein I saw the scattered leaves of the universe in one volume composed.” We must now ask what this has to do with the arts and music. In searching for an answer we recall that it is the experience of many persons that great art allows us a glimpse of our world without our “selves” superimposed onto it. This is explored by Iris Murdoch in The Sovereignty of Good where she discusses the power of art that is not mediocre as directing the “attention ... outward, away from self.”14 As a result, what is truly beautiful is inaccessible and separate from us, and from life and nature and the temporal process. As an aspect of the Good, art is separate from say justice, morals and other virtues because of its extra dimension and its ability to encapsulate (in Murdoch’s disconcerting simile) an “absolute pointlessness”. But according to Murdoch, the pointlessness of art is not the pointlessness of a game; it is the pointlessness of human life itself, and form in art is properly the simulation of the self-contained aimlessness of the universe. Good art reveals what we are usually too selfish and too timid to recognize, the minute and absolutely random detail of the world, and reveals it together with a sense of unity and form.15 Dante’s words consolidate the essential mystery of the “pointless” affirmation in a tangible, earthly form of the higher Good. It is a metaphysical paradigm which was widely held in the Greek world. Following on from this we learn from Plotinus that the arts are not to be slighted on the ground that they create by imitation of natural objects. From Plotinus we recognise that the arts give us bare reproduction of the things seen but go beyond to the Ideas from which nature itself derives. They make good where nature is defective, having the vision of beauty in themselves. So the cause of painters and sculptors is happily retrieved. More importantly there is a justification here of the thesis which forms the central concern of this present book, which is the belief that the work of art, and here specifically music, reveals something of which the natural world is an imperfect image or symbol, and can reveal it more luminously if not more truly than inartistic nature.

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The writings of Plotinus reflect a more exclusive and wholehearted mysticism than is to be found in Plato. In his fifty-four essays, or Tractates, which were later arranged in six Enneads, Plotinus outlines a sometimes very obscure and idiosyncratic philosophy. Behind the visible world as its ultimate source and ground is what Plotinus calls the One, which is ultimate reality in its “first hypostasis” and which is beyond all conception and knowledge. This is variously described as the Good, or the Infinite. Different functions of the One are known as its second and third hypostasis, the second hypostasis being Intellect or Mind, the Divine Knower (nous), the Platonic Forms (or ideas), thus the archetypes and prototypical patterns of the visible world. The third hypostasis is the All-Soul (psyche), or principle of creativity and life. These three hypostases make up a single transcendent Being, from which all reality proceeds by emanation. Plotinus tries to overcome the Platonic dualism of Being and Becoming by connecting what belongs respectively to greater and lesser reality. As Monroe C. Beardsley points out in Aesthetics from Classical Greece to the Present, Plotinus’s metaphors of Being overflow, like a spring, and of a central source of light that grows dimmer with the distance from it we may think of the various parts of reality, including nature and the visible world, as participating in the light of Being and Becoming in one sense overcome by this conception of all things as ordered in a continuous degree of greater and lesser reality, but the contrast between the Visible and the Intelligible World remains in the distinction between nature and the Forms of the Second Hypostasis.16

For Plotinus the beauty of the visible world is its mirroring of the invisible and art can reveal an “Authentic Beauty” or “Beyond Beauty” (even though, paradoxically, to achieve “Absolute Beauty” is not to see it!) His observations on music, although cryptic and fantasy-laden, are fascinating in their assertion of important verities: Any skill which, beginning with the observation of the symmetry of living things, grows to the symmetry of all life, will be a portion of the Power There which observes and meditates the symmetry reigning among all beings in the Intellectual Cosmos. Thus all music - since its thought is upon melody and rhythm - must be the earthly representation of the music there is in the rhythm of the Ideal Realm.17

It is in the spontaneity of artistic expression that we see reflected the important concept of emanation, a difficult idea (for our purposes

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identical perhaps with “immanence”) in which Plato’s thoughts became crystallised in the work of Plotinus and others. In Plato’s Republic VI.508 the term aporroia was introduced and this came to play a central role in the cosmology of Neoplatonism. It was applied originally to the emission of light and heat by the sun. Later it was adapted, in particular by Plotinus, to describe the derivation of the many from the One. It found its way into Christian theology through the work of Pseudo-Dionysius the Areopagite and his Western translator and interpreter, John Scotus Eriugena, and a number of other thinkers. Dionysius the Areopagite, and much later John Scotus Eriugena, appropriated the concern of Neoplatonism to make the existence of the world intelligible by relating it to the being of the One from whom it took its origin. They sought to revise the Christian understanding of creation in the light of this. Aquinas pursued their endeavour with greater circumspection but with clear acknowledgement of the source of their inspiration. He introduces the topic of creation by referring to “the procession” of the creatures from God.18 He writes of “a prolongation, as it were, into the lives of men of the … processiones, within the Blessed Trinity.” Furthermore, “the coming forth of a divine Person comes before and is more perfect than that of the creature, for a divine Person issues as the full likeness of its principle whereas the creature is but a partial likeness.”19 As Keith Ward explains: If Thomas means to say that the same act by which God understands the divine self, by which God is, is the act by which God wills the world, then this world is in all its detail, part of God’s being what it is. If this world is contingent, then God must be contingent in some respect.20

The most serious objection to the concept of emanation from the viewpoint of Christian orthodoxy is that in its original usage it implies a continuity of being, or nature, between the original source and that which emanates from it, such as to obliterate or weaken the radical distinction between the Creator and the creature, which is held to be basic to Biblical faith. Emanation comes close to the concept of generation; in fact, the original model of emanation, namely the derivation of light from a luminary, was frequently used even in Christological debates of the early church as an illustration of the generation of the Son (meaning that it is the same “in being” as the

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source), and it eventually found its way into the Nicene Creed in the phrase “light from light”. But that was specifically in relation to the Son. The point was that that which is derived from God by generation is indistinguishable or inseparable from its source. In contrast, that which is created is of another substance or being. The process of emanation in the Neoplatonic world scheme does not result in an identity of being between the emanant and its source, but in a diminution, or dilution, which progresses as the emanent moves further from its source, until it reaches the nadir of nothingness. One who named the rungs of an ascending progressive ladder was St.Augustine and he listed the hierarchic chain as follows: bodily animation, sense, art, virtue, tranquillity, the entrance, observation. Elsewhere this progression takes the form: “of the body, through the body, about the body, toward the soul, in the soul, toward God, with God.”21 The Christian doctrine of creation is often imbued with a paradox which nicely balances the pantheistic absorption of things into divinity by the recognition of God’s likeness everywhere, and the theory of God’s sublime aloofness and distinction from finite things. The transcendental and the immanent are played off ambiguously against each other. Clearly, if things are like him then they must be beautiful, but in a strictly limited degree. Hence while things may aspire to becoming the One, they must resign themselves to becoming mere “harmonies” of the One. Therefore, if God has communicated a likeness of his own beauty then there may be degrees of likeness to God resulting in a hierarchy of beauty. Working this out in a modern context is demanding to say the least, and fraught with a hazard previously mentioned, namely that of asserting as truth what has been conditioned by one’s own (often unreliable) psychological motivation and agenda. St. Augustine also wrote about imitations of God’s beauty. In many places in the De Ordine and Soliloquia St. Augustine addressed God as he in, by, and through whom all good and beautiful things have their qualities. We note this because, among the early fathers, St. Augustine was the one most concerned with aesthetic matters, although he seems to have had a divided mind about the importance of beauty, for he clearly felt that earthly beauty may prove to be a trap. In one place he deplores the satisfaction in musical harmony “for the sake of vulgar pleasure.”22 (Knowing exactly what he means is of course impossible for us in our ignorance of what sort of sounds he

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refers to). He sees a danger in men being too enamoured of transitory earthly satisfactions. In particular, physical beauty is regarded as the lowest grade of beauty and not comparable to beauty of soul. For a classical development of the Augustinian view we go to St. Thomas Aquinas who, in a famous passage in the Summa Theologiae23 formulated the three conditions that are required in order to ascribe beauty to anything: integrity or completeness (integritas sive perfectio), right proportion or consonance (debita proportio sive consonantia), and radiance (claritas). Aquinas’ formulation was essentially a theological one since he associates beauty with the Son: wholeness, because he truly possesses the nature of the perfect Father; consonance, because he is the Word; and radiance, because he is the Word, the radiant light of understanding. This applies to both natural and artistic beauty and Aquinas generally insists that all three conditions are required. But clearly there are many instances where only one or two are applicable. A verdant meadow in spring may not be fully beautiful. It may have radiance and perhaps a sense of completeness but lack harmony (although that would not be needed for us to perceive its beauty). In art criticism we may judiciously accept Aquinas’ trio of conditions and, if so, this would serve to justify an assertion from a much later period, namely Hegel’s claim that the beauty of art is higher than that of nature. But here we come up against essential differences between one art and another. Perhaps Aquinas’ analysis may be more appropriate to the visual arts or to things in which form is a fundamental consideration. This would certainly reflect the general tone of much ancient and medieval aesthetics. In Aquinas’ opinion, although a creature or some aspect of nature or a work of art may represent and resemble God to the extent that it has some perfection, it clearly does not represent him as it might something else in the same species or genus. Aquinas accepts the impossibility of any straightforward comparison of earthly things with God. Like some other theologians he claims that God’s nature is simple, for he is not composed of matter and form, and his essence and existence are the same. This leads him to predict that the perfections which pre-exist in God in a unified and simple way are represented differently in creatures and things and in a diverse and manifold way.24 He was able thus to speak of creation’s likeness to God without treating him as one being alongside others and without

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losing sight of the religious requirement that the object of worship far surpasses any other reality. If “beautiful” and “beauty” are attributed to God and to things or creatures in different ways, then God gives beauty to things or creatures according to their proper nature. In other words, the process is analogical. Each kind of thing is good or beautiful in its own way. Therefore, instead of looking for a nature or form that, in its beauty, is common to diverse beings, we should rather look at the context and admit that there is no single and unique referent. To borrow an idea from Wittgenstein, things may have a “family resemblance” and a network of similarities rather than a common definition. Later Thomists coined the phrase Analogy of Proper Proportionality to describe the word frames which can help to clarify analogous resemblances. The analogy is founded on, The ontological (transcendental) relation in which each being stands to every other being in virtue of the very act of existence whereby all that is exists. Beings are analogical in be-ing. That is to say every being exercises the act of existence in proportion to its essence. The analogy of proper proportionality alone accounts for the diversity of beings and their unity in being 25

The notion is similarly expressed by Maritain when he says: Like the one, the true and the good, the beautiful is being itself considered from a certain aspect; it is a property of being ... Thus everything is beautiful, just as everything is good, at least in a certain relation. And as being is everywhere present and everywhere varied the beautiful likewise is diffused everywhere and is everywhere varied.26

That all three conditions in Aquinas’ trio need not be met is surely feasible. For instance, doesn’t the integrity of many works of literature and music, especially in the Romantic period, eschew formal beauty, as is often suggested? Perhaps, or perhaps not. If chaos and shapelessness are absent, and in art that is almost always the case, then surely some formal coherence (beauty) is present. We are only too aware of the overriding importance of meaning and feeling in a Mahler symphony, and Aquinas’ trio of conditions may seem weak and limited in this, as in many another, romantic context. Also, we may not expect a modern work to have radiance; in fact, we are only too aware that there is that phenomenon for which Yeats’s phrase “terrible beauty” is well suited. But underlying this, of course is the possibility that here too, paradoxically, there is a “radiance.” And this

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is by no means a twentieth-century experience, for there is profundity and emotion to be found in those great works of art to which the term “beautiful” seems inappropriate. Beethoven’s Grosse Fuge, Shakespeare’s King Lear, and Grünewald’s Crucifixion are all far removed from our time, and clearly we need either to extend our concept of beauty in our discussion of them or to bring in different concepts which should have the same status as beauty. In so doing we are essentially concerned with artistic truth, and a connection seems essential with those other affective and moving qualities of art, with art’s ability to stir our feelings and imagination and its capacity to enlarge our emotional range. We may distinguish different media, too, looking perhaps for imagination and moral insight in literature, emotion in music, and so on. Some arts reflect the world of nature whilst others look more to the inner world, corresponding perhaps to the different realms of spiritual experience. To leap many centuries we note that it was Leibniz (more than any other modern philosopher) who echoed Aquinas in taking seriously the idea of a creation with God as author and man profiting therefrom. He wrote: In God is found not only the source of existence, but also that of essences, insofar as they are real. In other words, He is the ground of what is real in the possible. For the Understanding of God is the region of the eternal truths and of the ideas on which they depend; and without Him there would be nothing real in the possibilities of things, and not only would there be nothing in existence, but nothing would even be possible.27

Since God is omniscient Leibniz’s concept of the “substance” is not in any way approximate but is complete in every detail and with regard to every one of its properties. Every possible substance, not only the ones proceeding to a finite form in this world, is represented in the mind of God by what Leibniz calls its complete individual notion. And every unfolding of a substance's “programme” has an inexorable inevitability. In view of its specifications every substance contains a law of the continuation of the series of its own operations, but complete knowledge of a substance is known only to God, not to us. One of the key ideas of Leibniz's ways of establishing the existence of God is his assertion that possibles could not exist without the existence of a Being who could produce the possible.28 This is no novel idea, deriving as it does from Aquinas’s fifth proof for the

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existence of God, whereby things are seen to achieve their end by design rather than fortuitously. It follows that whatever lacks knowledge cannot achieve its end without direction from some intelligent Being, which we call God. Nineteenth-century thinkers were well aware of the different modes inhabited by the different art forms. For our purposes we shall concentrate on one eminent nineteenth-century figure who draws these strands together. In so doing we can move from a general view of metaphysics to a more specific consideration of the ontological power of music. Arthur Schopenhauer’s philosophy, more than any other’s, holds a strange fascination for musicians, in particular his assertion that there are strict limits on the reach of the intellect and that the abstraction of reason, even when useful, cannot possibly be taken as an indication of the nature of reality. Schopenhauer published his major work, Die Welt als Wille und Vorstellung (The World as Will and Representation) at the age of 30. It is a survey of the whole of human activity and knowledge in the light of a philosophical attitude that saw the universe, in all its variety and richness, as something to be transcended. Unlike many philosophers, and in direct opposition to those for whom philosophy is a purely verbal, conceptual activity, Schopenhauer’s work is rooted both in the burgeoning romanticism of his time and in his personal experiences. This existential activity identified him more with creative artists than with philosophers. Although immensely erudite, he was never an academic in the professional sense, and this was summed up in his student days when he became disillusioned with his teachers Fichte (in particular) and Schleiermacher. He is often assumed to be a deeply pessimistic writer. A perpetual conflict certainly existed in him between feeling and reason, between the subjective and the objective, inevitably perhaps because of his emphasis on the Will and determinism. The main elements of his philosophy were formulated by intuition early in life. For Schopenhauer the universe is a cosmic illusion brought about by what he called the Will (the fundamental reality underlying all knowledge and reason).29 This manifestation, the “thing-in-itself ”, inhabits one’s consciousness and expresses itself in archetypal ideas. One can be released from bondage to the Will and its productions only if it can be extinguished from consciousness. This has been falsely interpreted by many as extinction in nothingness.

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Furthermore, Schopenhauer’s universe is hierarchic ranging from the pure Will down to its most unconscious productions. We all have the potential to know its inner workings, and it is “art, the work of genius”30 in particular, which gives the closest idea of what the Will itself is like. Artistic endeavours have the Platonic Ideas as their models, and these Ideas are the very essence of the world. This aesthetic attitude infuses Schopenhauer’s philosophy, and, despite Schopenhauer’s very limited knowledge of it, music is elevated above all the arts. The other arts represent it at second or third hand - for they only depict its “productions.” That so many of his closest philosophical predecessors had failed to say much about art and its relation to a higher existence troubled Schopenhauer, who could really only look to Plato and Kant for any truly significant contribution, and Plato’s work, in Schopenhauer’s view, was tainted by his hostility towards art. (This came about, as we have seen, because of Plato’s view that works of art are mere imitations of things and events in the phenomenal world). Schopenhauer formulated a doctrine which categorised the Will’s self-objectification in the world of phenomena into four categories: inorganic matter, plant life, animal life and human life, with a progression in terms of value and significance from lower to higher.31 Schopenhauer saw the different arts connected to the appropriate category. The medium most appropriate for the communication of a perception of the beautiful differs according to the grade of the Will’s objectification to which the object seen as being beautiful belongs.32 For instance, the art most appropriate for communicating insights in inorganic matter or inanimate nature is architecture. When such things as flowers and trees are seen as beautiful, this is usually conveyed by painting and, indirectly, by verbal description. In animal life the physical presence of animate objects, their solidity and mass, make them more clearly expressed in the three dimensional form of sculpture. In the highest category, that of humans, language comes into its own. In particular, the power of drama is inexorable, combining as it does the dramatic unfolding of events in time simultaneously with the articulation of inner thoughts. The verbal arts stand almost supreme in the artistic hierarchy corresponding to the grades of the Will’s objectification. But the highest of all the arts is music, which is regarded by Schopenhauer as having a special quality. Presumably, for

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Schopenhauer, this quality makes music essentially different in kind from the other arts.33 Unlike the other arts it does not find its subject matter in perceptions of anything in the world of phenomena. All works of art that are not music, says Schopenhauer, either represent objects or events in the phenomenal world or are decorative or have a practical use. The very fact of music’s separation from the phenomenal world has led some people to regard it as other-wordly, a view endorsed by Schopenhauer. According to him, all the arts except music communicate knowledge of something which is intermediate between the noumenon [the “thing-in-itself”] and phenomena, namely Platonic Ideas.34

Music by-passes the Platonic Ideas, and unlike the other arts speaks of the noumenon directly. And since the noumenon is an indivisible and undifferentiable whole then music is a direct articulation of it and a manifestation of the whole of it. It is therefore an alternative to the Ideas. So profound is this power that music provides a symbolic alternative to the world. And not so symbolic either, for it succeeds concretely in doing what philosophers do in abstraction. It is the most direct representation of the Will, indeed it is the Will made audible, a non-conceptual representation of an inner life. Philosophy itself is no more than a translation into conceptual terms of what music expresses, giving some rationale to what, in music, we sense purely intuitively. For Schopenhauer music seems to be the romantic reincarnation of the ancient notion of universal harmony. He describes it as, in the highest degree a universal language, which is related indeed to the universality of concepts, much as these are related to the particular things. Yet its universality is by no means that empty universality of abstraction, but of a quite different kind; it is united with thorough and unmistakable distinctness. In this respect it is like geometrical figures and numbers, which are the universal forms of all possible objects of experience and are a priori applicable to them all, and yet are not abstract but perceptible and thoroughly definite.35

He goes on: We could just as well call the world embodied music as embodied will; this is the reason why music makes every picture, indeed, every scene from real life and from the world, at once appear in enhanced significance, and this, of

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course, all the greater, the more analogous its melody is to the inner spirit of the given phenomenon.36

Thus one can say that Schopenhauer’s view of music contains within it a “revelation” theory of the meaning of music. Music’s self-evident capacity to parallel, or speak for a transcendental reality presupposes that the revelation is somehow not expressible, since this lies outside or beyond rational discourse. Schopenhauer acknowledged this as follows: I recognise ... that it is essentially impossible to demonstrate this explanation, for it assumes and establishes a relation of music as a representation to that which of its essence can never be representation, and claims to regard music as the copy of an original that can itself never be directly represented.37

Because he was unable to adequately support his assertion of music’s special powers it is not surprising that Schopenhauer failed to develop his arguments in the form of convincing ideas in a body of propositions. It is true that he exhorts his readers “to listen often to music with constant reflection on this [theory].”38 But no more. All he does is tell us that music is a copy of the Will itself. Sadly, the innumerable correspondences that he draws between music and the phenomenal world lack conviction because of the gap that exists between the world as a representation (as phenomenal) and as Will (an impersonal and undifferentiated energy that is the direct manifestation of the noumenal). He wants to have it both ways, it seems. The dilemma he is in is that he wishes to assert that musical revelation is ineffable and yet he wants to philosophise about it. But the two disciplines are different: as we know, philosophy is essentially conceptual, while art is both conceptual and perceptual. Schopenhauer’s dilemma was understood, at least in part, much later by more than one Process philosopher. For instance, Susanne Langer, in Philosophy in a New Key, acknowledged that the essentially abstract and ambivalent nature of music gives it a capacity to express the life of feelings in general.39 Following from her argument that “music can reveal the nature of feelings with a detail and truth that language cannot approach”,40 she pulls back from claims, such as those found in Schopenhauer, that feelings have a further reference, namely to a noumenal reality. In so doing she avoids stepping beyond what is consistent with her theory of art,

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which, unlike Schopenhauer’s, eschews metaphysical assumptions in favour of advocating no more than music’s presentational symbolism as a paradigm of a function shared by all the arts. As a pupil of Whitehead Langer would have been aware of the importance of perception not least since there was an assumption that Whitehead (at least partly following Leibniz, Schopenhauer, Bergson and others) was a panpsychist. This is despite the fact that he never seems to have employed the term “panpsychism” in relation to himself. Although he regarded himself as a realist Whitehead often seems to be in support of panpsychism and accepted that in the quantum nature of energy there was at least an elementary life consisting of creativity, aim and (to use his own striking term) “enjoyment”, however rudimentary. Since Whitehead regarded the fundamental units of existence as in some way experiential then he can undoubtedly be described as an exponent of panpsychism. But before we attempt to see whether Whitehead’s teaching renders the world more comprehensible on the assumption that every object is imbued with a soul or mind it will be fruitful to view the matter from a different direction. In the next chapter we shall appraise the work of Victor Zuckerkandl who in his Sound and Symbol 41 attempted to reverse the traditional relationship between music and philosophy, not by exploring music through recourse to aesthetic theory (such as we may see in Schopenhauer and, more obliquely in Whitehead or some other Process philosopher) but rather through deriving an aesthetic, indeed an entire metaphysical stance, from a detailed examination of music itself. Notes 1. Real Presences (London 1989), p.23. 2.

See pp.81ff.

3. ibid., p.86. 4. ibid. 5. ibid., p87. 6. ibid. 7. ibid.

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8. The Idea of the Holy, tr. John W.Harvey (London 1928), p.50. 9. (Lewisburg 1972). 10. See Martin’s reference, ibid., p.134. 11. See Immanuel Kant, Critique of the Power of Judgement, “Analytic of the Beautiful”, ed. Paul Guyer, tr. Paul Guyer and Eric Matthews (Cambridge 2000),pp.114-116. 12. Ion 534c-d. tr. Trevor J. Saunders Early Socratic Dialogues (London 1987), p.55. 13. Iris Murdoch, The Fire and the Sun: Why Plato Banished the Artists (Oxford 1977), p.56 14. (London 1970), p.66. 15. ibid, p.86. 16. Monroe C. Beardsley, Aesthetics from Classical Greece to the Present (Alabama 1966), p.79. 17. Plotinus, The Enneads, tr.Stephen MacKenna, rev. by B.S.Page (London 1956), V, ix,11; p.441. 18. St. Thomas Aquinas, Summa Theologiae, tr. Thomas Gilby (London 1963), Vol.1,1a.1,p.89. 19. ibid., Vol. V111,1a.45.6,p.51. 20. Keith Ward, Religion and Creation (Oxford 1996), p.232. 21. See the analysis by Katharine Gilbert and Helmut Kuhn, A History of Esthetics (Bloomington 1954), p.146. 22. See Augustine The City of God, ed. and tr. R. W.Dyson (Cambridge1998) Bk.XVII, Ch.XIV, p. 802. 23. St. Thomas Aquinas, Summa Theologiae, tr. T.C.O’Brien (London 1976), Vol.7,1a, 39, p.133. 24. ibid., Vol 3,1a, 13.2, p.55. 25. G.B.Phelan, St. Thomas and Analogy (Milwaukee 1943), p.39. 26. J.Maritain, Art and Scholasticism, tr. J.W.Evans (New York 1962), p.30.

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27. See Nicholas Rescher’s translation in The Philosophy of Leibniz (New Jersey 1967),p.14. 28. See C.I.Gerhardts, Die philosophischen Schriften von G.W.Leibniz (Berlin 187590), III, p.572 as cited by Rescher in The Philosophy of Leibniz. 29. Bryan Magee offers a lucid definition of the problematic term “Will” in his The Philosophy of Schopenhauer, revised edn., (Oxford 1997), pp.124-5. 30. Arthur Schopenhauer, The World as Will and Representation tr. E.F.J.Payne, (New York 1969),Vol.1, p.184. 31. ibid., Chapters 23 and 24. 32. Magee, op.cit., p.176.

33. Schopenhauer, op.cit., Vol.1, p.256.

34. See Magee, op.cit., p.182. 35. Schopenhauer, op. cit., Vol 1, p.262. 36. ibid., p.262-3. 37. ibid., Vol. 1, p.257. 38. ibid. 39. (Cambridge USA 1957), pp.243 and 246-57. 40. ibid., p.235. 41. Victor Zuckerkandl, Sound and Symbol (London 1956), pp.363-4.

Chapter Two Music as Sublime Organism Some of the issues raised so far are common to all the arts. Now we should enquire as to what is music’s province and what makes it unique. To start, there are some elementary facts. Among the various sensory experiences we possess, musical experience is the only one that belongs predominantly to our own lives. Light and colour, sound, smell, taste, solids, fluids, gases, the heat and the cold, are all to be found in nature outside ourselves. The whistle of the wind is also found in nature and outside ourselves but could be described as a musical experience only by some exaggeration. Generally speaking music has a decisive border, its transcendence not being found elsewhere in nature. Musical sound is set apart, and its traditional connection with the soul and with feelings has divorced it from the intellect, at least as far as its essence is concerned. Its outward, technical manifestation absorbs the theorists, provided the ultimate question is not posed - how is music possible? This is more profound even than it looks, for in it is hidden a deeper question, namely what is the nature of this world if it contains this extraordinary phenomenon called “music”, which admittedly is a term open to various definitions? Traditionally philosophy has not been enthusiastic to find an answer, since its energies have been focused in different areas. Truth, Virtue and Beauty, the three subjects of Logic /Epistemology, Ethics and Aesthetics respectively will not suffice to explain the essence of music, even when all three can be made to cohere in an interdisciplinary way. By itself, the aesthetic response falls short because it tends to confine itself to judgements of taste, aesthetic value and theories of beauty. These are not the categories that concern us here, except insofar as they relate to a metaphysical source (i.e as outside sound per se). We start with melody, or at least the individual notes that might make up a melody. Here is our first mystery - what is it that differentiates a nondescript musical phrase (albeit that is put together

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so as to have a logical structure) from a truly great melody such as we might find in any mature work by Mozart or Schubert? Whatever may be the answer, it is clearly not as intelligible as a similar one in, say, language. If I change “the cat is on the mat” to “the mat is on the cat”, the difference between the two statements is manifestly obvious. The difference in sound is perceptible to anyone, while the difference in meaning is perceptible only to someone who understands English. Similarly, if the opening theme of Schubert's Unfinished Symphony has one note changed in it, then this too is immediately noticed by all, perhaps even by a tone-deaf person. But what is it that actually changes in the melody when its notes are changed? In the comparable case in language we can give a sensible explanation. In the case of music we find ourselves unable to account for it, while appreciating the grammatical change that has taken place. The analogy between language and music is a fruitful one and will be explored later in some detail. We may succeed in explaining Schubert's inspired choice of notes by a technical discussion. This might clarify what is required to achieve competence in melody writing. But whether Schubert's melodic genius can be rationalised thus is doubtful. In any case we are at present less concerned with melodic genius than with the underlying forces at work in melodies good and bad. In all melody we notice common forces at work, comparable to that exerted between magnetic needle and magnetic pole. Every musical note belongs to a field of musical gravity, is drawn in a particular direction, and nowhere is this more clearly seen than in the Schubert piece referred to. A cogent discussion of this and other musical issues appears in the writings of Victor Zuckerkandl.1 In Sound and Symbol the author defines the proper musical quality of the notes as a “dynamic quality” that permits notes to become conveyors of meaning. The notes by themselves as vibrating strings or vibrations of air are objective phenomena, essentially without dynamic quality, and therefore phenomena of the external world easily measured by scientific means, indeed translatable to the visual dimension by means of an oscilloscope. Other properties, such as pitch, intensity, colour or volume can also be measured. But these are only physical manifestations. Clearly there is something in the notes of a melody to which nothing in the context of the physical world corresponds. This is the important feature, that which we recognise as having artistic

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value. But it is invisible, intangible, and does not fit into the general context of the physical world. Here lies the dilemma - we hear dynamic forces at play in a melody, their existence is beyond doubt, but even though they are perceived via the physical world they are not, according to Zuckerkandl, a part of the physical world. In another important book, Psychological Studies,2 Theodor Lipps made a connection between the dynamic qualities of notes and physical processes, and his “theory of pulses” has been advocated by Zuckerkandl and others as a rationale for deriving tonal dynamism from the numerical ratios of the harmonic series. Any note, as produced on any instrument, is accompanied almost imperceptibly by a varying number of simultaneously sounding attendant notes called harmonics, overtones or upper partials. Thus the note C may be accompanied by the C next above, the G above that, the C above that, the E above that, and so on, the intervals between the notes getting smaller as the series ascends. The first seven harmonics of C give a chord which in the harmonic system is the dominant seventh of the key of F major, a sound therefore that historically demands resolution to a new fundamental, F. There is a story told about the musicologist Donald Tovey's inclination to hear strong unison Cs as self-evidently “in” F major, because of the gravitating pull exerted by the almost imperceptible overtone B flat, the seventh harmonic of C. In turn, the ensuing F would hold its own seventh, E flat, as a subversive force pulling it towards the key of B flat, and so on down a spiral of ever lower fifths and increasing flats into a hellish realm of double flats. This may account for the evil associations of the seventh as expounded by writers like Louis-Claude de Saint-Martin (1743-1803). He was essentially a theosophist who examined the duality inherent in musical intervals by a fanciful analogy with macrocosmic entities, where the perfection of God is represented by the pure octave, but the disturbance effected by the seventh became the source of all evil.3 In such areas of poetic speculation such as this it is not difficult to find contradictory viewpoints, one of which aimed to deter Goethe from rejecting the flat seventh because of its supposed failure to fit in with the laws of harmony. Bettina Brentano Von Arnim (1785-1859) wrote to him castigating him for his misunderstanding of the crucial role of the seventh as a harmonic catalyst: The flat seventh does not harmonize certainly, and is without sensible basis; it is the divine leader, - the Mediator between sensual and heavenly Nature; it

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Music as Sublime Organism has assumed flesh and bone, to free the spirit to tone, and if it were not, all tones would remain in limbo ... the flat seventh by its resolution leads, which pray to it for delivery, in a thousand different ways, to their source - divine spirit.4

To return to plain facts, and providing that we have here a tempered scale, we can go down in a cyclic pattern through all twelve keys and then arrive back at the starting point. Thus the whole cycle can be regarded as represented in potential by the sounding of one note. The scale system illustrates a different aspect, and the more obvious one of the dynamic relations between notes. A note's stability as part of a group is dependent on its relationship to the chosen tonic, at least in classical music. In particular, the striving upwards of the leading note B to C represents a powerful assertion of this dynamic principle. In addition one can also describe musical notes in mathematical terms. Taking the seven diatonic notes in a major scale we notice that, in terms of intervals, purity of sound is related to the simplicity of the ratios of the frequencies of the notes that constitute those intervals. The interval of the fifth has the ratio 3:2, and its inversion, the fourth, 4:3; the major third 5:4, and its inversion, the minor sixth 5:3, and so on. But nothing in the physical phenomenon of a note corresponds to its musical quality, and therefore Lipps began an inquiry into the exact mathematical order of the relation between notes. He sought to discover whether such an analysis (involving that which occurs between one note and the next) would enlighten us about the inherent dynamic qualities over and above the purely vibrational differences of individual notes. He recognised a psychological tendency for the vibrations to set in motion a 1-2 rhythm, or a pulse whose oscillation is fundamentally stable. If another note is added which vibrates twice as fast as the first so that the two notes have the ratio 1:2, then there is no fundamental contradiction - it still sounds like the same note, but at a different place, namely the octave above. But if the frequencies of the two notes have a different ratio, say that of 2:3 or 4:5, the pulse of the second note will not fit the first, or at least it will sound a different pitch. Lipps' theory was that in every such “disturbance” there was a tendency to return to a position of equilibrium, so that when the frequencies of two notes are in such a ratio that on one side we have 2 or a power of 2, i.e. 4, 8, 16, and on the other 3 or 5, or 3 x 3 or 3 x 5, there exists a natural tendency on the part of the 3s, 5s, and so on, to

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move towards the power of 2, to seek resolution there as a natural centre of gravity. Zuckerkandl’s arguments are helped by his careful scrutiny of Lipps’ theories. In Sound and Symbol Zuckerkandl maintains that the frequencies of the first two notes of the opening of Schubert's Unfinished Symphony (B and C sharp) have the ratios 8:9, thus there must be a tendency from the note C sharp to the note B, the former seeking the latter as its home base. It seems that, according to Lipps, the disturbances in the relationship of pulses and their subsequent removal (certainly as far as classical music is concerned) accounts for the play of forces which is found in melody. It is a theory that has much to commend it, especially when the argument is extended to embrace the functions of key in our Western tonal system. Here, a different gravitational pull from the one Lipps describes can be seen. Now we consider not the notes B and C sharp per se, but B as 1 and C sharp as 2, the first and second degrees of the B minor scale; 2 points beyond itself to 1, and this directional pointing is found in each note of the scale. When we hear notes, we place them in the seven-note system. In developing Lipps' hypothesis Victor Zuckerkandl noticed that owing to their greater stability 3 and 5 serve their most unstable adjacent notes, especially the higher, as the nearest points of support. 4 tends to resolve on 3, 6 to 5; 4 gravitates towards 1 across 3, 6 across 5 and so on. Since our Schubert example is in the minor we should point out that the effect in the minor mode is different from the major, (a complex topic in itself). The fifth note of Schubert's melody, A, is a minor seventh and thus predisposed to fall to 6 rather than, say, to rise to 8. As we explore the various gravitational forces at work in an unaccompanied melody such as this one, we become ever more aware of the elusive and complex character of these forces, for if we compare similar situations like 4-3 with 6-5 we notice essential differences such as to confirm the subtlety of our tonal system. A difference exists between melody and harmony insofar as we assume that any reasonably musically literate person can construct a harmonic progression or a tonal scheme. This is the reason why harmony and counterpoint are such eminently teachable subjects. But knowing full well that it is perhaps a gift from the gods we rarely attempt to teach melody. The intellectual basis which we find in harmony and counterpoint is foreign to melodic invention. Heinrich Schenker's analytical system surely obeys a correct intuition in

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looking for quasi-melodic outlines behind classical pieces, but it never succeeds in defining why the melodic invention of works should be so often seductive, for his system is essentially to do with formal structure. Harmonies therefore are generally simple discoveries. But melody often entails creation at the highest level of the imagination, and the composer as creator need not feel that his own participation in that creative process is less metaphysically significant because of the personal gifts which he alone exercises. Where a composer's own creations lose value and indeed credibility is when they are mechanical inventions. This is the issue raised by all methodically contrived music from early canons to motivic organisation of a 12 note series. Sadly, many modern scores have elevated the constructive processes above the genuinely musical revelations of the inner ear, a fault which, for example, Bach the great constructor never succumbed to, even in his wildest forays into constructionism. The organic process which is called melody symbolises certain fundamental characteristics of the natural world, most obviously biological structures (however improbable this might seem). The biologist Jakob Von Uexküll in his Theoretische Biologie5 saw the action of “melodic laws” in organisms as a “genetic melody”, (for instance in the way fish develop.) This poetic analogy underlies a serious scientific point about the genesis of organisms. The scientific aspect of music we have been concerned with so far is that of physical laws. But the creative aspect of music would seem to relate music just as convincingly with a science fundamentally different from physics, namely biology. Certainly, there is in biology as in physics and chemistry a dependence on causality. But physical causality is not apparent when, for instance, an egg is cut in two and two new whole organisms are the result. The individual parts of the new organisms have no correspondence with the individual parts of the egg, so there is no causal chain here - it is a purely biological process. While conceding that this apparently mysterious process can be scientifically accounted for, there appears to be a miraculous place-transcending order at work that is not dissimilar to that found in music. Uexküll makes a further identification of musical process with biology on two levels - firstly the level of nature, the way life is organised (whether life as feeling and thought as in music or as an organic process as in biology), secondly, the metaphysical level, where both music and biology in rather similar fashions simulate a form of creativity that is

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mysteriously endowed with an immaterial power that is both in this world and beyond it. We can only imagine the scepticism such fanciful notions would elicit from die-hard academic musical analysts! We shall now turn to harmony. While always being aware that it was essentially no more than a bit of fancy and fantasy we note how venerable is the history of the triad's symbolism, particularly among the German theorists of the Renaissance and afterwards. For Johannes Lippius in 1612 the common chord symbolised the Holy Trinity, the true and unitrisonic root of all the most perfect and most complete harmonies that can exist in the world ... the image of that great mystery, the divine and solely adorable Unitrinity.6

Andreas Werckmeister (1645-1706), a German provincial organist and theorist, extended this to four octaves and made a correspondence with the four successive periods of divine revelation. Octave I (harmonics 1, 2) now symbolise God the Father as he was before Creation; II (harmonics 2, 3, 4) the time of the Old Testament, when the Trinity was concealed; III (harmonics 4, 5, 6, 8) the time of the New Testament, in which the Trinity was revealed; IV (harmonics 8, 9, 10, 12, 15, 16) the melody of the Christian life, in earth and heaven. His association of these ascending octaves with what he called the “trumpet scale” (the trumpet's harmonics) gave it a resplendently apocalyptic gloss, and it was significant here that the dissonant harmonics 7, 11, 13, 14 were excluded as representing sin.7 Such an approach is strange to us, yet the awesome mysteries of harmony still prevail in modern analysis as we will now endeavour to show. Clearly there is in harmony a prodigious and diverse sound-world which phenomenally extends the range of our discussion. One acoustic property of chords is that when the component notes merge the resulting harmony becomes a single complex sensation. The dynamic qualities we have noticed in individual notes are perpetuated in harmony according to the position of the notes. CEG can be described as 1.3.5., but the presence of a key means that the numerical function can change according to what key you are in. Therefore CEG is 5.7.2. when we are in F major, or 4.6.1 when in G major, and so on. The sense of direction prevailing in the individual notes is more complex than in melody alone. In general, the tonal pull in a chordal context is more ambiguous than in melody because here the chord itself possesses a tension of its own. Some chords exert a greater

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gravitational pull than others. The tonic chord 1.3.5. is clearly the home base for other chords, while the dominant chord as we have noted, and especially the dominant seventh, 5.7.2.4., finds the pull towards the tonic irresistible (at least in music later than the 16th century). Until the end of the nineteenth century, in the majority of cases, the dominant seventh chord was followed by the tonic, and final cadences were often formed by this progression. We have maintained that the dynamic force is a mysterious element which lies in the notes as they progress in time from one note to the next, or from one chord to the next. In contrapuntal music we still have a strong chordal element in the vertical superposition of the notes, but many would argue that here the horizontal sweep has, or at least pretends to have, primacy over the harmonic event. Our convention is to use the name of an interval (second, fifth, octave and so on) to describe not only the distance between two notes but also the connection between them, which may either be successively as in melody, or simultaneously as in harmony. The movement from one note to another or from one chord to another is far more than it is at first glance in, say, the hymn-tune “St Anne”, where there is a progression from the chord E flat to A flat to E flat to C minor to A flat to B flat to E flat. Here there is an extra dimension in the very act of moving away from the tonic chord to a related area before returning to the tonic. This horizontal motion adds to the dynamism we have already seen in individual notes, and where there is harmony there must surely be an enhanced effect which opens up a vast new dimension of tonal potential. A chord is not just the sum of its notes, and a triad's depth of meaning cannot be explained by aggregating its three components. In both melody and harmony we can deduce why the language of diatonic music takes the form so familiar to us. By extending our argument to more complicated areas it is possible to come to similar, if more complex, conclusions about chromatic music. With atonality the conscious rejection or contradiction of these gravitational forces is an issue in itself. Indeed this analytical method gives no explanation of chromaticism, which of course has been present in Western music for longer than we realise. Bach was the composer of chromatic music par excellence, and even in the apparently still harmonic waters of the classical period the chromatic subtleties of Haydn and Mozart and Schubert suggest that the “pulse

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theory” of Lipps and its extension to harmony provides a rather inadequate rationale. We have noted the uniquely insubstantial quality of music. The notion that there may be quantifiable, verifiable correlations between rhythm, pitch, timbre, harmonic resolutions or dissonance, or the fact that the number and mathematical progression of vibrations are functional, does not conceal the essential unreality of music as a kind of constant flickering of presence and absence together. Although we hear forces, we can find no material phenomena to which music correlates. In the external world body and force are dependent upon each other, and we know of forces only through their material effects. Even here the actual nature of the force may be imperceptible. Yet we clearly deduce it from material traces. We have already noted that in music too there are material forces, the wave-producing vibration of a string or column of air. But these physical properties have nothing to do with the dynamic properties of music as previously discussed. In music it is precisely the fact that its forces are invisible, and have no matter, which makes logical deduction ineffective. Because of its derivation from the harmonic series, tonal music would seem to have a superior claim to the divine than non-tonal music. But we must note that the very expansive, adventurous character of art, its continuously developing state and novel creations, makes it logically impossible to ensure any set of defining properties, especially in a world wide context. Indeed, for many music lovers tonal music does not (only) indicate a music derived from diatonicism but also modes, ragas etc. Similarly, the ontological distancing of serialism from the harmonic series may at first sight tend to undermine the metaphysical validity of it and other non-tonal systems. But many would dispute this, for the very existence of 12-note chromaticism and complex ragas make them also eternal objects and, as such, with sufficient metaphysical validity as wellsprings for human creativity (as our recognition of a number of masterpieces, twelve-note and non-Western respectively, would seem to confirm). While objects generally recognised as being of special aesthetic interest have in common some distinguishing trait (what Mozart and Stockhausen produced is the same in that it is music), such a trait cannot be a defining characteristic. How does all this fit our assertion of music as an immanent expression of a divine creator? The truth is that there is a nonphysical

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element in the external world which is neither to be understood by examining technical phenomena nor to be seen as merely a projection of our emotions. It has an autonomy of its own, which the great Process philosopher Charles Hartshorne described as an “external psychic”, a psychic force outside ourselves. If we listen to the opening of the Schubert symphony we not only hear the notes B, C sharp, D, B, A, F sharp and so on, but the characterisation of these notes into a solemn and brooding phrase low in the cellos and double basses. And this has an emotional effect. Many listeners would see this as the whole experience. But in addition to this is that which is neither physical nor emotional, namely the dynamic force, the relationship in motion of 1 2 3 1 7 5 6 etc, the degrees of the scale explored by Schubert's opening. As we have previously maintained, this dynamic force is a separate and mysterious power, fundamental to musical expression and yet to which many listeners are oblivious, for in no way is it a creation of the listener. One could say also that it is not consciously created by the composer, for he is often bound to use it without understanding how it works. Nevertheless we must always remember that the piece belongs to a specific culture and context. Its phrase-length marks it as belonging to a Western canon; and since it ends on the dominant it clearly belongs to the 18th century. Leibniz's famous description of music is apposite: “music is a secret arithmetic of the soul unknowing of the fact that it is counting” (nescientia se numerare). This concealment may account for the problems which face aestheticians when dealing with music, and indeed the other arts, (as we shall see later in Chapter 6). For we can doubtless see potent forces which are invisible dynamic agents for equilibrium and tension not only in music but in the visual arts and architecture or in literature. This extra dimension we have noted will be elusive. We may, for instance, find it difficult to define in the visual arts precisely because the eye, which has such a central role in constructing the world of material things, may not easily penetrate the nonmaterial in the guise of purely dynamic phenomena. In asking what it is that lends enchantment to a melody by Schubert, (and in his case we could cite almost any melody by this most gifted of all melodists), Zuckerkandl maintained that the key to understanding the process lies primarily not in the relation of the notes to any feeling of ours but rather in the relation of the note B to C sharp and so on. And this autonomy of the notes can be proven, for the

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dynamic power is evident even when the context is not musical, in the playing of a scale, for instance, (but always accepting that our scales are also constructs i.e. conceptions belonging to our culture but having evolved from physical laws). This has absorbed a number of influential musical commentators in their various attempts at rationalisation. Leonard Bernstein, for instance, in his televised Harvard Lectures8 probes the deep structures inherent in music and makes cogent analogies with Chomskyan linguistic theories. But the crucial issue of music's immanent meaning is not satisfactorily pursued by him beyond purely emotive descriptions. Yet the comparison with language provides a fruitful area for Bernstein to attempt a hermeneutics of music. In language as well as music, the meaning is often inexpressible by other means, and at least this mystery is shared by music and language. But as we shall note in Chapter 4 a word and its meaning, in the sense of what it is saying, are independent things, the word being a series of signs for a meaning that is separate. There is no equivalence in music. A musical meaning resides in the note; meaning and sign are indivisible and the musical meaning cannot reside elsewhere. The flickering of presence and absence is nowhere more tantalising than in this compounding of abstract meaning with real sound. Whatever emotion we may feel as listeners may not necessarily be an accurate reflection of the meaning of the notes, whose import lies in the notes and not in us. Zuckerkandl argues that while it is possible to translate from one language to another it is not possible to translate from one music to another because language has a finite world of things whereas musical notes themselves are what they mean. He continues, Hence too the number of words, of the smallest meaning units of language, corresponds roughly to the number of things: languages are rich in words, whereas twelve tones suffice to say everything that has ever been said.9

(Clearly Zuckerkandl is mistaken here, as will be apparent to us every time we listen to, say, a richly expressive 19-note raga). As we shall note later, if music generates its own meaning from inside itself, then words lead away from themselves to a separate conceptual idea. In the opinion of many, this is what brings the musical experience close to the religious dimension. Just as a religious symbol provides a direct apprehension of God, so does a musical note provide a direct sense of experiencing another

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world. Whether or not we can call this God is dependent on how allinclusive we are prepared to be in our speculations about religion, for religious belief is such a personal matter. While the presence of God may be self-evident to the believer, the unbeliever will perceive nothing. At least in music we can be sure that there is an “invisible” dynamic force of some significance to music lovers. This force is clearly heard and exists in all music (including trivial pieces). In this respect the numinous quality in a musical context is more directly perceptible than in a religious one. Perhaps this is why music (and not always of a certain rigorously disciplined kind, as we have already noticed) has been central to worship. Of all the arts one might find represented in heaven, music and the singing of angels would seem to take pride of place. We should also include rhythm in our discussion. It is possibly the most fundamental element of all, as Roger Sessions implied when he said, “Basically music is not so much sound as motion”. Rhythmic motion in music is a subject that affects the present discussion because it is to do with what happens so as to connect the notes. Rhythmic movement is less concerned with the notes, which in themselves do not move, than with the relationship between one note and the next. Fundamentally, rhythm is to do with time, and if we are to seek to provide an ontology of time in music we must deal with its principal manifestation, which is rhythm. In combination with melody and harmony, rhythm constitutes the trinity of basic elements that are fused in music. But unlike melody and harmony, which are found only in music, rhythm is a universal property, and found in the inanimate as well as the animate, in the microscopic as well as in the macrocosmic. In music two types of rhythmic force can be seen, rhythm as commonly understood on the one hand, and, on the other, metre, which is a process for demarcating beats. They both cohere, since metre groups rhythms into (usually) equal portions. Zuckerkandl makes a good analogy whereby a comparison is made between the motion of a machine on the one hand and man on the other: the machine runs metrically, man walks rhythmically.10 It is the interplay of rhythm with metre which accounts for much of the driving intensity of many pieces. The general organisation of works into formal structures owes much to the polarising effect of metre, intensified as it must always be by the constantly rejuvenating power of rhythm. Symmetries are established and contradicted and there is diminution

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and augmentation involving variants of pre-established motifs and themes. Rhythmic dynamic forces have a life of their own, but these combine with the previously described tonal dynamic forces to produce a complex synthesis of musical argument which we recognise as the “form” of a work. On the smallest as on the largest scale, all the technical paraphernalia of music interact to make a synthesis, with certain ground rules involving tonal and rhythmic dynamic forces. It might seem that time itself is an innocent bystander in all this, a mere servant for all this energy. Isn't it a somewhat neutral vessel through which the music travels? Not necessarily. When a piece comes to its end we feel that, in addition to us responding to the richly argued musical discourse, the passing of time itself has been a participating element. The rhythmic power is exerted not by the beats but in what happens between the beats, from beat to beat, so that time seems to actively participate, to intervene. This is an unorthodox view of time. Even such an original thinker as Schopenhauer avoided ascribing such significance to it. (In The World as Will and Idea he describes time in itself as empty and without properties, and in similar vein we have William James's observation, that “empty time's own changes are not sufficient for the awareness of change to be aroused.”) The performing musician will reject this notion, for he is constantly relating his work to time as an active force. This bears some relation to ourselves as beings who, from heartbeat to heartbeat, live a rhythmic life, whether we are musicians or not. We might ask whether the rhythmic forces we have been discussing are not processes in our own bodies (rather than without) were it not for the very particular data which informs even the simplest musical piece, which proves rhythm’s autonomy and thus separates it from our feelings and the movements of our own bodies. If metre and rhythm follow on from the concept of time, then time itself, as a concept, will not be beyond our comprehension. For if we have understood musical rhythm then we can understand time, at least insofar as rhythm is an integral factor in its passing. In Sound and Symbol, Zuckerkandl, like many other writers on music, perceptively compares two concepts of time, physical time and musical time, and shows fundamental differences between them. On the one hand, while physical time is “order, form of experience”, musical time is “content of experience.” While physical time “measures events”, musical time “produces events.” While physical time is “divisible into equal parts”,

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musical time “knows no equality of parts.” While physical time “is perpetual transience”, musical time “knows nothing of transience.”11 Therefore, through musical notes and their rhythms, time becomes a concrete reality, and musical rhythm is the most effective way of making time an experience in itself. The realisation of time belongs to music for in music we perceive effects of time rather than in time. Zuckerkandl's final analogy between physical time and musical time raises the issue of the equality of parts. This needs explanation, for it illustrates how unphysical is music's measure of time. One definition of physical time equates it with the motion of a body taken as the measure of the motion of another body, hence a comparison of two bodies, of matter in space, not of times. Equality of time is crucial, of course, in the musical sense of good rhythm meaning “keeping in time.” But in ensuring that time units are kept equal we note that this does not relate to space, and again we ask what is the nature of this musical equality of time? Is it the equal succession of beats, or of bars, or of phrases? Often there is arithmetically an equality, but every musician knows that deviations from metrical equality do not disturb us if the rhythmic (or time) variation makes musical sense. When music imposes a rhythmic quality on equal lengths of time it often rejects equal time (meaning man's measurement of time, and involving spatial measurements). Zuckerkandl deals with the poignant issue of the transience of time as an indicator of man's mortality and suggests that musical time tends to counter this transience (transience being one of the fundamental features of physical time). He quotes a number of classic statements about the passing of time, from Locke's cryptic “Time: a perpetual perishing” to Schopenhauer's “Time is that by the power of which everything at every instant turns to nothing in our hands”. He goes on to ask the provocative question: To us, temporality and transience are words for the same thing, and only the timeless does not pass. It might be asked why, then, one aspect of this twofold process imposes itself on us so much more than the other; for the same time that turns the now into a no-longer has, after all, first made the not-yet a now. Yet we never talk about anything but time passing; no one says, “Time becomes.”12

As we shall discover later, the notion of time “becoming” is the crux of so much that is fundamental to Process thought. Since music

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disputes the hour-glass idea of time it thus questions the entire conceptual notion of it. Music actively moves into the future in a manner rather different from other phenomena. The need for a phrase to be answered by a succeeding one is in itself a reaching out into the future. Language behaves similarly, a sentence inexorably proceeding so as to draw the future closer, making time “become”. But it is the material concepts which language handles which does this. In music it is the singularly immaterial flux of sound which provides compulsive anticipation of what is to come in time. Of the many differences between language and music none is more striking than the continuously revelatory effect of musical surprises. In language, a surprising statement is usually only a surprise the first time, while in music we continue to be startled by surprise events after having heard them many times before. It is this capacity, found only in music and in the very finest pieces of literature, which helps to confirm the idea of time itself being enhanced by its rhythmic manipulation in the hands of Bach or Mozart, or indeed Shakespeare or Dante. Zuckerkandl shows us that in such contexts time is more than a mere container for events. Music is certainly an experience of the present, but it is a present in which the past and the future are stored somehow simultaneously, as one of the more difficult passages by Henri Bergson attempts to suggest. In Zuckerkandl’s discussion on Bergson he quotes the following passage from Durée et simultanéité : A melody to which we listen with our eyes closed and think of nothing else, is very close to coinciding with this time which is the very fluidity of our inner life; but it still has too many qualities, too much definition, and we should first have to obliterate the differences between the tones, then the distinctive characteristics of tone itself, retain of it only the continuation of that which precedes in that which follows, the uninterrupted transition, multiplicity without divisibility, and succession without separation, in order at last to find fundamental time. Such is duration immediately perceived, without which we should have no idea of time. 13

Bergson claims that time is a process of the inner world and is to be understood psychologically. But it is not in me, it is in the music. So musical time does not reside in the psyche after all. Yet its connection with us is real - it is co-rhythmic with physiological time, with the durations of our body rhythms, with life itself. It is a living time, which can “remember”. Here in Bergson too there is a rejection of spatial measurement of time. (He sees “spatialised time” as concerned

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with an “instant” as a “point” in time, and of duration as an interval that extends between two points - thus measured by spatial representation). The immateriality of notes make them compatible for functioning in time, for notes are not qualities, they are a selfsufficient inherence in time involving a direct perception of time. As soon as the note is heard we are drawn directly into time. Hearing the notes means hearing time. We can appreciate this by analogy with the visual dimension - if I see a landscape the duration of my experience is not an element of the sensation. It is not duration that I see, it is landscape. But in listening to a note I hear in it duration per se, and music not only possesses duration but contains temporal extension as a fundamental defining quality Before we leave this area of inquiry we need to discuss briefly musical space and silence. The relationship of time to space in music is a vexed one. Schopenhauer maintained that music is perceived solely in and through time, to the complete exclusion of space. Zuckerkandl contradicts this when he discusses harmony, whose notes, although merging into a single chord, do not disappear in it; each remains in existence as a separate component of the chord and, in simple cases, can easily be heard in the chord even by untrained ears. What keeps apart simultaneously sounding notes so that they can jointly form a chord? Simultaneously appearing colours coalesce into a mixed colour, unless, that is, they appear in different places, unless space keeps them apart. It appears as if the fact of simultaneity of different notes would in some way bring space as its indispensable prerequisite into music.14 The same argument is presented with counterpoint, its texture arising from the connection of several voices proceeding side by side. In its most elementary form this correlation between time and space (space, of course, being only a metaphor not an essence) is seen in a unison passage sung by a mixed choir, for here the men sing exactly the same part as the women but sound an octave lower. This is the same music but spatially a different experience. For Zuckerkandl this involves a very special experience of space, and this is supported by our habit of describing music “spatially” in almost all our common descriptions of it. If we experience the complex simultaneity of a chord as a vertical event in a contrapuntal passage we still perceive a single flow of music in time. Contrapuntal lines in Bach, even when their separation is clarified by their being allotted to different tone

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colours, still maintain a cogent unity - four melodies integrated into a single texture. There are four separate meanings too, but these bow to the overriding precedence of a unified expression. Such is the subtlety of time's hold on this that we can still perceive and appreciate the four separate elements of this essentially divisible whole. A musical note's connection with space, as ordinarily conceived, is seen in its manifestation as a performed event, perhaps in public, or at least in a space. But the note immediately detaches itself from its material source, and this divorce from spatiality is one of its physical and metaphysical characteristics. Zuckerkandl makes a distinction between notes and thought, and points out that, whereas there is no within-without in thought, there is this distinction in a musical note. Only thoughts are indifferent to space. But the creative imagination of the composer or of a performer is similarly immaterial and this lack of materiality in the creative act is the essence of all musical composition. So, as we have already maintained, a piece of music inhabits two worlds, the inner psychological world and the real world of its performance, that of the twanging gut and measured breath on the reed. Sound is imparted into the air, is localised in space, and occupies and integrates space before we encounter it. But if the ear is aware of space in music, then, to use Zuckerkandl's phrase, it is “a space without place”. It entirely lacks the three-dimensionality of optical space where there is occupancy by objects. But many might argue that this is an over-simplification, after all isn’t it also music when you sit in a chair and read it? To turn now to silence, we notice that one of the peculiar experiences in music is the eloquent effect of silence, when silence is a structural element in the motion of a piece. In one passage in Bach's motet Jesu meine Freude there are rests which are used functionally to stop the music prior to an outpouring of motion in the form of a vibrantly surging sweep of counterpoint. The context here is so rhythmically unified that the rests contribute as much as the music to the motion. In other words, musically the rests are not silent, they are full of meaning, are pregnant pauses. This procedure is not confined to music, for in speech also there can be eloquently structural rests, and where great poetry has pauses the effect is similar to that in music. This reinforces our claim that dynamic force is found not just here in this note and there in the next note, but in the transition from one to another. What takes place in between is processive, the lifeblood of

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musical motion (and afterwards too, as in that special moment before the applause). We have naturally seen time as music's province and our discussion of the other arts has been limited to a passing reference to literature. Clearly, many of the points made above have validity in relation to dance and we shall deal with this in later chapters. It is also conceivable that those arts which seem not to be connected with time as a process, which do not use time as music does, may have a mysterious underlying connection with time as an active agent. For instance, in his book A Whiteheadian Aesthetic , Donald W. Sherburne makes a case for reconsidering the different functions of time in the performer and non-performer arts respectively. He confirms much of what has been discussed above when he writes: In the performer arts an objectification is a discursive entity that requires the passage of time for its performance and then fades from actuality into objective immortality, while in architecture and the non-performer arts an objectification, once secured, is an enduring object indifferent to time.15

He goes on to point out a peculiar tendency for the arts within each category to “approximate to those within the other”. He notes a tendency in viewing a painting, statue or cathedral to be in a certain chronological sequence like the sequence in a musical performance. From the opposite point of view, he cites the allegation (it is no more than that and not authenticated) that Mozart could hear a symphony complete in his head in the flash of an instant to prove that the temporal arts demand a familiarity on the part of the contemplator which permits him to gather the discursiveness of the performance into a unity of presence parallel to that which predominates in the nontemporal arts.16

In suggesting that the discursiveness of the temporal arts must be overcome before the objectified proposition “can be fully grasped” Sherburne lends support to Schenkerian analysis, where an instantaneously graphic explanation of a musical work is aimed for. Conversely, he seeks to urge the sequential appreciation of nontemporal arts if the subject is to have the right impact on the viewer. Why this needs to take place is not explained, except in a general statement to the effect that the basic aesthetic tension of unity within contrast is exemplified by this approximation of arts within one category to those within the other. “Music has contrast built into it,

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hence the composer struggles for unity; architecture has unity built into it, hence the architect struggles for contrasts.”17 In conclusion, therefore, the artistic universe as a whole has a temporal dimension that is more than momentary, for it can be perceived as a distinct structure. If one remains conscious of the poignant reality of real time in which one is inexorably moving towards death, one apprehends the joy of art's own time as being profoundly meaningful. In stepping from one chronology to another it is as if we step from time to eternity. The reality of our “living towards death”, as Heidegger described our condition, is suspended. This explains the liberation and peace that is found, a true catharsis, even when the artistic subject prehended is apparently of a gloomy nature. Notes 1. Sound and Symbol (1956) and Man the Musician (1973). 2. (Baltimore 1926). 3. See Godwin’s discussion, op.cit., p.174. 4. Bettina Brentano von Arnim, Goethe’s Correspondence with a Child (London 1839), Vol.1, p.282. Discussed in Godwin, op.cit., p.175-6. 5. Discussed in Zuckerkandl, Sound and Symbol, p.263-4. 6. Andreas Werckmeister, Musicae mathematicae hodegus curiosus (Frankfurt and Leipzig 1687, reprinted Olms 1972). Discussed in Godwin, op.cit., p.185. 7. ibid. 8. The Unanswered Question (Harvard 1976). 9. Zuckerkandl, op.cit., p.68. 10. ibid., p.170. 11. ibid., p, 202. 12. ibid., p.224. 13. See Durée et simultanéité (Paris 1922), quoted in Zuckerkandl, op. cit., p.244.

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14. op.cit., p.268. 15. A Whiteheadian Aesthetic (Tennessee 1970), p.131. 16. ibid. 17. ibid.

Chapter Three Process Philosophy Before discussing music any further we shall explore some general philosophical arguments arising out of Process and scrutinize briefly the ideas of the first and greatest Process philosopher, Alfred North Whitehead. But for Whitehead to be cited in any discussion on aesthetics needs some explanation, for there is very little reference to art or aesthetics in his work. Since he was one of a small group of thinkers whose influence is felt far beyond the confines of their own specialisms his philosophical writings provide an inexhaustible mine of suggestion, despite their difficulty and stylistic elusiveness. (Whitehead himself maintained that he was the only person ever to have read the chapter on “Abstraction” in his Science and the Modern World, and Dorothy Emmett in an obituary notice said, “There are some who have done so. But they must be very few!”) When he was elected to the Professorship of Philosophy at Harvard in 1924, at the late age of 63 and following a phenomenally distinguished career as a scientist, he embarked upon a fruitful period of activity both as an original philosophical thinker and as the teacher of such illustrious figures as Susanne Langer, Paul Weiss, F.C.S. Northrop and Charles Hartshorne. What soon became apparent in Whitehead the philosopher was how relevant his scientific discoveries were to his philosophical thought, as is apparent in his idea of forces at work (process) as fundamental to reality. In his famous book Process and Reality: An Essay in Cosmology (1929)1 we have an exposition of what he described as his “Philosophy of Organism”. Here he asserts that ultimate components of reality are “events” in time, not static situations or particles of matter. An event is never instantaneous, for it always lasts over a certain duration, (although perhaps an infinitesimally short period of time, as when a molecule in this paper reacts to another). This is an event and a process in time. An instant of time and a point in space have no place in his scheme. Thus, with events we do not talk of how things are (what they are made of) but of how things become. The process of events, their “becoming” is fundamental. Those events of which the world is made are called “actual entities”. In older philosophies substance plays a fundamental role, but unlike substance

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(which endures), an actual entity has no permanence. And as if to emphasise this point he, in typical neologistic fashion, describes an actual entity not as a subject but as a superject, thus suggesting its emergence from antecedent entities to itself. The provenance of this concept in classical antiquity is immediately apparent when we recall Heraclitus’ famous assertion that no man could step twice in the same river. Here is encapsulated the hypothesis that the only absolute which exists is change and only process and change can be counted on to be the basis of reality. The actual entity “becomes” as it absorbs influences from other entities in its environment, including God. God also can become. This absorption or takeover is termed “prehension”, literally meaning “grasping”. So prehension is a ferment of “qualitative valuation” which need not necessarily be conscious. The table on which I am writing prehends its surroundings, since its molecules react to others. Whether one can romanticise this and see in it the workings of a mind or rudimentary consciousness evidenced by the simple transfer of energy is not a matter for the present discussion. The entity prehends objects from its environment. Those objects are said to exert “causal efficacy” on the subject. But this is not some simple, easily understood effect, for to begin with it need not be conscious. In “seeing”, for instance, the eye’s enjoyment of a reddish feeling is intensified and transmuted and interpreted by complex occasions of the brain into definite colours and other instances of qualitative “eternal object.” The original physical feeling of causal efficacy is submerged but not eliminated by an inrush of conceptual feelings. Furthermore, conceptual prehensions allow the objective scale of values given by the primordial nature of God to enter the decision, and it is then that we have a display of qualities presented to us. Whitehead calls this experience “perception in the mode of “presentational immediacy,” The becoming of an actual entity is called a “concrescence”. This is an integration as a result of prehending other things or as a result of experiencing the causal efficacy of other things on it. Actual entities, sometimes termed “actual occasions”, (which, because of the implication of temporality might be a more appropriate term) are the final real things of which the world is made up. There is no going behind actual entities/occasions to find anything more real. “God is an actual entity, and so is the most trivial puff of existence in far-off empty space.”2 There may be gradations of importance, or diversities of function, but in principle all are on the same level.

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When the concrescence is complete, an actual entity’s or actual occasion’s private life, during which it has been prehending, comes to an end. In perishing it embarks on a public career and the cycle starts again. This novel occasion now becomes the object for another subject to prehend, and, if consciously, with aspirations of a kind of immortality. While ordinary objects may be physically prehended, eternal objects are conceptually prehended. As a foundation for this we have eternal objects. Whitehead sees eternal objects as ingredients in an experience and rather similar to Plato's ideal forms. They are patterns and qualities like squareness, blueness, hope or love. Whitehead's definition of eternal objects has its source in early Greek theory, for to him “eternal objects of the objective species are the mathematical Platonic forms.”3 But here he is referring to the objective forms of numerical relationships and geometrical shapes. What was noted in Chapter 2 concerning the physical coherence of music naturally fits in with this. But eternal objects of the subjective species function in a more complicated manner. They are the qualitative clothing to the raw quantitative data of the objective species. Such a subjective species is “an emotion, or an intensity, or an adversion, or an aversion, or a pleasure, or a pain,”4 and so on. So-called secondary qualities are eternal objects of the subjective species, as are (per se) pains, likes, dislikes, etc. These eternal objects of the subjective species appear at the private end of prehension, but they may be transmitted into a characteristic of the datum objectified. A complex illustration from music will show how subtle this can be. The bare essentials of harmony may be reduced to one particular scale system which is an eternal object of the objective species, but it is made meaningful in a series of harmonies or in the coherence of a complete piece so that the eternal object achieves a subjective status. Any succeeding rationalisation of this provides a further objectification of the whole structure, both its quantitative data and its qualitative clothing. Musical analysts may not be aware of it but this rationalisation is the function of musical analysis. Naturally, the more probing the analysis then the more it will provide a fundamental explanation of a piece. When an actual entity undergoes the developing process (concrescence) it acquires a definite character to the exclusion of other possible characters by selecting some eternal objects (rather than others) to conceptually prehend. So if I say that this pencil is green, then this is a proposition where the subject is a society (nexus, or group) of molecular actual entities and the predicate is the eternal

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object “green”. The fusion of the two is the combining of something real with something ideal. An eternal object refers only to the purely general among undetermined actual entities. In itself an eternal object evades any selection among actualities.5 On the other hand, the datum of a physical feeling is either one actual entity or, if the feeling be complex, a determinate nexus of actual entities. This datum is unique and specific, a “this” as opposed to “any.” In this synthesis [of eternal object and actual entity within a proposition] the eternal object has suffered the elimination of its absolute generality of reference.6

According to Whitehead both the eternal object and the actual entity find their reasons for being in God. For Whitehead, God is the “aboriginal condition” upon which all actual occasions are dependent. Without God the forms of definiteness (artistic and otherwise) would be “indistinguishable from nonentity”. In a limited sense of the word “create”, God can be said to “create” all actual entities and Whitehead insists that God has a crucial role in the birth of each one. In playing this role, God does in a very real sense participate, though Whitehead warns us not to be misled by the suggestion that the diverse creativity of the universe is to be attributed to God's volition.7 For Whitehead what is real is the actual entities/occasions. But we must remember that groupings of occasions (nexus) are abstractions. We must beware of attributing reality to nexus lest we commit the “Fallacy of Misplaced Concreteness.”8 It may be hard-core common sense to believe that what I am writing on is this desk. But the desk categorises other substances, including the microscopic. Whitehead argues that the desk does not pertain to my experience in the most concrete way, but rather to abstractions from the categories of substances contained in it, hence the Fallacy. If we can free ourselves from too much reliance on the common abstractions underlying our perception of substances then we can perceive aspects of life and reality which we have hitherto ignored, like those molecules within this desk that I write on, that have as much reality as the desk. Thus, the sequence from microcosmic actual entities/occasions through various stages towards macrocosmic entities is a sequence from reality to appearance. God’s persuasive (rather than coercive) wisdom imbues the initial aim of every concrescence. This occurs at the start of each occasion’s reaction to the influence from the past. The initial aim “determines the

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initial gradations of relevance of eternal objects for conceptual feelings with its initial conceptual valuations, and with its physical purposes”,9 and God’s all-embracing conceptual valuation is harnessed to the particular possibilities available for the initial feeling. Whitehead wrote: there is constituted the concrescent subject in its primary phase with its dipolar constitution, physical and mental, indissoluble.10

As we have said, from this point onwards the concrescence determines its own definiteness and this is the general law. Whitehead always asserted the freedom of non-divine subjects, whether that be me gardening or Bach, with awesome awareness, penning a fugue as one of more than a thousand works indicative of a profound understanding of what can be produced from the overtone series. The three concepts referred to by Whitehead as the formative elements are creativity, eternal objects, and God. God is the third formative element and one of Whitehead's most impressive achievements is to show how God binds actual occasions and eternal objects into one coherent system, with God in His role of “the outcome of creativity, as the foundation of order, and as the goad towards novelty.”11 Since artistic creation has frequently been linked to the notion of a divine madness or inspiration it is useful to find in Whitehead a rational account of the nature and function of God so that we can specify in a more precise way the relationship between God and artistic creation. His concept of God emerges from a metaphysical demand for a unique actual entity which links actuality and potentiality. In other words it supplies a First Principle to relate the eternal models to the actual definite forms. This provides an explanation for why things need to exist. In artistic terms significant creations seem to have importance, yet since they form no part of a useful commercial function we may not be able to argue for their relevance. But, as Whitehead notes, nothing, within any limited type of experience, can give intelligence to shape our ideas of any entity at the base of all actual things, unless the general character of things requires that there be such an entity.12 (My italics).

This means that the general character of things requires that there be a God. But God does not interfere, he is not a deus ex machina, for this would not conform with a logical metaphysical system such as Whitehead envisages. Yet Whitehead's God is central to his

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metaphysical system and not at all arbitrary: God is not to be treated as an exception to all metaphysical principles, invoked to save their collapse, he is their chief exemplification. Whitehead's doctrine of the primordial nature of God strengthens the claim that God's conceptual valuation is identical with the web of relationships constituted by the relationships forged by eternal objects: The things which are temporal arise by their participation in the things which are eternal. The two sets are mediated by a thing which combines the actuality of what is temporal with the timelessness of what is potential. This final entity [God] is the divine element in the world, by which the barren inefficient disjunction of abstract potentialities obtains primordially the efficient conjunction of ideal realization ... By reason of the actuality of this primordial valuation of pure potentials, each eternal object has definite, effective relevance to each concrescent process. Apart from such orderings, there would be a complete disjunction of eternal objects realized in the temporal world. Novelty would be meaningless, and inconceivable. 13

The conclusion emerges that the three formative elements are interwoven into a mutual interdependence. This implies that without eternal objects God's primordial existence is impossible, for eternal objects are the primordial “definiteness” apart from which no existence or creativity, even in the primordial instance of God, is possible. Actuality presupposes definiteness, and God must also be definite. In his A Whiteheadian Aesthetic, Donald Sherburne makes a common-sense analogy, as follows: It takes pistons, a sparking device, and some fuel to result in an operating, pulsing, dynamic engine. If any of these three be lacking, there is no dynamic system. Remove the sparking device or the fuel and you still have pistons, but pistons resting in their casings are lifeless and pointless when compared to the vibrating, thrusting pistons of a dynamic system. Likewise, eternal objects in the “isolation indistinguishable from nonentity” are inert, lifeless, and ungraded in relevance when compared to eternal objects linked by the web of relational essences which is God's primordial vision.14

God's relationship to actual occasions couples them with the abstract model which is an eternal object. This coupling is called a proposition, and gives to God a “common quality”. But it is only God who can conjure up conceptual feelings that do not depend upon prior physical feelings: unfettered conceptual valuation, “infinite” in Spinoza's sense of that term, is only possible once in the universe.15

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Conversely, the artist does not create ex nihilo; his vision is not unfettered or infinite as is that of God. But his creativity presupposes God and therefore the artist is a discoverer (a view which, by the way, was sharply contradicted by Croce when he maintained that artistic creation implied absolute novelty and a bringing into being ex nihilo). Whitehead's theory, therefore, is that an artist discovers a proposition. How rich a process and how subtle it is can be shown by all the attendant features of the process, for example, by the contextual influence of what Whitehead calls “conceptual reversion”. Conceptual reversions are feelings partially identical with and partially diverse from the eternal objects constituting the data which one is confronted with. This profoundly subtle concept is crucial in artistic creation since it is the element which implies that the artist has freedom of choice. A conceputal reversion was defined simply by Hume in his well-known discussion of the missing shade of blue: even though one has never seen a particular shade of blue, one can, given other shades of blue, conceptually supply the missing shade. Thus, creativity thrives “on a positive prehension of relevant alternatives.”16 Many artists surely cannot “conceptually supply”, but if we accept the notion as feasible then this forms an intriguing element in creativity. The final artistic product is the artist’s, and in a particular form that can be called novel. The eternal object acts only as a wellspring. What we mean by describing artistic creation as discovery is that when the artist, the innovator, dives down into the inner flux to draw up a crystallised shape which he endeavours to fix, this becomes a discovery when he has expressed it because we recognise it as having a universal truth. So the divine inspiration is not something appealed to ad hoc in Whitehead's system, it is rather an underlying metaphysical requirement linking the creative surge of actuality in all its gradations from God to “the most trivial puff of existence in far-off empty space”! An important characteristic of creativity in Whitehead's system was the necessity to recognise the “ultimate” without denying actuality to the individualisations of the ultimate. In his doctrine the “ultimate” is the basic activity of self-creation generic to all individual actual entities. That is to say, it is the generic activity conceived in abstraction from the individual instances of that activity. This “ultimate”, this generic activity, Whitehead terms “creativity.” Creativity must transcend each individual actual creature even though it is not itself “actual”. Thus is secured the conception of a connected “universe.” And thus is secured the character of the universe as a

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process, for its ultimate character is that of a self-creating activity. The individual actual entities are the creatures of this universal creativity in the sense that the ultimate, creativity, individualises itself in the individual creatures. So creativity is neither a thing nor an entity, it is a selective principle which expresses the relationship between “one” and “many.” It expresses the relationship whereby “the term ‘many’ presupposes the term ‘one’, and the term ‘one’ presupposes the term ‘many.’ ”17 For Whitehead, creativity is that ultimate principle by which the many, which are the universe disjunctively, become the one actual occasion, which is the universe conjunctively.18

Whitehead also describes this principle more simply: “It lies in the nature of things that the many enter into complex unity.”19 It would seem, therefore, that the universe abhors a many; it is just an ultimate fact that the universe cannot tolerate a disjunctive diversity, as many thinkers (such as Lovelock recently with his Gaia theory) have sought to prove. Since creativity brings together the actual creations of man and the divine principle from which those creations derive there is here both a concrete togetherness and novelty. According to Whitehead both things must happen simultaneously, for to produce togetherness is to produce novelty and vice versa. As we have noted, The ultimate metaphysical principle is the advance from disjunction to conjunction, creating a novel entity other than the entities given in disjunction.20

And this is fundamental to Whitehead's doctrine of process. For it is because creativity links in the same set of relationships the production of togetherness and the production of novelty that an on-going process is built into the philosophy of organism. Of course, the eternal objects are essentially aloof from change in that it is of their essence to be eternal. But they are involved in change in the sense that the very process of becoming, which is any given actual occasion, depends on the control of the selected eternal object. There cannot be anything “novel”, (that is, different from what is already “actual”) unless there be a “potential” for it. Something “novel” cannot come into existence out of nowhere; it must be a “given” as an “unrealized potentiality.” Whitehead shows us that this unrealized potentiality must be constituted by entities; the word “unrealized” simply underlines the

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contrast of potentiality with actuality. Thus the notion of novelty can have no meaning unless there be entities which are pure potentials, and which are the eternal objects. To conclude, in Whitehead’s universe God affects the world by providing each emerging actual entity with its subjective aim. Divine activity is imparted to mundane actual entities through God’s consequent nature weaving itself across his primordial nature. For Whitehead, God is dipolar, both transcendent and immanent, and in the second capacity, dynamic rather than statically immutable. The immanent God returns a dynamism back into the world through the shaping of subjective aims. As Whitehead puts it: The consequent nature of God, composed of a multiplicity of elements with individual self-realization ... passes back into the temporal world and qualifies this world so that each temporal actuality includes it as an immediate fact of relevant experience ... What is done in the world is transformed into a reality in heaven and ... passes back into the world ... In this sense, God is the great companion - the fellow-sufferer who understands.21

Primordial envisagement of eternal objects is necessary to make our inferior envisagement of them possible. We have noted that the three formative elements are creativity, eternal objects, and God. In the next two chapters we shall consider the relationship between them and how the binding of actuality with potentiality can work in music. And as we explore how Whitehead’s logical methodology can be supplemented by aesthetic intuition we recall Whitehead's own warning against letting scientific domination and analysis eviscerate the “aesthetic needs of civilised society.” Whitehead always maintained that the vivid but transient values of art are permanent and that it is scarcely possible to overvalue their importance in an age which threatens to go down in its materialism and lack of awareness of ultimate issues. Notes 1. In this book all the references are to the edition revised by Griffin and Sherburne (New York 1978). 2. ibid., p.18. 3. ibid., p.291. 4. ibid. 5. ibid., p.256.

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6. ibid., p.258. 7. ibid., p.225 8. See, for instance, A.F.Whitehead, Science and the Modern World (Cambridge UK 1927), p.64. 9. Process and Reality, p.244. 10. ibid. 11. ibid , p.88. 12. Science and the Modern World, p.207-8. 13. Process and Reality, p.40. 14. A Whiteheadian Aesthetic, p.40. 15. Process and Reality, p.247. 16. This is discussed in Process and Reality, p.249. 17. ibid., p.21. 18. ibid. 19. ibid.

20. ibid. 21. ibid., p.350-1.

Chapter Four Music and Process The value of Whitehead's system as a cauldron from which others can draw ideas in order to apply them to their own respective areas of enquiry is undisputed. The general or universal nature of his concepts ensure their relevance in all areas of reality. Strangely, as we have noted, it is in only one area, that of Process theology or philosophy, that his speculations have been influential. Process theology is largely the result of the way Whitehead, along with Charles Hartshorne, succeeded in influencing members of the School of Divinity at Chicago during the 1930s and later. It is only recently, and in a very limited way, that Process has featured in writings about art. Among the most significant contributions is F. David Martin's book Art and the Religious Experience: The Language of the Sacred, which we have previously mentioned in Chapter 1. This work is redolent of the Whiteheadian approach. For example, in attempting to explain the fundamental essence of the different arts Martin concludes that a fine balance and interchangeability of “causal efficacy”and “presentational immediacy” can be perceived in different art forms. He echoes Donald W. Sherburne (see above, p.60) when he writes: Music more than any other art is perceived mainly in the mode of causal efficacy. Abstract painting more than any other art is perceived mainly in the mode of presentational immediacy. Thus music appears in part elsewhere, whereas abstractions appear to be all here. In listening to music, we experience presentational immediacy because we hear the presently sounding tones. But there can be no “holding” and we are swept up in the flow of process. In seeing an abstract painting we experience causal efficacy because

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This extract gives an idea of the modus operandi in adapting Whitehead's theories to a chosen area of analysis. In the context of the present discussion we need to focus on the fundamental point of Martin's argument, that this is a religious quest. His procedure is to carry ultimate questions into the actual context of specific works of art. And if we are to follow him successfully we must be aware of certain elementary facts about sense and perceive them in a Whiteheadian manner and without committing the fallacy of misplaced concreteness. For example, if we consider sounds and ponder on their nature we might argue that when I hear a door shutting, the sensation is not primarily (in the commonsense judgement) an abstract acoustic one. I know what a door is, have heard one bang before, and recognise the common factor. In Whiteheadian terms I, the subject, have already prehended the object and by means of the “mental pole” interpreted it. Consequently, if we are to be useful transcendentalists we may have to be aware of the prehensions and try to listen away from things, listen through things, perceive the inner core of an aural (and indeed visual and other) sensa, to the depth dimension of whatever it is, the referent. Some will see this as somewhat comparable with Heidegger's notion of “Being” as the depth dimension of all “beings”, Being giving enduring value and ultimate significance to beings. George Steiner has written of Heidegger’s doctrine of existence as one of “radical astonishment”, in the way that, “Being” and “being” are the pivot, the core of “lit darkness” to which every path leads, whatever its starting point. 2

Following on from this, and very much in his own terminology, Whitehead tells us that although the ontical (the secular) and the ontological (or religious) are distinguishable, they are not separable. For we must remember that God is an actual entity. So can we ever be sure where the ontical ends and the ontological begins? We may at least tentatively attempt to answer this by scrutinising the materials of our chosen art of music, and look at common experiences of music. To avoid a confusion about “meanings” we will consider pure music only (not programme music). We also need to bear in mind the

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traditional rift between the Referentialists and the Non-referentialists among musicologists and aestheticians, and remember that most aestheticians tend to belong to the second category, being either Formalists (like Hanslick or Gurney) or Absolute Expressionists (like Leonard Meyer). For the Formalists, tonal structures have meanings which are strictly musical. The Absolute Expressionists take a softer line. They affirm the evocation of emotion by the musical meanings, but this emotion is strictly musical, so musical meaning is intramusical for them too. The Referential Expressionists on the other hand claim that musical meanings legitimately refer to the extra-musical world, whether that be ontical or ontological. This theory owes its unpopularity presumably to the implication that somehow one shouldn't listen to music as such at all, rather daydream of swirling torrents and great vistas of the natural world - anything extra-musical in fact (a common perception among non-musical people). We may not favour the theory, but in the present context we may choose to review it and give at least some credence to it, albeit in a rather unorthodox way. This is because the whole point of our discussion is art referring to something else. F. David Martin's bold compression of Whitehead's thought is often useful, and one example recalls our conclusions about time and temporality in Chapter 2: Music more than any other art forces us to feel causal efficacy, the compulsion of process, the dominating control of the physically given over possibilities throughout the concrescence of an experience. The form of music binds the past and future and present so tightly that as we listen we are thrust out of the ordinary modes of experience, in which time rather than temporality dominates. Ecstatic temporality, the rhythmic unity of past-present-future, is the most essential manifestation of the Being of human beings.3

With its similarities to the assertions by Zuckerkandl, the implication here is that music can make us feel process directly because musical notes are presented successively. But successive unfolding is found in other arts too. As we noted in Chapter 2, music's special claim over other art forms surely lies in its abstract nature. As we have stressed, the notes convey internal or embodied meanings, at least in pure music where there are no designative allusions. It appears that only music has both characteristics, namely a successive unfolding and abstraction. But before elaborating on this special claim

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which is made for music, Leonard B. Meyer's differentiation between designative and embodied meaning should be explained.4 In language, when a word refers to an object this is a designative meaning. Embodied meaning occurs when the stimulus and the referent are the same. A note, a phrase, or a section of music has embodied meaning because it points to and makes us expect another musical (not extramusical) event. Embodied meanings are the internal relationships of an art form, and in pure music and abstract painting it is the very lack of a designative meaning that distinguishes them respectively from programme music and representational painting. But, admittedly, designative meanings can be attached by us to them. Designative meaning is strong in literature, film and dance (in dance, the bodies themselves have a designative meaning). Whether having a designative meaning weakens our sense of the fundamental compulsion of process is a vexed question - it might form a distraction inimical to the experiencing of process, at least in the form we associate with music. Martin succeeds in conveying this peculiar engagement or participation in process via music by recalling a striking passage from Sartre's The Psychology of Imagination where the author succinctly observes that music neither dates nor locates. I am listening to the Seventh Symphony. For me that 'Seventh Symphony' does not exist in time, I do not grasp it as a dated event, as an artistic manifestation which is unrolling itself in Châtelet auditorium on the 17th of November, 1938. If I hear Furtwaengler tomorrow or eight days later conduct another orchestra performing the same symphony, I am in the presence of the same symphony once more. Only it is being played either better or worse … I do not think of the event as an actuality and dated, and on condition that I listen to the succession of themes as an absolute succession and not as a real succession which is unfolding itself, for instance, on the occasion when Peter pays a visit to this or that friend. In the degree to which I hear the symphony it is not here, between these walls, at the tip of the violin bows. Nor is it “in the past” as if I thought: this is the work that matured in the mind of Beethoven on such a date. It has its own time, that is, it possesses an inner time [process], which runs from the first tone of the allegro to the last tone of the finale, but this time is not a succession of a preceding time which it continues and which happened “before” the beginning of the allegro; nor is it followed by a time which will come “after” the finale. The Seventh Symphony is in no way in time.5

In Problems of Art6 Susanne Langer makes a distinction between musical time and clock time, with musical time possessing a

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“complexity” and “variability” which is more similar to body time, with its passage of vital functions and the tensions of “lived events”. We have already noted that music certainly seems to give meaning to time, and through it we experience the present in a special way, directed as we are towards the future anticipated by our expectations. Thus if the ontical categories of time and place, and all the habits of everyday existence are not designated, then (to revert to quasi-poetic Heideggerian terminology) we may then be open to Being. When discussing music in more detail F. David Martin's treatment of standard works is sometimes disconcerting. For instance, in clarifying the ontological implications contained in music he compares Bach's “48” Preludes and Fugues (i.e. all of them as a single group) with the Art of Fugue and with the St. Matthew Passion, all three works being reduced by Martin to single, rigidly uniform types. We may agree with him that technically the Passion is a form of programme music for liturgical use, its designative meaning referring specifically to religious events and doctrines. But he goes on rather provocatively to say: Yet music can have a religious programme and even be put to liturgical use and still not be religious, except in the sense that all works of art are religious insofar as they reveal something of the mystery of Being in their seeming inexhaustibility ... There must be a more essential or further inner continuity [my italics] between the music and the religious dimension.7

Unfortunately he is not clear about the “how” of this inner continuity. He points out that the Art of Fugue and the “48” lack religious programmes. But, curiously, he seems to perceive some transcendental element in the Art of Fugue that is missing in the “48” Preludes and Fugues. For he asks, isn’t it possible that the Art of Fugue possesses an inner continuity with the religious dimension that the “48” lack? This is a very problematic assertion, and again we need to ask what exactly is the nature of this inner continuity. With this question poised in suspended animation we could perhaps digress for a moment in order to refer to another area of art where Martin's arguments prove more convincing and certainly more logical. This might help us answer the present question. In discussing painting, Martin recalls the ground-rules set by Tillich, namely Tillich's distinction between “signs” and “symbols”, where “sign” designates ontical (secular) reality and “symbol” designates

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ontological (religious) reality. There is a further distinction too, that between “conventional” signs and “iconic” signs. We also have “conventional” symbols and “iconic” symbols. The meaning of a conventional sign is arbitrarily attached to it, perhaps by social convention, like x and y in mathematics. The sign's value is its transparency, since one sees through it to the message conveyed as when using a non-onomatopeic word. An iconic sign on the other hand incorporates characteristics significantly similar to the referent, like a stickman. In language the onomatopeic word “rattle”, because it resembles the sound of a rattle, is an iconic sign. There is a designative meaning here too and thus this sign is also transparent. Martin then moves to the world of symbols with an analogy between signs and symbols as follows. He cites another human image very far removed from our stickman, namely Christ in Grünewald's Crucifixion. He says of it: “our sight is ensnared, we attend carefully to the embodied meanings.” The designative meaning is very obvious, while the embodied meaning is the divinity and suffering in the lines. Whereas the stickman is a “transparent icon”, Grünewald's Christ is a “translucent icon." The referent of a translucent icon, unlike that of a transparent icon, cannot be understood independently of careful attention to the icon.8

This is where a work of art attains ontological significance, and there is no doubt that works of art possess this translucent iconicity. While Grünewald's Christ has conventional symbols it also has iconic symbols. Martin asserts that without the addition of conventional symbols it will be very difficult for an iconic symbol to function as a religious one. For how can one prove that certain brush strokes in a painting have iconic symbolism? Martin's answer is that if the primary subject matter is ontological, then, and only then can the work be appropriately described as religious. But how does one determine whether a work is ontologically oriented? The answer has usually been – “if conventional symbols are present.” But what if it is not a painting of Christ, or the Cross, or anything like that? Let us say Picasso's Guernica (to cite an example of Martin's). There are no conventional symbols in it which might specifically indicate the religious dimension. We must ask therefore whether it has iconic symbolism, even if only implicitly. Does it not point to a further

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reality in its devastating representation of what the ontical is like when it becomes man's supreme value, which, admittedly, is a point Martin makes? One can assert that Guernica does suggest something other than the secular values of Franco's fascism, a something other than the awful image of a bull signifying totalitarianism. But this “other” image is not explicitly indicated, despite the fact that one is helped in a possible interpretation by the presence of recognisable figures. This raises the issue of how to extend this ontological enquiry to paintings which are completely abstract, or indeed to abstract or pure music. Tillich himself was moved to see in Guernica an ontological dimension, and, as Martin reminds us, it was Tillich who argued that there was more religion in Cézanne's apple than in Hofman's Jesus!9 Similarly, we recall that it was George Bernard Shaw who argued that the “Choral” Symphony was more relevant to the devout believer than Brahms’s Requiem. To return to the question which remains unanswered, seen now in relation to our discussion of paintings, we note Martin's conclusion which greatly complicates the premise whereby the St. Matthew Passion and, say, a secular work like the Art of Fugue are coupled together in an ontological category and regarded as translucently iconic whereas the “48” is categorised as ontical. For he maintains that not only is there a difference between the Passion and the Art of Fugue, (because of the religious programme of the Passion) there is also a distinction to be made between the Art of Fugue and the “48”, with the former at least implicitly seen to possess “an inner continuity with the religious dimension”. He amplifies this as follows: In most of the work - Contrapuncti 1-11, 14, 17-18 and above all 19 (the unfinished quadruple fugue) there is in the structure of the embodied meanings an unearthly inevitability about the resolution of the tensions that is iconic with the sense of reverence and peace that accompanies coercive experiences of Being. For example, in the opening 16 measures of Contrapunctus 11 the 3 note phrases that form the subject sound in isolation somewhat baseless and suspended. Despite their majestic pace, there is unfulfilled tension, anxiety in each one. Yet this theme of 4 measures is centred around the tonic pitch, and when it arrives at the D there is a sense of quiet release, although there is no final release until the last chord of the fugue. The Well Tempered Clavier [i.e. the “48” Preludes and Fugues] on the other hand, despite its perhaps equally powerful icons of inexhaustibility and temporality generally lacks icons of religious feeling . . .10

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Later, he admits – “often no doubt we will differ about such judgements”! Clearly, Martin’s highly programmatic arguments do not convince and are compromised by a too vivid and easily led imagination. The conclusions one can make from them suggest the need for a more careful scrutiny of the musical materials than is found in the analysis. First, if music is an iconic symbol and translucent, showing us a world beyond, then very careful attention must be paid to the actual harmonic and rhythmic characteristics. After all, if God is somehow to be evoked and perhaps even experienced through the icon then the icon itself must be carefully assessed. When one does this it soon becomes apparent that what is really under scrutiny is the language of music as a whole, not just one “secular” piece and the way it differs from another secular one. Some will argue quite convincingly against this by exaggeratedly stressing that a metaphysical distinction is apparent between the Art of Fugue and some example other than the “48”, for instance some banal pop music. We may indeed concur and plausibly dismiss the pop music as failing, through its embodied meanings, to inform us or make us aware of ecstatic temporality because of an alleged triteness of meanings and their failure either to make significant demands upon our imagination or to conjure up a translucent iconicity. But such general statements may be so weighed down with cultural and religious preconceptions and prejudice as to be rather suspect and one reason for this may be the lack of a detailed assessment of the actual music. What if we found that a piece of pop had the same chord structure as a beautiful (transcendentally beautiful) piece by Mozart? What criteria apply then, even when there is meticulous regard for musical materials? So, comparing pieces has its pitfalls, and the comparison between the Art of Fugue and the “48” is no exception. Perhaps therefore we should look at music as a whole (rather than draw conclusions from individual pieces in relation to other pieces) and do so in the light of a modification of an observation by Susanne Langer when she said: The tonal structures we call “music” bear a close logical similarity to the forms of human feeling - forms of growth and of attenuation, flowing and stowing, conflict and resolution, speed, arrest, terrific excitement, calm or subtle activation and dreamy lapses - not joy and sorrow perhaps, but the poignancy of either and both . . . Music is a tonal analogue of emotive life.11

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Unlike Langer I would claim that the iconic designations of music as a whole are not necessarily restricted to the structure of feelings. By means of powerful internal connections which seem inexhaustible the very structure of music (so much that is possible out of so few notes) suggests that music as an analogue of feeling is too restricted a definition.12 To begin with, the fundamental technical basis is an eternal object found in nature and bequeathed by God to us, and as we have previously noted at length, that is the harmonic series. Our approach might be to ponder what the world must be like if between us and the world the phenomenon of music can occur. How must I consider the world, how must I consider myself, if I am to understand the reality of music? This may not have much to do with conventional analysis of a particular piece of music, so concerned are we with certain fundamentals common to all music. And it is fascinating how musical notes, although derived from something very material like the harmonic series, do not correlate with any material phenomena when they are in horizontal motion or vertical grouping. As we have noted in Chapter 2, acoustical phenomena and one's auditory apparatus are indeed material but they have nothing to do with the “meaning” of the sounds in our particular area of enquiry. We might impose a private meaning on the sounds, of course, and we might be helped to appreciate the music by the designative meanings or conventional symbols in it. But one should be cautious in the present context of this personal interpretation, for claims have been made, somewhat provocatively, by Charles Hartshorne and other Process philosophers that the element of feeling is more closely bound up with the “outer world” component than might at first be assumed. As Hartshorne has pointed out in discussing colour (and the comparable point remains true of music) “the ‘gaiety’ of yellow ... is the yellowness of the yellow.”13 As we have already seen, Whitehead emphasises God's immanence in the world. This occurs in three ways, and these provide cornerstones for new avenues of enquiry. First, God supplies every entity with its basic conceptual aim. Second, he is present with the entity throughout its concrescence in its world. Third, as the entity prehends God, so is he an influence on it, and his own consequent nature is duly affected. As Zuckerkandl has suggested at the very end of his book, our epilogue becomes the prologue to a new study. In this context no passage could be more appropriate to close our journey

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from Greek thought to Whiteheadian metaphysics than the following from Johannes Kepler which Karl Popper quotes as a hymn of praise to the music created by man, to the polyphonic music that was in Kepler's time still a fairly recent discovery. In taking as his starting point his theory of the movement of heavenly bodies and the divine music which results therefrom we find a poetic celebration of the great issue which concerns us. Kepler writes: Thus the heavenly motions are nothing but a kind of perennial concert, rational rather than audible or vocal. They move through the tension of dissonances which are like syncopations or suspensions with their resolutions (by which men imitate the corresponding dissonances of nature), reaching secure and predetermined closures ... And by these marks they distinguish and articulate the immensity of time. Thus there is no marvel greater or more sublime than the rules of singing in harmony together in several parts, unknown to the ancients but at last discovered by man, the ape of his Creator; so that, through the skilful symphony of many voices, he should actually conjure up in a short part of an hour the vision of the world's total perpetuity in time; and that, in the sweetest sense of bliss enjoyed through Music, the echo of God, he should almost reach the contentment which God the Maker has in his Own works.14

In the next chapter we shall focus on a fragment of music by J.S.Bach. By examining it in a metaphysical context our method will differ from that of conventional analysis. By appraising it specifically with an affective awareness of its ontological implications according to Whiteheadian precepts, we may thus be able to discern whether it is rational to perceive within it God’s “persuasive” role. Notes 1. p.147. 2. George Steiner, Heidegger (London 1978), p.31. 3.

Martin, op.cit., pp.94-5.

4. See his Emotion and Meaning in Music (Chicago 1956), pp.2 ff. 5. See Martin, op.cit., p.104 and Sartre, The Psychology of the Imagination (New York 1948), pp.279 ff. 6. (New York 1957), p.37.

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7. Martin, op.cit., p.113. 8. ibid., pp.116-7. 9. loc. cit., p.160. 10. ibid., p.124. 11. Feeling and Form (New York 1953), p.27. 12. This is also Martin’s view, op.cit., p.122. 13. Charles Hartshorne, The Philosophy and Psychology of Sensation (Chicago 1934), p.7. 14. Quoted in The Times Higher Educational Supplement (July 24, 1992), pp.15 and 19.

Chapter Five A Whiteheadian Aesthetic and a Musical Paradigm In considering a musical case-study to illustrate how the procedures of Process Philosophy can be applied we recall Whitehead’s advice to take some part of our personal experience to provide clues as to how the real and the conceptual can be merged. To do this we need to clarify the concept of prehension. As we have noted there are two aspects to prehension. Prehensions of other actual occasions are physical prehensions and prehensions of eternal objects are mental or conceptual prehensions. Both aspects appropriate elements of the universe which in themselves are other than the subject, and in so doing synthesise these elements. Physical prehensions are always the data of the past, called by Whitehead “stubborn facts”, about the world as it was. These facts process inexorably into the new actual occasion. But high grade organisms enjoy another kind of takeover from the past, namely what man does when prehending concepts. This emotional response has been touched upon in our discussion of Martin’s views, and it makes up the mental pole of prehension. In order to make the leap from inorganic to living societies Whitehead makes a sharp distinction between the physical and mental pole of each actual occasion.1 The physical pole is responsible for the automatic evolution of material reality, and is more or less devoid of “novelty.” The mental pole on the other hand has an element of subjectivity, is most striking in imaginative thought and is the source of all creative advance in the universe. In prehending concepts we sense an objective scale of values in the form of eternal objects. As we have noted, eternal objects are efficacious in all types of prehension, ranging from sub-atomic phenomena to advanced societies, including human activities. The omniscient God includes all possibilities available for the concrescence of an actual occasion. These possibilities encompass the

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range of eternal objects that are relevant to the concrescence. According to Whitehead, it is through God’s “appetition” that a selection of the relevant eternal objects is allowed to ingress into its concrescence, so that, “the things which are temporal arise by their participation in the things which are eternal.”2 In his chapter on “Abstraction” in Science and the Modern World (1925), previously referred to at the start of Chapter 3, Whitehead comprehends an eternal object in two ways: on the one hand, vis-à-vis its particular individuality in its own unique and peculiar form, and on the other, in its general relationships to other eternal objects “as apt for realisation in actual occasions.”3 The general relationship to other eternal objects implies that the eternal object varies from one occasion to another in respect to the differences of its mode of ingression, for every actual occasion is defined as to its character by how these possibilities are actualised for the occasion.4

Thus actualisation is a selection among possibilities. More accurately, it is a selection issuing in a gradation of possibilities in respect to their realisation in that occasion. Whitehead calls this principle of selective limitation the relational essence. Furthermore, for eternal objects to be relevant to process there is required a togetherness of eternal objects. According to Whitehead, this togetherness must be an aspect of God. To explain how this organic process works, we shall turn to one aspect of reality, to art, and to some abstract music by J. S. Bach, a famous piece with no programmatic reference which might complicate our interpretation of its meaning.5 We chose this nonprogrammatic piece because abstract music represents process in an unambiguous way. Naturally, in order to illustrate Whitehead’s speculations, such is the universality of his philosophy that we could have chosen any aspect of reality. But our aim is specifically to explore a medium whose power possesses a dimension that, in the final analysis, lies beyond the world of concepts. The discussion later on God’s persuasive role may help to relate the aesthetic and the religious aspects, bearing in mind that our exploration of the continuum between temporality and eternity, between matter and spirit, between man and the “wholly other” will always respond to the numinous power concealed in real things, like, for example, pieces of music. For Whitehead’s advice was to start from some section of our experience in the belief that the knower, the percipient event, provides

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the clue to nature in general. Thus, in art the potentiality for becoming is no mere abstract concept. All actual occasions are dipolar, and the physical and conceptual must work hand in hand with an outcome that is real, and that produces a real experience. In art, creative advance into novelty is underpinned by the individual choices of the artist and his jealous involvement with inclusion and exclusion. J.S. Bach, Prelude 1, The Well-Tempered Clavier.

In relation to dipolar reality we can regard the opening note of Bach’s Prelude 1 in C major from the Well-Tempered Clavier as an individual essence, as middle C, 256 cycles per second. But as the root of the C major triad this C has a determinate i.e. a relational essence to other features of the tonality of C. Here, C is the tonic and there is a fundamental axis of C (tonic) and G (dominant), both notes being eternal objects in mutual relation. A congruence exists between these predisposed tonal forces present in nature, and the creative manipulation of the creative artist (drawing in other notes and chords) so as to make a coherent pattern of 35 bars ending conclusively, as it began, on a C major harmony. As the composition develops, the relational essence is extended, at least with regard to the choice of notes and the tonal progress. As in some other Preludes, the rhythmic progress is very regular and repetitive, and even minimalist until 3 bars from the end, the result of constructing the piece throughout on a simple broken chord formula. We can follow the relational aspect in great detail, from the initial departure in bar 2 from C to a D seventh chord in third inversion whose relation to C is as a pseudo-dominant (it is not a major chord) to C’s own dominant, G major. The fundamental ploy of presenting chords 1, 5 and 2 (C major, G major and D minor) in relation to each other is characterised and enhanced by Bach’s decision in bar 2 to hold the C root so that it becomes the

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seventh of the D chord, thus exerting a compulsive tension demanding resolution down to B in bar 3. The eternal object C (note), while remaining in the same place, has now changed its function, (a common procedure in tonal music, whose importance was discussed in Chapter 2). This is indicative of what happens generally in music, where tonal progressions similar to what is found here facilitate subtle interrelationships between different notes whose functions change constantly, and which also bestow on an unchanging note (like the C here) a change in tonal, and therefore expressive, function. To describe this in Whiteheadian terms, we can say that while these chords are built on the determinate relationships of the overtone series (approximate tunings only), the specific instances of these harmonies are actual entities that have ingressed from the eternal object C major or, indeed, from the note C, which has a “patience” for the ingression. This is complicated by the fact that, according to Whitehead’s hypothesis, every eternal object is systematically related to every other eternal object. A relationship between eternal objects is a fact which concerns every relata, and cannot be isolated as involving only one of the relata. Accordingly there is a general fact of systematic mutual relatedness inherent in the “character of possibility.” The realm of eternal objects is properly described as a “realm”, because each eternal object has its status in the general systematic complex of mutual relatedness. In referring to the relationship of eternal objects to actual occasions, Whitehead wrote: The general principle which expresses A’s ingression in the particular actual occasion a is the indeterminateness which stands in the essence of A as to its ingression into a, and is the determinateness which stands in the essence of a as to the ingression of A into a. Thus the synthetic prehension, which is a, is the solution of the indeterminateness of A into the determinateness of a. Accordingly the relationship between A and a is external as regards A and is internal as regards a. 6

In a powerful paper in Review of Metaphysics Charles Hartshorne expressed this perhaps in a more congenial form as follows: But, though the all-inclusive cannot, in its inclusiveness, be absolute, yet since it includes all things, it can perfectly well include something absolute. For to be included is, we have argued, an external relation, a relation of which the included is a term, but not subject. Therefore, the absolute can exist in the supremely relative, in serene independence, serene exemption from relativity. For it is not the absolute which has the relation ‘in’ the actual relative, but

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rather and only the relative which as the relation, “containing” the absolute; just as it is the particular subject which has the cognitive relation to the object, while the latter is only nominally “in” this relation. And, indeed, since an abstraction cannot actually know, it can only, when we speak of it, be something known, an object. Thus the absolute is a divine object in the divine subject and for the divine subject. It is an essence not an existence. Nevertheless, it may yet be that God’s existence follows from his essence, if by “his existence” we mean only that there is some existence embodying the divine essence. 7

Thus the eternal objects are ingressed by selection, and prehending them involves the grading of possibilities. At all microcosmic levels this is highly complex, and with regard to our musical example there will be a multitude of graded possibilities as each harmony progresses to the next. On a wider canvas, this grading of possibilities is quite striking in the overall form of Prelude 1. Since its evolution as a piece has been documented, it is possible to study some revisions and expansions that suggest an ongoing grading of possibilities by Bach, effected with the cooperation of his eldest son W.F. Bach, for whom the piece was originally intended. This takes us into the world of musicology. From an initial version of 24 bars the piece was expanded to 27 bars before assuming its final definitive form of 35 bars. An examination of the various different versions shows the final masterpiece emerging as an extension of the possibilities suggested by the simple basic material. The insight this gives into Bach’s uniquely powerful control over tonal possibilities, not to mention the lyrical inspiration of it all, is a revelation that needs no further comment here.8 Implicit are the hidden possibilities, other valid choices available for Bach, and not just those seen in the two less accomplished versions of this Prelude. (Whitehead’s term for an unrealised possibility was “conceptual reversion” and Bach’s two sketches suggest the nature of such possibilities. But of course these are more than just conceptual, for they actually exist in manuscript). Bach did not exhaust all the possibilities conceptually; he was concerned with one only, which is the final and perfect version. We may assume that excellent possibilities remain unrealised, despite the feeling we might have that this Prelude is unique and exists finally in a very satisfactory form. But in noting the different versions we naturally see that, between any form and another, there is inevitably a continuum of possible intermediate forms. There are alternative suggestions, “untrue propositions”9 which lie undisclosed. To

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comment further on these undisclosed possibilities seems fruitless, as Whitehead’s pupil Charles Hartshorne implied when he said, “counting to infinity is an incomplete process,” (meaning, presumably, “incompletable.”) Like Whitehead himself, we must accept that reality is found in actual occasions, and only in them. As was said in the previous chapter, since creativity brings together the actual creations of man and the divine principles from which those creations derive, there is both a concrete togetherness and novelty to it. According to Whitehead, both things must happen simultaneously, for to produce togetherness is to produce novelty and vice versa, and with some imagination we can reach out to what this means by scrutinizing worthwhile examples of actual occasions like Bach’s Prelude. The ultimate metaphysical principle is the advance from disjunction to conjunction, creating a novel entity other than the entities given in disjunction.10

This is fundamental to Whitehead’s doctrine of process. To recapitulate, we can say that the eternal objects of course are not subject to change, in that it is of their essence to be eternal. But they are involved in change insofar as the very process of becoming, which is any given actual occasion, depends on the control of the selected eternal object or objects. There cannot be anything novel (that is, different from what is already actual) unless there is a potential for it. While bestowing the infinite possibilities of the eternal objects according to various principles of value, God reins them all into a coherent harmony so that all actuality is harmoniously graded. God therefore functions as the principle of limitation, imposing order on the infinite possibilities of the eternal objects. In Science and the Modern World Whitehead asserted that God is an explanation: “God is not concrete, but he is the ground for concrete actuality.”11 As noted in Chapter 3, some years later, in Process and Reality, there is a remarkable and unexplained shift to the assertion, consistently made thereafter, of God as an actual entity: “God is an actual entity and so is the most trivial puff of existence in far-off empty space.”12 Whitehead clearly regarded his original idea of the inscrutable and lonely God as a fundamental inconsistency, and incompatible with one of the aims in Process and Reality, namely to rid philosophical discourse of what hitherto had been “enmeshed in the fallacy of misplaced

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concreteness.” In the three notions - actual entity, prehension, nexus [a collection of entities] - an endeavour was made to consistently base philosophical thought upon the most concrete elements in our experience.13 If God is himself conceived as an actual entity who works as an agent for maximising and harmonising values, then in this form he is enduring, and, as an enduring subject, he relates temporally and in a temporal world; for God’s mode of relationship with other subjects is through his actions having an effect upon the world and its agents, and modifying the world in accordance with his intentions. This logically entails a self-imposed limitation upon his absoluteness; for if he acts in the temporal world then he makes himself available to receive, in the very same field, the acts of non-divine agents. This also implies both a reaching out by God and his dependence on others. If the world needs God, then God needs the world. If God is no exception to metaphysical principles, and if his authority is seen to be restricted and curtailed by this self-imposed consequential nature then one rational argument for it is the assertion that a creator God must have a social bond which he has created, notably with higher organisms such as ourselves. In other words, why not follow the dynamics of creative involvement in which creator and created affect each other selectively? As some writers have put it, to be fully God He needs the universe. If, after creating the universe, the divine reality was exempt from the multifarious diversity of his creation, then what is the point of the creation and what is the universe’s purpose? Since God is actual, he must include in himself a synthesis of the total universe. Therefore, God is immanent in the world and is an ordering entity whose purpose is the attainment of value in the temporal world. The ordering entity is a necessary element in the metaphysical situation presented by the actual world. We have noted previously that Whitehead emphasises the togetherness of eternal objects on which creative order depends. This precise monism, in which all reality is unified, was at the core of Hartshorne’s panentheism (literally pan-en-theism), which validated God’s transcendence by maintaining that everything exists in God. God contains all. On the other hand such is the freedom allowed to the concrescing entity that, while the initial aim is infused by God directly, the actual occasion’s subjective aim refers to the active appropriation by the concrescing entity of what it decides freely to

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take as its own personal goal guiding it towards its characteristic action. God then becomes the source of the systematic introduction of novelty into the world process and for the co-ordination of all the varied activities of a harmoniously evolving world order. Whitehead asserts that, apart from the intervention of God, there could be nothing new in the world and no order in the world. The course of creation would be a dead level of ineffectiveness with all balance and intensity progressively excluded by the cross-currents of incompatibility. If this is correct, truth in art is possible only if it conforms to the patterns at the microcosmic level. Art is not a realm apart from the fundamental structures of God’s universe. It is indissolubly linked to reality, and hence to the world. So we can be sure that a work of art is loaded with ulteriority. Whitehead seems to admit that he cannot provide a rational, verbal conclusion to the argument when he tells us: The relata in Reality must lie below the stale presuppositions of verbal thought. The Truth of supreme Beauty lies beyond the dictionary meanings of words.14

Perhaps it is through scrutinizing masterpieces such as our simple example from the Well-Tempered Clavier that we are able so often to come to terms with powerful undercurrents of ulteriority that are so pervasive in the different realms of human and indeed natural activity. But what of the other arts, and what is their ontological status in relation to what seems to be a special position accorded to music? In considering the relationship between the different arts we recall Walter Pater’s pithy assertion, “All art aspires towards the condition of music.” Since Pater’s time this has been somewhat wilfully deployed as an apologia for a unique power, sometimes felt as numinous, which music possesses. In this context we shall, in the next chapter, explore what possible claims can be made for arts other than music. Notes 1. See Process and Reality, p.108 and many other places where the mental pole is discussed. 2. Process and Reality, p. 40. 3. p.197.

A Whiteheadian Aesthetic and a Musical Paradigm 4. ibid., pp.198. 5. But many years after Bach’s time this piece, the first Prelude from the WellTempered Clavier, assumed a programmatic religious meaning when Gounod borrowed it to make an instrumental accompaniment to his Ave Maria. 6. Science and the Modern World, p.199. 7. “God as Absolute Yet Related to All,” Review of Metaphysics (New Haven 1947), Vol.1 No.1, p.46. 8. Similarly, the idea of Michelangelo “releasing” a figure from the rock is a familiar one to a number of artists, working in all forms, who might regard themselves as artistic vessels or conduits. 9. See Science and the Modern World, p.196. 10. Process and Reality, p.21. 11. p.222. 12. Process and Reality, p.18. 13. ibid. 14. A.N.Whitehead, Adventures of Ideas (Cambridge UK 1933) p.343.

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Chapter Six Music, the Other Arts and Process In making the necessary comparison between different art forms we note a number of reasons why Pater's dictum poses grave difficulties, at least in literature. Pater asserted that the ideal condition of art is for the matter to be inseparable from the form, so that the more effectively the material is fused in form the more splendid the work of art. In literature this is difficult and perhaps impossible to achieve. In the novel, poetry and drama the very fact of their reliance on specific references to life, i.e. their fundamental concern with life values, is what gives them coherence. Unlike music, literature strives with difficulty to attain a purely structural and formal coherence without necessarily drawing in the extrinsic, from life. The flow of words would have little value were they to be appreciated for their sounds alone, as is most often the case with music, at least instrumental music. In Chapter 4 we learnt that the sense of music is inherent, its meaning wholly intrinsic (embodied) while words and sentences are designative and cannot achieve coherence independently of their referents, images, facts and meanings from life. In his writings I.A.Richards expounded at length on how the auditory arrangement of vowels, consonants, phonemes and words have a design which needs to be more than simply sound content. A poem is not really a perfect fusion of content (meaning) and poetic technique (form). The poetic line is self-evidently independent of the poetic rhythm despite the wonderful examples that exist where one feels that a perfect unity has been achieved. In his Practical Criticism1 Richards, in a rather droll fashion, compares two trivial lines and points out the immense difference between: “Deep into a gloomy grot” and “Peep into a roomy cot.” He explains that the difference is not lessened by the

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comparatively slight contrast between the sounds of each line. A student's contradiction of this (along the lines, “I should never bother about the sense, the sound is enough for me”) provoked Richards to drive home the point by composing a poem made up of nonsense syllables as a “double” or “dummy” to Milton's On the Morning of Christ's Nativity, xv, starting: “J.Drootlan-Sussling Benn/Mill-down Leduren N./Telamba-taras oderainto weiring/Awersey zet bidreen.”2 Changing Milton's content to what is clearly non-representational illustrates the chasm which exists between poetry and music. While the coherence of the sound is the sine qua non of the meaning of a piece of music, in literature the sound of words and sentences cannot achieve coherence independently of their referents. There is a similar case to be made with relation to painting, at least concerning representational works. In the same way that Mozart's Symphony no.40 is not “about” anything as Paradise Lost is, it is also not “of” anything as the Mona Lisa is. We might not be so confident of this assertion if we chose Berlioz's Symphonie Fantastique or Beethoven's Pastoral Symphony, with their representational implications (conveyed, incidentally, and unlike Beethoven's Ninth, without specific recourse to words). In his book Real Presences: Is There Anything In What We Say? George Steiner, with characteristically rhetorical verbal pyrotechnics, aims to grapple with the distinctions which exist between the theoretical functions when directed to surface forms and content, and those same functions when directed towards the depth content. Towards the end of his book his central concern with music comes to the fore. Pater is revisited (“In music form is content, content form.”3) But he goes further than Pater. The “depth content” of music for Steiner is a power or meaning which is spiritual, and with a depth of being such as to prompt the question “can there be art in the absence of ‘the rival Maker?’”4 For Steiner God is the premise for all worthwhile aesthetic activity. He makes a “wager” on meaning and understanding in the arts which he describes as “a wager on transcendence.”5 This is done in faith, i.e with an awareness that while proof is not possible, the arguments may be convincing enough to

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persuade Steiner’s readers of the involvement of a transcendental participant. In this scenario it would be plausible to see the artist himself as a god: “God is in reality nothing but another artist ... declared Picasso, whose own appetite for invention, for self-recreation was, indeed, that of a demiurge.”6 Matisse was even more direct (“Yes, but I am God.”) And James Joyce's simile in A Portrait of the Artist as a Young Man conjures up a mysterious disaffection: The artist, like the God of creation, remains within or behind or beyond or above his handiwork, invisible, refined out of existence, indifferent, pairing his fingernails.7

The aura is of an otherness, an awe-fullness whose source is felt as the Maker. And it is a transcendental source not just in music but in other arts too, although they seem to be less adequately underwritten by the sacred. For Steiner, rationality dictates that this is no more than presupposition: it is clearly a wager - the postulate cannot be proven. Steiner intimates that we must respond to the world as if to the “real presence” of the transcendental. He continuously admits that his opinions are just speculative and, to use the language of linguistic philosophy, “verification transcendent”. But seeing an art as transcendental, on the one hand, and, on the other, seeing God directly at work in the art form are two rather different things. We can be drawn through the mediating power of a poem or a painting or a piece of music to a higher plane than we might expect from the rationallogical apparatus of the art in question; the work in question might leap out of nothingness . . . [so that] its enunciatory shape so new, so singular, to its begetter, literally [ leaves] the previous world behind.8

This does not necessarily mean that God's hand can be seen. But this is exactly what Steiner surmises; for him this transcendentalism is divine. The “quantum leap between the character as letter and the character as presence” 9 is not of an aesthetic order (or only of an aesthetic order), it is specifically metaphysical, divine. He is unfazed by the fact that God has absented Himself so that, as Simone Weil

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said, “truth is secret.” And since his absence is essentially indescribable - being ineffable - then the question is raised whether anything at all can be said about such an intractable matter. Steiner perseveres over 200 pages and more, in impressionistic fashion, encouraged by the fact that by charting the known in this world one may be able to fathom the mystery of the unknowable. If the intimations lie too deep for words, at least an attempt at specificity and careful attention to the “semantic markers” of different art forms may provide ontological clarification. Steiner sees the pigments or incisions which externalize Grünewald's Issenheim triptych or Brancusi's Bird, or the notes, tempo markings etc. which “actualize” Schubert's posthumous Quintet as a re-enactment, reincarnation via spiritual and technical means of that which human questioning, solitude, inventiveness, apprehension of time and of death can intuit of the fiat of creation, out of which, inexplicably, have come the self and the world into which we are cast. 10

He continues by acknowledging the specific role of music as a paradox which unites the palpable with the inexpressible. When reviewing the book in The Times Literary Supplement, Roger Scruton reacted to Steiner's extolling of the supremacy of musical expression as follows: “Small hope, then, for the tone-deaf in Steiner's Church.”11 This is not altogether fair, since, as we have noted, Steiner sees a “carrying over” of the inexplicable in the more discursive or representational arts, especially where religion is specifically welded to myth. He cites different (very different) aspects of the one question that is ineradicable in man: is there or is there not God? as posed by Victor Hugo's late epics on God and on Satan, Faulkner's Light in August, Melville's Moby Dick and Dostoevsky’s The Brothers Karamazov (in the parable of the Grand Inquisitor.)12 But whether the ineffability is apparent specifically in the semantic markers of literature, as they are in music, must surely be open to question. If the ineffable is directly sensed in arts other than music then shouldn't they contain the ineffable intrinsically, like music, in their semantic markers? In painting, perhaps this can be seen both in representational

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and modern abstract works. Or can it? Steiner asks a question, rather similar to ours concerning poetry, about representational painting's ability (or shortcomings) in this respect. He asks, In what possible regard ... can we attach transcendent dimensions to a stilllife, to the portrait, to the numberless depictions of the natural and domestic settings in which we lead our non-metaphysical lives?13

We can attempt to answer this question by judging the capacity for transcendence in representational and non-representational art respectively. To take representational art first, we can take no more trivial artifacts as a subject for painting, but in this case redolent with meaning, than a worn-out pair of shoes. Van Gogh painted them and Heidegger meditated on them14 in a manner which brought out the integral reality beyond scientific analysis, (and also in a manner which anticipates the influential role Heidegger was to have on postmodernism). To use Heideggerian terminology the shoes have an inherent “thereness” or meaning which cannot be externalized because the meaning is “within-it.” In them can be sensed the life and purpose of the peasant who wore them day in day out over many years. We read into the picture what it is for a man to live in a particular way. The shoes must be understood on the basis of what is at work in Van Gogh's painting and not in just the “thingly” character of the pair of shoes. The pair is a thing plus. The question is posed: what is man and what is humanity if these shoes are according to Heidegger's explanation? In attempting to disclose the “truth of beings” Heidegger expresses a deep-seated need often present in the work of aestheticians and art critics to disclose meaning that is hidden in spite of the specificity of the image! Heidegger argues that such a simple revelation is inherent in every work of art. In Van Gogh's painting there is a formal self-sufficiency on the side of the object, of the pair of shoes. It is shoes that are depicted; but they are enhanced immeasurably by the artist revealing the creative dynamic by means of light and colour. It is because of the experience of van Gogh (and many another secular artist) that we should not be drawn so easily to accord a special status to explicitly religious works. For Heidegger

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“world” and “earth” clearly presuppose a metaphysical challenge. Because of this, being representational has more value because it is grounded in man's experience and therefore is redolent of life values. Paradoxically, according to this belief, the closer the art is to life, via its representational nature, the more authentic value it seems to have, and by implication the more transcendental it is. Similarly, the absorption of the object into its affective world is explored also (and, again, impressionistically) by Mikel Dufrenne when he describes the soft delicate tranquillity which is expressed by the interiors of Vermeer ... not contained between the walls which the painting encloses. It radiates upon an infinity of absent objects and constitutes the visage of a world of which it is the potentiality.15

With reference to representational art Paul Tillich resolutely disputes Heidegger's contention. While accepting that art indicates the character of a spiritual situation, and that its symbols have something of a revelatory character not found in scientific conceptualisation, which “must suppress the symbolical in favour of objective adequacy,”16 he maintains that the forms of the “naturalistic and impressionistic tendency” in art are “the perfect forms of selfsufficient finitude, in naturalism on the side of the object, [but] in impressionism on the side of the subject”, albeit with great creative power and with the force of symbolism. But nowhere does one break through to the eternal, to the unconditioned content of reality which lies beyond the antithesis of subject and object.17 In contrast, when we turn to abstract art we find that planes, lines and colours do not just express what he describes as “life values”, but represent both “world values” and “life values.” For shapes and mathematical forms are inherent in life and earth and have been artistically interpreted in works of seemingly mystical transparency. Therefore, for Tillich, when the dissolution of the natural forms of objects took on a geometric character: planes, lines and cubes ... received an almost mystical transparency. In this case, as in expressionism in general, the self-sufficient form of existence was

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broken through. A transcendent world is not depicted as in the arts of the ancients but the transcendental reference in things to that which lies beyond them is expressed.18

Clearly, a transcendent world is not depicted here in the same way as in romantic or impressionistic art, but the transcendental reference to that which lies beyond is unmistakable. The inherent quality of a work, its capacity to evoke the Other is found in what is intrinsic rather than extrinsic. The semantic meaning therefore achieves an autonomy and becomes full of meaning because the other-worldly reality is embodied in it. In the same way that, according to Heidegger, Van Gogh liberates experience from the drag of social and biological purposiveness, so for Tillich does Mondrian liberate intelligence from the constraints of mathematical proofs and scientific verification. To return to literature, and to admit that the semantic incompatibility we have noticed in representational and non-representational painting is no hindrance to our argument that Steiner's wager may be justified, we can test the nature of our assertion by considering “presence” in one small corner of the work of a notable pantheist, William Wordsworth. In his book, Wordsworth's Theory of Poetry, J.A.W Heffernan maintains that, For the rest of his life [Wordsworth] firmly believed that when a poet transforms visible universe by the power of his imagination he imitates the creative action of nature herself.19

The poet's connection with nature, furthermore, is seen as a quasidivine manifestation. Wordsworth's imagination works by analogy. In a well-known passage in Book X111 of The Prelude, “Wordsworth's ascent of Snowdon”, the poet describes what he saw from the peak, and it is a great moment in poetry. The certainty of its declaration that there is an imagination in nature analogous to that in man is aweinspiring. In its consideration of nature's capacity to transform “as if with an imaginative power” we see traced the analogy between the

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mind of man and nature. Heffernan seizes on the “as if” line (actually found only in a fragmentary draft) and uses it to provide a clue to one of the most vexing questions raised by that passage: just what is the “mighty Mind” of the early version, or the lower-case “mind” of the later one? The answer, I think, can be best approached by means of an algebraic proportion. What Wordsworth witnessed at Snowdon was the transforming effect of mist and moonlight upon distant hills. This effect struck him as very similar to the transforming effect that he, as a poet, often had upon the images he used in his poetry. In poetry, he believed, such an effect was produced by the imagination. But what produced it in nature? We have three givens and one unknown - all the requisites for a standard algebraic proportion:

human imagination __________________ transformation of ages in poetry

=

X _____________ transformation of natural objects in actual experience

In ordinary English, the human imagination is to the transformation of images in poetry as X is to the transformation of natural objects in actual experience. With a formula something like this, not articulated but certainly felt, Wordsworth groped his way toward a definition of X, the unknown factor. What he concluded, I think, was this: the transformation of natural objects before his very eyes was “presumptive evidence” - a favourite phrase of Wordsworth's - that something like the human imagination was at work upon them. It was a mighty mind, archetype of the human imagination; it exercised itself on natural objects “as if” with imaginative power. What Wordsworth saw at Snowdon was an image, emblem, or shadow of that mind, a demonstration of its power for the human senses. But only in the visible demonstration - only in the emblem - could he perceive the mighty mind. In the Platonic language of the later Prelude, therefore, he ascended from “sense ...to ideal form.”(XIV,76) ... Can we give the “mind” a specific name? It is extremely tempting to call it God ... But in fairness to Wordsworth we must resist ... In the early version of the Prelude Wordsworth tells us that the mighty Mind is exalted by “the sense of God”(XIII,72), which surely implies that it is not identical with God. Further, even though Wordsworth seems to separate the human imagination from the “Power” of nature, which is its “Counterpart/ And Brother'”(X111, 89-90), he does not clearly separate it from the “mighty Mind.”20

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The poem, with its specific statements conjuring up the divine (and obviously done conceptually), is of a different order from what can be found (nonconceptually) in music or in non-representational painting. And in the same way that Tillich doubts the noumenal capacity of naturalistic painting so does poetry, it would seem, in its specificity, also lack a capacity that is transcendental to the degree that music can be. Speech lacks the direct contact with the ineffable. To return to Steiner’s book, there, as we have seen, God is very much part of the equation. But in his rhetorical manner Steiner never succeeds in clarifying the exact nature of God's participation. One reason for this is that his process is emotional rather than rational. His mode of address fails to explain certain logical aspects that would have thrown some light on the problem. Instead, his book inhabits a dim penumbral region full of vague, inarticulate feelings imbued with an alienating piety. Clearly a more logically coherent structure for imbuing works of art with transcendental values is called for. One convincing way of doing this must surely be via Process philosophy. Steiner's thesis would have benefitted from an injection of rationalism into its colourfully empirical observations. Such a rational approach is provided by Process whereby feeling and rationality are carefully balanced. For Whitehead observed somewhere that no one has ever been a pure empiricist and, likewise, no one has ever been a pure rationalist. Finding the proper balance appropriate to the circumstances (Aristotle's mean) is the challenge, and we will now consider briefly how Process’s approach to the arts is framed within a universal, centred vision of reality, of all actual entities in the world. In adapting these universal truths to art we should note that Whitehead's axiology is remarkable in giving aesthetic value a primacy over moral value. He claimed that the most fundamental order of reality is aesthetic and that “The real world is good when it is beautiful.”21 In turning to a literary gloss on this aesthetic position - and to note, say, Wordsworth's (and many others') cloaking of philosophy in art while responding to the imaginative world which they create, we perceive a basic insight that man is wholly “in nature.” He is thus to be

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perceived in a cosmological perspective in which, according to Whitehead, all philosophical problems are to be raised and resolved. In Whiteheadian language, when we read The Prelude we may be drawn towards seeing through it towards a theory of “propositions” (Whitehead's term) involving the transcendental. Its text can be regarded as a configuration of linguistic symbols which tend to elicit a hybrid physical feeling of God, in respect to God's conceptual feeling which is immediately relevant to the universe "given" for that concrescence.22

Its nature is “a derived conceptual feeling which reproduces for the subject the data and valuation of God's conceptual feeling.”23 Few would doubt that Wordsworth’s way of expressing this has a more agreeable tone than Whitehead’s, but the latter’s precision of thought and expression has immense value in the way God is portrayed as himself experiencing reality in a sentient manner, so that he (as superjective) becomes a sense-datum for other actual entities. So authoritative and influential was Whitehead's teaching that, at least among his acolytes in the USA, Process philosophy has assumed a significance comparable to many of the most important philosophical movements of the last three or four hundred years. Since, today, postmodernist deconstruction would seem to be the unavoidable framework of all discourse, it is logical at this point to have a coda to our chapter and enquire how postmodernism might respond, in its avowedly sceptical and anti-authoritarianism manner, to a movement such as Process, that offers universal explanation of important phenomena. To start, Process's bold reconstruction of the idea of God would surely upset irreligious deconstructors, who, anxious to see the horizon wiped clean of all traces of divinity, might espouse a creativity untrammelled by the “normative” factors of Process's “grand narrative.” Contrary to expectations, however, there are at least three leading proponents of Process, David Ray Griffin, Charles Birch and John B. Cobb, who have aimed to show Process's strong postmodern quality. Whitehead's comments in the 1930s and 40s in relation to inexactitude of language prompted Cobb and others to make a connection with the postmodernist idea of instability of language, and Whitehead's

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observations in Science and the Modern World strongly suggest a break with modernity. Incidentally his critiques generally are somewhat comparable, if expressed very differently, to Heidegger's, who has been acknowledged as a key precursor of French deconstruction. In his paper “The ‘End of the Grand Metanarratives of Progress’?” Raymond Younis argues that Whiteheads' affirmation of “inexactness” seems to anticipate the indeterminacy of meaning affirmed by the likes of Lyotard and Derrida. These are not identical positions to be sure, since Derrida seems to be interested in pointing out cases of indeterminacy in arguments and assertions in which systematic coherence or rigour are rendered problematic, and since Lyotard seems to be interested in affirming the failures or the insufficiency of “grand metanarratives” which are employed to legitimise certain restrictive Western methodologies and which, as he would have it, are inextricable from metaphysics and its speculative content.24

While Cobb sees the deconstructive model as rather like peeling the onion, Process postmodernism has a different model for renewal, deriving from Whitehead's detailed account of creativity - the many becoming the one and increased by one - in a pluralism implying an unmasking, a deconstruction that positively reacts to the many, generously aiming to relate all aspects without attacking established norm. This is less of the “peeling the onion” type, more of “seeking insights into the inexhaustible reality of the plenum of events, wherever those insights can be found.”25 Notes 1. I.A.Richards, Practical Criticism (London 1964), p. 231. 2. ibid., p.232. Of course, we could cite Edward Lear to exemplify that value can be found in nonsense, but this is not really the point here. 3. Real Presences, p. 217. 4. See the dust-jacket of Real Presences. 5. ibid., p.214.

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6. ibid., p.209. 7. ibid. 8. ibid., p.202. 9. ibid., p. 211. 10. ibid., p.215. 11. The Times Literary Supplement, May 19, 1989, p.534. 12. See Steiner, op.cit., p.220. 13. ibid., p. 224. 14. Martin Heidegger, “The Origin of the Work of Art” (1936), tr. Hofstadter Poetry, Language, Thought (New York 1971), pp.17-87. Previously Steiner had acknowledged the potency of Van Gogh's “almost raging insistence that the placing of the piquant, of ‘the yellow that is somehow inside the shadow of the blue’, is, in the severest observance of the term, a metaphysical act, an encounter with the opaque and precedent authority of essence.” Real Presences, p.211. 15. Mike Dufrenne, The Phenomenology of Aesthetic Experience, tr.E.S.Casey et al.(Evanston 1972), p.181. 16. Paul Tillich, The Religious Situation, tr. H.R.Niebuhr (Cleveland 1956), p.85. 17. ibid., pp.86-7. 18. ibid., p.88. 19. J.A.W.Heffernan, Wordsworth's Theory of Poetry: The Transforming Imagination (Ithaca 1969), p.105. 20. ibid., pp. 102-4. 21. Adventures of Ideas, p.345. 22. Process and Reality, p.225. 23. ibid.

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24. Raymond Younis, “The ‘End of the Grand Metanarratives of Progress’?”A paper given at the Australasian Association for Process Thought Inaugural Conference, Sydney, May 1997. 25. John B. Cobb, “Two Types of Postmodernism: Deconstruction and Process”, Theology Today, Vol 47, No.2 (July 1990), p.149.

Conclusion Readers may be anticipating an examination of a rather obvious issue, namely the interaction between music and theology, or at least the more recent developments in this field. They will probably conclude that my reticence about this comes from the general preference shown in this book for the phenomenalistic over the theological. However, one eminently logical theologian, Paul Tillich, has made a ground-breaking contribution in setting an agenda for the role of the arts in theological work; and, similarly, because F. David Martin is a Process theologian (and a Tillichian), his work naturally has been critically reviewed in Chapters 1 and 4. As is apparent in the Introduction and Chapter 1 several theologians in previous centuries have treated music and the arts with theological seriousness, but most of their modern successors have either neglected the topic or tended to confine their deliberations on aesthetics to ethical matters. They have generally restricted themselves (as Tillich himself did in Systematic Theology) to the role of the arts in the life of the institutional church. At this point we must remind ourselves that theological aesthetics are to do with the full panoply of aesthetic considerations in a religious tradition, thought, worship and practice. Consideration of the arts is just one aspect of this wide-ranging category within theology. It is surely right to strike a cautionary note on the work of theologians during the last half century. When religious thinkers write about art we sense a method of approach from within a religion, and often their work seems to dissolve into history and sociology. They have tended to avoid philosophical enterprise, perhaps because the logical criteria of philosophy are thought to be somewhat irrelevant to them. Since theology is neither a science nor a branch of formal logic, as A.J.Ayer contended in Language, Truth and Logic, it could be abandoned to a limbo outside the scope of positive knowledge and significant inquiry.1 In contrast, the more phenomenalistic attitude in the present book is an examination “from without” the bounds of established religion.

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In an examination from without you aim to use your reason creatively, in the sense that you bring forth ideas which are not simply re-arrangements of data arrived at through sense perception. Furthermore, some of us will have noted that our experiences of music and art, via an empirical process, have a mysterious quality, an ulteriority which goes beyond a mere desire for enjoyment. In listening creatively to music we do not just enjoy it, or merely project something into the object of our admiration by imagination, rather we feel within it something peculiarly profound. In this respect we are not reacting very differently from the theological aesthetician, but we do not carry his institutional baggage. Sometimes a work of art will have such a striking emotional effect as to directly bring us face to face with higher realities like our mortality, or, as the passage quoted from Alister Hardy at the beginning of the book exemplifies, with God. But even when the conviction is so strong that the experience is of profound importance we can never be absolutely sure that all is not imagination because there is here, in the absence of scientific verification, a fear that what has been achieved may after all be a nonsense because of the perceived irrationality. Many would agree that advancement towards a rational, scientific knowledge of God is impossible because of the incompatibility between two ways God can be known, through the senses on the one hand, as a system of concepts on the other, the age-old tussle between faith and reason, theology and philosophy. There is a great difference between the kind of assent that is required by a philosopher and the kind of assent that is invited by the theologian. Since faith embodies wisdom of a tradition or authority or revelation, then it is perceived as not demonstrable by reason. Consequently, much of the content of theological aesthetics, indeed of theology per se, is prompted extrinsically through infallibly inspired scriptures. Coupled with the weight of institutional teaching are certain mysteries which soar above human reason, so as to question the nature of their coherence and, especially, verifiability. Concerning coherence we may recall Heidegger’s summing up of the problem when he acknowledged that whereas theology gives thought to faith, thought full of faith is not faithful to thinking. It rather blindly answers to God. In Heidegger’s words, “faith and thinking cannot be made to coincide.” 2

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During the last half century theologians, and Process theologians in particular, have been coming to terms with and possibly discomfited by all this. They have endeavoured to answer the question whether God is an object that enters into our immediate awareness through a possible experience or is He rather only an object of speculation, purely a system of concepts known through the logical consistency of propositions. If He is purely a system of concepts can He also be an object of sensuous experience? Or are they incompatible? Although Process has tended to concentrate on the second possibility, that of rationalising the divine presence, it is not necessarily the case that the polemical thrust of Process philosophy has neglected the claims of belief “in” rather than “about” God Following on from this one can elaborate on the psychological ramifications, based on fear, which are implicit in beliefs not being provable. The powerful Latin proverb timor fecit deos (fear created gods) is redolent of man’s existential anxiety and encapsulates the Freudian analysis about religion being largely projection. For Freud religious faith was seen as no more than a wish-fulfilling illusion.3 He claimed that a large portion of the mythical conception of the world which is central to most religions is nothing but a psychological projection onto the outer world. The unclear inner perception of man's own psychic apparatus incites him to illusionary thoughts about immortality and the hereafter, and these become projections of a psychic interior which carries with it a vast luggage of psychomythology. Thus God is largely a creation of man, who projected into God his own human characteristics. Psychologically speaking the belief in a personal God is ultimately nothing but the belief in an elevated father image.4 This desire for a father, according to Freud, leads naturally to religion. Freud’s theory that religion is a projection of man’s desires resembles ideas previously voiced by D.F.Strauss and Feuerbach. For them too religion was the dream of human and not of divine development. Consequently, man thereby can transcend himself, and religion is a comforting means for objectifying man’s own essence in ideal terms. Therefore, the Christian idea of the incarnation is nothing but the reflection of the dream of man to become god. But as a counterargument to this, as Anthony Storr points out in discussing Freud, this general approach to the issues arose from a very narrow position and a psychological shortcoming which “as he [Freud] himself admits, is incapable of understanding

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ecstatic and mystical experiences which for many people are the origin of ‘religious’ feelings.” 5 So much for the cautionary note. If we are to counter the accusation that our reaching out to the spiritual dimension is mere projection we need to establish our defence along a broad front, and include facts that are provable and scientific if this is at all possible. But to give scientific credence to what lies in the metaphysical domain may tend to reduce the essential mystery of our exercise, as might be the case when we read Zuckerkandl for instance. The predicament is that if knowledge of the ontological becomes possible then its inexhaustibility would surely be reduced to the exhaustible. Nevertheless it seems important to define God in terms of concrete experience, as is certainly the case in any Whiteheadian reference to God. Achieving plausibility is clearly problematic. Inevitably, accusations of self delusion and irrationality have been levelled against many cogent writers for neglecting to supply “irrefutable proofs,” among them even the “irrational” trio of Bergson, William James and Dewey (Whitehead’s colleagues in radical empiricism). But they were defended resolutely by none other than the arch rationalist Whitehead when he remarked (in connection with all three) that “one of my preoccupations has been to rescue their type of thought from the charge of anti-intellectualism, which rightly or wrongly has been associated with it.”6 It is to be hoped therefore that the process whereby art goes beyond the rational structures of logic is available to us. There is often a defence of this by Whitehead and his followers, including his pupil Susanne Langer, who wrote: One can sometimes prove the consistency of concepts, and inconsistency can always he logically demonstrated; but one cannot prove the excellence of a concept, even if it be logically impeccable, except pragmatically, by operating with it successfully.7

Operating successfully may often involve “felt beliefs.” As such these are essentially beliefs “in” rather than beliefs “that” or beliefs “about.” We must therefore proceed to ask what is the nature of beliefs “in.” The general submission to a process of scientific verification that is normally required by society is usually via some form of repeatability. Ensuring repeatability causes systems other than scientific ones to have a serious verification problem. Some writers have sought to deal with this dilemma by producing, somewhat paradoxically, logical

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arguments in support of “felt truths”, and none more persuasively than Tillich and Whitehead. Tillich cautioned us8 against making the experimental and repeatable, scientific method of verification the exclusive pattern of all verification. In more than one place he boldly asserted that verification of the experiential type, as opposed to the experimental, has the advantage that it need not halt and disrupt the totality of a life process in order to distil calculable elements out of it (which, apparently, experimental verification must always do). From this we can deduce that the verifying experiences of a nonexperimental character can be truer to life, though presumably less exact and definite. The question posed by such a belief is whether introducing the experiential into metaphysics allays our inhibitions about the intelligibility of such an argument as Steiner's, previously discussed, which was presented, as noted above, in rather a shadow cast by his admission of its “verification transcendence.” Process philosophers generally would have the necessary confidence that others lack in this context. They would assert their belief “in” the very notion of non-conceptual thinking as plausible and bound up with our nature and the nature of our universe. We might not expect non-conceptual thinking in the non-theologian Whitehead, but he as well as Tillich occasionally deplored the tendency of logicians to ignore all but the narrow class of propositions which interest them directly. In Process and Reality he made this very striking suggestion: The fact that propositions were first considered in connection with logic, and the moralistic preference for true propositions, have obscured the role of propositions in the actual world. Logicians only discuss the judgement of propositions. Indeed some philosophers fail to distinguish propositions from judgements; … But in the real world it is more important that a proposition be interesting than that it be true. The importance of truth is that it adds to interest.9

This ambiguous and paradoxical statement raises a question as to whether Whitehead believed that an “ultimate” mode of reasoning (in all fields of inquiry) has a somewhat different norm of deduction and induction than is normally acceptable. Indeed, are there modes which are neither deductive nor inductive? Also, more radically, are not deductive and inductive reasoning themselves dependent on modes of reasoning which are neither deductive nor inductive? If so, this will

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produce a defence of modern theology with its perceived distrust of reason. And if we go back to the passage quoted from Alister Hardy we sense that a comment made on revelation and faith by John Hick goes some way towards strengthening the validity of perceptual, experiential knowledge. In his Philosophy of Religion Hick argues that just as our knowledge of the physical world is ultimately based upon sense perception, so any religious knowledge must ultimately be based upon aspects of human experience as the source of the basic religious data. He writes: Thus, reason can never replace experience as the source of the basic religious data ...[Reason] must seek to understand the implications of what is known by faith: in a famous phrase of Anselm this is “faith seeking understanding” ... Once certain “facts of faith” are acknowledged or confessed by a religious community the task of the theologians is to draw out their implications, relating them both to one another and to human knowledge in other fields.10

Standing in the tradition of Anselm, Karl Barth supported this point by contending that theology needs to reconsider faith: “testing and rethinking it in the light of its enduring foundation, object and content …What distinguishes theology from blind assent is just its special character as ‘faith seeking understanding.’”11 Similarly, revelation can be consonant with reason because, as has been shown, the world bears some revelatory marks of the world’s dependence on God for its existence and order. Over the centuries Christianity has developed many different conceptions of the difference between reason and revelation, but has never deviated from the belief that vision of ultimate reality, which for Platonists is knowledge in its purest sense (noesis), is not achievable by use of intellect alone. To carry this point to a different area, where the demands of logic and reason would seem to be paramount, we note that Whitehead also asserted that perceptual knowledge is just as much a factor in mathematical insight or scientific discovery, (but obviously not in its final fashioning). It is understandable that mathematicians have frequently seen their activities as akin to artistic creation. This may be because mathematical discovery (so mathematicians would tell us) is not completely a matter of logic. Apparently it can often result from mysterious powers in which the unconscious recognition of other, hidden connections plays a part. Thus, a truly creative scientist will choose one pattern for beauty's sake out of innumerable possibilities.12

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It may be strange to see an aesthetic beauty at the core of certain scientific discoveries, but a definition of beauty is neither limited to art nor, conversely, is it the whole of an aesthetic theory. In seeking to understand art we must concern ourselves with many different aspects of it spread out on a vast canvas, including, among other things, understanding aesthetic experience, artistic creation, and its ontological status and function. Furthermore, our tendency to view music and the arts against the widest possible canvas is justified by Whitehead's example in applying his metaphysics so broadly. He once argued that one of the motives of a complete cosmology was to construct a system of ideas which brings the aesthetic, moral, and religious interests into relation with those concepts of the world which have their origin in natural science.13

Above all there was an instinctive aim to centre reality in the aesthetic experience. When he wrote the following passage in Religion in the Making Whitehead clearly had a concept of the aesthetic which is really metaphysical. Whether this is no more than a pious assertion will be a matter of opinion: The metaphysical doctrine, here expounded, finds the foundations of the world in the aesthetic experience, rather than – as with Kant – in the cognitive and conceptive experience. All order is therefore aesthetic order, and the moral order is merely certain aspects of aesthetic order. The actual world is the outcome of the aesthetic order, and the aesthetic order is derived from the immanence of God.14

In contrast to demonstrated truths, another problem faced when communicating felt truths is that this is done via symbolism and metaphor. Even the arch-rationalist Whitehead conceded the inevitability of this. The transparency of felt truths to the ontological cannot be expressed other than poetically, for in discussing them there is no literal explanation, only another kind of symbol or metaphor. As we have noted in Tillich, the strength of felt truths as distinct from demonstrated truths lies in their conformity to the lived experience. The dismembered rationality of analysis which characterises techniques of abstract thinking has its value, but in the final analysis one senses that to measure and count is not to see. It follows that once Whitehead has exhausted nearly every logical abstraction in Process and Reality he eventually defines God’s presence in rather different

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Conclusion

language, which is metaphorical and essentially in aesthetic terms. Even in Process and Reality there is a palpable change in his expression to a more poetic style as he digresses fancifully on the four symbolic figures in the Medici chapel in Florence, - Michelangelo’s masterpieces of statuary … exhibit the everlasting elements in the passage of fact … forever showing the essences in the nature of things.15

He goes on: “It implants timelessness on what is passing”, it becomes “the moving image of eternity.”16 This is Whitehead relaxing into an impressionistic mode, and, as a result, the comment is not particularly instructive. We ask, in what way does the scene implant timelessness, and how? At this point (to use Whitehead’s own words from another source which compounds the direct with the oblique), “The basis of experience is emotional. Stated more generally, the basic fact is the rise of an affective tone originating from things whose relevance is a given.”17 In this vein we are not any more dealing with a cut-and-dried metaphysic. On the contrary, Whitehead strives to integrate various applications and displays an open-ness to approaches drawn from other visions of reality. Intuition obviously is not dismissed. For Whitehead, intuition was very important and, following Bergson, was analysed by him as “the feeling derived from the synthesis of the conceptual prehension with the physical prehension from which it has been derived.”18 Intuition operates in various realms. As we have previously noted, it may be directed towards the type of awareness which is more “mathematical”, or to such aspects as the moral sense of the rightness of things or to the artist's empathetic awareness, or to the religious perception. What is important here is the balance between rational generalisation and more emotional empirical investigation. For Whitehead showed that to concentrate entirely on any one field of interest would be to impoverish one's grasp of the totality of things. This is how he accounted for speaking about deity in abstraction from the world while at the same time thinking of God always in terms derived from and relative to his creative activity in the world. When Whitehead refers to Michelangelo or to Wordsworth in Process and Reality he is articulating many another’s testimony to the numinous power of art to convey a reality which is concealed behind the appearance of things. Elsewhere he speaks of great art

Conclusion

117

transforming “the soul into the permanent realisation of values extending beyond its former self.”19 From the coercive power of such a participative experience as this flows more specific religious beliefs or feelings of ultimate concern. We detect this in very many sources and very engagingly in Karl Barth’s effusive acknowledgement of the role Mozart had in his life. In 1956 Barth published a short book of writings about Mozart where he stated that if he ever went to heaven he would first of all seek out Mozart, and only then enquire about Augustine, Aquinas, Luther, Calvin and Schleiermacher. His reason for according a special place to a figure who was neither a pillar of the church nor particularly devout had previously been voiced by him in his Church Dogmatics. In a fulsome eulogy to Mozart he asked: Why is it possible to hold that Mozart has a place in theology, especially in the doctrine of creation and also eschatology, although he was not a father of the Church, does not seem to have been a particularly active Christian, and was a Roman Catholic, apparently leading what might appear to us a rather frivolous existence when not occupied in his work? It is possible to give him this position because he knew something about creation in its total goodness that neither the real fathers of the Church nor our Reformers, neither the orthodox nor Liberals, neither the exponents of natural theology nor those heavily armed with the “Word of God”, and certainly not the Existentialists, nor indeed any other great musicians before and after him, either know or can express and maintain as he did.20

Barth’s claim that Mozart “saw the whole context of providence” was certainly in response to a creativity that was mysterious and inexplicable. Perhaps we instinctively sense that it emanates from “outside” Mozart. In any case, and in the final analysis, and however much we may revere him, we may suspect that what is fundamental in Mozart’s music can be regarded as if totally independent of a composer called Mozart. This, of course, is in “the final analysis,” and in the final analysis, as a result of what we have learnt from Whitehead and others, whether they be Process philosophers or not, we can postulate that this fundamental quality is God. Notes 1. See Chapter 6 of A.J.Ayer’s Language, Truth and Logic (London 1971). 2. Martin Heidegger, The Piety of Thinking, tr. James G. Hart and John C. Maraldo (Bloomington 1976), p.67.

118

Conclusion

3. The Complete Psychological Works of Sigmund Freud, tr. and ed. James Strachey (London 1961), Vol.XXI, p.85. 4. Ibid., Vol.XIII, p.147ff. and elsewhere. 5. Anthony Storr, Freud (Oxford 1989), p.9. 6. Process and Reality, p.xii. 7. Reflections on Art (Baltimore 1958), p.xii. 8. See Systematic Theology (London 1953), I, p.114. 9. Process and Reality, p.259. 10. John Hick, Philosophy of Religion (Englewood Cliffs 1963), pp. 76-7. 11. Karl Barth, Evangelical Theology (New York 1964), p.36. 12. For instance, the playing with “beautiful” possibilities was an element in Watson and Crick's discovery of the structure of DNA as related in Watson's book The Double Helix. 13. Process and Reality, p.xii. 14. p.91-2. 15. Process and Reality, p338. 16. ibid. 17. Adventures of Ideas, p.226. 18. Process and Reality, p.33. 19. Science and the Modern World, p.252. 20. Karl Barth, Church Dogmatics, tr. G.W.Bromiley and R.J.Ehrlich (Edinburgh 1961), Vol.III, Part III, pp.297-8.

Selected Bibliography Aquinas, St. Thomas. 1964. Summa Theologiae. (vol.1, tr. Thomas Gilby). London: Blackfriars. — 1970. Summa Theologiae. (vol.7, tr. T.C.O’Brien). London: Blackfriars. Augustine.1998. The City of God. (ed. and tr. R. W.Dyson).Cambridge: Cambridge University Press. Ayer, A.J. 1946. Language, Truth and Logic. London: Gollancz. Barth, Karl. 1961.Church Dogmatics. (tr. G.W.Bromiley and R.J.Ehrlich). Edinburgh: T&T Clark. Barth, Karl. 1964. Evangelical Theology:An Introduction. New York: Rinehart & Winston. Beardsley, Monroe C. 1966. Aesthetics from Classical Greece to the Present. Alabama: University of Alabama Press. Bernstein, Leonard. 1976. The Unanswered Question. Cambridge USA: Harvard University Press. Cobb, John B. 1990. “Two Types of Postmodernism: Deconstruction and Process” in Theology Today, Vol 47, No.2. Princeton: Princeton Theological Seminary. Dufrenne, Mikel. 1972. The Phenomenology of Aesthetic Experience. (tr. E.S.Casey et al.). Evanston Ill: Northwestern University Press. Freud, Sigmund. 1961. The Complete Psychological Works of Sigmund Freud. (tr. and ed. James Strachey). London: Hogarth Press. Gilbert, Katharine and Kuhn, Helmut. 1954. A History of Esthetics. Bloomington: Indiana University Press. Godwin, Joscelyn. 1995. Harmonies of Heaven and Earth. (RochesterVT: Inner Traditions International. Hardy, Alister. 1979. The Spiritual Nature of Man. Oxford: Clarendon Press. Hartshorne, Charles. 1934. The Philosophy and Psychology of Sensation. Chicago: University of Chicago Press. J.A.W.Heffernan, J.1969. Wordsworth's Theory of Poetry: The Transforming Imagination. Ithaca: Cornell University Press. Heidegger, Martin. 1936. “The Origin of the Work of Art” in Poetry, Language, Thought. (tr. Hofstadter). NewYork: Harper & Row. —The Piety of Thinking.1976. (tr. James G. Hart and John C. Maraldo). Bloomington: Indiana University Press. Hick, John. 1963. Philosophy of Religion.Englewood Cliffs: NJ Prentice-Hall. Jenny, Hans. 1967. Kymatik. Basel: Basilius Presse. Kant, Immanuel. 2000. “Analytic of the Beautiful” in Critique of the Power of Judgement. (ed.Paul Guyer, tr. Paul Guyer and Eric Matthews). Cambridge: Cambridge University Press. Langer, Susanne. 1942. Philosophy in a New Key. Cambridge USA: Harvard University Press. — Feeling and Form. 1953. New York: Charles Scribner’s & Sons. Leibniz, G.W. 1927. Discourse on Metaphysics, Correspondence with Arnauld, and Monadology. (tr. Montgomery). Chicago: Open Court Publishing. Lipps, Theodor. 1926. Psychological Studies. Baltimore: Williams & Wilkins.

120

Selected Bibliography

Magee, Bryan. 1997. The Philosophy of Schopenhauer. Oxford: Clarendon Press. Maritain, J. 1962. Art and Scholasticism. (tr. J.W.Evans). New York: Charles Scribner’s & Sons. Martin, F. David. 1972. Art and the Religious Experience: The Language of the Sacred. Lewisburg: Bucknell University Press. Messiaen, Olivier. 1977. Recherches et expériences spirituelle. Paris: Leduc. Meyer, Leonard B. 1956. Emotion and Meaning in Music. Chicago: University of Chicago Press. Murdoch, Iris. 1970. The Sovereignty of Good. London: Routledge & Kegan Paul. —The Fire and the Sun: Why Plato Banished the Artists. 1977. Oxford: Clarendon Press. Otto, Rudolf. 1924. The Idea of the Holy. (tr. John W.Harvey). Oxford: Oxford University Press. Phelan, G.B. 1943. St. Thomas and Analogy . Milwaukee: Marquette University Press. Plato. 1953. Republic, Symposium and Timaeus in The Dialogues of Plato (vols.1, 2 &3 respectively, tr. B. Jowett). Oxford: Clarendon Press. —1987. Ion in Early Socratic Dialogues. (tr. Trevor. J. Saunders). London: Harmondsworth-Penguin. Plotinus. 1956. The Enneads. (tr. Stephen MacKenna, rev. by B.S.Page). London: Faber& Faber. Rescher, Nicholas. 1967. The Philosophy of Leibniz. Englewood Cliffs NJ: PrenticeHall. Sartre, Jean-Paul. 1948. The Psychology of the Imagination. New York: Philosophical Library. Schopenhauer, Arthur. 1969. The World as Will and Representation. (tr. E.F.J.Payne). New York: Dover. Sherburne, Donald W. 1961. A Whiteheadian Aesthetic. New Haven: Yale University Press. Steiner, George. 1978. Heidegger. London: Collins. —1989. Real Presences. London: Faber & Faber. Storr, Anthony. 1989. Freud. Oxford: Oxford University Press. Tillich, Paul. 1953. Systematic Theology. Oxford: Oxford University Press. — The Religious Situation. 1956. (tr. H.R.Niebuhr). Cleveland: H. Holt. Ward, Keith. 1996. Religion and Creation. Oxford: Oxford University Press. Whitehead, Alfred North. 1929. Process and Reality (rev.edn., eds Griffin and Sherburne, 1978). New York: Macmillan. —1927. Religion in the Making. Cambridge: Cambridge University Press. —1927. Science and the Modern World. Cambridge: Cambridge University Press. —1933. Adventures of Ideas. New York: New American. Younis, Raymond. “The ‘End of the Grand Metanarratives of Progress’?” presented at the Australasian Association for Process Thought Inaugural Conference (Sydney, May 1997). Zuckerkandl, Victor. 1956. Sound and Symbol. London: Routledge & Kegan Paul. —1973. Man the Musician. Princeton: Princeton University Press.

Index of Names Apollo, 17 Aquinas, St. Thomas, 6, 7, 31, 33-5, 117 Aristotle, 7, 27, 103 Aron, 21 Arrau, Claudio 5 Augustine, St. 6, 32-3, 117 Ayer, A. J 109 Bach, J.S. 8, 11, 22, 23, 57ff., 67, 77ff., 80, 86-90, 92 Bach, W.F. 89 Barth, Karl 114, 117 Beardsley, Monroe C. 30 Beethoven, Ludwig van 35, 96 Bergson, Henri 40, 57, 112, 116 Berlioz, Hector 96 Bernstein, Leonard 53 Birch, Charles 104 Brahms, Johannes 77 Brancusi, Constantin 98 Brendel, Alfred 5 Brentano von Arnim, Bettina 45 Calvin, John 117 Cézanne, Paul 79 Chomsky, Noam 53 Christ, Jesus 22, 78 Cobb, John B. 104-5 Croce, Benedetto 69 Dante, Alighieri 29, 57 Derrida, Jacques 105 Dewey, John 112 Dickens, Charles 12 Dostoevsky, Fyodor 98 Dufrenne, Mikel 100 Emmett, Dorothy 63 Eriugena, John Scotus 31 Faulkner, William 98 Feuerbach, Ludwig 111 Fichte, Johann Gottlieb 36 Fo-Hi 22 Forte, Allen 14 Freud, Sigmund 111 Furtwaengler, Wilhelm 76 Gilson, Etienne 15 God, passim Godwin, Joscelyn 6, 16-7, 22

Gounod, Charles 93n. Gregory, St. 18, 22-3 Griffin, David Ray 104 Grünewald, Matthias 35, 80, 98 Gurney, Edmund 75 Hanslick, Eduard 75 Hardy, Alister 11, 110, 114 Hartshorne, Charles 52, 63, 76, 88-90 Haydn, Joseph 50 Heffernan, J.A.W. 8, 101-2 Hegel, G.W.F. 33 Heidegger, Martin 8, 74, 77, 99-101 Heraclitus 64 Hick, John 114 Hofman, Wlastimil 79 Hugo, Victor 98 Hume, David 69 Jackendoff, Ray 14 James, William 55, 112 Jenny, Hans 16 Joyce, James 97 Kant, Emmanuel 6, 24, 37, 115 Kepler, Johannes 82 Kircher, Athanasius 17 La Rue, Jan 14 Langer, Susanne 13, 39-40, 63, 76, 80-1, 112 Lear, Edward 105n. Leibniz, Gottfried 18, 35, 40, 52 Lennon, John 23-4 Lerdahl, Fred 14 Lippius, Johannes 49 Lipps, Theodor 45-7, 50 Locke, John 56 Lovelock, James 70 Luke, St. 22 Luther, Martin 117 Lyotard, Jean-Francois 105 Mahler, Gustav 14, 34 Maritain, Jacques 34 Martianus, Capella 17 Martin, F. David 8, 22-24, 73-80, 109 Matisse, Henri 97 McCartney, Paul 23-4 Melville, Herman 98 Mendelssohn, Felix 6

122 Messiaen, Olivier 19 Meyer, Leonard B. 75 Michelangelo Buonarroti 93n., 116 Milton, John 96 Mondrian, Piet 101 Moses 21 Mozart, W.A. 44, 50-1, 57, 60, 96, 117 Murdoch, Iris 26, 29 Nordoff, Paul 18 Northrop, F.C.S. 63 Orpheus 22 Otto, Rudolf 6, 11, 23 Pater, Walter 92, 95-6 Pérotin 22 Picasso, Pablo 78 Plato 6, 13, 22, 25, 25-32, 37-8, 65, 102, 114 Plotinus 6, 29-31 Popper, Karl 82 Porta, G.B. 17 Pseudo-Dionysius, 31 Pythagoras 26 Richards, I.A. 95 Robbins, Clive 18 Saint-Martin, L-C. de 45 Sarasvati 22 Sartre, Jean-Paul 76 Schenker, Heinrich 14, 47, 60 Schleiermacher, F.D.E. 36, 117 Schnabel, Artur 5 Schneider, Marius 18 Schoenberg, Arnold 21 Schopenhauer, Arthur 6, 12, 36-40, 55-8

Index Schubert, Franz 44, 47, 50, 52, 98 Scruton, Roger 98 Sessions, Roger 54 Shakespeare, William 35, 57 Shaw, G. Bernard 79 Sherburne, David 60, 68 Socrates 13 Solomon 5 Spinoza, B. 68 Steiner, George 8, 21, 74, 96-103, 113 Steiner, Rudolf 18 Stockhausen, Karlheinz 51 Storr, Anthony 111 Strauss, D.F. 111 Tillich, Paul 79, 79, 100-1, 103, 109, 113, 115 Tovey, Donald 45 Uexküll, J. von 48 Van Gogh, Vincent 99, 101 Vermeer, Johannes 100 Ward, Keith 31 Weil, Simone 97-98 Weiss, Paul 63 Werckmeister, Andreas 49 Whitehead, Alfred North 5, 7-8, 12, 15, 40, 63ff., 81, 85ff., 103-5, 112ff. Wilde, Oscar 15 Wordsworth, William 14, 99-101, 114 Yeats, W.B. 34 Younis, Raymond 105 Zuckerkandl, Victor 40, 44, 47, 52-9, 81, 112

Music and Mathematics From Pythagoras to Fractals

Edited by Eva Li

__ . _---_ .. _._.. _... .. _--_ ...-

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_-----~

Music and Mathentatics From Pythagoras to Fractals John Fauvel Raymond Flood and Robin Wilson

Preface

From ancient Greek times, music has been seen as a mathematical art. Some of the physical, theoretical, cosmological, physiological, acoustic, compositional, analytical and other implications of the rela­ tionship are explored in this book, which is suitable both for musical mathematicians and for musicians interested in mathematics, as well as for the general reader and listener. In a collection of wide-ranging papers, with full use of illustrative material, leading scholars join in demonstrating and analysing the con­ tinued vitality and vigour of the traditions arising from the ancient beliefs that music and mathematics are fundamentally sister sciences. This particular relationship is one that has long been of deep fascina­ tion to many people, and yet there has been no book addressing these issues with the breadth and multi-focused approach offered here. This volume is devoted to the memory of John Fauvel, Neil Bibby, Charles Taylor and Robert Sherlaw Johnson, whose untimely deaths occurred while this book was being completed.

Eva Li

CONTENTS

Music and mathematics: an overview Susan Wollenberg

Part I: Music and mathematics through history 11 1. Tuning and temperament: closing the spiral 13 Neil Bibby 2. Musical cosmology: Kepler and his readers 29 J. V. Field Part II: The mathematics of musical sound 45 3. The science of musical sound 47 Charles Taylor 4. Faggot's fretful fiasco 61 Ian Stewart 5. Helmholtz: combinational tones and consonance David Fowler Part III: Mathematical structure in music 89 6. The geometry of music 91 Wilfrid Hodges 7. Ringing the changes: bells and mathematics Dermot Roaf and Arthur White 8. Composing with numbers: sets, rows and magic squares 131 Jonathan Cross Part IV: The composer speaks 147 9. Microtones and projective planes Carlton Gamer and Robin Wilson 10. Composing with fractals 163 Robert Sherlaw Johnson Notes on contributors

173

Notes, references, and further reading Acknowledgements Index

187

149

183

177

113

77

And so they have handed down to us clear knowledge of the speed of the heavenly bodies and their risings and settings, of geometry, numbers and, not least, of the science of music. For these sciences seem to be related. ARCHYTAS OF TARENTUM, EARLY FOURTH CENTURY

BC

'We must maintain the principle we laid down when dealing with astronomy, that our pupils must not leave their studies incomplete or stop short of the final objective. They can do this just as much in harmonics as they could in astronomy, by wasting their time on measuring audible concords and notes.' 'Lord, yes, and pretty silly they look', he said. 'They talk about "intervals" of sound, and listen as cartjitlly as

if they were trying to hear a conversation next door.

And some say they can distinguish a note between two others, which gives them a minimum unit of measurement, while others maintain that there's no diffi:rence between the notes in question. They are all using their ears instead of their minds.' 'You mean those people who torment catgut, and try to wring the truth out of it by twisting it on pegs. '

PLATO, FOURTH CENTURY

BC

The Pythagoreans considered all mathematical science to be divided into four parts; one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in its relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantity as such, music the relations between quantities, geometry magnitude at rest, spherics magnitude inherently moving.

PROCLUS, FIFTH CENTURY This science [mathematics] is the easiest. This is clearly proved by the fact that mathematics is not beyond the intellectual grasp of anyone. For the people at large and those wholly illiterate know how to draw figures and compute and sing, all of which are mathematical operations.

ROGER BACON, c.1265 I do present you with a man of mine, Cunning in music and in mathematics, To instruct her fUlly in those sciences, Whereof, I know, she is not ignorant.

WILLIAM SHAKESPEARE, 1594

May not Music be described as the Mathematic of Sense, Mathematic as the Music of reason? The soul of each the same! Thus the musician feels Mathematic, the mathematician thinks Music,-Music the dream, Mathematic the working life,-each to receive its consummation from the other.

JAMES JOSEPH SYLVESTER, 1865 Mathematics and music, the most sharply contrasted fields of intellectual activity which can be found, and yet related, supporting each other, as

if to show forth the

secret connection which ties together all the activities of our mind . .. H. VON HELMHOLTZ, 1884 Music is the arithmetic of sounds as optics is the geometry of light.

CLAUDE DEBUSSY, c.1900 Quite suddenly a young violinist appeared on a balcony above the courtyard. There was a hush as, high above us, he struck up the first great D minor chords of Bach's

Chaconne. All at once, and with utter certainty, I had found my link with the centre . .. The clear phrases of the Chaconne touched me like a cool wind, breaking through the mist and revealing the towering structures beyond. There had always been a path to the central order in the language of music, ... today no less than in Plato's day and in Bach's. That I now knew from my own experience.

WALTER HEISENBERG, 1971 When Professor Spitta, the great expert on Bach, explained to [Ethel Voynich (Lily Boole)] that in tuning, the third and fourth notes of the octave had to be just a little off or otherwise the octave would not fit, she suddenly "began to hate God and to despise the Almighty Creator of all things visible and invisible who couldn't make even eight notes fit", and she remained devoutly atheistic for the rest of her days. When Anne Freemantle told her many years later that Einstein had shown that it was only in our space-time continuum that the octave does not fit, the ninety-six year old Voynich replied reflectively, "Yes, perhaps I was a bit hasty."

DES MAcHALE, 1985

Music and mathematics: an overVIew Susan Wollenberg

Mathematics and music have traditionally been closely connected. The seventeenth century has been seen by historians as a crucial turning-point, when music was changing from science to art, and science was moving from theoretical to practical. Many connections between science and music can be traced for this period. In the nineteenth and twentieth centuries, the development of the science of music and of mathematical approaches to composition further extended the connections between the two fields. Essentially, the essays in this book share the concern of commentators throughout the ages with the investigation of the power of music. Musicke I here call that Science, which of the Greeks is called Harmonie. Musicke is a Mathematical Science, which teacheth, by sense and reason, perfectly to judge, and order the diversities of soundes hye and low. JOHN DEE (1570)

In the traditional arrangement of knowledge and teaching in universities, music was one of the seven liberal arts, along with the other quadrivium subjects of arithmetic, geometry and astronomy. This woodcut dates from 1504.

The invitation to write an introduction to this collection offered a welcome opportunity to reflect on some of the historical, scientific, and artistic approaches that have been developed in the linking of mathematics and music. The two have traditionally been so closely connected that it is their separation that elicits surprise. During the late sixteenth and early seventeenth centuries when music began to be recognized more as an art and to be treated pedagogically as language and analysed in expressive terms, it might have been expected to lose thereby some of its scientific connotations; yet in fact the science of music went on to develop with renewed impetus. This introduction sets out to explore, via a variety of texts, some of the many historical and compositional manifestations of the links between mathematics and music. (This endeavour cannot be other than selective: the field is vast, ranging from ancient theory and early developments in structure such as those of the medieval motet, to the new ideas of post-tonal music and experimental musical techniques explored over the past century.) In what follows, the field is viewed particularly from the perspective of a music historian with a special interest in the history of music in its educational dimension.

Music and mathematics

Aspects of notation and content In contemplating the two disciplines, mathematics and music (and taking music here essentially to mean the Western 'Classical' tradition), it is clear to the observer from the outset that they share some of their most basic properties. Both are primarily (although not exclusively) dependent on a specialized system of notation within which they are first encoded by those who write them, and then decoded by those who read (and, in the case of music, perform) them. Their notations are both ancient and modern, rooted in many centuries of usage while at the same time incorporating fresh developments and newly-contrived systems to accommodate the changing patterns of mathematical and musical thought. Musical notation can be traced back to the ancient Greek alphabet system. A series of significant stages came in the development of notations within both the Western and Eastern churches during the medieval period. In the eleventh to thirteenth centuries more precise schemes were codified, including Guido d'Arezzo's new method of staff notation and the incorporation of rhythmic indications. By the time of the late sixteenth and the seventeenth centuries, most of the essential features of musical notation as it is commonly understood today were in place within a centrally established tradition. Subsequent additions were mainly in the nature of surface detail, although of considerable importance, as with the expanded range of performance instructions in the nineteenth century. The twentieth century, with its emphasis on experimental music, saw a precipitate rise in new forms of notation. In a comparable way, mathematical notation has developed over a period of at least 2500 years and, in doing so, has inevitably drawn from various traditions and sources. In music, the relationship between notation and the content it conveys is sometimes more complex than might at first appear. Notation has not invariably fulfllled the role merely of servant to content. While it is generally true that notational schemes evolved in response to the demands posed by new ideas and new ways of thinking, it is also possible that experiments in notation may have been closely fused with the development of such ideas, or may even have preceded-and inspiredtheir creation. In mathematics, too, the relationship has subtle nuances. Notation developed in one context could prove extremely useful in another (seemingly quite different) context. (A well-known example of this is the use of tensor notation in general relativity.) In one notable case, notation formed part of the focus of a professional dispute, when a prolonged feud developed between Newton and Leibniz as to which of them invented the differential calculus, together with the different notation used by each.

2

Music and mathematics: an overview

In the course of their history, mathematics and music have been brought together in some curious ways. The Fantasy Machine demonstrated in 1753 by the German mathematician Johann Friedrich Unger to the Berlin Academy of Sciences, under Leonhard Euler's presidency, was designed to preserve musical improvisations; in the words of an English inventor, the Revd John Creed, on whose behalf a similar idea was presented to the Royal Society in London in 1747, with this device the 'most transient Graces' could be 'mathematically delineated'. Unger claimed to have had the idea as early as 1745, although Charles Burney (in his essay 'A machine for recording music') attributed priority of invention to Creed. Although it aroused considerable interest and support among the intelligentsia, and 'was tried out by several wellknown musicians' in the mid-eighteenth century, the machine was ultimately not a success.

Music as science: the historical dimension Throughout the history of mathematical science, mathematicians have felt the lure of music as a subject of scientific investigation; an intricate network of speculative and experimental ideas has resulted. Taking a historical view, Penelope Gouk has voiced her concern that such terms as 'mathematical sciences' are 'routinely used as essentially unproblematical categories which are self-evidently distinct from the arts and humanities ... Since music is today regarded as an art rather than a science, it is hardly surprising that the topic should be disregarded by historians of science'. Her book remedies this situation with resounding success, inviting a reconsideration of the way joint histories are told. Within the scope of a work based primarily on seventeenth-century England, Gouk's references range from Pythagoras (in particular, Pythagorean tuning and the doctrine of universal harmony that 'formed the basis of the mathematical sciences') to Rene Descartes ('the arithmetical foundation of consonance') and beyond. Descartes' Compendium (1618) was translated as Renatus Des-Cartes excellent compendium of musick and animadversions of the author (1653) by the English mathematician William Brouncker. Brouncker himself was 'the first English mathematician to apply logarithms (invented c.1614) to the musical division'. Thus he entered into a scientific dialogue with the work of Descartes, contesting the latter's findings. At the period when music was changing from science to art (retaining a foot in both camps), science itself was moving from theoretical to practical. The seventeenth century has been seen by historians as a crucial turning-point, with the emergence of a 'recognizable scientific community' and the institutionalization of science. The founding of the Royal Society of London in 1660 formed a key point in the development

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Newton's spectrum scale.

It is interesting to note that such keyboards were actually built: Handel, for example, played a 31-note organ in the Netherlands. This multiplicity of keys is necessary because successive transpositions of the scale of just intonation generate even more notes between those of the basic setJ than they did for the set P. In this case each transposition produces a new 'black' note, as in the Pythagorean case, but an extra new note is produced, a syntonic comma sharper for upward transpositions and flatter for downward. This arises, as we have seen, because one of the fifth intervals in the just scale is narrow-the interval D-A has ratio f : ~ or~, which is less than %. In musical terminology, the old submediant is too flat to serve as the new supertonic. The more transpositions take place, the worse the problems get. The effect of successive upward and downward transpositions of the basic just scale J is summarized overleaf. In practice, modulations into remote keys were not usual at this time (partly, no doubt, for this reason): however, even to use the keys near to C in just intonation required two extra notes per modulation. The systems discussed so far imply infinitely many keys, with the spiral of fifths continuing infinitely, both outwards and inwards: the Pythagorean system P*, with notes generated by octaves and perfect fifths, and the just system J*, with notes generated by octaves, perfect fifths and major thirds, both yield infinite sets. So far as the construction of keyboard instruments was concerned, this was not an encouraging state of affairs. Many attempts were made to develop tuning systems that overcame the difficulties of Zarlino's just system. Amongst these, Francesco Salinas (1530-90) proposed a system called mean-tone, in which the two whole tones of Zarlino's system (~ and -¥') were replaced by their geometric mean, thus giving a whole tone interval of L5. The interval of the third remained a pure consonance of %, while the fifth had a ratio of \5, which is approximately 1.4953: this is a little less than t giving a rather flat fifth. Isaac Newton also spent much time trying to select the best ratios. Believing that seven notes in the octave and seven colours in the spectrum were too much of a coincidence, he even produced a 23

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