The Music Instinct

The Music Instinct How Music Works and Why We Can’t Do Without It 

BY THE SAME AUTHOR 

 Designing the Molecular World: Chemistry at the Frontier   Made to Measure:  New Materials for the 21st Century  Life’s Matrix:  A Biography of Water  The Self-Made Tapestry:  Pattern Formation in Nature Bright Earth:  Art and the Invention of Color   Molecules:  A Very Short Introduction The Elements:  A Very Short Introduction Critical Mass: How One Thing Leads to Another   Elegant Solutions: Ten Beautiful Experiments in Chemistry The Devil’s Doctor:  Paracelsus and the World of Renaissance Magic and Science  Nature’s Patterns:  A Tapestry in Three Parts Universe of Stone:  A Biography of Chartres Cathedral

The Music Instinct How Music Works and Why We Can’t Do Without It 

philip ball

1 2010

3 Oxford University Press, Inc., publishes works that further Oxford University’s objective of excellence in research, scholarship, and education. Oxford New York    Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in   Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam

Copyright © 2010 by Philip Ball Published by Oxford University Press, Inc. 198 Madison Avenue, New York, New York 10016 www.oup.com Oxford is a registered trademark of Oxford University Press  All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Library of Congress Cataloging-in-Publication Data Ball, Philip, 1962–  The music instinct : how music works and why we can't do without it / Philip Ball. p. cm. Includes bibliographical references and index. ISBN 978-0-19-975427-4 1. Music—Philosophy and aesthetics. 2. Music and science. I. Title. ML3800.B2085 2010 781'.1—dc22 2010017795

1 3 5 7 9 8 6 4 2 Printed in the United States of America on acid-free paper

Contents

Preface

vii Author’s Note

1 Prelude: Prelude: The Harm Harmoniou oniouss Unive Universe rse  An Introduction

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2 Overtu Overture: re: Why We Sin Sing  g  What is music and where does it come from?

9

3 Staccato: Staccato: The Atom Atomss of Musi Musicc What are musical notes and how do we decide which to use?

32

4 Andante: Andante: What What’s ’s In a Tune Tune??  Do melodies follow rules, and if so, which?

91

5 Legato: Legato: Kee Keeping ping It Toge Together ther How do we decode the sound?

137

6 Tutti: Tutti: All Toge Together ther Now How do we use more than one note at a time?

163

7 Con Moto: Slave to the Rhyt Rhythm hm What gives music its pulse?

207

8 Pizzicato Pizzicato:: The Colou Colourr of Musi Musicc Why do instruments sound different, and how does that affect the music?

228

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9 Misterioso: All In the Mind Which bits of the brain do we use for music?

240

10 Appassionato: Light My Fire How does music convey and elicit emotion?

254

11 Capriccioso: Going In and Out of Style What are musical styles? Is music about notes, or patterns, or textures?

322

12 Parlando: Why Music Talks to Us Is music a language? Or is it closer to the non-verbal arts?

355

13 Serioso: The Meaning of Music What are composers and musicians trying to say? Can music in itself say anything at all?

381

Coda: The Condition of Music

409

Credits Notes Bibliography Index

413 415 425 443

 Pre f ace

‘Must the majo majority rity b  bee made “unmusi unmusiccal al”” so that a few may  b  beeco come me more “musi musiccal al””?’ This q uestio uestion, in Jo John Blac Blacking’s seminal 1973 19 73 boo  book  k  H ow Musical I s Man?, apparently sums up the status of mu musi sicc in Wester Western n culture: it is co comp mpo osed sed b  b y a tiny mino minority and perf ormed rmed b  b y a slightly larger one, and these are the peo pe ople we call ‘musi musiccians’. But Blac Bla cking  points to to the co contradi ntradiccti tio on inherent in the way that music music is at the same time utterly pervasive in this culture: at supermarkets and airpo airp orts, in mo movies and on televisi televisio on (every pro programme must have its theme tune) tune), at impo important cerem eremo onies, and no now, on the private, porta b  ble le sounds undsccapes that snake u b  biiq uito uitously fro from poc ocket ket to to ear. ‘“ ‘“My My”” soc ociety’, iety’, says Blac Bla cking, ‘c ‘claims laims that only a limited num b  ber er of pe peo ople are music musical, yet it b it  behaves ehaves as if all peo pe ople po possessed the b the  basi asicc capa apaccity witho with out whic which no musi musiccal traditio tradition can exist  –   – the the capa apaccity to to listen to and distinguish patterns of sound.’ He implies that this assumptio assumpti on urther: ‘his’ soc society iety presuppo presupposes shared gro ground in the way g oes still f urther: tho th ose patterns will  b  bee interpreted, understoo underst ood, d, respo responded to to.  And of  co course urse these assumptio assumptions are justified: we do have this capa apaccity to to hear music music, and to to devel develo op a cultural co consensus nsensus a bo  bout ut ho how to resp respo ond to it. Yet we have, in the West at least, dec de cided that these mental fac faculties are so so co comm mmo onpla nplacce that they are hardly wo worth no noting, let alo alone cele b  brating  rating o or designating as ‘musi musiccal’ attri butes.  butes. Blac Blacking’s experiencces amo experien among Afric African cultur ultures es in whic which musicmusic-making making was far less rigidly appo app orti rtio oned ned b  between etween ‘pr pro odu duccers’ and ‘co ‘consumers’ nsumers’ –   – where, where, indeed, tho those categ ories were so sometimes meaningless  –  helped him to appre apprecciate the oddness of this situatio situation. Perso Personally, I suspec suspect that it might in any event  b  bee easy to to overplay that sc schism, whic which, to the extent that it exists at all, may pro pr ove to t o  b  bee partly a transient aspec aspect of 

the emergenc emergence of mass media. Bef ore music music co could uld  b  bee re reco corded rded and  brroad  b adccast, peo people made it themselves. And no n ow it is inc increasingly easy and cheap to to make and b and brroad adccast it yo yourself, huge num b  bers ers are do doing  so. Yet we still tend to to as asccri be  be primac primac y of music musicality to to the ‘pr pro odu ducctio ti on’ mode. In this  boo  book k I hope to sh sho ow why the ‘c ‘capa apaccity to to listen to and distinguish patterns of sound’, whic which we nearly all po p ossess, is the essenc essence of music musicality ality.. The boo The  book k is a bo  bout ut how this capa apaccity arises.  And I want to to suggest that, while hearing great music musi c played played b  b y great perf ormers is an inco incompara mpara b  ble le pleasure, this is no n ot the only way to to get enjo enjo yment and satisfac satisfacti tio on fr fro om music music. Beccause the q uestio Be uestion of how music music does what it do does is so so phen pheno omenally co compli mpliccated and elusive, one co could uld easily co constru nstrucct an illusio illusion of  cleverness  b y pointing  out flaws in the answers offered so so far. I hope it will b will bee clear that this is no not my intentio intention. Every Everyo one has stro strong  opini pinio ons on these matters, and thank g oodness oodness f or that. In a su b je  jecct of this nature, ideas and views that differ fro fr om one’s own sho should no not  bee targets f or demo  b demoliti litio on,  b  but ut whetsto whetstones f or sharpening  one’s own tho th oughts. And sinc since it is likely that everyo everyone will find so something with whicch to disagree in this boo whi this  book, k, I ho hope that readers will feel the same way. For helpful advic advice and disc discussi ussio on, pro providing material, and f or general suppo supp ort or even just g ood ood intentio intentions, I am grateful to t o Aniruddh Patel, Stefan K oels elscch, Jaso Jason Warren, Isa b  belle elle Peretz, Glenn Sc S chellen b  berg, erg, Oliver Sac Sacks and David Huro Huron. I am once again muc much inde b  bted ted to to my agent Clare Alexander f or her enco encouragement, uragement, insight and inco in compar mpar-a b  ble le co com m b  binati inatio on of experienc experience, diplo diploma macc y and reso resolve. I am thankful to  b  bee in the safe and suppo supportive edito editorial hands of Will Sulkin and  Jö  J örg Hensgen at Bo Bodley Head. And I cherish the music music that Julia and Mei Lan b Lan  bring ring into into our home. I sh sho ould like to to dedi dediccate this boo this  book k to every everyo one with who whom I have made music music.

Philip Ball Lond ndo on Novem b  ber er 200 0099

 Author’s Note

To listen to the musical examples illustrated in this book, please visit www.oup.com/us/themusicinstinct

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1 Prelude The Harmonious Univer se  An Int ro  duct ion

Fourteen billion miles away from Earth, Johann Se bastian Bach’s music is heading towards new listeners. An alien civilization encountering  the V o yager 1 or 2 spacecraft, launched in 1977 and now drifting  beyond our solar system, will discover a g olden gramophone record on which they can listen to Glenn Gould playing the Prelude and Fugue in C from the second book of  The Well-Tempered Clavier . You couldn’t fit much on a long -playing record in 1977, but there was no room f or a more extensive record collection – the main mission of the spacecraft was to photograph and study the planets, not to serve as an interstellar mobile music li brary. All the same, offering  extraterrestrials this glimpse of Bach’s masterwork while denying them the rest of it seems almost an act of  cruelty. On the other hand, one scientist feared that including Bach’s entire oeuvre might come across as an act of  cosmic boasting. Recipients of  the V o yager  g olden record will also  be a ble to listen to the music of Mozart, Stravinsky and Beethoven, as well as Indonesian gamelan, songs of Solomon Islanders and Navajo Native  Americans, and, delightfully, Blind Willie Johnson perf orming  ‘Dark  Was the Night, Cold Was the Ground’. (They are denied the Beatles; apparently EMI couldn’t see how to maintain copyright on other worlds.) What are we thinking of, sending music to the stars? Why should we assume that intelligent life f orms that may have no human attri butes, perhaps not even a sense of  hearing, could comprehend what

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happens if  –  f ollowing the pictorial instructions included with the discs – you spin the V o yager  g olden records and put the needle in the groove? That q uestion is, in a sense, what this book is all a bout. Why is the succession of sounds that we call music comprehensi ble? What do we mean when we say that we do (or don’t) ‘understand’ it? Why does it seem to us to have meaning, as well as aesthetic and emotional content? And can we assume, as the V o yager  scientists have done implicitly, that these aspects of  music are communica ble to others outside our own culture, or even our own species? I s music universal?   A gli b argument f or the universality of music would say that it is at root mathematical, as Pythag oras proposed in the sixth century BC, so that any advanced civilization could ‘decode’ it from the vi brations excited in a stylus. But that is far too simplistic. Music is not a natural phenomenon but a human construct. Despite claims to the contrary, no other species is known to create or respond to music as such. Music is u biq uitous in human culture. We know of societies without writing, and even without visual art  –  but none, it seems, lack some f orm of  music. But unlike the case of language, there is no generally agreed reason why that should be so. The evidence suggests it is an inevita ble product of intelligence coupled to hearing,  but if so, we lack an explanation f or why this is. It is deeply puzzling why these complex mixtures of acoustic freq uencies and amplitudes make any sense to us, let alone why they move us to jo  y and tears. But little b  y little, that is becoming a less mysterious q uestion. When we listen to music, even casually, our  brains are working awfully hard, perf orming clever feats of filtering, ordering and prediction, automatically and unconsciously. No, music is not simply a kind of mathematics. It is the most remarka ble blend of art and science, logic and emotion, physics and psychology, known to us. In this  book I will explore what we do and don’t know a bout how music works its magic.

Confectionery f or the mind? ‘Music is auditory cheesecake, an exq uisite confection crafted to tickle

prelude

3

the sensitive spots of at least six of  our mental faculties,’ claimed cognitive scientist Steven Pinker in his 1997 book H ow t he Mind W orks. He went on: Compared with language, vision, social reasoning, and physical knowhow, music could vanish from our species and the rest of  our lifestyle would  be virtually unchanged. Music appears to  be a pure pleasure technology, a cocktail of recreational drugs that we ingest through the ear to stimulate a mass of pleasure circuits at once.

These claims provoked predicta ble outrage. Imagine it, comparing  Bach’s B minor Mass to the Ecstasy pills of  clu b culture! And  b y suggesting that music could vanish from our species, Pinker seemed to some to  be implying that he wouldn’t much mind if it did. So Pinker’s remarks were interpreted as a challenge to prove that music has a fundamental evolutionary value, that it has somehow helped us to survive as a species, that we are genetically predisposed to be musicmakers and music-lovers. It seemed as though the very dignity and value of  music itself was at stake. Pinker responded to all of this with understanda ble weariness. No one was suggesting, he said, that music could only be taken seriously as an art f orm if it could be shown to be somehow evolutionarily beneficial. There are plenty of aspects of human culture that clearly did not arise as adaptive behaviour and yet which are deeply important components of  our lives. Literac  y is one: an evolutionary psychologist who argues that writing is obviously adaptive because it preserves vital inf ormation in a way that can be relia bly passed on to our offspring is making  a hopeless case, because writing is simply too recent an innovation to have any dedicated genetic component. We can read and write because we have the req uisite intrinsic skills  –  vision and pattern recognition, language, dexterity  – and not because we have literac y genes.  Joseph Carroll, professor of English at the University of MissouriSt Louis, has offered a more su bstantial reply to Pinker.  ‘Art, music and literature are not merely the products of  cognitive fluidity,’ he says. ‘They are important means b y which we cultivate and regulate the complex cognitive machinery on which our more highly developed functions depend.’ These arts aren’t at all like stimulati on of the taste buds – they em body emotions and ideas:

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They are f orms of  communication, and what they communicate are the q ualities of experience. Someone deprived of such experience would have artificially imposed on him a deficienc y similar to that which is imposed on autistic children through an innate neurological defect . . . a child deprived of all experience with art and literature would still have innate capacities f or social interaction, but these capacities would remain  brutishly latent. The architecture of his or her own inner life and that of  other people would remain dully obscure. In the place of  meaningful pattern in the organization of emotions and the structure of human needs and purposes, such a child would perhaps scarcely rise a bove the level of reactive impulse.

This is the classical argument of the ennobling nature of art, which g oes back to Plato. The problem is that it is awfully difficult to prove. Carroll cites the example of the Smallweeds in Dickens’ Bleak H ouse, who ‘discarded all amusements, discountenanced all story books, fairy tales, fictions, and fa bles, and  banished all levities whatsoever’. The Smallweed children are, as a result, ‘complete little men and women [who] have  been observed to  bear a likeness to old monkeys with something depressing on their minds’. But that is all so much literary invention; and more to the point, the a bsence of art in the lives of  the Smallweed children is obviously a symptom of their general lack  of love and nurture, not a cause of it. Do we have any real evidence that being deprived of music would impoverish our spirit and diminish our humanity? In this  book I suggest why, even though there is something to  be said f or both Pinker’s and Carroll’s positions, they both miss the point. While it is possi ble in principle to disprove Pinker’s thesis (and while, as we’ll see, there are already reasons to suspect that it is indeed wrong ), it is a mistake to think that this would somehow esta blish the fundamental value of music. Neither do we need to show that Carroll is right – that exclusion of music leads to a brutish nature – to prove that we can’t g o without it. After all, the reverse is not true:  beastliness and a finely honed musical aesthetic may coexist, as personified  b  y Anthony Burgess’ Alex in   A Clockwork Orange, not to mention Hitler’s notorious love of Wagner. It is misguided to think that music enriches us in the mechanical manner of a nutrient. The fact is that

prelude

5

it is meaningless to imagine a culture that has no music, because music is an inevita ble product of human intelligence, regardless of whether or not that arrives as a genetic inheritance. The human mind q uite naturally possesses the mental apparatus f or musicality, and it will make use of these tools whether we consciously will it or not. Music isn’t something we as a species do  b y choice  – it is ingrained in our auditory, cognitive and motor functions, and is implicit in the way we construct our sonic landscape. Even if Pinker is correct (as he may  be) that music serves no adaptive purpose,  you could not  eliminat e it   f ro  m our cult ures wit hout changing our brains. Boethius seemed to understand this in the early sixth century  AD: music, he said, ‘is so naturally united with us that we cannot be free from it even if we so desired’. For that very reason, Pinker is also wrong to suggest that music is simply hedonistic. (Besides, however much cheesecake or recreational drugs we consume, we do not there b  y exercise our intellect or our humanity –  q uite the reverse, one might say.) Here is the surprising  thing: music does not  have to be en jo yed. That sounds terri ble,  but it is a fact. I don’t mean simply that everyone does not enjo y every possi ble sort of music; that’s obviously true. I mean that we don’t just listen to music f or pleasure. In some cultures that doesn’t seem to  be the primary function, and it has  been de bated whether an aesthetic response to music is at all universal. Of  course, there are also many reasons f or eating other than hunger –  but it is far from clear that the main reason f or music is enjo  yment in the same way that the main reason f or eating is survival. Happily, though, on the whole we do enjo y music, and one of the major themes of this  book is to find out why. But the pleasure may well be a conseq uence, not a cause, of music-making. Pinker’s ‘auditory cheesecake’ is itself a side effect of  our urge to find music in our auditory environment, although in fact the image of a guzzling diner is a bsurdly inappropriate to span the range from an indigenous tri besperson singing a ritual chant to a composer of the hard avantgarde plotting  out his mathematical music in the 1970s. We have a music instinct as much as a language instinct. It might be genetically hard-wired, or it might not. Either way, we can’t suppress it, let alone meaningfully talk  of taking it away. What’s more, it no longer makes much sense to reduce this instinct to some primitive urging  on the savannah, any more than it makes

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sense to ‘explain’ the minutiae of courtship, personal grooming, extramarital affairs, romantic fiction and Ot hello on our urge to reproduce. Cultures ela borate basic instincts out of all recognition or proportion, even inverting what one might presume to be their biological origin (if such a thing exists). Does it really make any sense to apply Pinker’s phrase, or indeed Carroll’s argument, to John Cage’s 4’33”, or to Motörhead pla ying ‘Overkill’ at a volume close to the pain threshold?

Whose music?  Although my survey ranges across cultures, much of it will draw on Western music. This is only in part because it is the music with which I am (and proba bly most readers will  be) most familiar. More importantly, it is the  best-studied system of highly developed ‘art music’, and so provides the richest source so far of inf ormation a bout how music is processed. Yet  b  y exploring non-Western music, I hope not only to avoid the common error (many composers have made it) of  asserting universal relevance to culturally specific concepts,  but also to  bring to light those aspects of music that do seem to have some cross-cultural validity. I shall look in particular at some highly developed and sophisticated non-Western f orms of music, such as Indian classical music and Indonesian g amelan.* I will also show that ‘more sophisticated’ does not b y any means imply ‘better’, and that art music is no more highly developed in some respects than traditional or f olk  music. Indeed, I will not on the whole be attempting to make judgements a bout music in an artistic or aesthetic sense, although we will find some clear, ob jective indications of why certain types of music seem to be more satisfying and enriching than others. I hope this book  might encourage you, as researching it encouraged me, to listen again to music that you previously dismissed as too boring, too complicated, too dry, too slushy, or just plain incomprehensi ble. I dou bt that there is a single one of us whose musical horizons could not be broadened with a little more understanding of what the music is doing and why. * In a recent study of the ‘complexity’ of musical styles, gamelan scored highest: an emphatic reminder that we should not associate the geographic u biq uity of Western music with superiority.

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7

Music is not a luxury The fact that we humans are  bound to  be musical come what may could be taken as advocac y f or a laissez-faire attitude to music education. And it’s true that children who don’t venture near an instrument and never have a music lesson at school are as likely as anyone else to end up plugged into their iPods. But to neglect music education is to stunt development and to deny opportunity. If we don’t teach our children to cook, they won’t starve, but we can’t expect them to take much delight in f ood, or to  be a ble to discover how to distinguish g ood fare from bad. Music is the same. And no one needs to be taught what  to cook, but only how. Whether or not Joseph Carroll is right to assert that deprivation of  music makes us lumpen  brutes, there is no q uestion that the provision of music enriches in countless ways. One of the most remark a ble illustrations of that is the National System of Youth and Children’s Orchestras of Venezuela (commonly known simply as El Sistema), which has offered music tuition to around 250,000 impoverished Venezuelan children. Its 200 youth orchestras have provided a haven from crime and drugs f or young people in the  barrios, and the flag ship Simón Bolívar Youth Orchestra plays with a passion and musicality that is the envy of more ‘developed’ nations. In part, the social  benefits of El Sistema no dou bt stem from the mere fact that it supplies some degree of structure and security in lives that had precious little  bef ore – perhaps f oot ball or literac y schemes would have similar effects. But it seems hard to dou bt that the music itself, generally taken from the European classical repertoire, has instilled a f ocus, curiosity and optimism in the young Venezuelan players. In contrast, music education in the West is often seen as elitist and irrelevant, a drudge that promises little in the way of either satisfaction or inspiration. At best, it is something that children do if they have the spare time and resources. Yet music ought to be a central and indispensa ble facet of a rounded education. For one thing, we will see that it is a gymnasium f or the mind. No other activity seems to use so many parts of the  brain at once, nor to promote their integration (the tiresome, cod-psycholog ical classification of people as ‘left brain’ or ‘right brain’ is demolished

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where music is concerned). The spurious ‘Mozart Effect’ aside (see Chapter 9), it is clearly esta blished that music education has a positive effect on general intellect. It is also a potentially socializing activity, and one that most young people are interested in, often passionately.  And sensitive music teaching (as opposed to hothousing of little virtuosos) will bring out one of music’s most valua ble attri butes, which is the nurturing and education of emotion. The case f or musical education should not rest on its ‘improving’ q ualities, however, even if these are real. The fact is that music no less than literac y gives access to endless wonders. To cultivate those avenues is to facilitate life-enhancing experience. But what usually happens instead? Children stop singing and dancing, they get em barrassed a bout their piano lessons (if they’re lucky enough to be of fered them) and frustrated that they don’t sound like the stars on MTV. As adults, they deny that they possess having  any musicality (despite the extraordinary skills needed to listen to and appreciate just a bout any music), they jokingly attri bute to themselves the rare clinical condition of tone-deafness. They proba bly do not know that there are cultures in the world where to say ‘I’m not musical’ would be meaningless, akin to saying ‘I’m not alive’. This book is a bout that too.

2 Overture Why We Sing  What  is music and where does it come  f ro  m?

Hadn’t I  better explain what I am talking a bout, when I am talking  a bout music? That would seem a sensi ble preliminary, but I am g oing  to decline it. Just why I do so should become clear when I  begin to explore shortly the different f orms that music takes in different cultures,  but let me say right away that there is no meaningful definition of  music that doesn’t exclude some or other aspect of it. The most notorious counter-example to most definitions is John Cage’s silent opus 4’33” (a work that is more accurately descri bed as specifying that the perf ormer play no notes). Some might, with reason, argue that this is not music but a conceptual artwork * –  but that risks straying towards arid semantics. Such eccentricities aside, one definition of music that seeks to acknowledge its cultural and historical diversity, proposed b y musicologist Ian Cross, runs as f ollows: Musics can be defined as those temporally patterned human activities, individual and social, that involve the production and perception of  sound and have no evident and immediate efficac y or fixed consensual reference.

 And of  course you can at once choose your own favourite nitpick  –  f or example, that this includes a person idly scuffing his shoes at the street corner. ‘Evident and immediate efficac  y’ in particular raises enormous q uestions. But perhaps most significantly, you need only * Philosopher Stephen Davies does just that in an illuminating and dogma-free discussion, while concluding that ‘we should acknowledge the originality and importance of  Cage’s contri bution to our understanding of music and of the philosophy of the arts’. 4’33”, he says, ‘challenges the boundary between noise and music’, but ‘is likely to include more of the f ormer’.

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start listening to Sam Cooke or Ravel to sense that straining f or a definition of music is a vapid exercise that tells us nothing important a bout what it is or why we listen. Such definitions tend to consider music as an acoustic phenomenon, with the result that they seek distinctions between musical and non-musical sound. ‘Organized sound’ isn’t a bad working description of music, so long as you recognize that this definition would make no sense to some cultures, and that it excludes some types of music and includes sounds not generally considered to be music.* Yet whatever you think of the twentieth-century Western avant-garde, it served as a reminder that this sort of exercise in definition is futile. Music can be made from mistuned radio sets, from the incidental noises of  a concert hall, from the hum of machinery. No one says you have to like it. There’s a g ood argument that music is better defined in sociolog ical and cultural than in acoustic terms. It’s a thing we do. It is universal only in the sense that every culture seems to have it. But a bout what music is, and what purpose it serves, we can make no other generalizations. Some cultures make music b y banging on drums, blocks, pieces of  metal: they value rhythm (and perhaps tim bre) a bove melody. In others, the main instrument is the human voice; in others, music is insepara ble from dance. In some cultures, music is reserved f or special occasions; in others, people create a more or less continual musical soundtrack to their lives. Some reserve a term like ‘music’ only f or a su bset of the apparently musical things they do. Some analyse music in obsessive detail; others are puzzled b y any need to discuss it. Perhaps most significantly, there is no reason to suppose that all musics should share any particular trait in common – that music has universal features.   As semiologist Jean Molino has put it, ‘Nothing guarantees that all f orms of human music contain a nucleus of  common properties that would be invariant since the origination of music.’

*There’s a g ood case f or saying that a via ble definition of music doesn’t have to be all-inclusive, but should simply apply to the central instances of the art. Of  course, that in itself provokes q uestions;  but I sympathize with the idea that we need feel no great obligation to encompass extreme experiments in our definitions.

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Music in the world One of the strongest ob jections to Steven Pinker’s characterization of  music as ‘auditory cheesecake’ is its ethnocentricity: it implies that all people listen to music simply because they like to do so. That is proba bly not true even in Western culture, where a type of music might f or example serve as a badge of affiliation to a su bculture, or proclaim a regime’s military might. And music may serve very specific social functions that do not obviousl  y demand (and perhaps do not involve) aesthetic judgements. For the Kaluli people of Papua New Guinea, music allows communion with the dead. The music of the Venda people in South Africa helps to define social relations.   And music is not merely structured sound. The word f or ‘music’ in the language of the Ig  bo people of Nigeria is synonymous with ‘dance’, and in Lesotho there is no distinction  between dance and song. In parts of su b-Saharan Africa, music without a steady rhythm, to which one cannot theref ore dance, is not considered music at all,  but instead a f orm of lamentation. Ethnomusicologists have documented an a bundance of social functions f or music: it expresses emotion, induces pleasure, accompanies dance, validates rituals and institutions, promotes social sta bility. The last of these is not merely a matter of  ‘bringing people together’ – music can serve as a socially sanctioned outlet f or negative or controversial  behaviours too. In some African cultures, the ‘protest song’ is tolerated as a f orm of political dissent that could not be voiced in speech or text. And in Bali, musicians and dancers may enact socially disruptive emotions such as rage so as to discharge them pu blicly in a way that serves the community. In Senegal, the low-caste  griots of the Wolof people play music to and dance f or the nobles in an emotional way. The  griots are considered expressive and excita ble, the nobles cool and detached. These musical perf ormances ena ble both groups to maintain the stereotypes, which may have nothing to do with the true nature of the individuals. The music stands proxy f or the emotions of the nobles, to ward against apathy, without them having to break their mask and actually display such attri butes. Music can be a vehicle f or communication, sometimes with exq ui-

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site precision. The ‘talking drums’ of African cultures are legendary, and may be used to convey q uite specific inf ormation in intricate codes almost like Morse, which seem to  be tied to the pitch structure of   African tonal languages. Villagers might  burst into laughter during a xylophone perf ormance as the musician uses his instrument to make a joke a bout a particular mem ber of the tri be. Everyone gets it  –  except, sometimes, the butt. The music of the Sirionó Indians of Bolivia, meanwhile, seems extremely simple: each song is a short phrase containing just a handful of  closely spaced pitches. The function of this music seems to  be entertainment rather than ritual,  but in some ways that ob jective works on a far deeper level than it does in the West. Each mem ber of a tri be has a ‘signature’ tune that f orms the  basis of all he sings, and these songs are voiced in the morning and evening almost as a kind of  conversation, a way of saying  ‘here I am again’. Here’s a musical culture of which composer Paul Hindemith would surely have approved when he wrote that ‘Music that has nothing else as its purpose should neither be written nor be used.’ In many of these cases, music serves a sym bolic purpose. It has  been tacitly agreed in advance what the ‘meaning’ of the music is, and no one is too bothered a bout judging how ‘well’ the music meets that g oal – the mere fact of the perf ormance guarantees it. Yet whether such a purpose involves any element of pleasure is a difficult q uestion. It has sometimes  been claimed that some cultures show no aesthetic response to music,  but other ethnomusicologists consider this a prejudiced view: the a bsence of  critics, fanzines and discussion groups doesn’t mean the listeners don’t assess and enjo  y what they hear. Such disagreements may themselves  be a conseq uence of  imposing alien categ ories on the musical experience. It has  been claimed that composers among the Basongye people of  the Cong o have no explicit intention of  creating music that others will admire, partly because there is nothing to be judged: they deem music to be an intrinsic g ood, not something that might be ‘g ood’ or ‘bad’. Some ethnologists say that art criticism in general has no place in African tri bal culture, since it is taken f or granted that what we call art is a positive activity that meets essential needs. Meanwhile, David Mc Allester, a pioneer in the study of music in pre-Colum bian American societies, suggests that aesthetic judgements in Native Americans are

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commonly tied to function: people like particular songs because they are associated with enjo ya ble ceremonies. (He says that some people in these cultures also express preferences f or songs that are more easily learnt.) The Canadian ethnomusicologist Colin McPhee claimed in 1935 that Balinese music is utilitarian, ‘not to  be listened to in itself’ and containing no emotion. Rather, he said, it is simply, like flowers or incense, a necessary component of  ceremony, as though someone had said ‘We need three hours of music here’ in the same way that they might specify the necessary dimensions of the meeting hall.  Anthropologist Margaret Mead later argued that this did not mean listeners derive no enjo yment from the perf ormance, but she suggested that this pleasure came from the perf ormance aspects itself  –  from ‘the way in which music is played rather than the music’. No one would, in that sense, be saying ‘Oh, I love this song’. Yet these responses may have  been the result of the Western observers’ distance from Balinese culture; certainly, modern listeners to gamelan seem to derive aesthetic satisfaction from it. The ethnomusicologist Marc Benamou cautions that aesthetic and emotional judgements a bout music can be tricky to compare across cultures: Javanese people don’t necessarily recognize the same categ ories of musical affect (happy/sad, say) as those in the West. In any event, the Basongye people consider music to be insepara ble from g ood feelings – they say they make music in order to be happy, or to express that happiness: ‘When you are content, you sing.’ But that’s a more complex statement than it sounds; it is as if the emotion defines music rather than stimulates it, f or music is not something  that can be made in anger: ‘When you are angry, you shout.’ What’s more, any notion that Basongye music is there b  y a spontaneous out burst of pure jo  y is complicated  b  y the claim of  one tri besman that ‘When one shouts, he is not thinking ; when he sings, he is thinking.’ All this suggests that Basongye music has a su btle and sophisticated social function that can’t easily be descri bed b y analogies with the West. The Basongye readily admit that music can  be utilitarian too: another reason f or making it, they say, is to be paid. In some cultures it is a trada ble commodity, a f orm of wealth. In New Guinea, tri bal people might sell dances from village to village, bundled up with new

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f orms of  clothing and some  bits and pieces of magic. The Navajo Native Americans can own songs and sell them to others. And this, at least, is hardly unfamiliar in the West. Neither is the sacred aspect of music and song. A further reason f or making music, say the Basongye, is that God (whom they call Efile Mukulu) tells them to do so. The Yirkalla a borigines of Arnhem Land in Australia hear sacred song words in the ba bbling of  ba bies. To them, songs are never composed but only discovered: all songs exist already. Where music is used f or ritual purposes, a concern with accurac y may  become almost obsessive, f or a ceremony that is conducted incorrectly loses its power. If a single error is made in the song accompanying a Navajo ritual, the whole thing has to  be started again  –  a standard that even the most exacting  of Western concert perf ormers hardly feels a need to uphold. The purely functional roles of music are also evident in its association with healing. The ancient Egyptians regarded music as ‘physic f or the soul’, and the He brews used it to treat physical and mental distur bance – an early f orm of music therapy. The Greek philosopher Thales is said to have used music to cure a ‘plague’ of anxiety suffered  b  y the Spartans. According to Plutarch, Thales’ songs dispelled the affliction with concord and harmony, in an echo of the magical healing  powers attri buted to the music Orpheus sang while playing his lyre. That myth is also reflected in the Bi ble: Now the Spirit of the Lord had departed from Saul, and an evil spirit from the Lord tormented him . . . Whenever the spirit of God came upon Saul, David would take up his harp and play. Then relief would come to Saul; he would feel better, and the evil spirit would leave him.

In antiq uity and the Middle Ages, music was deemed (at least b y the intelligentsia) to have a primarily moral rather than an aesthetic, much less a hedonistic, purpose. It was perf ormed not f or enjo yment  but to guide the soul. For Plato and Aristotle, this made music a tool that could either promote social harmony or, if improperly used, discord. (It’s no coincidence that those are both musical terms.) For the early Christian writer Boethius in the sixth century, music was to be judged ‘b y means of  reason and the senses’, not b y the heart, and this made it the province of the philosopher rather than the artist. None of this

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is to deny that these classi lassiccal listeners too took k pleasure fro from music music,  b  but ut that pleasure was suppo supposed to to  b  bee a means, no not an end. No No wonder St  Augustine wo worried that peo people listening to t o religi religio ous singing might b might  bee ‘more mo moved ed b  b y the singing than b than b y what is sung’. Phil Philo osopher R oger Scrut ruto on argues that music music still has the capa apaccity to to pr pro ovide mo moral educ educatio ti on: Through melo Thro melody, harmo harmony ny,, and rhythm, we enter en ter a world where others exist  b  besides esides the self, a wo world that is full of feeling  b feeling  but ut also also ordered, discciplined dis iplined b  but ut free. That is why music musi c is a chara haraccter ter--f orming f orce.

In this view, music music has as part of its func functi tio on an educ educative and soc social ial-izing value, and I have so s ome sympathy with that.* that. * Facced with all this Fa th is diversity, diversity, ethno ethn omusi musico collog ists have have lo l ong tended to av avo oid any q uest uest f or universals in the f orms and categ ories of  musicc . Yet musi Yet there t here do seem to t o b  bee so some overlaps and paral parallels lels b  between etween traditio traditi ons. Afric Afri can music music , f or example, can an b  bee crudely divided into int o two tw o types, divided b divided  b y a bo a  boundary undary that lies alo al ong the so southern edge of the Sahara. Sahara. To To the no north, the music music is primarily voc vocal al and mo m onopho ph oni nicc , suppo supported rted b  b y a dro drone or rhythmic rhythmic acc cco ompaniment. There is a lo lot of im impr pro ovisati visatio on and ornamentati rnamentatio on of th thee voc vocal al line, often using mic mi c rot ones. In su bsu b-Saharan Saharan Afric Afri c a, in co contrast, ntrast, music musi c is usually perf ormed in gro gr oups,  b  being eing po polyph lypho oni nicc an and d often harmoharmonized and making use of  co complex, mplex, multilayered rhythmic rhythmi c patterns.   And the mo modes of singing are q uite uite different: fullfull -th thrroated in the south, nasal in the no n orth. The musico musi collogist Alan Lo L omax argued that these distinc distin cti tio ons reflec refle ct cultural attitudes to t owards co coo opera pera-tio ti on, sex, hierarc hierar chy and class, and that the two two styles are in fac fa ct representative of twin pro progenit genito ors of all music musi cal traditio traditi ons. He pro pr oposed that a f or m  b  based ased on (mostly male) male ) impr impro ovised so s olos, with free rhythm and co complex, mplex, highly ornamented melo mel odies, sprung up in eastern Si beria,  beria, while su bsu b-Saharan Saharan Afric Africa gave  b  birth irth to a ‘feminized’, manymany -voiced, rhythmic rhythmi cally regular style. Fro Fr om these twin roo roots ts Lomax claimed to t o dis disccern the  b  bra ran nching  of ten families of music musical styles thro thr ough ugho out the wo world. Altho Alth ough few * I have less sympathy f or Scrut ruto on’s suggestio suggestion that bo that  both th music music and mo morals are on the dec decline line –   – see see p.335 p.335..

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ethnomusi ethno musico collogists no now acc accept ept this idea, the b the basi asicc traits that Lo L omax identifies can indeed b indeed bee reco recognized gnized in the music musi cs of man many y disparate disparate cultures. The sc scien iencce of music music co cogniti gnitio on is starting to t o make the q uestio uestion of universals respec respe cta b  ble le again. Perhaps this is  b  beecause it has tended to  b  break reak do down music music int into o the simplest struc stru ctural elements, suc su ch as pitcch and to pit tone and rhythm, the perc percepti eptio on and organizati rganizatio on of whi hicch would seem to t o  b  bee an essential part of any listener’s a b a bility ility to to trans trans-f orm sound into into musi musicc regardless of th thee func functi tio on that it serves. This appro appr oach can only get so so far, ho however,  b  beecause even the issue of  what we perc perceive is no not simply a matter of audito auditory aco cousti usticcs: just as emo emoti tio onal, soc social ial and cultural fac factors may pro promote selec selective hearing o hearing  of language, so so they impinge on music music. A Western listener can hear just a bo  bout ut any music music on the radio radio and make so some kind of  assessment of it witho without kno knowing anything a bo  bout ut the co comp mpo oser, perf ormer, perio peri od or co context ntext of the music music. This wo would  b  bee an alien noti tio on to some preliterate soc s ocieties ieties suc such as the Baso Basongye or the Flathead Native Americ Ameri cans, f or wh who om a respo response to to, and even a reco re cogniti gnitio on of, music music depends on co context, ntext, on the reaso reason why it is  being  b eing played and heard. To To ask, as music music psy psycchologists ro routinely do do of their test su b je  jeccts, ho how one feels a bo  bout ut partic particular intervals or rhythms has no no meaning f or these peo people ple –   – th tho ose are no not, to them, q uestio uestions a bo  bout ut music music at all. That’s one reaso reason why studies in music music co cogniti gnitio on have f ocused ocused almo alm ost entirely on the music music of large and generally industrialized cultures: it is no n ot only lo logisti gisticcally diffic diffi cult  b  but ut also also potentially am b  bigu iguo ous to test the perc percepti eptio on of and respo response to to musi musicc am amo ong  tri bal  bal soc ocieties. ieties. Highly develo devel oped music musical traditio traditions usually have a rather explic explicit set of rules f or co comp mpo ositi sitio on, perf orman rmancce and analysis  –  to put it in co coldly ldly sc scientifi ientificc terms, we have a  b  better etter view of what the relevant varia b  bles les are. But given this lac la cuna, we have to to wonder whether a co cognitive gnitive sc scien iencce of mu musi sicc can really say anything universal a bo  bout ut it as a human ac activity. Jean Mo Molin lino o dou b  bts ts that there is muc much whyy we make music we can learn a bo  bout ut the q uestio uestion of  wh music  b  y studying  the ‘great’ music music of the Euro European classi lassiccal oeuvre –  he asserts that musicc used f or ritual and danc musi dan ce (even disco) disco),, as well as po p oetry, is mo more relevant to to that q uestio uestion. This is no not to say that co cognitive gnitive studies  b  based ased on the Western

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traditi on  –  whi traditio whicch means mo most of th tho ose disc discussed in this  boo  book  k  –   –  need  b  bee hopelessly paroc par ochial. hial. We’ll see that there is no n o reas reaso on to think, f or example, that Western sc s cales and music musi cal struc structures are someh meho ow pr proc ocessed essed with mental apparatus uniq  uni q uely uely designed f or that purpo purpose, any mo more than the English language has dedic dedi cated modules that co could uld no not  b  bee used f or other languages. And b And  b y asking  how Western listeners co cope pe in co cognitive gnitive terms with no n on-Western musicc, we can gain insight into musi int o the general mec me chanisms the human  brain  b rain uses to t o organize so s ound. Besides, the Western music musi cal traditradi tio ti on, while having no no claim to to prima primacc  y, is unq  unq uestio uestiona b  bly ly one of  the mo most sophisti phisticcated in the wo world, and wo worth explo exploring in its own right. In fac fact, music music co cognitive gnitive studies are helping to t o dismantle the old prejudicces of et prejudi ethn hno omusi musico collog y. While Wh ile ev even en muc mu ch of the early early work  in this field had the virtue of  challenging  centuries of presumed Western music musical supremac suprema c y  y,,* it nevertheless tended to t o assert an exccepti ex eptio onalism of the so sort voiced  b y one of  the f ounders of the field, Bruno Brun o Nettl, who wh o in 195 1956 defined ethno ethn omusi musico collogy as ‘the scien iencce that deals with the music musi c of pe peo oples outside of Western civilizati ivilizatio on’. A modern definitio definiti on chara haraccterizes it instead as ‘the study of soc ocial ial and cultural aspec aspe cts of mu musi sicc and danc dance in loc local al and glob gl obal al co contexts’, ntexts’, whic which rightly implies that Western music musi c is as mucch a part of the su b je mu  jecct as any other f or m. (Popular culture has   yet to to cat atcch up up,, whic which is why we have the a b  bsurd surd genre categ ory of  ‘world music musi c’, where the wo world is one in whic which a West is curi uri-ously a b  bsent. sent.)) As they prob pr obee deeper into int o su succh q uestio uestions as ho how musicc is linked to musi t o em emo oti tio on, researc researchers have b have beeco come me struc struck  b  b y ho h ow impo imp ortant it is to t o turn the ethno ethn omusi musico collogist’s lens on their own culture. Fo For acco ccording rding to to musi musicc psy psycchologist Jo John Slobo Sloboda, da, ‘It is a curi urio ous parad par ado ox that we prob pr obaa b  bly ly kno know . . . more a bo  bout ut the different purpo purp oses f or whic which music music is used within certain no n o nWestern soc s ocieties ieties than we do d o a bo  bout ut how it is used in Western consumer co nsumer soc societies.’ ieties.’ * It is a relief to to  b  bee free of the culture that ena b  bled led the early philo philosopher of music music Eduard Hanslic Hanslick to t o state in 1891 that So South Sea Islanders ‘rattle with woo wooden den staves and piec pieces of met metal al to to the acco accompaniment mpaniment of fea fearful rful ho howlings’, pro produ duccing  ing ‘‘no musi musicc at all’.

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In reawakening interest in universals, music musi c psy psycchology is also also revi revi-talizing an old q uestio uestion that ethno ethnomusi musico collogists have skirted with understanda b  ble le cauti autio on. Once you start to to ask ho how our ur b  brains rains make sense of music music, you can’t avo avoid the issue of  wh whyy they are a b  ble le to do so. And that summo summons f orth the mystery  b  behind ehind any survey of how musicc is used in different cultures to musi today: ho how and why did music music arise in the first plac place?

The first music musicians In 1866 the Linguistic Linguistic Soc ociety iety of Paris dec decided it had heard eno en ough dogmati gmaticc  b  biickering and vapid spec spe culati ulatio on a bo  bout ut the origins of  language, and dec decided to to  b  ban an fro from its meetings any papers on the topi picc. If you survey mo modern disc discussi ussio ons a bo  bout ut the origins of music music  –  not just a parallel q uestio uestion  b  but ut most prob probaa b  bly ly a related one  –  you might have to to co con ncede that the Linguistic Linguisti c Soc ociety iety of Paris knew knew what what it was do doing. As seems to to  b  bee the case with an y academi ademicc en enq  q uiry, uiry, the stridenc stridenc y with whic which points of view are asserted seems to t o  b  bear ear an inverse relatio relati on to to the q uantity uantity and q uality uality of su supp ppo orting evidenc evidence.  And a bo  bout ut the origins of music music, we have almo almost no eviden evidencce whatwhatsoever. Musicc in human culture is certainly very anc Musi ancient. Several flutes made of  f  bo  bone ne have  b  been een f ound fro from the Sto Stone Age  –  that’s to to say, the Palaeo Palaeolithi lithicc peri perio od, deep into into the last ic ice age. The oldest candi andi-date kno known so far is carved fro from the bo the  bone ne of a young  ung ccave  b  bear ear and dates to to ar aro ound 44 44,,000 years ag o. It was f ound in 1995 1995 in Slo Slovenia, and has two two holes with the suggestio suggestion of a third, and perhaps ano an other on the opp ppo osite side. When  b  bllown at one end and fingered, it will pro pr odu ducce a diverse range of pitc pitches. It’s po possi ble  ble that this ob je  jecct isn’t an instrument,  b  but ut a  bo  bone ne puncpunctured b tured  b y the sharp teeth of some carniv arnivo ore whic which gnawed it later. But the ho holes appear to to  b  bee carefully made, with no no cra raccking at the edges, and it wo would uld b  bee rather surprising if they had b had  been een f ormed in just these placces witho pla without shattering the  bo  bone ne or presenting too too mu mucch of a mouthful f or any chewer. Besides, there is no n o dou b  btt that bo that  bone ne flutes were made in the Sto Stone Age. Several unam b  bigu iguo ous examples have b have been een

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unearthed in the Swa b  bian ian Jura in Germany dating fro from aro around 40 40,,000   years ag o, in inccluding  one more or less co complete mplete and rather elegant flute made fro from a  b  bird ird  bo  bone ne (Figure 2.1) 2.1). These instruments sho sh ow that humans had already  b  y this time rather tho thoroughly integrated musicc int musi into o their everyday lives. Yet why sho should our anc ancest esto ors have wanted or needed music music, espeespecially during an ic i ce age when merely surviving fro fr om one day to to the next was hard eno enough? Charles Darwin offered one of the earliest spec spe culati ulatio ons a bo  bout ut why humans first made music music. He co couldn’t uldn’t igno ignore the puzzle it seemed to to pose f or ev evo oluti lutio onar  y explanations of human  b  behavi ehavio our, and in his  Descent  t of  of  Man (18 1877) 77) he wro wrote:  As neither the enjo enjo yment no nor the capa apaccity of pr pro odu duccing music musical no notes are fac faculties of the least direc direct use to to man in referenc reference to his ordinary ha b  bits its of life, they must b must  bee ranked amo amongst the mo most mysterio mysterious with whicch he is endo whi endowed. They are present, tho though in a very rude and as it appears almo almost latent co conditi nditio on, in men of all rac races, even the mo most savage.

In other wo words, Darwin viewed musicmusi c-making making as an evo evolved lved b  behav ehav-iour witho without ob obvi vio ous adaptive value. He was, ho h owev wever er,, familiar fam iliar with other apparently useless adaptatio adaptati ons, and he  b  believed elieved his evo evolu lu-tio ti onary theo theory co could uld explain them. He argued that music musi c had no nothing  to do with nat ural ural sele seleccti tio on (‘ (‘survival survival of the fittest’) fittest’),  b  but ut co could uld  b  bee

 Figure  2.1  A  A bo  bone ne flute disco discovered vered b  b y Nic Nicholas Co Conrad nrad of the University of  Tüb übingen ingen and his coco-w workers in 200 2008, 8, during exc excavati avatio ons at Ho Hohle Fels Cav avee in the Swa b  bian ian Jura. It is tho thought to to  b  bee a bo  bout ut 40 40,,000 years old. (Image: H. Jensen/ Jensen/University of Tüb übingen. ingen.))

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acco ccounted unted f or  b  y his parallel no noti tio on of  se x ual ual sele seleccti tio on, in whic which organisms gain a repro repr odu ducctive advantage no not  b  y living lo longer  b  but ut  b y having mo more succ success ess at mating. He co considered nsidered the music musi c of  our anccest an esto ors to  b  bee a f or m of exhi biti  bitio onist display or pr pro owess akin to to the mating  ‘songs’ and ‘dan dancces’ of some animals. This hypo hypothesis can acco ccomm mmo odate the fac fact that music music is not just of no ‘dire direcct use’  but  b ut is seemingly antianti -adaptive: it takes time to t o learn an instrument and to to sit aro around playing it, whic whi ch early humans or ho h ominids might  bee expec  b expected to to have spent mo more pro produ ducctively in hunting and gathgath ering. The eff ort pays off, ho howe wever ver,, if the music musi cian’s skill makes him more attrac attractive. (We can, f or these purpo purposes, assume a ‘him’, sinc since these sexual displays are, in animals, a nimals, the preserve of the male male..) Why, tho th ough, sho should an a b  bility ility to to make music music  b  bee deemed sexy? One possi ble  ble answer is that it displays coo coordinati rdinatio on, determinatio determination, g ood ood hearing, and perhaps stamina (some cultur ultures es engage in very lengthy musiccal ritual) musi ritual), all of whi hicch are argua b  bly ly features that a female might wish to to find in her offspring. In this view, music musi c is like the peacoc pea cock’s k’s tail: an ela bo  borate rate display that is useless, and indeed a hindranc hindran ce, in itself  b itself   but ut whic which sends out a signal of  ‘g ood ood genes’. The pio pi oneering   Americcan  Ameri an b  behavi ehavio oural neuro neurologist No Norman Gesc Geschwind hwind b  believed elieved that musiccal a b musi  bility ility is a genuine predic predi ctor of male rep reprr odu ducctive pro prowess,  beecause (he argued)  b argued)  bo  both th are pro promoted  b  y high levels of f oetal testo test oster stero one. Altho Although this h yp  ypo othesis was develo devel oped  b  bef  ef ore we knew muc much a bo  bout ut the links b links  between etween  b  brain rain anato anatomy and music musicality (there’s still muc mu ch we do don’t kno know, as yo you’ll see) see), it is so sometimes still asserted to t oday in suppo supp ort of Darwin’s sexualsexual -sele seleccti tio on origin of  musicc. musi  And indeed this idea isn’t witho without merit. But its mo modern adherents too often mistake the acc accumulati umulatio on of ad hoc arguments f or the co colle llecctio ti on of scientifi ientificc eviden evidencce. e.** One researc researcher po points out, f or instanc instance, *One argument adduc *One adduced  b  y psyc psychologists Vanessa Sluming and Jo John Manning has at least the virtue of  f  b  being eing amusing: they f ound in 2000 2000 that, averaged over eleven con co ncerts of  classi lassiccal music music, there were signific significantly mo more wo women in the seats nearer the (pred predo ominantly male) male) orchestras than in the  b  baack rows  –  a genteel f orm, they implied, of the female hysteria that greeted the Beatles in co con ncert. Sluming and Manning admitted that the hypo hypothesis might, ho however, need to to take into into acco ccount unt how many of these wo women were prepre-men meno opausal. I suspec suspect they may have f ound this inf ormati rmatio on hard to to acq uire uire at classi lassiccal rec recitals.

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that just a bo  bout ut all co complex, mplex, varied and interesting so s ounds pro produ ducced  b y other animals are made f or the purpo purposes of  co courtship, urtship, so so why no not humans? This wo would seem eq  eq ually ually to to argue that every phrase we utter has the aim of attrac attracting a mate, whic which I rather do dou b  btt was true even of  f C Casan asano ova. In any ev event, ent, the claim is no not even even true tr ue as stated: monkeys and apes do don’t appear to to use calls f or sexual purpo purposes. And ‘primitive’ songs are b are b y no no means the tri bal  bal eq  eq uivalents uivalents of  ‘Let’s Spend the Night Together’: tho those of the Australian A bo  borigines, rigines, f or example, express the singer’s feelings as a mem b mem ber er of the co comm mmunity. unity. If music music really did stem fro fr om sexual selec selecti tio on, we might reaso reasona b  bly ly expec expect that music musicians will have mo more children (o (orr children who who survive  b  better etter)). Do they? We have no no idea, and no no one seems too too con co ncerned to to find out. Even mo more regretta b  bly ly,, sup supp porters of the sexual sexual-seleccti sele tio on hypo hypothesis seem to to find it extrao extraordinarily diffic difficult to to refrain fro fr om drawing a fac facile analo analogy with the li bidinal  bidinal exc excesses of roc ock k stars  –  whi whicch is why I suggest we view this as the ‘Hendrix theo theory’ of  musicc’s origins. Yes, Jimi Hendrix had plenty of sexual co musi con nq uests uests (th tho ough he sired few children hildren))  b  bef  ef ore his untimely death (there b y, in evo ev oluti lutio onary terms, making the dangero danger ous drugs and drink a pric pri ce potentially wo worth paying )  –  but  but if there’s one thing wo worse than theotheorizing  b rizing   b  y anec anecdote, it is theo theorizing  rizing  b  b y cele b  brity rity anec anecdote. Fo For every succh case, there is a co su counter unter--example. We do don’t kno know mu mucch a bo  bout ut the sexual adventures of tr tro ou b  bad ado ours, urs, b  but ut mo most Western Western music music in the Middle Ages was prac practised tised b  b y (supp suppo osedly sedly)) celi bate  bate mo monks. In so some  Africcan soc  Afri societies, ieties, music musicians are regarded as lazy and unrelia b unrelia ble le –   – p poo oorr marriage pro prospe speccts, in other wo words. (Some seem to to find tho those char har-oût  is no acteristi teristiccs in themselves aphro aphr odisia disiacc, b  but ut chacun à son g oût  no evolu lu-tio ti onary theo theory either.) either.) Besides, if music music is an adaptatio adaptation via sexual selec selecti tio on, we might expecct it to expe to  b  bee de dev vel elo oped to to different degrees in men and wo women. There’s no no eviden evidencce that it is (even tho though there may b may  bee slight differdifferencces in ho en how music music is proc processed essed in the b the  brain rain –   – see see p. 24 249). We kno know of no other example of sexual selec selecti tio on that is manifested the same an’’t  be uniq  way in  bo  both th sexes. This do doesn’t mean that music music can uniq ue ue in that respec respect, t, b  but ut it do does warrant so some scepti epticcism a bo  bout ut the idea. There’s no no la lacck  k o of alternative hypo hypotheses f or the origin of music music. One key q uestio uestion is whether whether human music music has any co conne nneccti tio on to to the ‘songs’ that so some animals, fro from b  birds irds to to whales, pro produ ducce. Some peo people

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might bee happy to might b to call these ‘songs’ music music simply simply b  beecause they so sound a b  bit it like it; it; and it hardly seems impo imp ortant to to dissuade them, pro pr ovided we acc ccept ept that b that birds irdso ong does not b  beeco come me music music merely merely b  beecause Olivier Messiaen transc transcri bed  bed it as suc such (and  b  beecause co countless untless earlier comp co mpo osers, inc including Beetho Beethoven, mimic mimicked it aco acousti usticcally in their comp co mpo ositi sitio ons ns)). But as will b will  beeco come me inc increasingly clear, music music is no not just a series of  pit pitcches, and neither is it a so s ound designed to to impart inf ormatio mati on. One co could, uld, in theo theory, enco encode de any message in music music, merely  b  y assigning no notes to to letters. If yo you kn kno ow the co code, de, the Bi ble  ble co could uld  bee co  b communi mmuniccated that way. But it wo wouldn’t  b  bee the Bi ble  ble rendered in ‘musi musicc’, ’, b  beecause it wo would uld b  bee music musically empty. Most animal so sound is of this enco encoding ding type: the so sounds have desig nated meanings, serving as warning signals or mating  calls or summo summ onses to to the yo young. What is striking and suggestive a bo a bout ut b  bird ird and whale so songs is that they are no not ob obvi vio ousl  y like this: they aren’t mere sc screams or wh whoo oops, ps, b  but ut co consist nsist of phrases with with distin distinct pitc pitch and rhythm patterns, whic which are permutated to t o pr pro odu ducce co complex mplex so sound signals so sometimes many minutes or even ho hours lo long. It seems clear that these seq  seq uenc uences do don’t in themselves enco en code de semantic semantic inf ormati rmatio on: song  b  birds irds do don’t mean one thing when they repeat a phrase twic twi ce, and ano an other with three repeats. In this sense, no n o animal makes lexic lexically meaningful co com m b  binati inatio ons of so s ound und –   – senten sentencces es,, if you like, whic which deriv derivee a new meaning fro from the co com m b  bined ined meanings of  the co comp mpo onent parts. This challenges any no noti tio on that animal so song is like human language  –  but  but what a bo  bout ut human music music? As we’ll see, the q uestio uestions of wh whethe etherr musicc may have either a grammar or any semantic musi semantic meaning are ho hotly contested, co ntested,  b  but ut neither has yet  b  been een sho shown to  b  bee an essential chara haraccteristicc of music teristi music. So S ong  b  birds, irds, whic which co comprise mprise nearly half  of all kno known  bird  b ird spec species, tend to to create their so songs ngs b  b y the shuffling and co com m b  bina ina-tio ti on of sh sho ort phrases. In this way they can create a huge reperto repertoire ire –   –  sometimes hundreds of songs, eac each one apparently remem b  bered ered and repeata b  ble le –   – fr fro om a small invento inventory of  f  b  basi asicc fragments. Yet the so s ongs don’t eac each have a distinc distinct meaning ; rather, it seems that the aim is merely to to create senso sensory diversity, to t o pr pro odu ducce a ‘new’ so song that will capture the attentio attention of potential mates thro through no novelty. (In an ec echo of Darwin’s sexualsexual-sele seleccti tio on hypo hypothesis, the females of some of the song  b  bird ird spec species with the mo most co comple mplexx so songs, suc such as sedge war b  blers lers and starlings, may choo oose se males with the mo most ela bo  borate rate so songs. ngs.)) This

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is certainly paralleled in so s ome music music, partic particularly that of the Western Classi lassiccal perio period, in whic which many stoc stock k phrases (su succh as arpeggio arpeggios, turns and so so f orth rth)) re reccur in different seq  seq uenc uences. There are, no nonetheless, all so sorts of  ob je  jeccti tio ons to the idea that this makes b makes  birds irdso ong  ng ‘‘like music music’. For one thing, the so soni nicc  b  building  uilding  b  blloc ocks ks of  f  b  birds irdso ong  ng co contain ntain no none of the no note te--too-n note implic implicati atio ons of Mozart: there is no no indi indiccati atio on that spec specifi ificc pit pitcches imply whic which others will f oll llo ow. And there is no no indi indiccati atio on that  b  birds irdso ong has the hierarc hierarchi hiccal struccture of human music stru music, in whic which even the simplest tunes tend to to have ‘nested’ phrase struc stru cture reminisc reminiscent of the way way language wo works. (I will explo explore this no noti tio on, as well as the validity and pitfalls of  f co compar mpar-iso is ons with language, in Chapter 12.) 12.) Birds Birdso ong is b is  basi asiccally just a string  of little  b  bursts ursts of sound: no no more than one thing after ano another. ther.** Furthermo Furtherm ore, animal ‘song’ is typic typically no non-voliti litio onal,  b  but ut is stimustimulated  b  y seaso seasonal and ho horm rmo onal changes. One can nevertheless argue that an a b a bility ility to to create and remem b  ber er different arrangements of soni nicc units is a nec necessary prec precurs urso or to t o bo  both th musicc and language. Even there, ho musi however, we must take care. Do Don’ n’tt imagine that  b  birds irds and humans share so s ome pro protoo-musi musiccal anc ancest esto or: the a b  bility ility to to learn voc vocal al reperto repertoires of  ‘song’ seems to to have evo evolved separately in primates and b and  birds, irds, and indeed has evo evolved at least twic twice amo am ong  birds  birds themselves as well as separately in b in  bats, ats, whales and seals. No other primates sing, b sing,  but ut chimpanzees pro produ ducce a struc structured call kno kn own as a pantpant-hoo oot, t, whic which seems to to differ fro from one creature to to ano an other: eac each has a signature tune. Co Compared mpared with b with birds, irds, chimps alwa a lways ys sing essentially the same ‘song’. But  bo  both th sexes ‘sing’ in all of the primate spec species that sho show this b this  behavi ehavio our (a bo  bout ut one in ten) ten), and they acco ccompany mpany that ac activity with ritualized mo m ovements suc such as drumming, drumming, sto st omping and shaking  bran  brancches, resem b  bling ling the b the behavi ehavio ours that humans sho sh ow in music musical co contexts. ntexts.† (They do don’t, ho however, keep a steady  b  beat. eat.)) * Whale so song  does seem to to have so some element of hierarc hierarchi hiccal organizati rganizatio on. That doesn’t mean whale so song is ‘musi musicc’ either,  b  but ut it do does  b  bring ring it so somewhat closer to to that status. So Some philo philosophers of music music insist, ho however, that music music can only  b  bee a human attri bute  bute b  b  y definitio definition, sinc since listening to to it as suc such re req  q uires uires imaginatio imagination. † Linguist Tec Tecumseh Fitc Fitch thinks that primate drumming, whic whi ch is so sometimes condu co nduccted in a spo spontane ntaneo ous and playful manner, co could uld b  bee closely related to to human perccussive musicper music-making. making. But we do don’t kno know whether ape drummers can ‘get with a  b  beat’ eat’ –   – see see pp. 225–  225– 227 227.

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Perhaps the most interesting aspect of primate singing is that the pant-hoot doesn’t connote anything in particular, or at least nothing  with a guaranteed meaning. Instead, it seems to be an expressive sound, a vehicle f or emotion. Chimps pant-hoot when they are excited, or perhaps merely to say ‘here I am’. African apes also use their voices more f or affective than f or inf ormative reasons, unlike the coded calls of many other animals. This has led some researchers to speculate a bout whether music stemmed from emotive rather than semantic signalling. Might there have then been a time when vocalization contained a  bit of  both inf ormation and emotion? Of course, language clearly does so today, particularly in poetry (which also shares with music the properties of rhythm and metre). But  bef ore language crystallized into consensual f orms, one might conceiva bly have achieved a lot of  communication and interaction with a ‘musilanguage’ that verged on the semantic while emplo ying the emotional arsenal of simple music. This ancestral merging  of language and music is a popular theory, and it also boasts Darwin’s imprimatur. He wrote: it appears proba ble that the progenitors of man, either the males or females or both sexes, bef ore acq uiring the power of expressing their mutual love in articulate language, endeavoured to charm each other with musical notes and rhythm.

But the idea is older still: Jean- Jacq ues R ousseau expressed something  like it in the eighteenth century, suggesting that our ancestors may have used music-like vocalization to convey passions  bef ore they  became a ble to express their thoughts.  Adherents of the musilanguage hypothesis point to the analogies that have been drawn between the structures of language and music.  Although these are still  being de bated,  both do use com binatorial syntax – the rule-based com bination of  basic acoustic building  blocks  –  and intonational phrasing using pitch and rhythm. Steven Brown of the Karolinska Institute in Sweden suggests that one can identify a continuum of f orms  between language and music, progressing  through heightened speech, poetry and operatic recitative to song, musical sym bolism (where semantic meaning is conveyed through devices such as descending melodic contours to denote ‘falling’) and

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finally ‘pure’ instrumental music. ‘Music and language have just too many important similarities f or these to be chance occurrences alone,’ claims Brown. He believes that a musilanguage could have served as a launching stage f or  both music and language if it contained three essential features: lexical tone (the use of pitch to convey semantic meaning ), com binatorial f ormation of small phrases, and expressive phrasing principles, which add emphasis and connote emotion (f or example, fast tempos to convey happiness, and slow to convey sadness).   A remnant of such musilanguage might  be perceived in the socalled Auchmartin and Enermartin of some Ecuadorian tri bes, which are f orms of song -speech used respectively  b y strangers meeting on a jungle path and b y groups of men to promote courage bef ore battle. More generally, perhaps relics of musilanguage survive in tonal languages, and in the way songs and rhythmic poems are often used in preliterate cultures to encode important knowledge. Here the musicality aids memory: it’s generally much easier to memorize poetry than text, and we typically find song lyrics easier to recall when we sing rather than say them. (We’ll look later at some of the possi ble neurological reasons f or this.)  A curious variant of the ‘musical communication’ hypothesis was put f orward  b  y the Hungarian-Dutch psychologist Géza R évész, a friend of Béla Bartók, who pointed out that a song -like voice has acoustic f eatures that allow it to carry over greater distances than a speech-like voice. You might say that this makes the earliest music a kind of yodel – if you like, the ‘Lonely Goatherd’ theory of music’s origins. One of the most obvious features of music the world over is that it tends to be a group activity. Even when perf ormed b y a select few, music commonl  y happens in places and contexts in which it creates social cohesion, f or example in religion and ritual or in dance and communal singing. One of the clearest descriptions of this role was given  b  y the English social anthropologist Alfred Radcliffe-Brown in his study of dance among people of the Andaman Islands in the Bay of Bengal: The dance produces a condition in which the unity, harmony and concord of the community are at a maximum, and in which they are

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intensely felt b y every mem ber. It is to produce this condition, I would maintain, that is the primary social function of the dance . . . For the dance aff ords an opportunity f or the direct action of the community upon the individual, and we have seen that it exercises in the individual those sentiments b y which the social harmony is maintained.

This function has led some to suspect that we shouldn’t be searching  f or music’s origins in the  benefits it might confer on individuals,  but rather, in how it is advantageous to an entire society or culture (and thus indirect ly the individual). This is, you might say, the ‘New Seekers theory’ of music’s origins: ‘I’d like to teach the world to sing’. The music psychologist Juan R oederer puts it a little more soberly: The role of music in superstitions or sexual rites, religion, ideological proselytism, and military arousal clearly demonstrates the value of  music as a means of esta blishing  behavioural coherenc y in masses of  people. In the distant past this would indeed have had an important survival value, as an increasingly complex human environment demanded coherent, collective actions on the part of groups of human society.

The notion of  ‘group selection’ as an evolutionary f orce, where b y  behaviours are selected because they benefit a group, has had a controversial history, and remains so today. The q uestion of how much advantage you get from helping those only distantly related to you, or not related at all but nonetheless sharing common g oals, is a very su btle one. All the same, the theory that music’s adaptive value lay in the way it  brought communities together and promoted social cohesion enjo ys wide support.* A ‘social’ element is f ound in primate calls, which seem to help mem bers of a group locate one another.   And music in tri bal societies often has communal functions: f or example, it’s said that Venda tri bespeople can tell from a song what the singer is doing. The men of the Mekranoti tri be of Amazon Indians devote several hours a day to group singing, especially very * There is in fact nothing necessarily incompati ble with an origin of music in social cohesion and one in sexual selection, f or individuals that take the lead in social musicmaking gain status.

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early in the morning. Everyone is expected to attend these communal sessions, in which the singing possi bly keeps the groggy men awake so that they can  be alert to attacks from enemy tri bes. That would certainly give music-making a survival value  – and indeed, it would  be odd to devote this much time to an activity that did not have some adaptive  benefit. Rhythmic sounds provide a great vehicle f or synchronization and coordination of activity  –  witness (say the theory’s advocates) the u biq uity of  ‘work songs’. And even when nothing tangi bly ‘useful’ comes of group participation in music, it promotes a lasting sense of togetherness. Again, contemporary parallels offer themselves with treacherous alacrity: look at the way adolescent su bcultures esta blish their identity through allegiance and shared listening to specific modes of music. Japanese researcher Hajime Fukui has f ound that people have lower testosterone levels when listening to their favourite music, which he interprets as an indication of  music’s socializing  function, promoting sexual self -control and lowering aggression. Those notions seem sq uarely contradicted b y rave parties and mosh pits, of  course,  but it’s q uestiona ble whether we can deduce much a bout music’s origins from the antics of Western teenagers. More importantly, Fukui’s findings fail to tell us whether changes in listeners’ testosterone levels are prompted  b  y music as such or  b y the f act that they are hearing their favourite kind. Rather more convincingly, the almost universal use of music in communal ritual might  be understood on the basis that its a bility to arouse emotion and teeter on the brink of meaning, without any such meaning ever becoming apparent at the semantic level (and we’ll look  at that contentious claim later), seems to recommend it f or expressing  or representing numinous concepts. Stravinsky seems to have shared this view, saying that ‘the prof ound meaning  of music and its essential aim . . . is to promote a communion, a union of man with his fellow man and with the Supreme Being’. Sexual display, group bonding, transmission of inf ormation: it all sounds rather, well, male. Another hypothesis aims to relocate the musical impulse in the maternal,  b y pointing  out that infants are much more receptive to speech when conveyed in the singsong tones du bbed ‘motherese’, and that mothers of all cultures use this instinctively. (So do fathers and si blings, although an infant’s exposure to

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this kind of  communication would usually come mostly from the mother.) And ba bies seem to come eq uipped with the mental apparatus f or discerning simple musical attri butes: they can discriminate from the time of   birth  between upward and downward musical contours, and within two months they can detect a change in pitch of just a semitone. If   better mother-child communication  –  not just semantic  but emotional – leads to better-adjusted and more cognitively a ble adults who do well in the world, then there is a potential selective advantage to a predisposition to musicality.* But one can also interpret at least some features of motherese in purely linguistic terms: it facilitates language learning  b  y helping to emphasize contrasts  between different vowels and consonants, f or instance. And the descending  pitch contours that characterize lulla bies throughout the world are also f ound in speech typically used to soothe a child. Furthermore, it’s not easy to explain how traits shaped  b y oneon-one infant interactions find their way into adult social ritual. Musicologist Ellen Dissanayake suggests that the music-like sensitivities and competencies developed in the mother-infant interaction ‘were f ound  b  y evolving human groups to  be emotionally affecting  and functionally effective when used and when further shaped and ela borated in culturally created ceremonial rituals where they served a similar purpose  –  to attune or synchronize, emotionally conjoin, and enculturate the participants’. That seems something  of a leap of faith, and surely invites the q uestion of why often (although  b y no means universally) it is men who have traditionally engaged in the production of music. Even less comf orta ble is the suggestion that an origin of music in infanthood explains why (Western) popular songs use childish words such as ‘ba b y’ to express sentiment, an idea that tempts me to call this the ‘R onettes theory’ of music’s origins: ‘Be My Ba b y’. Might it be that to ask ‘what is the origin of music?’ is simply to ask the wrong  q uestion? Some palaeontologists and archaeologists consider that the transition from our ape-like ancestors to humans *Some Freudian psychologists, such as Heinz K ohut, have stood this argument on its head, suggesting that music is theref ore a f orm of infantile regression, al beit one that has been made socially and aesthetically accepta ble.

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 – what they call hominization  – involved the appearance of such a rich complex of traits, such as language, arithmetic, logic, society and self -consciousness, in such a short time that it makes little sense to consider them independent of  one another. Either they are all part of the same basic phenomenon, or the emergence of  one made all the others inevita ble. In a similar vein, Jean Molino argues that, as there seems to  be no universal definition of music, we can’t reasona bly say that something  called music emerged in evolution,  but only that certain human capacities and tendencies appeared which have gradually f ound expression in what we now consider types of music.

Pinker redux To almost all of this theorizing a bout origins, one can only say: yes, it sounds plausi ble. You could be right there. May be it’s unfair to point out (as one nonetheless must) that all these ideas are more or less impossi ble to prove. After all, no one has access to a Palaeolithic society. But it’s unf ortunately rather rare to hear hypotheses a bout music’s origins asserted with anything less than firm conviction, and rather common (as I’ve hinted) to find them supported  b y cherry-picking  from the vast and diverse ways in which music is made and used throughout the world  –  or worse still,  b  y anecdotes from Western popular culture, in which music has surely become a more artificial, a bstracted, and fashion-bound medium than in any other culture. More trou bling still is the sense that these speculations are  being  offered in desperate determination to prove that music has been hardwired into our  brains  b  y evolution  –  to show, in other words, that Steven Pinker is wrong to portray music as a kind of aesthetic parasite. One can’t help feeling that an evolutionary role f or music is often seen as the only way it can be aff orded its true dignity. Even worse is the implication that if we understand where music came from, we will understand what it is a bout. Whether or not Pinker is right a bout why we have music, he is right to say that the de bate should not  become a surrogate f or arguing over the value of music. When evolutionary  biology  becomes the ar biter of artistic worth, we are in  big  trou ble.

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The fact is that at this point there are no compelling scientific arguments against Pinker’s position. We will see later that there are a few tentative indications that music might indeed  be a genuine, adaptive ‘instinct’,  but that case is far from secure. My view is that we should approach this interesting  q uestion as one that is utterly irrelevant to our reasons f or treasuring music, there b  y jettisoning  the emotive  baggage with which it has  been  burdened.  Auditory ‘ cheesecake’ is a phrase carefully chosen f or polemical effect, but it’s dou btf ul that Pinker meant it as any kind of artistic or aesthetic  judgement, and we’d do him a favour to assume he did not. As f or William James, who regarded music as a ‘mere incidental peculiarity of the nervous system’, it seems that this unf ortunate philosopher strained in vain to make much sense of music (he may have  been one of the rare individuals who is genuinely tone-deaf ), and so his dismissive comment is more an expression of   bafflement than a prof ound insight. Richard Dawkins has rightly said that a q uestion does not become meaningful simply because it can be articulated, and I suspect that is true of Pinker’s suggestion that music ‘could vanish from our species and the rest of  our lifestyle would be virtually unchanged’. Aniruddh Patel of The Neurosciences Institute in San Dieg o regards music as a transf ormative technology  – one whose appearance so alters its host culture that there is no g oing  back. ‘The notion’, he says, that something is either a product of  biological adaptation or a frill [‘cheesecake’] is  based on a false dichotomy. Music may be a human invention, but if so, it resem bles the a bility to make and control fire: It is something we invented that transf orms human life. Indeed, it is more remarka ble than fire making in some ways, because not only is it a product of  our brain’s mental capacities, it also has the power to change our brain.

In this view, you might as well imagine that we could give up theatre or sport, which eq ually don’t seem essential f or our survival (though again, one can tell superficially plausi ble stories a bout why they might  be adaptive). It is no surprise, then, that we know of no culture that lacks music. I agree with Patel,  but would g o further. It’s not only that music

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is too deeply em bedded in our cultures to be extracted. It is too deeply em bedded in our brains. Regardless of whether evolution has given our brains musical modules, it seems to have given us intrinsic proclivities f or extracting music from the world. Music is a part of what we are and how we perceive the world. Let’s now start to see why.

3 Staccato The Atoms of  Music What  are musical not es and how do we decide which to use?

‘Organized sound’ might strike you as a pretty neat definition of music. But the phrase was coined b y the French-born avant-garde composer Edgar Varèse, who wrote music in the early twentieth century that many of his contemporaries would not have accepted as ‘music’ at all. And Varèse wasn’t seeking a catchy general definition that could  be applied to anything from Monteverdi to Lead belly; rather, he used the description to dist inguish his bold sonic explorations from conventional music. His compositions called f or howling sirens, the ghostly electronic wail of the theremin, and electronically taped am bient noises: rum bling, scraping, jangling, honking and the churning  of  machines. He gave these works pseudoscientific names: Inté grales, I onisat ion,  Densit  y  21.5. ‘I decided’, he said, ‘to call my music “org anized sound” and myself, not a musician,  but a “worker in rhythms, freq uencies and intensities”.’ If  t hat  was meant to apply to Mozart too, it would seem to make him something like a cross  between a la boratory technician and an industrial la bourer. But Varèse didn’t regard himself as an iconoclast. He traced his heritage to music’s ancient practices, and professed admiration f or the music of the Gothic Middle Ages. This seems appropriate in many ways, f or the composers and musical scholars of antiq uity shared his view of music as a kind of technical crafting  of sound. Unlike the nineteenth-century R omantics, they would have had no problem with a discussion of music in terms of acoustic freq uencies and intensities. I suspect many people share the romantic sense that music is a product of numinous inspiration, and are apt to feel disheartened, even appalled, when it is fragmented and seemingly reduced to a

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matter of mere acoustics, of the physics and biology of sound and audition. If that seems at first to be the business of this chapter, I hope you will soon see that it isn’t really so. But I don’t intend to apologise for a digression into the mathematics, physics and physiology of acoustic science by justifying it as an unavoidable introduction to the raw materials of music. It is much more interesting than that. I will admit, however, that while dissection is as necessary in musicology as it is in biology, it is likewise apt to leave us contemplating a pile of lifeless parts. A better metaphor than the anatomical is the geographical: music is a journey through musical space, a process that unfolds in time and the effect of which depends on how clearly we can see where we are and how well we recall where we have come from. Only the vista ahead is obscure to us; but our sense of journey depends implicitly on our anticipation of what it might contain. And just as a journey is not made from trees and rocks and sky, music is not a series of acoustic facts; in fact, it is not acoustic at all. I can’t emphasize this enough. It is fine to call music ‘organized sound’, so long as we recognize that this organization is not determined solely by the composer or performer: it emerges from a collaboration in which the listener too plays an active part. Nonetheless, this chapter is not merely about the cold facts of the ‘sound’ that Varèse sought, in his idiosyncratic way, to organize. It is about how nature and culture interact to produce the diverse palettes of notes that most traditions draw on in creating their sonic art. There is very little that is preordained in this palette – contrary to common  belief, it is not determined by nature. We are free to choose the notes of music, and that’s what makes the choices interesting. They crystallized in Western music into the notes of the modern piano, which repeat in octave cycles with twelve notes each. Not everyone accedes to that arrangement. The maverick American composer Harry Partch (1901–74), searching for a system better adapted to the nuances of the human voice, devised a microtonal scale of 43 pitch steps per octave (he also experimented with 29-, 37- and 41-note scales). The music Partch wrote was played on special instruments that he designed and   built himself, bearing exotic names such as the chromelodeon, the   bloboy and the zymo-xyl. It sounds frighteningly experimental, but Partch’s music is actually not as formidable or jarring as one might

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expect, especially if you’ve had any exposure to gamelan and South East Asian percussion orchestras. The point is not necessarily which notes we choose,  but the fact that we choose them at all. Painters understand that notion. They have in principle an infinite range of  colours at their disposal, especially in modern times with the chromatic explosion of synthetic chemistry. And yet painters don’t use all the colours at once, and indeed many have used a remarka bly restrictive selection. Mondrian limited himself  mostly to the three primaries red, yellow and  blue to fill his black -ruled grids, and Kasimir Malevich worked with similar self -imposed restrictions. For Yves Klein, one colour was enough; Franz Kline’s art was typically  black  on white. There was nothing  new in this: the Impressionists rejected tertiary colours, and the Greeks and R omans tended to use just red, yellow, black and white. Why? It’s impossi ble to generalize, but both in antiq uity and modernity it seems likely that the limited palette aided clarity and comprehensi bility, and helped to f ocus attention on the components that mattered: shape and f orm. That is perhaps even more true in music,  because the notes carry a heavy cognitive burden. To make sense of  music, we need to  be a ble to see how they are relat ed –  which are the most important, say, and which are peripheral. We need to understand them not just as stepping stones in musical space,  but as a family group with a hierarchy of roles.

Making waves Most of the music in the world is made from notes. And to a g ood approximation, we hear each note as a  pitch with a specific acoustic freq uenc  y. Notes sounded in succession create a melody, while notes sounded simultaneously produce harmony. The su b jective q uality of  the note – crudely, what instrument it sounds like – is its t imbre. The duration and timing of notes, meanwhile, define the rhyt hm of  music. With these ingredients, musicians compile ‘global’ structures: songs and symphonies, jingles and operas, compositions that typically belong  to a certain f orm, style and genre. Most music is experienced as vi brations in air. That’s to say, some ob ject is struck, plucked or  blown, or driven  b y oscillating electro-

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magnetic fields, so that it vi brates at specific freq uencies. These motions then induce sympathetic vi brations in the surrounding air that radiate away from the source like ripples in water. Unlike waves on the sea surface, the vi brations of air are not undulations in height; they are changes in the air’s density. At the ‘peaks’ of sound waves, the air is compressed to greater density than it would be in a soundless space; at the ‘troughs’, the air is less dense (rarefied) (Figure 3.1). The same is true of acoustic waves passing through other su bstances, such as water or wood: the vi brations are waves of material density. Earpieces attached to porta ble electronic devices sit in contact with the tissues of the ear and transmit vi brations to them directly. The perceived pitch of a sound  becomes higher as the freq uenc y of the acoustic vi brations increases. A freq uenc y of  440 vi brations per second  –  the ‘concert pitch’ to which Western pitched instruments are conventionally tuned  –  corresponds to the A note a bove middle C. Scientists use units of hertz (Hz) to denote the num ber of vi brations per second: concert A has a freq uenc y of  440 Hz. We can hear freq uencies down to 20 Hz,  below which we feel rather than hear them. Freq uencies just below the lower threshold of hearing are called

 Figure 3.1 Sound waves in air are waves of greater or lesser air density.

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infrasound, and are produced b y some natural processes such as surf, earthq uakes and storms. They seem to stimulate strange psycholog ical responses, particularly feelings of unease, revulsion, anxiety and awe, and have been credited with inducing ‘supernatural’ experiences. Infrasound has been used f or its unsettling effect in some contemporary music, f or example in the soundtrack to the French shocker movie Irr éver sible. As a way of using music to induce emotion, that somehow seems like cheating. The upper freq uenc y limit of human hearing is typically a bout 20,000 Hz,  but tends to be lower in older people  because our ear’s sound sensor cells stiffen with age. Higher freq uencies than this (ultrasound) are inaudi ble to humans,  but are detected  b  y many other animals:  bats use them f or echolocation. Between these extremes, human hearing typically spans a gamut of a bout ten octaves. On the 88-note piano, the lowest A growls at 27.5 Hz, and the top C is a shrill 4,186 Hz. We find it harder to make out a single well-defined pitch f or notes at either extreme of the piano than f or those in the middle – which is why most music is played there, and of  course why it is the middle of the key board at all. The human male speaking voice has a typical freq uenc y of around 110 Hz, and the female voice an octave higher, 220 Hz; so when men and women sing together ‘in unison’, they are actually singing in octave harmony.

How we hear Converting acoustic vibrations in the air to a nerve signal that is sent off for processing in the brain is the job of the cochlea, a spiral chamber of bone in the inner ear that looks like a tiny snail shell (Figure 3.2). Housed within it is a long membrane sheet called the basilar membrane, covered with sound-sensitive ‘hair cells’, so called because of the little tuft-like protrusions that poke above their surface. These cells are like mechanical switches: when the ‘hairs’ are set waving by acoustic vibrations in the fluid that fills the cochlea, the movement pulls open tiny pores in the cell walls, letting in electrically charged metal atoms from salt in the surrounding fluid that change the electrical state of the cell. This

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produces nerve signals that surge along nerve fibres leading to the brain. Different hair cells respond to different sound frequencies, and they are arranged over the basilar membrane in a manner remarkably similar to the way piano strings are laid out on the soundboard: the basilar membrane resonates to low-frequency sounds at one end and progressively higher frequencies as we move along it. All this is the easy part of auditory cognition – it converts sound into electrical signals, rather as a microphone does. Our perception of  the sound depends on how those signals are processed. One of the first steps is to decode the pitches, which is done surprisingly directly: each part of the basilar membrane seems to have a dedicated set of  Temporal bone

Semicircular  canals

Malleus

Stapes Incus

Tympanic membrane (eardrum)

Cochlea Auditory nerve

Tympanic cavity

2,000 Hz 1,500 Hz 3,000 Hz 400 Hz

600 Hz

Cochlear duct

200 Hz 800 Hz 1,000 Hz

20,000 Hz

Basilar  membrane

7,000 Hz 5,000 Hz

 Figure 3.2 The anatomy of the ear.

4,000 Hz

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neurons in the brain to pick up the activity. These pitch-selective neurons sit in the primary auditory cortex, the part of the brain where pitch is processed. It’s very unusual for a perceptual stimulus to have this one-to-one mapping in the brain – we have no comparable neurons that, for example, respond to specific tastes, smells or colours.

How music is written The ability to read music is sometimes regarded with awe, as though it offers privileged insights into the world of music from which noninitiates are excluded. The fact that many popular and jazz musicians could not read a note – Erroll Garner and Buddy Rich, for example, virtuosos both – only adds to this notion: if  they  couldn’t do it, it must surely be a gargantuan feat. Well, it isn’t. The plain truth is that many self-taught musicians simply never felt the need to learn this skill. But it is not hard at all, at least to the extent of becoming able to name a note. A facility for reading complex music fast enough to play it on sight is indeed a technical skill that requires practice, as is the ability to ‘hear’ in one’s head what is written on the page. But you will not need to do that in order to understand and benefit from the musical quotations reproduced in this book. And in any case, they can all be heard online at www.bodleyhead.co.uk/musicinstinct. Reading music is perhaps most easily explained with reference to the piano, on which there is a transparent relationship between written notes and the piano keys – every written note corresponds to a specific key. The musical stave – the five horizontal lines on which notes are suspended – is just a representation of a piano stood on its side, with the high notes uppermost. Of course there are a lot more notes on the piano than there are lines on a stave, but the two staves in written music cover the notes most commonly used (Figure 3.3) – one typically played with the left hand, the other with the right. For notes outside this range, the staves are extended locally with extra lines. Each of the white-note keys of the piano is assigned a place on these staves, successively either between or on the stave lines. The

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 Figure 3.3 The musical clefs and staves. Notes higher on the stave indicate notes ‘higher’ on the piano. Every note either sits on a stave line or between them.

ornate ‘clef’ signs that appear at the start of the stave – the baroque treble clef on the upper stave, the coiled bass clef on the lower – are merely symbols to tell you where the correspondence between stave lines and piano keys is anchored. The treble clef looks a little like a fancy ‘g’, and its lower body circles the stave line corresponding to the note G above middle C. The bass clef is a stylized F, and its two dots straddle the stave line corresponding to the F below middle C (Figure 3.3). Other types of clef are sometimes used that define different ‘origins’ on the staves, but we needn’t be concerned with them. What about the black notes on the piano? These are indicated by so-called accidentals – the sharp and flat signs G and H – next to a note of a particular pitch, indicating that this note should be played either on the black note above (sharp) or below (flat). There is some redundancy in this system, because it means that the black notes have more than one ‘identity’. That above F, for example, is simultaneously F G and GH (Figure 3.3). And for white notes that do not have a black note immediately adjacent in a certain direction, a sharp or a flat becomes another white note: BG, for instance, is the same as C. We will see shortly where this notation for accidentals came from, and also how the ‘multiple identities’ of the various notes have a complex history and a subtle role to play in how we conceptualize music. The notes go in a repeating cycle as they ascend. Rising from concert A, for example, we find the white notes B, C, D, E, F, G – and then A again. This second A is an octave above the first: eight notes higher as we rise up the musical scale. We’ll see below precisely what that means. Each particular note can be given a unique label by numbering those in each octave, starting from the lowest A on

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the piano keyboard (AO). This makes middle C equivalent to C4, and concert pitch A4. The blobs denoting notes take on different appearances in a musical score (Figure 3.4) – sometimes filled in ( Q), sometimes empty (W), some with wavy tails attached, some linked by bars or accompanied by dots or so on. These markings indicate the note’s duration: whether they last a whole beat, or several beats, or a fraction of a beat. And there are other objects arrayed on the staves. Some (such as A and S) denote rests, which are beats or fractions of a beat during which no notes sound. Arching lines might designate ties, which show that a note is to be prolonged over both of the note durations at each end; or they might tell the musician about patterns of phrasing, meaning how notes are to be articulated in groups. There are rhythmic codes here too. The numbers at the start of a stave are the time signature, which indicates how many notes of a particular duration should appear in each of the bars denoted by vertical lines. In essence, they tell us whether we count the rhythm (more properly, the metre – see Chapter 7) in groups of two, three, four or more beats. Music scores are littered with other signs too, indicating such matters as dynamics (where to get louder or softer), accents, trills and so forth. This isn’t the place for a comprehensive account of what music notation means; Figure 3.4 shows the main symbols that will suffice to understand most of the musical extracts I quote. To keep matters simple, I have generally stripped them down to their bare essentials rather than following the composers’ scores rigorously. I hope that will not trouble purists. Bar line

Time signature

Dynamics (getting louder)

Treble clef  Phrasing Dynamics (Pianissimo: very soft)

 pp

Articulation (staccato)

sf   cres

-

-

cen - do

decresc.

 p

Tie

Bass clef 

sf   Key signature

sf  

Rests

Phrasing Dynamics (getting louder)

Dynamics (Sforzando: abrupt accent)

 Figure 3.4 Basic elements of written music.

Rest

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 Arranging the sonic staircase In principle, the relationship between the pitch and acoustic freq uenc y of a musical note seems simple: the higher the freq uenc y, the higher the pitch. But a striking aspect of music in nearly every culture is that its notes are discret e. There are an infinite num ber of pitches within the freq uenc y range audi ble to humans, since the difference between two freq uencies can  be made as small as you like. Although there comes a point at which we can no longer distinguish  between two very closel y spaced tones, just as there are limits to the resolution with which we can discriminate ob jects visually, there are conseq uently very many ‘notes’ that we could arrange into music. Why do we use only a su bset of them, and how is that su bset selected? Nature seems to have imposed a  basic division of this continuous pitch scale: the octave. If you play any note on the piano and then play the same note an octave higher, you will hear it as a ‘higher version’ of  the original note. This is so commonplace that it seems barely remark a ble. Anyone who has ever picked out a simple melody on a piano with tentative prods of a finger will have discovered that the same melody can be played, with the same pattern of key strokes, an octave higher or lower. The octave is itself enshrined on the piano in the shape and arrangement of the keys: novice pianists learn to recognize the L shape of  Cs and Fs, and the c yclic clustering of two and three black notes. But octave eq uivalence is deeply strange. It is a perceptual experience uniq ue to music: there is no analog ous repeat pattern in visual perception, or in taste.* In what way is middle C ‘like’ the C a bove * It is often remarked that the two extremes of the visi ble spectrum of light – red and violet – match up, so that the spectrum seems to come full circle. There is no obvious reason why this should be so: the freq uencies of light corresponding to the two colours are unrelated. The circularity of colour space is, however, a genuine perceptual phenomenon, which has been tremendously useful to colour theorists in permitting them to construct closed ‘colour wheels’ f or purposes of classification. It is an artificial construction, however: the ‘colour’ just as visi ble light turns into infrared does not really look  identical to the colour as violet  becomes ultraviolet. And in any case, there is no repetitive c yclicity here as there is in pitch perception – colour has, at best, only ‘one octave’. Nonetheless, a semi-mystical conviction that colour and sound must be related wave-determined phenomena was what led Isaac Newton to postulate seven divisions of the rain bow,  b  y analogy to the seven notes of the musical scale. This ar bitrary Newtonian scheme of  colour categ ories is still taught as ob jective fact today.

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or below it – what q uality remains unchanged? Most people would say ‘they sound the same’  –  but what does that mean? Clearly they are not the same. Perhaps one might say that the two notes sound g ood or pleasing together, but that only generates more q uestions. Pythag oras is attri buted with the discovery of how octave pitches are related to one another. The apocryphal story has it that the Greek philosopher once walked into a  blacksmiths’ f orge where notes rang  out as the smiths’ hammers struck their anvils, and he noticed that there was a mathematical relationship between the relative pitches and the size (the masses) of the anvils that produced them. When he went on to investigate the sounds made b y plucking  taut wires or strings, Pythag oras is said to have f ound that tones which sound harmonious together, such as octaves, have simple ratios of their freq uencies. The octave is the simplest of all: a note an octave a bove another has dou ble the freq uenc y of  the first. This is eq uivalent to saying that the higher note has hal f  the wavelength of the lower. We can visualize the relationship in terms of the lengths of the plucked string. If you halve the length of the vi brating string  b y putting   your finger on its midpoint, you dou ble the freq uenc y and generate a note an octave higher. This is easily done on a guitar: the fret that produces an octave higher than the open string is located exactly halfway between the contacts of the string at the head and the bridge (Figure 3.5a). The next higher octave has a freq uenc y that is dou bled ag ain, making  it 2  2 = 4 times that of the original note. The freq uenc y of A6, say, is 4  440 = 1,760 Hz. You will get such a dou ble-octave jump on a guitar string  b  y pressing down three-q uarters of the way along the string and plucking the upper q uarter. And so it g oes on: each successive octave entails another dou bling  of the original freq uenc y.  Just a bout every musical system that we know of is based on a division of pitch space into octaves: it seems to  be a fundamental characteristic of human pitch perception. We’ll see later the likely reas on why. But what a bout the notes in  between the octaves? Again, legend credits Pythag oras with an explanation f or how these are chosen in Western scales, although in fact this knowledge was surely older. If 

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a Fretted string

Open string

1 2

1

Vibration of open string

Vibration of string fretted at the midpoint: an octave higher

b Fretted string

Open string

2

3

1 c Fretted string

Open string

3 4

1  Figure 3.5  An octave can be produced on a plucked string  b y fretting it halfway along its length (a). The two notes have wavelengths in the ratio 2:1, and freq uencies in the ratio 1:2. Fretting a third of the way along produces a note a perfect fifth a bove the open string (b), and fretting a q uarter of the way along produces a perfect f ourth (c).

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 you put your finger a third of the way along a vi brating string and pluck the longer segment – now two-thirds as long as the open string   –  you get a note raised  b  y less than an octave (Figure 3.5b). Most people will agree that this note fits pleasingly with that of the open string  – it sounds harmonious. The note is the fifth of a major scale that begins on the open string ; in do-re-mi terminology it is the note so. If the open string is tuned to middle C, this new note is the G a bove. The distance, or int erval,  between these two notes is called a perfect fifth (see Box: Scales and int ervals).

Scales and intervals The set of pitches from which a tradition constructs its music is called a scale. As we’ve seen, the notes of a scale have discrete pitches in the continuous space of all possible pitches. We can think of the smoothly varying pitch of, say, the rising wail of a siren as a kind of ascending slope of frequency, while a scale is more like a staircase or ladder. Western music uses scales inherited from Greek tradition, called diatonic scales (‘diatonic’ means ‘progressing through tones’), in which there are seven tones between each octave. Just about all of Western music between the late Renaissance and the early twentieth century was based on two general classes of  diatonic scale: the major and minor. The major scale is the sequence picked out, in the key of C, by all the white notes (Figure 3.6). There are several different minor scales.

 Figure 3.6 The major and minor diatonic scales.

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Each note of a diatonic scale has a technical name. I will explain and occasionally use these later, but for the present purpose we need only recognize the first: the note on which the scale starts, which is called the tonic . In the key of C, for example, C is the tonic. I will often refer to the other notes of the scale not by their technical names but by their ordering in the scale: the second note (D in the scale of C major) is 2, the third is 3 and so on. Likewise, I’ll sometimes call the tonic 1. That way we can avoid either having to use technical terms or having to specify a key. As well as the seven notes of the diatonic scales, there are five others in one octave span – for example, all the black notes scattered among the C major scale. These notes lie outside the scale, but most tonal Western music makes occasional use of them. The scale that includes all twelve notes is called a chromatic  scale, and when tonal music deviates from the tones of the diatonic scale, it is said to be chromatic. A pitch step between one note and that immediately above – B to C, say, or F to F G – is called a semitone, while a step of two semitones (F to G, or C to D, say) is called a tone. This is a somewhat confusing terminology, because a ‘tone’ can also refer simply to any pitched musical sound – but I hope the distinctions will be clear from the context. Any two notes are separated by an interval, which is defined by the corresponding number of steps in the scale. Thus the interval between the tonic note and the fifth note of the scale – C to G, say – is called a fifth (Figure 3.7). For technical reasons it is called a  perfect  fifth. Aside from the fourth and fifth, other intervals come in two different variants, depending on whether they involve a note from the major scale or the note a semitone below, which is often a note from a minor scale. An example of a major-third interval is the step from C to E, while the corresponding minor third is C to E H (Figure 3.7). The only interval not covered within this terminology is that between the tonic and the sharpened 4 or, equivalently, the flattened 5 – from C to FG or GH, for example. This is sometimes called an augmented fourth or flattened fifth interval, but more commonly it is known as the tritone interval, because it is reached by three pitch steps of a whole tone: C ©D©E©FG. Intervals can also span more than an octave: that between C4 and D5,

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 Figure 3.7 The intervals of the diatonic scales.

for example, is an octave plus a second, or nine scale degrees, and is called a (major) ninth. Arguably one could denote this step as 1©9; but the 9 here is also the second note of the scale starting an octave higher, and so is more commonly written as 2’, the prime denoting the start of a new octave. The octave interval is, in this notation, 1©1’. Any specific interval always spans a set number of semitone steps between the lower and upper notes: a major third corresponds to four semitone steps, a minor third to three, say. So it is all really just a matter of counting. Where things get a little complex is that intervals aren’t always defined with reference to the tonic note of the key in which they appear. Consider the interval E to G, say. This is a minor third: G is four semitones above E, and is also the third note of the E minor scale. But this doesn’t mean that the E©G step is somehow confined to music in E minor. It is also a step between the 3 and 5 of the C major scale, for example, and between the 7 and 2’ of F major.

Thus an interval of a fifth separates pitches whose freq uencies are in the ratio of  3:2. Having decided that this interval is pleasing to the ear, the f ollowers of Pythag oras deduced from this a general principle: pitches whose freq uencies are related  b y simple ratios sound ‘g ood’, which is to say, they are considered consonant. (The real relationship  between ‘consonance’ and what we perceive is more complex, as we’ll see.) For the consonant perfect f ourth  – C to F, say – the pitches are in the freq uenc  y ratio 4:3 (Figure 3.5c). The freq uenc y of F is f ourthirds that of the C below it. These three simple freq uenc  y ratios  –  2:1, 3:2 and 4:3  –  give us three notes related to the original one: an octave, a perfect fifth and a f ourth a bove, or 1’, 5 and 4. In the key of  C, these are C’, G and F.  And so we have the beginnings of a scale, a set of notes that seem to f it together harmoniously and which we can arrange into music. One

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 Figure 3.8 Getting from C to D in steps of fifths and octaves. The resulting  freq uenc y ratio is 9/8.

might then explore the notes that f ollow from other simple ratios, such as 5:4 and 6:5. We’ll come to that shortly. But it isn’t how the Greeks proceeded. They recognized that just these three intervals alone can provide a basis f or generating other scale notes, because one can apply the same mathematical transf ormations on the ‘new’ notes 5 and 4. For clarity, let’s stay with the specific versions of these notes in C – that is, G and F. We can raise G b y a perfect f ifth b y increasing  its freq uenc y in the ratio 3:2 (multiplying  b y 3/2). Relative to the orig inal C, this new note has a freq uenc y greater b y a factor 3/2 × 3/2, or 9/4, and it corresponds to the note D’. Now if we f old this new note back into the octave span C©C’ b y dropping it an octave (halving  its freq uenc y), we find that we have a note 9/8 times the freq uenc y of the tonic C, corresponding to the D a bove (Figure 3.8). We can get to this D another way from just steps of f ourths and fifths:  b  y stepping up a perfect fifth to G, and then down a perfect f ourth. I won’t g o through the maths, but that too brings us to a note with a freq uenc y 9/8 that of the tonic. Consistenc y! So we have a scale C, D, F, G, C’. But there are  big gaps  between D and F, and  between G and C’. We can fill them b y taking step sizes eq ual to that  between C and D, or  between F and G, which are  both freq uenc y increments of 9/8. Applying this to D gives us an E with a freq uenc y ratio 81/64 that of  C, and applying it to G gives us an A at 27/16 the freq uenc y of  C. A further such step up from A gives B, with a ratio of 243/128. An eq uivalent way of getting these extra notes is simply to raise the tonic progressively in steps of a fifth – from C to G, G to D’, D’ to A’, A’ to E” and E” to B” (Figure 3.9) – and then to f old these notes back into the original octave span.   And there is our major scale. Closer inspection reveals that it has a curious, uneven pattern of pitch steps. The first two degrees, 1©2 and 2©3 are as wide as the steps 4©5 and 5©6, and all are eq ual to freq uenc y increments of 9/8. But the steps 3©4 and 7©1’ (E to F and B to C’, sa y)