Music and the Cognitive Sciences 1990 (Contemporary Music Review (M.E. Sharpe))

CONTEMPORARY MUSIC REVIEW Editor in chief Nigal Osborne Music and the Cognitive Sciences 1990 Issue Editors Ian Cross ...

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CONTEMPORARY MUSIC REVIEW Editor in chief Nigal Osborne Music and the Cognitive Sciences 1990

Issue Editors Ian Cross and Irène Deliège Volume 9 Proceedings of Cambridge Conference on Music and the Cognitive Sciences, 1990

harwood academic publishers Published in Switzerland

CONTEMPORARY MUSIC REVIEW Editor in Chief Nigel Osborne (UK) Regional Editors Peter Nelson (UK) Stephen McAdams (France) Fred Lerdahl (USA) Jō Kondō (Japan) Tōru Takemitsu Editorial Boards UK: Paul Driver Alexander Goehr Oliver Knussen Bayan Northcott Anthony Payne USA: John Adams Jacob Druckman John Harbison Tod Machover JAPAN: Joaquim M Benitez, S.J. Shōno Susumu Tokumaru Yoshihiko USSR: Edward Artemyev Edison Denisov Yury Kholopov Alfred Schnittke Vsevolod Zaderatsky

This edition published in the Taylor & Francis e-Library, 2005. To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to http://www.ebookstore.tandf.co.uk/. Aims and Scope: Contemporary Music Review is a contemporary musicians’ journal. It provides a forum where new tendencies in composition can be discussed in both breadth and depth. Each issue will focus on a specific topic. The main concern of the journal will be composition today in all its aspects—its techniques, aesthetics and technology and its relationship with other disciplines and currents of thought. The publication may also serve as a vehicle to communicate actual musical materials. Notes for contributors can be found at the back of the journal. © 1993 Harwood Academic Publishers GmbH. All rights reserved. No part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system, without permission in writing from the Publisher. Ordering Information Each volume is comprised of an irregular number of parts depending upon size. Issues are available individually as well as by subscription. 1993 Volume: 7–8 Orders may be placed with your usual supplier or directly with Harwood Academic Publishers GmbH care of the addresses shown on the inside back cover. Journal subscriptions are sold on a per volume basis only. Claims for nonreceipt of issues will be honored free of charge if made within three months of publication of the issue. Subscriptions are available for microform editions; details will be furnished upon request. All issues are dispatched by airmail throughout the world. Subscription Rates Base list subscription price per volume: ECU 58.00 (US $69.00).* This price is available only to individuals whose library subscribes to the journal OR who warrant that the journal is for their own use and provide a home address for mailing. Orders must be sent directly to the Publisher and payment must be made by personal check or credit card. Separate rates apply to academic and corporate institutions. These rates may also include photocopy license and postage and handling charges. Special discounts are available to continuing subscribers through our Subscriber Incentive Plan (SIP). *ECU (European Currency Unit) is the worldwide base list currency rate; payment can be made by draft drawn on ECU currency in the amount shown or in local currency at the current conversion rate. The US Dollar rate is based on the ECU rate and applies to North American subscribers only. Subscribers from other territories should contact their agents or one of the offices listed on the inside back cover. To order direct and for enquiries, contact: Europe Y-Parc, Chemin de la Sallaz 1400 Yverdon, Switzerland Telephone: (024) 239–670 Fax: (024) 239–671

Far East (excluding Japan) Kent Ridge, PO Box 1180 Singapore 9111 Telephone: 741–6933 Fax: 741–6922 USA PO Box 786, Cooper Station New York, N.Y. 10276 Telephone: (212) 206–8900 Fax: (212) 645–2459 Japan Yohan Western Publications Distribution Agency 3–14–9, Okubo, Shinjuku-ku, Tokyo 169, Japan Telephone: (03) 3208–0181 Fax: (03) 3209–0288 License to Photocopy This publication and each of the articles contained herein are protected by copyright. The subscription rate for academic and corporate subscribers includes the Publisher’s licensing fee which allows the subscriber photocopy privileges beyond the “fair use” provision of most copyright laws. Please note, however, that the license does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotion purposes, for creating new collective works, for resale, or as agent, either express or implied, of another individual or company. A subscriber may apply to the Publisher for a waiver of the license fee. For licensing information, please write to Harwood Academic Publishers GmbH, Y-Parc, Chemin de la Sallaz, 1400 Yverdon, Switzerland. Reprints of Individual Articles Copies of individual articles may be obtained from the Publisher’s own document delivery service at the appropriate fees. Write to: SCAN, PO Box 786, Cooper Station, New York, NY 10276, USA or Y-Parc, Chemin de la Sallaz, 1400 Yverdon, Switzerland. Special Fax Service—USA: (212) 645– 2459 or Switzerland: (024) 239–671. Permission to reproduce and/or translate material contained in this journal must be obtained in writing from the Publisher. Please contact Rights and Permissions Officer, Harwood Academic Publishers GmbH, Y-Parc, Chemin de la Sallaz, 1400 Yverdon, Switzerland. Distributed by STBS—Publishers Distributor SEPTEMBER 1993 ISBN 0-203-39328-7 Master e-book ISBN

ISBN 0-203-39705-3 (OEB Format) ISBN 3-7186-54202 (Print Edition)

Contents Introduction: Cognitive science and music—an overview Ian CROSS and Irène DELIÈGE

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Music in Culture An interactive experimental method for the determination of musical scales in oral cultures: Application to the vocal music of the Aka Pygmies of Central Africa Simha AROM and Susanne FÜRNISS An interactive experimental method for the determination of musical scales in oral cultures: xylophone music of Central Africa Vincent DEHOUX and Frédéric VOISIN The influence of the tambura drone on the perception of proximity among scale types in North Indian classical music Kathryn VAUGHN

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Constraints on Music Cognition—Psychoacoustical Pitch properties of chords of octave-spaced tones Richard PARNCUTT

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Identification and blend of timbres as a basis for orchestration Roger A.KENDALL and Edward C.CARTERETTE

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What is the octave of a harmonically rich note? Roy D.PATTERSON, Robert MILROY and Michael ALLERHAND

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Brightness and octave position: are changes in spectral envelope and in tone height perceptually equivalent? Ken ROBINSON

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Constraints on Music Cognition—Neural A cognitive neuropsychological analysis of melody recall David W.PERRY Split-brain studies of music perception and cognition Mark Jude TRAMO

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Musical Structure in Cognition The influence of implicit harmony, rhythm and musical training on the abstraction of “tension-relaxation schemas” in tonal musical phrases 132 Emmanuel BIGAND Is the perception of melody governed by motivic arguments or by generative rules or by both? 150 Archie LEVEY Transformation, migration and restoration: shades of illusion in the perception of music Zofia KAMINSKA and Peter MAYER

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Associationism and musical soundtrack phenomena Annabel J.COHEN

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Rhythm perception: interactions between time and intensity Claire GERARD, Carolyn DRAKE and Marie-Claire BOTTE Mechanisms of cue extraction in memory for musical time Irène DELIEGE Generativity, mimesis and the human body in music performance Eric F.CLARKE

192 204

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Representations of Musical Structure Issues on the representation of time and structure in music Henkjan HONING

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A connectionist and a traditional AI quantizer, symbolic versus sub-symbolic models of rhythm perception Peter DESAIN

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Computer perception of phrase structure Robert ERASER

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Critical study of Sundberg’s rules for expression in the performance of melodies Peter van OOSTEN

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Contribution to the design of an expert system for the generation of tonal multiple counterpoint Agostino di SCIPIO

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Computer-aided comparison of syntax systems in three piano pieces by Debussy David MEREDITH

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Psychological analysis of musical composition: composition as design Ron ROOZENDAAL

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How do we perceive atonal music? Suggestions for a theoretical approach Michel IMBERTY

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Index

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Introduction: Cognitive science and music

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Introduction: Cognitive science and music—an overview Ian Cross and Irène Deliège Contemporary Music Review, 1993, Vol. 9, Parts 1 & 2, pp. 1–6 Photocopying permitted by license only

© 1993 Harwood Academic Publishers GmbH Printed in Malaysia

Over the last decade, cognitive science has increasingly come to be seen as offering an appropriate framework within which to explore and to explain issues in musical listening, performance, composition, development and analysis. There are a number of reasons for this. As cognitive science develops, it provides progressively more and more sophisticated and plausible accounts of the phenomena of mental life. Moreover, cognitive science appears to offer frameworks of understanding (or at least modes of enquiry) which appear largely “culturally-neutral”. This is of profound importance given the culturally-diffuse nature of music as it exists now in the West and the fact that most musicological frameworks of understanding can be thought of as highly ethnocentric and culturally-specific. In addition, a number of different dynamics are impelling what might be called the “computerisation” of music, or the embodiment of aspects of music in computer software and in hardware. This drive towards representing elements of music in computational terms is motivated by powerful aesthetic, educational and commercial imperatives. On the whole, the application of cognitive science to music can be thought of as being intended to bridge the gap between what music feels like—its experiential texture—and the language that is used to describe it and to teach it. To be more specific, the development of a cognitive science of music can help to span the disjunction that exists between the ways that music is experienced by listeners and by practising musicians and the rational frameworks of discourse that conventionally constitute music theory, i.e. that are used to describe and to define music. This development proceeds by seeking to provide accounts of music that are consonant with the concepts of computability and with empirically-derived evidence about musical perception, performance and creation. To approach music by means of cognitive science involves the scientific study of all aspects of the musical mind and of musical behaviour at all possible levels of explanation—be it neurophysiological, psychoacoustical or cognitive-psychological—by theoretical or empirical inquiry, and by means of computer modelling or by practical experiment. The objects of study—musical behaviour and the musical mind—can be conceived of as comprising the capacity to experience—and to learn to experience— patterns of events in time as music, and in the faculty of conceiving or producing, and of learning to conceive or produce, particular sequences of events as music.

Contemporary music review

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The idea of musical behaviour as an object of study is not unique to cognitive science. In fact, the cognitive science of music shares with ethnomusicology a concern with accounting for musical behaviours; however, while ethnomusicology tends to do so on the basis of the cultural and social function or utility of such behaviours, the cognitive sciences of music do so in terms of the inferred mental processes underlying such behaviours. Given this aim, it is not surprising that it is only in the last thirty years that music has become a focus of study for cognitive scientists, whether psychologists, computer scientists, philosophers or musicologists. After all, behaviour—particularly musical behaviour—is intrinsically evanescent. It is only in this century that have we have come to possess methods whereby we can reliably assess the representativeness of particular observed behaviours in respect of broader theoretical classes of behaviour, only in the last thirty years have we had appropriate metaphors in terms of which to express the mental processes that can be inferred as underlying the observed musical behaviours and only perhaps in the last twenty years have we had the technology to record and to examine musical behaviours economically and accurately. Despite these advances in the means of enquiry, until recently it might have been suggested (and sometimes was) that attempts to understand music in cognitive terms were inadequate. Studies were condemned as being over-reductionist (e.g., attempting to account for the cognition of melody in terms of the perception of single notes presented in isolation) or at being musically or psychologically simplistic. This can be traced to a lack of communication which existed between musicians and researchers in the cognitive sciences; the comments and critiques encountered by researchers were all too often directed as narrow issues of theory and method, whilst musicians were simply unaware of—or unable to comprehend the issues, methods and findings of cognitive studies. However, these circumstances have changed. As John Sloboda (1985) puts it “the psychology of music has come of age”. This “coming of age” he equates this with the appearance of Lerdahl and Jackendoff’s seminal Generative Theory of Tonal Music (1983), a text which constitutes a highly sophisticated attempt to provide a theory of tonal music consonant with the findings of cognitive psychology. Over the last decade research into music cognition has increasingly aspired—and frequently risen—to this level of sophistication, seeking to reflect an awareness of and a responsiveness to historical, analytical, practical and pedagogical perspectives on music. The constant need to stress the requirements to avoid over-reductionism and to strive for a high degree of “ecological validity” in studying music perception and production has diminished as psychologists, computer scientists and musicians have come together in communication and collaboration. The papers collected in this volume clearly reveal the range, diversity and sophistication of current cognitive-scientific accounts of music. These papers also attest to the growing realisation that one of the most significant contributions that cognitive science can make to the elucidation of music is in the exploration of music in its cultural context. In this volume it will be seen that the “culturally-neutral” character of cognitive-scientific explanation in combination with the close analysis that exemplifies ethnomusicological method can yield insights about music unattainable by other means. Bruner (1990) suggests that: “It is culture…that shapes human life and the human mind, that gives meaning to action by situating its underlying intentional states in an


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interpretive system. It does this by imposing the patterns inherent in the culture’s symbolic systems—its language and discourse modes, the forms of logical and narrative explication, and patterns of mutually dependent communal life.” The dynamics of the “forms of logical and narrative explication” that shape the mind within a given culture are rarely amenable to conscious introspection; they are usually not consciously-knowable by members of that culture. They can only be unravelled by means that are often oblique, but which are centred on cognitive-scientific method that is sensitively and imaginatively applied. A further powerful current in recent developments in the application of cognitive science to music that is evident in these papers is the drive towards the “computerisation” of music. Indeed, this can appear to be the governing force in these developments. This is unsurprising, given the confluence of intellectual, aesthetic, education and commercial imperatives that become manifest when one considers the interaction of music and cognitive science. Since its inception, one of the main engines of cognitive science has been the concept of computability, the idea that computational logic should constitute the principal criterion whereby to judge the efficacy or adequacy of theories of mind. This idea can exist in “harder” versions, wherein computational theory is taken to represent the fundamental substrate of mind (e.g., Churchland, 1986) or “softer” versions, in which computational logic serves as a functional metaphor in the description of mental processes (e.g. Bruner, 1990). This permeation of cognitive science by the concept of computability has increasingly determined the tools, methods and output of cognitive science. At the same time, the practical application of computers in music has recently sustained exponential growth. As technology has developed and advanced, computers have pervaded music at all levels, from the school to the studio, from the concert-hall to the field-trip. While the genesis of the use of computers in music lies in post-war musical aesthetics their current ubiquity arises from commercial interests responding to, and leading, consumer demand for accessible and populist musical tools. The broader utility of these tools in composition, performance and in music education is by-and-large a fortunate and highly-productive spin-off. There is obvious scope for exciting and innovative practical development in the coming-together of music and cognitive science. A cognitive-scientific understanding of the nature of perception and performance can help to shape new tools for composers and performers, providing new means of control over complex musical systems and structures. It can enhance and vastly expand the ways in which human and computer “performers” may interact. It might even help to mitigate the baleful influence on the development of computer-based learning systems that is exerted by those political ideologies for which cost-effectiveness is more important than any enrichment of the human experience that might arise from the process of learning. Overall, then, cognitive science has much to contribute to our understanding of music. It may even play some role in determining what we come to accept as music. However, even if we reject the proposition that cognitive science should be prescriptive in the domain of music, there is still space for it to make a major contribution to the frameworks


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of discourse in terms of which we describe and conceive of music. Music itself has value as a subject for the cognitive sciences; the understanding of a non-verbal auditory domain, rich in associative power, multifarious in form and culturally-emblematic surely has much to offer to the quest for a better understanding of the human mind. The papers in this volume demonstrate the breadth and complexity of some of what has already been achieved, and point towards some likely future developments.

Volume structure and contents This volume arises out of the 2nd International Conference on Music and the Cognitive Sciences, which was held in Cambridge in 1990. Its contents are laid out across six sections: Music in Culture, Psychoacoustical Constraints on Music Cognition, Neural Constraints on Music Cognition, Musical Structure in Cognition, Representations of Musical Structure and General Issues in Cognitive Musicology. These divisions arose from the ways in which papers submitted for the Cambridge Conference fitted into the four thematic areas proposed for that Conference—Music in Culture, Music in Action, Representing Musical Structure and Cognitive Musicology. In the first instance, these four themes chosen for the Conference were intended to embrace aspects of cognitive science which would be differentiable largely by the methods that they employed. Thus, it was felt, papers within the theme Music in Culture would be likely to reflect ethnomusicological practices (reliance on informants, immersion of researcher(s) in specific cultures via field-work, etc.): papers in Music in Action should reflect experimental work employing conventional psychological empirical methods: those in Representing Musical Structure would focus on issues in, and applications of, modelling music cognition via computer: and those in Cognitive Musicology should reflect the ways in which aspects of cognitive-scientific studies had fed back into the general theory and practice of music. However, the papers submitted for the Conference provided a different picture from that which had been anticipated. Most papers fell within the theme Music in Action, with those falling into Representing Musical Structure being the next most numerous. Those which dealt with issues of Music in Culture did so in fascinating and unexpected ways, while few papers actually demonstrated the applications of cognitive science to musicological concerns and thus fell under the heading of Cognitive Musicology. From the wealth of papers considered for this volume, it appeared most sensible to retain slightly altered versions of the four original themes but to split Music in Action into three categories: Psychoacoustical Constraints on Music Cognition, Neural Constraints on Music Cognition and Musical Structure and Cognition. This division acknowledges the differences in methodology which exist within the experimental tradition, and pointsup the ways in which psychoacoustical and neuropsychological studies sketch the boundaries of enquiry for cognitive science as a whole. The first section, Music in Culture, contains three papers. Two of these are by members of a group of French researchers, directed by Simha Arom, who have developed and applied new research methods to issues in African music that would appear otherwise intractable. The third paper, by Kathryn Vaughn, explores aspects of the perception and


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cognitive representation of North Indian music, using sophisticated experimental psychological techniques. The second section, Psychoacoustical Constraints on Music Cognition, contains papers which examine, respectively, the degree to which psychoacoustical considerations can be said to underlie our perceptions of harmonic structure (Parncutt), about timbral quality (Kendall and Carterette), and the interaction—or, perhaps, the ways in which we respond to real instrumental sonorities in making judgments relative inseparability-of pitch and timbre when considered from psychoacoustical perspectives (papers by Patterson, Milroy and Allerhand, and by Robinson). The next section, Neural Constraints on Music Cognition, contains papers by Perry and by Tramo, addressing aspects of our musical-perceptual and memory abilities via neurological data. The fourth section, Musical Structure in Cognition, starts with a paper by Bigand that explores the issue of how, in listening, we abstract those elements of musical structure that may well determine our emotional responses to music. A paper by Levey then studies our sensitivity to different types of music-theoretic relationships between melodies. The next paper, by Meyer and Kaminska, outlines a number of different experimental approaches to determining the similarities between musical and verbal processing. Cohen’s paper presents a rare study of ways in which musical sound contributes to our overall perception by examining the interaction of sound and vision via film. A paper by Gérard, Botte, and Drake then investigates the factors that play a role in our perception of rhythm. Following this, a paper by Deliège presents the results of a study of the ongoing perceptions that arise in the course of listening to a piece of music. The section ends with a paper by Clarke, in which an exploration of real and “artificial” (i.e. computer-generated) rubato provides clues as to the relation between musical structure and expression. The first two papers in the following section Representations of Musical Structure, by Honing and by Desain, present theoretical considerations of many of the issues addressed experimentally by Clarke within the framework of their functional connectionist model of rhythmic quantization processes. In contrast, Eraser’s subsequent paper adopts an explicitly grammatical approach to questions of how the cognitive representation of musical phrase structure might be modelled on computer. The paper by van Oosten returns to the connectionist framework to provide a critique of Sundberg’s model of musical performance. The section concludes with two papers examining, respectively, constraints on the computational representation of contrapuntal composition (di Scipio) and the formal representation of harmonic structure in music analysis (Meredith). The concluding section, General Issues in Cognitive Musicology, is comprised of three papers. The first, by Meeùs, explores issues in the development of a non-linguistically based semiotics of music. The second, by Roozendaal, reports an attempt to delineate the cognitive processes involved in the act of musical composition. Fittingly, the final paper of the volume is by Michel Imberty. At the Cambridge Conference, a meeting convened by Stephen McAdams led to the formation of the European Society for the Cognitive Sciences of Music (ESCOM). This body held its first formal colloquium and assembly in 1991, at which Professeur Imberty was elected to be its president. It is only fitting, then, that his paper on the perception of atonal music should round off the present volume. The editors would like to thank all of those who contributed to the organisation of the Cambridge Conference and the subsequent production of this volume. Thanks should go


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to all members of the Organising Committee, to all of those who chaired the sessions of the Conference and, in particular, to Marie-Isabelle Collart, Diana Stammers and Jane Woods for all of their administrative and practical assistance. The editors would also like to express their gratitude to the British Council and to the British Academy, without whose generosity the Conference could not have taken place.

References Bruner, J. (1990) Acts of Meaning. London: Harvard University Press. Churchland, P.S. (1986) Neurophilosophy. Cambridge, Mass.: M.I.T. Press. Lerdahl, F. and Jackendoff, R.A. (1983) A Generative Theory of Tonal Music. M.I.T. Press. Cambridge, Mass.: Sloboda, J. (1985) The Musical Mind. Oxford: Oxford University Press.

An interactive experimental method for the determination of musical scales

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Music in Culture An interactive experimental method for the determination of musical scales in oral cultures Application to the vocal music of the Aka Pygmies of Central Africa Simha Arom and Susanne Fürniss Lacito, CNRS, Paris Contemporary Music Review, 1993, Vol. 9, Parts 1 & 2, pp. 7–12 Photocopying permitted by license only


The contrapuntal vocal polyphony of the Aka Pygmies is based on a pentatonic scale but the nature of this scale is difficult to determine by ear. To overcome this problem and to circumvent difficulties of articulating such abstract concepts as musical scales which, for the Aka, are not subject to verbalisation, a method based on the use of a synthesiser was conceived and applied in a series of experiments among the Pygmies. In these experiments, polyphonic music of their own culture was simulated with different underlying scale models and submitted to their cultural judgment. This method was shown not only to cope with the initial problem but also to provoke a series of non-verbal interactions that open new dimensions for the study of cognitive aspects of musical systems in oral traditions. KEY WORDS: Ethnomusicology, methodology, modelling, scales, experimental research.

Aka Pygmy music is essentially vocal. It is characterized by a contrapuntal polyphony based on four constituent parts. Each of these four parts has a name in Aka language: mò tàngòlè, ngúé wà lémbò, ò sêsê and di yèí. Moreover, each of them can be distinguished


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from the others by several distinct traits: the presence or absence of words, its position in the sound space or the vocal technique with which it is executed. The mò tángòlè1 is the principal voice which begins the song and pronounces the incipit, the essential words of the song.2 This part is generally sung by a man. Ngúé wà lémbò which means literally “the mother of the song”, is (as the name indicates) the support of the song. This part has longer values than the other ones and, according to Aka theory, is a men’s part as well. The ò sêsê3 is a female middle voice characterized by a contrary movement to the mò tángòlè’s, with generally a descending melodic line. These three parts are sung with the chest voice. The fourth part, dì yèí, which means literally “yodelling”, is a yodelled part which is sung above all the other parts by the women. Aka music is an isoperiodic music, being embedded in invariant periodic cycles. These temporal matrices consist of regular and always even numbers of beats. The rigourousness of the periodic framework is attested by the recurrence of similar musical material in identical positions of each cycle. Each of the four parts has its own melodic scheme for every single song. This scheme serves as a referent for the several variations in terms of which it is realised. It consists of a minimal and non-varied version of the part, that is, a real pattern, determined by the presence of certain notes systematically located in certain positions within the cycle. With one exception, the contrapuntal repertoire of the Pygmies is based on poly rhythmic “blocks”, performed by several percussion instruments of which the pitches are not relevant (Arom 1985:408). This means that their singing has no reference whatever to any predetermined pitch. Seen from the perspective of its scale structure, this music can be considered as being sung a cappella. When listening to a polyphonic pygmy song there can be no doubt that it is based on a pentatonic system. Nevertheless, one can observe non-systematic phenomena in the realisation of the scale-degrees, the exact position of which are problematic. For example, although a semitone is never sung as a successive interval, it does appear in certain musical contexts. On the one hand, certain contiguous intervals are modified according to whether they are part of a rising or descending passage; on the other hand, the performance of part of a rising or descending passage; on the other hand, the performance of disjunct, yodelled intervals can give way to what appears now as a major sixth, now a minor seventh. The songs we analysed in this study 4, have been recorded by means of a re-recording technique5; the different constituent parts are not recorded simultaneously but successively, each of the singers hearing in his headphones the part or parts of the previous singer(s). By this means, each part of the polyphony can be isolated on a separate track of a tape (Arom 1976). When examining the relationship between the different—separately recorded—parts of a song, a divergence emerged between horizontal and vertical listening, which led to different conclusions. Thus, two scale-degrees which appeared an octave apart vertically were revealed to be forming an interval of a major seventh on the separate audition of the two parts which contained them. This means that a physically identical phenomenon with stable elements—as nothing physical varies on the tape—is being perceived in different ways. This last interval, a major seventh, creates a problem, since it is excluded from the anhemitonic pentatonic system.


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In order to interpret these kinds of phenomena, and to determine whether they were casual or structural, some acoustical analyses were carried out, starting with measurements of fundamental frequencies and the resulting intervals.6 However, this procedure did not uncover any systematic explanation of the observed phenomena; if in one case the seconds and sevenths were quite close to the Pythagorean system, in other cases they were closer to equipentatonic intervals. The possibility was also explored that the alternation of different vocal timbres associated with the use of specific vowels in the yodelled production of disjunct scale-degrees might account for the variations of pitch observed. However, an analysis based on this hypothesis provided no basis for an explanation of the observed interval usage. It was felt that a survey of scalar theories in the history of music since antiquity might suggest some scale models based on different orderings of scale-degrees within an octave, at least one of which might correspond to the musical scale of the Aka. A scale obtained by superimposition of fifths (c-g-d-a-e, Pythagorean system), a scale made of disjunct tetrachords (c-f/g-c) each divided into two equal intervals, together with some other scales, each corresponding to a different sectional sequence from the harmonic series, were considered. Here again, it was impossible to give preference to one of these models by the mere acoustical or musical analysis. Accordingly, it was thought that it might perhaps be better to try a method of analysis-by-synthesis. This would allow us to submit particular different scale models to the Pygmies’ own judgement. In order to communicate with the Aka on such an abstract level of musical theory, we had to take several steps towards them for to approach their own understanding as closely as possible. Only by the application of the Aka’s musical concepts—as known from earlier studies7—could we hope to find a point of intersection common to both sides. This was regarded as the basic step or origin of the methodology that will now be discussed. It was evident that a requirement existed for a purpose-designed toolkit with which interactive experiments in field conditions with the Aka themselves could be conducted. Any experiment should be based on contrapuntal pieces of their own culture, in which the different scale-models would be embodied. This latter aspect is of great importance; in cultures with implicit musical theory and without institutionalized musical apprenticeship, investigation of scale-structure has to be carried out in a concrete musical context, coming as close as possible to a traditional performance. The method used should ideally circumvent difficulties of articulating such abstract concepts as musical scales which, for the Aka, are not subject to verbalisation. It should further allow a nondirective investigation but at the same time elicit an answer to questions which, in certain respects, had not previously been posed. It was intended to discover which of the proposed scale models would be considered as adequate and which not. As we had many difficulties in synthesizing an acceptable vocal timbre8, we discarded the idea of imitating the human voice and contented ourselves with instrumental timbres developed from the pre-programmed timbres of a Yamaha DX7 IIFD synthesizer9. The latter enables the use of an integrated micro-tuning programme—fundamental for the application of our method—permitting extremely fine adjustments of pitch at 1/85th of a semitone (that is 1.17 cents). With this micro-tuning programme we were able to program the scale models which seemed to be the closest to those of Pygmy music and which we wanted to submit to the Aka’s judgement.


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Who were the judges? In an Aka community, musical practice is shared by all of its members. Each member of an encampment knows the totality of the repertoire. In this respect, everybody is equally performer, listener and judge. The encampment of Mbonzo, where we worked, consists of about 25 people and the majority of its members, i.e. about 15 persons, participated in our experiments. Not until we had reached Africa did Frédéric Voisin discover the sequencer which is integrated within the synthesizer and thanks to which we could transform it to a real “mediator” between Aka music and our hypotheses about it. Using tapes and transcriptions already to hand, it would become possible to simulate several versions of the same polyphonic song. However, before being able to undertake the experiments, properly speaking, it was necessary to get the Pygmies not to reject the very sound of the synthesizer from the outset. To do this, we had the idea of letting them hear some utterly different music which would share with theirs some common features. This was intended to avoid confusion between the following parameters: structural periodicity, vocal parts and timbre. The music chosen for this preliminary phase of the experiment was the opening of the Andante of the first movement of the Partita in C minor by J.S.Bach. It was performed by one of us on the synthesizer. In order to reproduce the principle of periodicity, the piece was put into a loop with a cycle of eight beats, at the end of which the same segment reappeared. We told our Pygmy participants, “You are going to hear a piece of our own music, but which works like your own songs. There are not four parts in this music as there are in yours, there are only two, which correspond to your mò tángòlè and ngúé wà lémbò. You will be able to follow them by listening, and it will help you to look at our musician’s hands.” Following this, we would need to get the Pygmies to recognise their own vocal music reconstituted via the synthesizer in a timbre noticeably different from that of the human voice. To try to help them to overcome this difficulty, we took the opening of the Andante and let them hear it at first with a very different timbre, like the sound of a bell. We repeated this piece several times with different timbres, until we converged on the timbre of one of their own instruments, a little wooden flute. At this stage, some Aka melodies being simulated by the synthesizer with this timbre were identified almost immediately. The Aka not only got used very quickly to the sound of the synthesizer and the reproduction of their vocal songs on an instrument, but also themselves spontaneously tried to play on the synthesizer. All experimental sessions were filmed in their entirety with a video camera. The scale experiment, properly speaking, consisted of letting the Aka listen to each of the simulated versions several times, each version having been programmed with one of the different scale models; they were asked, after each of these versions, to accept or to reject it. For this type of experiment, we chose two polyphonic songs, each of them having been programmed in two versions: one in a schematic form, that is, the mere polyphonic four-part pattern without any variation, and the other coming close to a conventional performance, with variations in every constituent part. Both versions were put into a loop in order to restore the periodic character of the music. The variations effected were


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chosen arbitrarily from the paradigms of every part’s proper variations, as the Aka usually do when singing in a real performance. In order to be sure that they concentrated their listening on the melodic structure of each part and on the vertical resultant of their superimposition, we asked each of them to follow his individual part while listening and to tell us if it was correct or not and if they agreed with its relation to the other parts. Apart from some remarks about rhythmic inaccuracies and the particular sound of the “voice of the machine”, there was no rejection either on the melodic axis nor on that of simultaneity. Several times and after having repeated very different versions from the point of view of the scale structure, the Aka said to us: “What the machine does and what we sing is the same thing”. The result of this series of experiments was completely unexpected: the Aka accepted every one—the totality—of the versions we had submitted to their judgement. In other words, they considered the ten different scale models as all being equivalent. Some of the Pygmies expressed the desire to try to play more on the synthesizer. This is why, on one occasion, we left them the instrument for three hours while we were absent from the camp. In the meantime, a fixed video camera filmed their exploration of the keyboard and their attempts to reproduce especially those melodies we had worked on that morning. Following this familiarisation with the synthesizer, we could integrate in our experiments the performance on the synthesizer by the Aka themselves, but always in presence of the other members of the encampment. To our great astonishment, this revealed that the vocal parts can start from any degree of the same pentatonic scale. Such liberties modify considerably each interval’s width with respect to the contour of each melody. Additionally, watching later the video of the Aka’s own experiments on the synthesizer while we were absent, we found the same phenomenon: one and the same melody was performed several times, starting each time from a different degree, but without changing the pentatonic system (see Figure 1).

Figure 1 “Mutations” of a melody, performed by the Aka when playing on the synthesizer.


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The Aka themselves performed melodies with several “transpositions”, or rather, “mutations” (involving the modification of some interval’s width within the same melody). This led us to the following hypotheses: if the key to the melodic structure of Aka Pygmy song is not to be found in the scales used, it can only be found in the progressive unfolding of the parts. The order of succession of the degrees in a pentatonic scale seems to prevail over the width of the intervals between them, subject to the condition that the melodic contour—which is characteristic for each and every song—be respected. A last experiment, which dealt specially with the recognition of melodic contours of each of the constituent parts, confirmed this hypothesis. Generally admitted theories about interval systems are based on the idea that a scale system—apart from the more-or-less large margins of tolerance it allows—consists of a mental template, a kind of mental grid, in which each degree of the scale has its predetermined, more-or-less fixed, position. The results of the experiments shown here may make such an idea questionable; indeed we found that Aka Pygmy music admits ten different scale models. The role of the synthesizer in the heuristics of this result is pre-eminent. It did not only permit us to investigate the issues that we had intended when preparing the field work. On the contrary, by allowing the Pygmies to participate as much as possible, the synthesizer provoked a series of interactions which reorientated and adjusted our research in other directions that we had not imagined before, such as the idea of investigating melodic contours. Thus, it appears that the application of a method of investigation to the study of scale systems which associates high technology with field work opens new dimensions for the study of cognitive aspects of musical systems in oral traditions.

Notes 1. literally “the one who counts”. 2. All the other parts are mostly sung with non-significant syllables. 3. literally “underneath”, which means inferior in hierarchy to the mò tángòlè. 4. Our corpus consisted of 8 polyphonic contrapuntal songs of 4 parts and 8 tale-songs, each of them recorded with different versions, the sum of which is 158 isolated parts. 5. They were collected during several field trips between 1974 and 1983 by the first author. 6. This was done by the second author at Hamburg’s Tonstudio of the Staatliche Hochschule für Musik und darstellende Kunst in 1987 with a sampler CASIO FZ-1, a synthesizer SYNTHI 100 (Electronic Music Studios London Ltd.) and a frequency-meter CA 51 N (Schurig). Other measurements were made at the Department of Music of the Hebrew University of Jerusalem on the Cohen-Katz-Melograph, and others again with the programme FØana2 of the workstation S_TOOLS at the Kommission für Schallforschung, Austrian Academy of Sciences. 7. The first author has worked on Pygmy music since 1971. 8. Knowing that the timbre of synthesized sounds could be problematic for the acceptability of the experiments, the second author first tried to sample Pygmy songs on a PDP 11.04 computer. By this means, the variation of scale-degrees would not have modified the characteristics of the voice timbre proper to the Pygmies. But the synthesis programmes at hand, based on the treatment of speech, were not accurate enough to be used for the simulation of singing; even the simple reproduction of the sampled melody was completely unsatisfying. 9. This was done by Frédéric Voisin.


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References Arom, S. (1976) The use of play-back techniques in the study of Oral polyphonies. Ethnomusicology, 20(3), 483–519. Arom, S. (1985) Polyphonies et polyrythmies instrumentales d’Afrique Centrale. Paris: SELAF. Arom, S. (1987) La musique des Pygmées. Le Courrier du CNRS, 69–70, 60. Arom, S. (1991) A synthesizer in the Central African bush: a method of interactive exploration of musical scales. In Für Ligeti. Die Referate des Ligeti-Kongresses Hamburg 1988. LaaberVerlag, pp. 163–178. Arom, S. & V.Dehoux (1978) Puisque personne ne sait à l’avance ce que tout autre que lui-même va chanter dans la seconde qui suit. Musique en jeu, 32, 67–71. Arom, S. & S.Fürniss (1991) The pentatonic system of the Aka-Pygmies of Central Africa. In Selected articles of the VIIth European Seminar on Ethnomusicology October 1990. Berlin: Intercultural Music Studies (in the press). Chailley, J. (1960) L’imbroglio des modes. Paris: A.Leduc. Chailley, J. (1964) Ethnomusicologie et harmonie classique. In Les Colloques de Wégimont IV, 1958–1960, pp. 249–269. Paris: Les Belles Lettres. Chailley, J. & J.Viret (1988) Le symbolisme de la gamme. Paris: Revue Musicale 408–409. Fürniss, S. (1991) Die Jodeltechnik der Aka-Pygmäen in Zentralafrika. Eine akustisch-phonetische Untersuchung. Berlin: Dietrich Reimer Verlag (in the press). Kubik G. (1985) African tone-systems: a reassessment. Yearbook for Traditional Music, 17, 31–63. Sallée, P. (1985) Quelques hypothèses, constatations et expériences à propos de l’échelle pentaphone de la musique des Pygmées Bibayak du Gabon. Paper presented at the European Seminar in Ethnomusicology, Belfast, March 1985.


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An interactive experimental method for the determination of musical scales in oral cultures Application to the xylophone music of Central Africa Vincent Dehoux and Frédéric Voisin Lacito-CNRS, Paris Contemporary Music Review, 1993, Vol. 9, Parts 1 & 2, pp. 13–19 Photocopying permitted by license only


When trying to determine the scalar system of the Centrafrican xylophones, one is confronted by the irrelevancy of physical measures which do not correspond to pitch as perceived, as well by the lack of verbalisation in respect of musical scales in these societies. In order to permit a field investigation into these scalar systems, we conceived an interactive experimental method founded upon the simulation of these instruments with a synthesizer. When the centrafrican musicians were playing the synthesizer like their own xylophones, we submitted to them tuning structures which also could be retuned by the musicians themselves. The analysis of the data generate a model of tuning structure which determine the interval ratios, the margin of tolerance, and the pertinent timbre structures of the xylophones. The results show various conceptions of scalar system corresponding to four centrafrican ethnic groups, specially in terms of pitch-and-timbre interaction. KEY WORDS: Centrafrican xylophones, experimentation, scalar system, pitch, timbre, synthesis, modelling.

The portable xylophone with multiple gourds resonators is in general use in Central Africa. This kind of xylophone always serves to accompany songs and is found in orchestral ensembles which include percussion instruments. While certain ethnic groups use the xylophone as the leading melodic soloist instrument, one can observe in other groups orchestral ensembles with two, three or four xylophones. The corpus collected since 1983 covers all types of possible formations, which are:


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ethnic groups using one xylophone: – the Manza who use one xylophone of five bars; – the Gbaya who use one xylophone of twelve bars. and ethnic groups using ensembles of several xylophones: – the Ngbaka-manza who use an ensemble of 3 xylophones (respectively, 9.7 and 4 bars); – the Banda Gbambiya who use an ensemble of 4 xylophones (respectively 8, 7, 7 and 5 bars). The xylophone musics studied use a scale close to a pentatonic anhemitonic scale. This scale is characterized by a division of the octave into five unequal intervals and above all by the lack of a semitone used as a melodic or successive interval.

The tuning of the xylophones When trying to determine the scale system used by the xylophones of Central Africa with precision, one is confronted by numerous difficulties such as, for example, the ambiguous nature of intervals. To attempt to overcome this problem, we have undertaken acoustical measurements1 from xylophone tunings recorded in the field. From the analysis of these measurements, it was not possible to establish a satisfactory and coherent interpretation. There seemed no firm grounds for any particular interpretation. The difficulties in the determination of the xylophones’ tuning appear equally due to the presence of two factors: the “roughness” of perceived pitch and the complexity of timbre. One of the intrinsic qualities of sounds produced by Central African xylophones is their roughness. In this case, the roughness can be considered as a group of “virtual” frequencies close to the fundamental frequency of each degree of the scale. It is a perceptual phenomenon due to the inharmonic structure of the spectrum, which. The complexity of timbre is tied to the specific organology of these xylophones. Each bar of the xylophones is coupled to its own resonator. On each resonator is placed a mirliton (a small buzzing membrane) of which the vibration is added to the bar’s own resonance. But if the mirliton’s forced vibration makes the perception of the pitch unambiguous, its strength is not the same in respect of the different bars of each xylophone. The perception of the intervals is consequently modified in proportion.

The scale of the vocal part Because of the difficulty of determining scale only from the tuning of the xylophones, and also because in every case the xylophones accompany sung melodies, we have approached the problem from the angle of the scales used in the vocal part. Listening to the vocal part, another phenomenon appears tied to the formal structure of the music. These songs are in a responsorial form. A fragment of the melody sung by the soloist singer is followed by a second fragment stated by a choir or by a second singer. The leader and choral vocal parts fall within, respectively, one higher and one lower register, which have some common degrees in a middle register. So, neither of the two


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protagonists cover all the range of the melody, but they divide it into two complementary registers in which the realisation of the scale-degrees is not the same form one register to the other. However, if neither the vocal nor the instrumental parts could help us in determining the scale used in the xylophone music, one might be able to assume a parallelism between the ambiguity of the tuning of the xylophone and the variable 1

Measurements made at the Musée de l’Homme in Paris, with the collaboration of Jean Schwarz, and at the IRCAM with the collaboration of Jean-Baptiste Barrière, also in Paris. 2 These last served as a reference point for out experiments.

realisation of the pitches in the vocal parts. The alternative possibilities would then be as follows: i) the scale is pentatonic with a large margin of tolerance in the realisation of the degrees ii) the scale is what we shall term a “composite scale”, in which each register has its own type of pentatonic scale linked together by common degrees; the passage from one register to the other brings a change of pentatonic mode.

An interactive simulation tool The choice between these two possibilities could only be established by a new investigation in the field, because the African musicians were the only ones who could provide evidence for or against the alternatives. For this purpose, it was necessary to establish a new field-work methodology able to address our requirements concerning scalar systems. As a result of a number of talks with specialists like John Chowning, Jean-Claude Risset and Louis Dandrel, Simha Arom had the idea of undertaking this field-work with the support of a Yamaha DX7 II synthesizer. This machine made available a combination of three facilities necessary for the research: (i) each key of the DX7 II could be “microtuned” to make all the scales needed, with a precision of ca. one cent (1/100 semitone): (ii) the successive order in which keyboard sounds were produced could be modified (an important facility as the topology of central African xylophones does not correspond to a continuous order of pitches as on, e.g. a piano keyboard): and (iii) novel timbres could be easily generated and modified (a condition indispensable in simulating the sound of each of the xylophones subjected to investigation). Moreover, all of the information concerning the results of the operations undertaken (programming and modifications) could be stored in the memory of the DX7 II. We considered following several different approaches in making use of the synthesizer in the field. The first idea was to present the synthesizer to the musicians as though it were a xylophone of a particular type, and to note the reactions of the musicians when we ourselves played examples of different scales. However, we were obliged to reject this approach because of the difficulty of entering into a discourse on abstract concepts like scale and timbre with the Central African musicians; considering the limited number of cases where the musicians have volunteered such information, our results would necessarily have to be treated with extreme caution.


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At this point, we thought to gauge the Central African musicians’ reactions not to “abstract” instrumental tunings, but to the music itself. To this end, we thought of playing a piece of music ourselves, with the help of transcriptions which the first author had made from his field recordings, and to change the scales on each playing. This approach would depend on our performing competence in a Central African repertoire; because of the strictness of the tempo and of the rhythmic articulation observed in this music, any mistake of rhythm could lead to an immediate rejection by the Central African musicians. So, our ideas on tunings and timbre might be rejected not because of the scales or sounds used, but because of the performance—if the wrong tempo or rhythmic articulation was introduced. Thus we arrived at the following conclusion: it was necessary for the musicians to play the synthesizer themselves as though it were one of their own xylophones. In order to make this possible, the keyboard of the synthesizer was transformed; its “western” configuration was made changeable according to the different typologies of Central African xylophones. Longish bars of plywood, large enough to be hit by mallets, were affixed to some of the keys of the DX7, projecting outwards from the keyboard; the keys not to be sounded were rendered mute. In this way, using Velcro to fasten the bars to the keys of the DX7, we were able to simulate at leisure as many types of xylophones on the synthesizer as necessary. Each xylophone player could thus imagine that he was in front of his own xylophone.

Experimental method The procedures used in our investigations in the field were the same for the different ethnic groups: the synthesizer was presented to a musician who was asked to play a piece of his own repertoire, and note was taken of whether or not he found acceptable the timbres and tunings that were provided. It should be stated that none of the xylophone players had any problems with the machine. During the experiments, the xylophone player was surrounded by several people, singers as well as other xylophone players. This was in order that their choice should be a reflection of a general consensus. Our approach always took the form of asking in the first place whether the musicians would accept or reject the tuning structures and timbres which had been programmed. As the sessions progressed, the musicians gave us more and more commentaries about their choices. We filmed our work in real time as the sessions took place, from the first moment that the musicians came into contact with the synthesizer until the end of the last work session. The video revealed the presentation order of the tuning structures, reactions and commentaries of the musicians and enabled us to record the different manipulations made on the synthesizer. Having determined the interactive principle of the experiments—using a genuine musical situation wherein the musicians played the DX7 as a “xylophone”—the focus can shift to the scales of xylophones. Since the problem was the same for each of the different ethnic groups, each experiment was based on the same theoretical tuning structures. These tuning structures were programmed into the DX7 before leaving for the field-work. Because of the influence of the xylophone’s timbre on its perceived pitch, we had to


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introduce into the tuning structures two other parameters: the degree of roughness and of inharmonicity of the xylophone tones. So, each theoretical tuning structure is a combination of three parameters: pitches (scalar tuning system), roughness, and inharmonicity. (i) Pitch Since our tuning structures make a distinction between pitch and roughness, we could consider pitches as fixed frequencies. These pitches correspond to different scalar systems according to our hypothesis: – five possible pentatonic anhemitonic systems – one possible pentatonic anhemitonic system incorporating a tritone (these were derived from a twelve-tone equitempered system) – one possible equipentatonic system – the original tunings of the xylophones, as determined from the acoustic measurement2 It appeared that it was necessary to develop in the field new tuning structures corresponding to the particular scale conceptions of each ethnic group, as revealed by the current experiments. Indeed the reactions of Central African musicians to the tuning structures were different from one group to the next. They concerned not only the scalar system of pitches, but also the inharmonicity of timbre. For example, the five-bar xylophone simulation of the Manza people had not less than 25 tuning structures, including several inversions and permutations of the original tuning. For the threexylophone ensemble of the Ngbaka-manza people, we programmed scales in which major sevenths or minor ninths replaced the octaves. (ii) Roughness Each scalar tuning structure could be combined with roughness, or not. The aim was to determine if roughness had an independent function in the structure of the scale itself, or if it is only due to the inharmonicity of the spectrum. In this last case, we had to concentrate on the timbre and its interaction with pitch. (iii) Inharmonicity After having synthesized on the DX7 an initial harmonic—periodic—timbre of a xylophone, we shifted step by step its harmonic components. This shifting concerned essentially the position of the second harmonic, which was progressively displaced from precise harmonicity within a range between +/−15 to 100 cents. With this operation, the timbre became more and more inharmonic. The difficulty was to maintain the impression of fusion of the timbre without any change in the other parameters except the harmonic ratios. Our collection contained twelve inharmonic degrees of the same timbre. Acoustical analyses of the spectra, of the synthesized timbres developed by ear and of the originals, gave us the opportunity of verifying the similarity of their spectral structures. Each theoretical tuning structure, as a combination of pitch, roughness and inharmonicity, was also submitted to the Central African xylophone players. Then, they could test the tuning structures by playing the xylophone simulation on the DX7, and accepting or rejecting each of these tuning structures. When musicians rejected a tuning structure, we asked them to retune the synthesizer, or to choose another timbre, or only to


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say what they considered as wrong. Sometimes, the tuning structure was so wrong that the xylophone players could not retune it, and said “everything is wrong, I can’t do anything”. Sometimes, just one bar of the tuning structure was wrong, and the musicians could retune it, lower or higher (thanks to the micro-tuning function of the DX7); also at times they expressed a wish to repair the “mirliton” on the gourd.

Results, and future perspectives The data were derived both from the synthesizer—pitch adjustments and timbre choices—and from the video—the reactions of the musicians. ‡These last served as a reference point for our experiments.

As all the experiments were filmed in real-time, the video allowed us not only to note a tuning structure as accepted or rejected, but also to determine what the musicians wanted to do. Their comments were important in order to validate models of their scale systems. As noted, we can see in an initial analysis that the conception of scale is quite different for each ethnic group. The importance given to the specific scalar systems used is greater when a single xylophone was played alone than when three or four xylophones were played as an ensemble. The distinction between harmonic and inharmonic timbres is also relevant for the Manza, Ngbaka-Manza and Gbaya populations, but not for the ensemble of four xylophones. Our current conclusion is that for the solo xylophone this harmonic/inharmonic distinction corresponds to different instrumental registers, some bars requiring a stricter harmonicity than others. For the three-xylophone ensemble, this distinction may correspond to different xylophones, a whole xylophone being less inharmonic than the others. Let us see now what kind of tuning structure model our data analysis suggests for the five bar xylophone. The rules of the scalar system are: a) the scale needs three types of intervals: – a major second (200 cents) – an equipentatonic interval (240 cents) – and a small minor third (285 cents), which can be replaced by a major second) – the margin of tolerance of these intervals is more or less 15 cents b) several combinations of these intervals are correct, while others are wrong c) the principal constraint is the pitch range across the bars: it must be between 900 cents and 940 cents, the mean adjusted pitch range being in the order of 930 cents d) the roughness is due to the inharmonicity of timbre, which must be avoided at the three highest pitches (or bars). e) the lower bars can be slightly inharmonic. We intend to verify these rules in our next field-work trip. Because the synthesizer became increasingly easy to handle for both the researchers and the African musicians, the experimental set-up is able to reveal knowledge which is not commonly verbalised in these Central African cultures. Here we provide an account


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of research which places the accent on the problems relating to musical systematics, but even so, such specific work leads quickly into a cognitive dimension. Indeed, it is important to note that the present work with the synthesizer was preceded by long familiarisation to the musics concerned. In other words, and insofar as this experimental format is characterized by processes involving much coming-and-going from one side to the other—from the researcher to the informant and back—it has become possible to imagine different protocols of investigation, reversing the conventional roles of the participants. Becoming the active protagonist in the research, the informant musician controls the flow of the processes of discovery according to his own musical behaviour. This kind of transformation of functions is one of the original aspects of this innovative experimental method in the field. The relation informant/researcher is now superseded by a new relation—informantmediator-researcher—in which, as its name indicates, the synthesizer takes charge in joining-up two behaviours which are radically different, suggesting a new kind of agreement between the participants in the research.

References Arom, S. (1985) Polyphonies et polyrythmies d’ Afrique Centrale, Paris SELAF. Arom, S. (1990) A synthesizer in the Central African Bush: a method of interactive exploration of musical scales, in für Ligeti. Die Referate des Ligeti-Kongress Hamburg 1988, Hamburger Jahrbuch für Musikwissenschaft 11 (in press). Dehoux, V. (1986) Chants à penser Gbaya (Centrafrique), Paris SELAF. Dehoux, V. & Voisin, F. (1990) Procédures d’analyse des échelles dans les musiques avec xylophones d’Afrique Centrale, in pre-publication of the VIIth European Seminar of Ethnomusicology. Berlin IICM. Jones, A.M. (1971) Africa and Indonesia, Leiden Netherland E.J.Brill. Pelletier, S. (1988) Description des échelles musicales d’ Afrique Centrale: problématique, hypothèses, heuristique, Mémoire de DEA.

Discography Arom, S.: Central African Republic, UNESCO “Atlas Musical” EMI 1653901. Duvelle, C.: Musicque Centrafricaine, OCORA, OC43, Radio-France. Tracey, H.: Xylophones, “Musical Instruments no. 5”, The Music of Africa series, Kaleidophone KMA 5.

The influence of the tambura drone on the perception of proximity

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The influence of the tambura drone on the perception of proximity among scale types in North Indian classical music Kathryn Vaughn Department of Ethnomusicology and Systematic Musicology, University of California, Los Angeles, USA Contemporary Music Review, 1993, Vol. 9, Parts 1 & 2, pp. 21–33 Photocopying permitted by license only


The unique character of the tambura drone is the result of a nonlinear interaction of the strings with the bridge of the instrument. The placement of juari, or “life giving” threads at the curved bridge causes the energy to spread into the higher partials. Experimental evidence indicates that the perception of timbre resulting from this acoustical property alters similarity judgments of pitches within the three most commonly used tambura tunings. The rags of North Indian classical music can be grouped into a system known as the Circle of Thats, based on 32 possible scales, of which 10 are the most commonly used. The perceptual relation among the ten scales and the three tambura drone tunings was investigated using multidimensional scaling and cluster analysis of experimental data from both North Indian and Western musicians. It was found that the perceptual relation among the ten scale types in the absence of the drone is very close to the theoretical Circle of Thats. In the presence of the PA-SA drone the scales tend to cluster on the basis of common tones, placement of gaps and tetrachord symmetry. Correlation between subjects was unrelated to original culture background but significantly related to length of time spent studying this musical tradition. KEY WORDS: Tambura drone, North Indian rag, nonlinear phenomena, psychoacoustics, figure ground pattern recognition, indigenous cognition.


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Introduction The classical music of India is based on both theoretical and acoustical systems. The classification of North Indian rags by scale type, or That (framework), is one such system. A series of experiments was designed to determine a possible perceptual basis for the system of That groupings, and to test cross-culturally what effect the psychoacoustical context provided by the tambura drone may have on the perception of proximity among the most commonly used Thats. The tambura is an unfretted, long-necked lute with four to six strings, used to accompany one or more melodic instruments with percussion. Characterized by a repeating bass pitch pattern and its unusual ‘wash’ of sound, it provides a shimmering backdrop which permeates the overlay of musical structure created by the other instruments with which it is used. The unique timbral modulation of the instrument. C.V.Raman (1920) showed that, in addition to those harmonics tambura drone is the result of the interaction of the strings with the bridge of the predicted by the YoungHelmholtz law, other partials which have a node at the point of excitation are also generated. This is due to the grazing contact between the string and the curved surface of the bridge. The angle at the point of contact is altered by placing threads of material known as the juari [‘life-giving’] threads between each string and the bridge of the instrument. The placement of the juari causes the energy to spread into the higher partials. It has been confirmed that the shimmering, “buzzing” sound of the sitar is due to the wrapping and unwrapping of the strings around the elastic boundary created by the parabolic shape of the bridge (Burridge, Kappraff & Morshedi, 1982). In the case of the tambura, the bridge is flatter but the addition of the juari creates a similar smoothly rounded shape. The resulting non-linear behavior of the strings creates variation in the string lengths. This produces amplitude modulation and frequency modulation sidebands from upper partials causing interactions between the individual strings, giving rise to harmonically related clumps (Benade & Messenger, 1982). Initial experimental evidence indicates that the perception of timbre created by addition of the juari threads alters similarity judgments between separate fundamental pitches of the tambura strings within the three primary tunings: {Pa Sa Sa SA} {Ma Sa Sa SA} {Ni Sa Sa SA}. Furthermore, these results suggest that timbre may be at least as strong a factor in rating similarity between single tones as is the fundamental pitch (Vaughn & Carterette, 1989). Function of the drone Emergence of the tambura drone in Indian music is documented from the sixteenth century. Its increasing use parallels a transition from a modal system with a movable “tonic” or base pitch, to a system of scales with variable intervals relative to a single basic tone. An equivalent transition occurred in European music as composition based on the “church modes”, with their moveable finalis tones, was gradually displaced in favor of the use of transposed modes known as “church keys” and eventually toward functional harmony. The rag and its time cycle, or tal, interact against the constant background of the drone. Jairazbhoy (1971) holds that need for resolution within a rag melody is affected by


23

two distinct types of consonant/dissonant polarities. The drone establishes the static framework wherein the relation between any note and the groundnote underlies the dynamic quality of the note, a perceptual aspect of which is the relative tension created and its tendency towards completion, or resolution. Indeed, the tambura does provide a continual unchanging bass pattern, but the constantly shifting emphasis along its rich spectrum simultaneously imbues the performance with a sense of constant fluctuation as well. As the strings are plucked successively in continual, unaccented iteration, the result is a dynamic complex of the tones that interact with each other and with the melodic line. In North Indian classical music the four-stringed bass tambura is most often used for accompaniment in one of three tunings known by the name of the altered string: Pa, Ma, or Ni. Pa

Sa

Sa

SA4

5

8

8

1

5th

Ma

Sa

Sa

SA4

4

8

8

1

4th

Ni

Sa

Sa

SA4

7

8

8

1

7th

The relative frequencies are as follows: Sa1

70 Hz

C#2

Ma

93 Hz

F#2

Pa

106 Hz

G#2

Ni

132 Hz

C2

SA4

140 Hz

C#3

Spectral analysis of these three tunings has shown that the distribution of power is strong and significantly harmonically related up through the 20th partial, to approximately 5000 Hz (Carterette, Vaughn & Jairazbhoy, 1989). If the spectrum of the tambura were to interact with the sitar on the level of pitch perception, specific tones of a given melodic pattern could be emphasized. For example, the PA SA drone, which establishes the ground note and the fifth, has partials at 742 Hz, the pitch of F#5, at an amplitude of 50 dB greater than the fundamental pitch of the PA string. This means the sitar scale (C#4– C#5) could have its natural fourth degree (F#4) enhanced at the octave of that tone.1 Therefore, one could expect similarity judgments between scales having a sharpened fourth degree and those having the natural fourth degree to be affected either positively or negatively by the addition of the fifth degree in the tambura drone tuning. Notwithstanding the timbre of the instrument, one would expect the addition of a fundamental at 106 Hz to add some measure of dissonance to those same sets of scales in any case.

A model for the relationship between Thats Circle of That The system of Thats formalized by Pandit V.N.Bhatkhande (1930) classified rags into ten major groups based on the set of tones from which each rag in that group was observed


24

to be composed. A cyclic component is inherent in Bhatkhande’s system since the categories he found were related to the assigned time of day each group of rags was (and for the most part still are) performed. Each twenty-four hour day is divided into two segments, from midnight to midday, so that one cycle repeats each twelve hour period. One cycle is subdivided into three main periods: 4

to

7

Sunrise and sunset {Transition from night to day}

7

to

10

Following sunrise and sunset {Morning/Evening}

10

to

4

Preceding sunrise and sunset {Day/Night}

The rags in each of these time “zones” fall into consecutive subsets which Bhatkhande identifies as: 4–5–6, those with a natural 3rd and natural 6th; 1–2–3, those with flatted 3rd and 6th degrees; 7–8–9, those with flatted 2nd and natural 7th degrees.2 Jairazbhoy proposed (1974) this classification system may be considered to have circular properties by the inter-That relation on musical characteristics such as a cycle of fourths, similar to the western circle of fifths. Hence the Circle of That.

Figure 1 Circle of Thats after Bhatkhande


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Note: That 9 is somewhat of a conundrum in that it has taken the place of a hypothetical That which was presumed to have used an altered fifth and is no longer in existence. Its place in the sequence can be considered to be unstable so that the location of 9 and 10 in the circle are interchangeable. Feature analysis of scale types A model of the ten scales, based on common tone relations, arrangement of successive intervals, and internal symmetry was created in order to determine how various strategies might affect the mapping of proximities among the modes. Figure 2 lists the ten Thats in traditional western notation, which, in spite of deviation from equal temperament, represents very well the relative differences between each of the modes. Figure 3 shows the same ten scales represented as shapes formed around the size of the gaps between the tones of each scale. The overlaid geometric contour represents the difference curve between each set of tones. Each profile represents the step size from note to note as a peak of either 1, 2, or 3 {semitone, whole tone, diminished 2nd}. The pitch series has been detrended so that the octave rise from C to C, present in all the scales, is not a factor in the analysis. Modelling the scale patterns in this way helps to visualize the component features which appear as each scale is heard through time. For instance, one can easily see that the beginning and ending slopes create some sense of symmetry or asymmetry. Also, a sequence of even step sizes creates a plateau in the difference contour. It is possible to derive a measure of distance between any two scales by numerically encoding the sequences in question. For instance, the ten Thats are seven tone subsets of the set of twelve possible tones. Sa

1

C

Re-komal

2

Db

Re

3

D

Ga-komal

4

Eb

Ga

5

E

Ma

6

F

Ma-tivr

7

F#

Pa

8

G

Dha-komal

9

Ab

Dha

10

A

Ni-komal

11

Bb

Ni

12

B

Bilaval That (major scale) can thus be represented as: 1

3

5

6

8

10

12

{C

D

E

Kalyan That (lydian mode) can be represented as the sequence

F

G

A

B}


1

3

5

7

8

10

12

{C

D

26

E

F#

G

A

B}

Based on this representation of the scales as profiles of tone sequences, the ‘distance’ between these two scales has a value of (1). Thus a matrix of distances between each pair of scales was derived.3 Similarly, two additional sets of distances were produced by encoding the scales on the basis of successive interval size (the size of each peak as in Figure 3) and on the differences between successive intervals. A simulated “perceptual space” for each condition was then determined by applying multidimensional scaling (MDS)4 to those calculations. Figure 4 is the two dimensional MDS solution which is derived from distances based on common tones. Figure 5 is derived from the gap-size solution based on size of successive intervals in each That. The resemblance between the Circle of That and the MDS solution for the common tones is striking, but quite logical if one considers that for the most part each That happens to be one tone different from its predecessor. The circular space is very similar to that of the color scale described by Shepherd (1962). The classes of data structures which give rise to “circumplexes” are discussed by Guttman (1954). The present data may arise from the Cartesian product of points on two simple underlying dimensions. Since there is no linear solution for more than three point which are consecutively separated by a distance of (1), two dimensions are necessary to describe the space. Further, the analysis clearly showed that the three dimensional solution yielded a negligible reduction in Kruskal stress, and the individual weights for the third dimension under INDSCALE were consistently insignificant.


Figure 2 The Thats

27


28

Figure 3 Profiles based on size of successive intervals and differences between intervals


Figure 4 Two dimensional perceptual space simulated using similarities based on number of common tones between Thats

29


30

Figure 5 Two dimensional space simulated using similarities based on comparison of successive gaps in each scale Experiments The experimental design was intended to discover the effect of the drone. However, the process seems to have uncovered additional evidence for a perceptual basis for the Circle of That. The work of Castellano, Bharucha & Krumhansl (1984) suggested that correlations of hierarchical ratings of tones from ten rag phrases, falling into eight of the Thats, could be represented by a somewhat circular MDS space.5 The common tone


31

space presented above in Figure 4 explains that circular relationship. However, the effect of the PA-SA drone is found to disturb that arrangement. General experimental procedures The ten scales and the PA-SA tambura drone, were played by Usted Imrat Khan and recorded separately on a Panasonic SV 250 Digital Audio Tape recorder and two Neumann FET 100 condenser microphones. Each scale was then combined with the drone in a professional recording studio using a Studer A-80 24 track recorder and SSL mixing console. The 20 stimuli were then digitally sampled to disk at 50000 samples per sec with 16 bit resolution. Playback was at the same rate as sampling and was smoothed and converted at a cut off of 20k. The group of subjects were experts in this music and included both Indian musicians and Westerners who had studied North Indian music for at least ten years and perform the music in a professional capacity. In all cases the number of years spent learning this musical tradition was at least 50% of the subject’s life. Random pairs of scales were presented to the subjects, who rated the similarity on a continuous scale ranging from 0 to 100 selecting a point on the computer screen corresponding to their choice. The data then was stored for analysis. Experiment 1: Scaling scales The purpose here was to see how the musician’s perceptual scaling of the Thats without the tambura drone in the background compared to the common tone and gap-size models described above, and to the Circle of Thats. All possible pairs of the ten modes, including identical pairs, were presented in random order to the group of experts. The two dimensional multidimensional scaling solution derived by Alscal is shown in Figure 6.6 The results show a striking resemblance to the Circle of Thats discussed above. The scales are dispersed in a circular manner from 1 (Bhairvi) to 10 (Tori), with number 9 (the conundrum) being slightly out of line, as would be expected for the reason given above. The spacing from one That to the next is consistent, except for the grouping of 7– 8–9–10, all of which contain at least one gap of a diminished 2nd (about three semitones). This grouping is supported by cluster analysis using the technique of overlapping clusters, which allows a non-exclusive clustering pattern. The first two groups to appear from this proximity matrix are divided between {7, 8, 9, 10} and {1, 2, 3, 4, 5, 6}, with no overlap. Experiment 2: Effect of the tambura drone The same group of subjects rated similarity among the Thats in the presence of the PASA drone. The order of presentation between experiments 1 and 2 was also randomized, the results of similarity scaling in the presence of the PA-SA drone, the most commonly used tambura drone tuning, are shown in Figure 7. Here the scales start to cluster more clearly into Bhatkande’s original groupings, i.e. {4–5–6} {1–2–3} {7–8–9–10}. A sub-division also appears between 7–8 and 9–10, with 10 moving somewhat closer to That number 1. It thus appears that the presence of the PA-SA drone creates a context in which the subjects categorize more strictly than in the


32

absence of the PA-SA drone. The tighter groupings seem to be related more by features, as in Figure 4, rather than by simply the number tones two scales have in common. Furthermore, there is some increase in the separation between the protomajor, protominor, and gapped scales. If one were to make a case for the influence of the tambura harmonics on these groupings, it would have to be limited to the strength of the major triad within the partial structure of the drone. Otherwise the natural seventh present in mode 10 (Tori) would set it further from mode 1 (Bhairvi) instead of closer to it. It is more likely that features become increasingly influential because the framework provided by the PA-SA drone gives the listener more information. The essential point here is that this most common of drone tunings does alter judgment of proximity, even within a highly trained group of subjects who claim that the PA-SA drone is such an integral part of the music they always assume its presence, even if it is not there. In general, the subjects asserted that they performed identically under both conditions. There was no significant difference between the musicians born and educated in India and the nonIndian Americans. However, initial analysis shows correlation across subject spaces for each condition (with and without the drone) is significant on the basis of the number of years spent studying this musical tradition.

Discussion It is clear that the tambura drone establishes a context on two levels: the first a tonal center, i.e. the harmony of the fundamental pitches; the second, a subtle reinforcement of the upper partials. A third factor, however, must also be considered. As the partials are strengthened at higher and higher frequencies, the apparent “buzziness” creates a separate effect. It is this aesthetically pleasing distortion which is most obvious to the listener. The buzz is a constant source of arousal, transforming the repetitive bass pitch pattern into the reference point for a binary distinction between the melody and the background pattern. Preliminary results on the additional two drone tunings Experiments using the NI SA tuning (7 8 8 1), which is the most dissonant of the three, shows similar results to PA-SA, with slight differences in distances within the subsets. However, the MDS solution for the MA SA tuning (4 8 8 1) places the Thats in an even more evenly distributed circular pattern than under the condition of no tambura. That 9 (Bhairav) comes much closer to 1 (Bhairvi). The ambiguity created by including the interval of the 4th in the drone is somewhat like modulation to the dominant and seems to create a new tonal center entirely. The results thus far indicate that modeling cognition of melodic patterns should include consideration of the performance context, i.e. the musical fabric, as well as


Figure 6 Perceptual space for the ten Thats without the tambura drone

33


34

Figure 7 Perceptual space for the ten Thats in the presence of the PS SA (I– V) drone influence of culturally specific prototypes which may have been learned by musicians and audiences. For the higher level music processing task presented here, amount of exposure to the performance practice was more a factor than the original cultural background of the musician. The listener’s integration of background and foreground information seems to enhance the encoding process, contributing cues regarding switching and summations between explicit and implicit levels of processing. Acknowledgements This research has been supported by grants from the Charles F.Scott Foundation and the Regents of the University of California. I would like to express my appreciation to the Ali


35

Akbar Khan College of Music and the Los Angeles Philharmonic Institute for their generous cooperation. Special thanks to Professors Nazir Jairazbhoy, Edward Carterette, Roger Kendall, Sue Carole De Vale, and Eric Holmann for their expert advice. I am deeply indebted to Ustadt Imrat Khan for contributing his invaluable time and consummate talent in support of this work.

Notes 1. I have measured the F#4 to be a frequency of 371 Hz, or 508 cents above the C#4 at 278 Hz. 2. Bhatkhande associates That number 10 (Tori) with the group 1–2–3 on the grounds that rag Tori is sometimes played with both natural and sharpened fourth degrees. 3. The distance matrix used for the MDS space presented here was derived by the CLUSTAN program which will give a distance matrix for any set of profile data using values between 0 and 1. 4. Multidimensional scaling is a class of mathematical methods which try to find a space of dimensional size n which best fits a set of points according to some minimum-error criterion. If n=1, a line fits the point; if 2, a plane; if 3, a cube or sphere, and so forth. The iterative criterion used here was for 2 dimensions. The task of interpreting the dimensions is of course, the problem peculiar to a given domain, in this case music and cognition. 5. Although there are some problematic issues in that excellent study (i.e. the use of transcriptions by Danielou who embedded his own notion of a hierarchy in his versions of the rag phrases, synthetic stimuli and some misinterpretation of Jairazbhoy’s theory) the results suggested that neither incorrect temperament nor “unreal” timbre would interfere with subjects’ recognition of the common tone relation between those eight Thats. 6. Disregard the order of 9 and 10. For purposes of illustration the points are joined by an interpolative smooth line fitting using a spline routine which fits a cubic spline that minimized a linear continuation of the sum of squares of the residuals of fit and the integral of the square of the 2nd derivative.

References Bhatkhande, V.N. (1930) A comparative study of some of the leading music systems of the 15th, 16th, 17th and 18th centuries—A series of articles published in Sangita, Lucknow. Benade, A.H. & Messenger, W.G. (1982) Sitar spectrum properties. Journal of the Acoustical Society of America, Supplement 1, 71, 583. Burridge, R., Kapproaff, J. & Morshedi, C. (1982) The sitar string: A vibrating string with a onesided inelastic constraint. SIAM Journal of Applied Mathematics, 42,1231–1251. Carterette, E.C., Vaughn, K. & Jairazbhoy, N.A. (1989) Perceptual, Acoustical and Musical Aspects of the Tambura Drone. Music Perception, 7, No. 2, 75–108. Castellano, M.A., Bharucha, J.J. & Krumhansl, C.L. (1984) Tonal Hierarchies in the Music of North India. Journal of Experimental Psychology, 113, No. 3, 394–412. Jairazbhoy, N.A. (1971) The rags of North Indian Music: Their structure and evolution. London: Faber & Faber. Raman, C.V.. On some Indian stringed instruments. (1920) Indian Association for the Cultivation of Science, 1920, 7, 29–33. Shepherd, R.N. (1962) The analysis of proximities: Multidimensional scaling with an unknown distance function. II. Psychometrika, 27, 219–246. Steblin, Rita (1983) A History of Key Characteristics in the 18th and 19th Centuries. Ann Arbor, Michigan: UMI Research Press.


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Vaughn, K. & Carterette, E.C. (1989) The effect on perception of tambura non-linearity. Proceedings of the First International Conference on Music Perception and Cognition, 1989, 187–191.

Constraints on music cognition

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Constraints on music cognition—psychoacoustical Pitch properties of chords of octave-spaced tones Richard Parncutt Department of Music Acoustics, Royal Institute of Technology, Stockholm, Sweden Contemporary Music Review, 1993, Vol. 9, Parts 1 & 2, pp. 35–50 Photocopying permitted by license only


Listeners were presented with simultaneities of 1, 2, 3, or 4 octave-spaced (Shepard tones). In Experiment 1, they were asked how many tones they heard in each chord (its multiplicity). In Experiment 2, they heard a chord followed by a tone, and were asked how well the tone went with the chord; this resulted in a tone profile for each chord. In Experiment 3, they heard successive pairs of chords, and were asked to rate their similarity. The experiments may be regarded as octave-generalized versions of experiments reported in Parncutt (1989). Results were modelled by adjusting and extending a psychoacoustical model for the root of a chord (Parncutt, 1988). The model predicts the multiplicity of a chord, the salience (probability of noticing) of each tone in a chord, and the strength of harmonic relationships between chords (pitch commonality). Implications for the theory of roots, implied scales, and harmonic relationships are discussed. KEY WORDS: Pitch salience, chord, root, tone profile, pitch commonality, similarity, multiplicity.


38

Introduction In Western music theory chords have roots, and imply scales. For example, a C added sixth chord (CEGA) normally has the root C, and implies the scale of C major. Roots and implied scales are usually somewhat ambiguous: a C6 chord may have other roots (such as A), or imply other scales (such as G major), depending on context. This paper investigates the roots and scales implied by musical chords by comparing the results of listening experiments with calculations according to a psychoacoustical model. The model accounts for roots and implied scale tones by means of a single parameter, pitch salience. Roots are supposed to have high pitch salience, or perceptual importance; additional, implied scale tones have intermediate pitch salience. The model further accounts for harmonic relationships, measured by similarity judgments of pairs of chords, by means of a parameter called pitch commonality. The model explains the sensory origins of roots, implied scales, and harmonic relationships, but neglects culturespecific effects such as conditioning by particular, arbitrary chord sequences. Octave-spaced tones were used in the experiments so as to enable octave-generalized aspects of music theory to be investigated as directly as possible. By building chords from octave-spaced tones, effects of octave register (pitch height) and voicing were minimized. Remaining register effects (such as the “tritone paradox” investigated by Deutsch, 1987) were avoided in Experiments 2 and 3 by random transposition of trials (see procedure sections). In this research, octave equivalence is regarded firstly as an axiom of music theory. As a perceptual phenomenon, it is assumed to be primarily learned from music (see e.g. Burns, 1981). It would appear to be unnecessary to postulate a neurophysiological basis for active equivalence, as e.g. Ohgushi (1983) has done, in order to account for octavegeneralized aspects of music theory. The paper begins by considering the number of simultaneously noticed tones in a chord, here called its multiplicity.1 This parameter is later used in the model to scale pitch saliences as absolute values, representing probabilities of noticing.

Experiment 1: Multiplicity The number of tones simultaneously noticed in a musical chord does not necessarily correspond to the number of pure tone components (Thurlow and Rawling, 1959) or complex tone components (DeWitt and Crowder, 1987; Parncutt, 1989). In the present experiment, sounds were constructed from octave-spaced tones (Shepard, 1964) and listeners were asked how many such tones they heard. Apart from providing some new experimental data, the experiment aimed to test the algorithm for pitch ambiguity in Parncutt (1988). A similar algorithm (for multiplicity) is presented below as part of a model for the salience of a chroma (pitch class) in an octavegeneralized chord, e.g. a chord made of octave-spaced tones. The multiplicity algorithm allows saliences to be expressed as absolute values: “probabilities of noticing” which may be compared across different chords.


39

Method Listeners. 26 adults participated in the experiment. Their musical experience (here measured in terms of the number of years spent regularly practising or performing music, either instrument or voice) had a mean of 11 years and a standard deviation of 10 years. Equipment. Waveforms were calculated by adding pure tone components in alternating cosine and sine phase (to reduce maximum amplitude) and transferred by analog signal to a digital sampling synthesizer (Casio FZ-1). During the experiment, sounds were called via MIDI by a Le_Lisp program running on a Macintosh II personal computer. They were amplified and reproduced over a loudspeaker in a sound-isolated room. Listeners responded by pressing keys on the computer keyboard. Sounds were compared of octave-spaced tones of equal amplitude. By contrast to the tones used by Shephard (1964), pure tone components had equal amplitude (before amplification) across the range 16 Hz to 16 kHz.2 All pure tone components were tuned to the standard equally-tempered scale, with A=440 Hz and no octave stretching. Twenty different sounds were presented, each in two different transpositions, six semitones apart. Pitches were chosen to produce a balance around the chroma cycle, and so not to emphasize any particular pitch. The 20 sounds consisted of one single octavespaced tone (monad), six dyads of octave-spaced tones (spanning intervals 1 to 6 semitones), five triads (037, 047, 048, 036 and 057) and eight tetrads (047Q, 037Q, 047L, 037L, 0369, 036Q, 057Q and 046Q).3 Sounds had durations of 0.2 s. All components in each sound started exactly simultaneously; this was important, as the auditory system is remarkably sensitive to asynchrony in onset times, and uses asynchrony to discriminate musical tones in performance (Rasch, 1978). Overall loudness was adjusted to a comfortable level by each listener. Procedure. In each trial, one of the 20 sounds was presented twice, with a pause of 0.5 s between presentations. The task was to indicate how many tones they heard in the sounds. No upper limit was set on their responses. Listeners could take as long as they wished to respond. They were asked, however, to respond spontaneously, without thinking too hard. It was stressed that this was not a test of musical ability. Each sound was presented twice, making a total of 40 trials. To avoid serial effects, trials were presented in a random order which was different for each listener. The experiment was preceded by a practice session. During the practice, listeners were told after they responded whether the chord had contained one, or more than one, (octave-spaced) tone. In the experiment proper, no feedback was given.

Results The non-musicians initially had some difficulty with the task, but after some practice found they were able to distinguish a small number of response categories (e.g. 1 to 3). Still, they were not sure that they actually heard all the tones that they guessed were present. Musicians’ responses generally covered larger ranges. Many said afterwards that they had responded on the basis of musical experience (e.g. responding “4” on


40

recognizing a seventh chord). All results correlated positively with the actual number of tones in the sounds, so none were eliminated from the analysis.

Figure 1 Points: mean responses (52 data per point). Bars: 95% confidence intervals. Squares: calculations according to (7) with kM=45, kW=3.9, and kS=0.91 (see below). Chord classes are indicated by intervals in semitones above the nominal root (e.g. “047”=major triad). Results are graphed in Fig. 1 as means and 95% confidence intervals of responses.4 Responses corresponded closely to the “actual” number of octave-spaced tones in each sound (but clearly not to the number of pure tone components) for the monad, dyads and triads. In the case of the monad, the result was not surprising, as listeners had been taught to recognize monads during the practice.5 The tetrads were heard to contain about 3.5 tones, agreeing with Huron’s (1989) finding that the accuracy of identifying the number of concurrent voices in polyphonic music drops markedly at the point where a three-voice texture is augmented to four voices. There was an additional tendency for consonant sounds to have lower, and dissonant to have higher, multiplicity. So, for example, dyad 05 (perfect fourth/ fifth) was heard to have significantly less (p0.05) if they differ by more than a 95% confidence deviation (i.e. the half-width of a 95% confidence interval) divided by root 2, provided the confidence deviation for the two experiments is about the same.


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5. In a different context (Parncutt, 1989), single octave-spaced tones were mostly heard to comprise between two and three tones. This is an example of the general rule that the perceived number of tones in a musical sound depends on context. 6. At medium to high sound levels, the masking pattern of a pure tone is considerably higher and longer on its upper than its lower side. However, at low levels the pattern is almost symmetrical with respect to critical-band rate (Zwicker and Jaroszewski, 1982). 7. In Parncutt (188), interval 3 was assigned a small root-support weight (1/10), as the third harmonic of interval 3 (3+7=10) corresponds to a harmonic (the seventh) of interval 0. It may therefore contribute to the root sensation. Here, octave-spaced tones were used, containing only harmonics 1, 2, 4, 8, 16, etc., so interval 3 could not contribute to the root— except, perhaps, by cultural conditioning. 8. Note that each parameter may be regarded as a measure of how analytically sound is perceived: kM at the level of spectral analysis (discrimination of pure tone components), kW at the level of “hearing out” of pure (as opposed to complex) tone components, and kS at the level of simultaneous perception of tones in a sound.

References Bharucha, J. & Krumhansl, C.L. (1983) The representation of harmonic structure in music: Hierarchies of stability as a function of context. Cognition, 13, 63–102. Burns, E.M. (1981) Circularity in relative pitch judgments for inharmonic complex tones: The Shepard demonstration revisited, again. Perception & Psychophysics, 30, 467–472. Butler, D. (1989) Describing the perception of tonality in music: A critique of the tonal hierarchy theory and a proposal for a theory of intervallic rivalry. Music Perception, 6, 219–242. Cuddy, L.L. & Badertscher, B. (1987) Recovery of the tonal hierarchy: Some comparisons across age and musical experience. Perception and Psychophysics, 41, 609–620. de la Motte, D. (1976) Harmonielehre. Kassel: Bärenreiter. Deutsch, D. (1987) The tritone paradox: Effects of spectral variables. Perception & Psychophysics, 41, 563–575. DeWitt, L.A. & Crowder, R.G. (1987) Tonal fusion of consonant musical intervals: The Oomph in Stumpf. Perception & Psychophysics, 41, 73–84. Fletcher, H. & Galt, R.H. (1950) The perception of speech and its relation to telephony. Journal of the Acoustical Society of America, 22, 89–151. Huron, D. (1989) Voice denumerability in polyphonic music of homogeneous timbres. Music Perception, 6, 361–382. Krumhansl, C.L. Kessler, E.J. (1982). Tracing the dynamic changes in perceived tonal organization in a spatial representation of musical keys. Psychological Review, 89, 334–368. Krumhansl, C.L. & Shepard, R.N. (1979) Quantification of the hierarchy of tonal functions within a diatonic context. Journal of Experimental Psychology: Human Perception and Performance, 5, 579–594. Ohgushi, K. (1983) The origin of tonality and a possible explanation of the octave enlargement phenomenon. Journal of the Acoustical Society of America, 73, 1694–100. Parncutt, R. (1988) Revision of Terhardt’s psychoacoustical model of the root(s) of a musical chord. Music Perception, 6, 65–94. Parncutt, R. (1989) Harmony: A Psychoacoustical Approach. Berlin: Springer-Verlag. Parncutt, R. (1990) Chromatic chord symbols. Computer Music Journal, 14 (2), 13–14. Pollack, I. (1987) Decoupling of auditory pitch and stimulus frequency. The Shepard demonstration revisited. Journal of the Acoustical Society of America, 63, 202–206. Rasch, R.A. (1978) The perception of simultaneous notes such as in polyphonic music. Acustica, 40, 21–33.


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Riemann, H. (1893) Vereinfachte Harmonielehre. London: Augener. Shepard, R.N. (1964) Circularity in judgments of relative pitch. Journal of the Acoustical Society of America, 36, 2346–2353. Shepard, R.N. (1982) Structural representations of musical pitch. In D.Deutsch (Ed.), The Psychology of Music, pp. 344–390. London: Academic Press. Sundberg, J. (1988) Computer synthesis of music performance. In J.A.Sloboda (Ed.), Generative Processes in Music. Oxford: Clarendon. Terhardt, E. (1982) Die psychoakustischen Grundlagen der musikalischen Akkordgrundtöne und deren algorithmische Bestimmung. In C.Dahlhaus & M.Krause (Eds.), Tiefendstruktur der Musik. Berlin: Technical University of Berlin. Terhardt, E., Stoll, G., Schermbach, R., & Parncutt, R. (1986) Tonhöhenmehrdeutigkeit, Tonverwandschaft und Identifikation von Sukzessivintervallen. Acustica, 61, 57–66. Terhardt, E., Stoll, G., & Seewann, M. (1982) Pitch of complex tonal signals according to virtual pitch theory: Tests, examples and predictions. Journal of the Acousticacl Society of America, 71, 671–678 (a). Terhardt, E., Stoll, G., & Seewann, M. (1982) Algorithm for the extraction of pitch and pitch salience from complex tonal signals. Journal of the Acoustical Society of America, 71, 679–688 (b). Terhardt, E., Stoll, G., Schermbach, R., & Parncutt, R. (1986) Tonhöhenmehrdeutigkeit, Tonverwandschaft und Identifikation von Sukzessivintervallen. Acustica, 61, 57–66. Thurlow, W.R. & Rawling, L.L. (1959) Discrimination of number of simultaneously sounding tones. Journal of the Acoustical Society of America, 31, 1332–1336. Zwicker, E. & Feldtkeller, R. (1967) Das Ohr als Nachrichtenempfänger, 2nd ed. Stuttgart: HirzelVerlag. Zwicker, E., Flottorp, G., & Stevens, S.S. (1957) Critical bandwidth in loudness summation. Journal of the Acoustical Society of America, 29, 548–557. Zwicker, E. & Jaroszewski, A. (1982) Inverse frequency dependence of simultaneous tone-on-tone masking patterns at low levels. Journal of the Acoustical Society of America, 71, 1508–1512.

Identification and blend of timbers as a basis for orchestration

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Identification and blend of timbres as a basis for orchestration Roger A.Kendall and Edward C.Carterette Departments of Ethnomusicology & Systematic Musicology and Psychology University of California, Los Angeles, USA Contemporary Music Review, 1993, Vol. 9, Parts 1 & 2, pp. 51–67 Photocopying permitted by license only


We report on a series of experiments directed toward questions concerning the timbres of simultaneous orchestral wind instruments. Following a background exposition on instrumentation and orchestration, we discuss previous experimental research on the properties of multiple timbres. To augment and explicate previous findings, we conducted two experiments: Experiment 1 was directed at subject ratings of the blend of oboe, trumpet, clarinet, alto saxophone, and flute dyads. Experiment 2 required subjects to identify the constituent instruments of a pair. Results demonstrated that increasing blend correlated with decreasing identification, and was related to the distribution of time-variant spectral energy. Oboe dyads, which were rated in other experiments as highly “nasal,” produced the lowest blend values and the highest identification. The findings are discussed in terms of a theoretical model of timbral combination and the possibilities for composition and musicological analysis. KEY WORDS: Timbre, tone color, wind instrument, orchestration, instrumentation, cognition, perceptual scaling, blend. Background The study of orchestration as an element of musical composition is, historically, a relatively recent event. In the Middle Ages and Renaissance, the assignment of instruments to parts was dictated largely by availability of resources; orchestration in the sense of a planned, structural use of instruments and instrument combinations was not employed. The Baroque era witnessed the increasing specificity of instrumental combinations. For example, Monteverdi suggests certain instrumental combinations for his opera Orfeo (1607). By the end of the Baroque, concert works might include parts for flutes, oboes, bassoons, horns, trumpets, timpani, and continuo, plus strings. The


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conception of the orchestra as consisting of contrasting families of timbres can be seen, for example, in Handel’s Music for the Royal Fireworks (1749). In the classical period, Mozart was innovative in his application of winds to solo melodic lines; his wind concerti, in fact, are beautifully crafted explorations of wind virtuosity. The origin of the scholarly study of orchestration, and its establishment as a study “independent of [and equal to] the three other great musical powers [i.e. melody, harmony, and rhythm],” can be attributed to Berlioz (1844/1856, p. 4). Instead of conceiving of orchestration as the application of instruments to already completed music, Berlioz saw orchestration as an essential part of the musical ideas themselves, an attitude expressed in the opening pages of A Treatise on Modern Instru-mentation and Orchestration (1844/1856, p. 4). Novel combinations of winds and strings abound in his music, for example, the trombone and flute trio in the “Hostias” and “Agnus Dei” of his Grande messe des morts [Requiem] (1837), and the opening woodwind and horn choir in the Symphonie Fantastique. His invention was remarkable, consider, for example, the instruction for muted clarinet enveloped in a leather bag in Lélio. Technological improvement of instruments, such as the Boehm flute, ca. 1850, and the invention of such important winds as the valved horn and trumpet, was the catalyst for compositional experimentation in orchestration. The winds have at least an equal footing with the strings in orchestral stature by the time of Debussy. Contemporary use of timbral combinations includes the innovations of such composers as Schoenberg in the Klangfarbenmelodie of the third of the Five Orchestral Pieces, op. 16 (1909), the structural use of timbre by Messiaen and Stockhausen, and the dodecaphonic organization of timbres in Slawson’s theoretical work and compositions in Sound Color (1985). It is startling that, with the increasing importance of timbre as a compositional force, particularly accelerated by computer synthesis, experimental studies of timbre perception are so rare. Partially to blame may be the pitch-centricity of Western scholarship, another factor may be the difficulty of manipulating the multidimensional timbral parameters of real instruments. In fact, much of the experimental timbre literature has used brief, steady-state, synthetic signals which are amenable to precise control and analysis. This work is in the tradition of Helmholtz (1863/ 1885/1954) whose subjective impressions of vowel and instrument timbres were quite insightful. Plomp (1976) reviews classical psychoacoustical studies on timbre, including his own work using single periods of musical instruments and organ stops. Temporal aspects of the acoustic spectrum, particularly the attack transient, have been extensively studied since Stumpf (1926); the criterial importance of the attack has been only recently challenged (Kendall, 1984). Very little timbre research has been conducted since Grey’s An Exploration of Musical Timbre (1975), which was based on real instruments. However influential this study has become, it has significant imperfections. Some unusual instruments were used, for example, soprano saxophone, Eb clarinet, bass clarinet, particularly considering that the more common members of the instrument family, such as Bb soprano clarinet, were not included. The trombone, bassoon, and cello were in moderately high registers, and the use of mutes and atypical bowing techniques should be noted. Another limitation was the brevity of the signals (ca. 330 msec) and the fact that line-segment resynthesized tones were employed (see Kendall & Carterette, 1991 for additional details).


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Recently, we have addressed many of these concerns in our explorations of simultaneously sounding wind instruments. Since most music is not monophonic, it is astonishing that little work has been done on perceptual aspects of simultaneously sounding instruments. To our knowledge, the first such experimental investigations were those of Carterette & Kendall (1989) and Kendall & Carterette (1989), which form the basis for the present work, discussed below.1 In addition, Sandell (1989a, 1989b) has reported preliminary work on the “blend” of “concurrent timbres” using 15 of Grey’s (1975) line-segment approximations of brief real instrument tones, whose limitations were just mentioned. Note that the combinations of timbres were mixed and adjusted computationally by Sandell, and not performed in duet; the resultant dyads were not equalized in loudness. Subjects rated the “blend” of all possible 120 pairs of 15 instruments. For each instrument its average blend with all other instruments was calculated. Some results of interest demonstrate that blend is related to the summed distribution of energy in the harmonic series of the two tones, with less blend correlated with more energy in higher harmonics contrasted to lower. Perceptual scaling of simultaneous timbres In a previous investigation, we required subjects to rate the degree of similarity among all combinations of five wind instruments: oboe, clarinet, flute, alto saxophone, and trumpet (Kendall & Carterette, 1991). We utilized six musical contexts: Unison, unison “melody” (consisting of scale degrees 3, 4, 5, 3 based on Bb4), major thirds (Bb4–D5), and harmonized melody (I–IV6–V6–I), the latter two contexts with both instruments of the pair as the soprano (we refer to the principal instrument order [e.g. OF=an oboe-flute dyad with flute in the soprano] as the noninverted major third and noninverted harmony contexts; the reversed instrument orders are called the inverted-instrument harmony and inverted-instrument major third contexts, e.g. FO. Therefore there are two contexts for each of the harmony and major third conditions). Duet performances by professional instrumentalists were digitally recorded in a concert hall; the resulting dyads were equalized in loudness (see Kendall & Carterette, 1991, for details). The ratings of similarity were subjected to a multidimensional scaling analysis (MDS). Briefly stated, the rating of similarity between two sounds is treated as a distance in some geometrical space. MDS attempts to find the “best” configuration of points in this space which minimizes the amount of error. The essential idea is easily illustrated (Figure 1). Suppose that the distance between A and B is 2; B and C is 10; A and C is 12. In this case, the configuration of points is best fit by Figure 1a, a line in one dimension. However, if the distance between A and B is 5; B and C is 9; A and C is 12, then (since AB+BC=14, rather than 12), the points are best fit by Figure 1b, a triangle in two dimensions.


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Figure 1 Illustration of one (a) and two (b) dimensional solutions for distances among three hypothetical stimulus points.

Figure 2 Three dimensional solution for wind instrument dyad similarity ratings for Bd4–D5 major third context. Subjects were nonmusic


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majors. O=oboe, F=flute, T=trumpet, S=saxophone, C=clarinet. For example a pair is represented by letter combination: OF is oboe-flute. The second instrument was the soprano (D5). Figure 2 graphs the three-dimensional solution for similarity ratings of the Bb4– D5 major third context. Notable is the clustering of wind dyads on the basis of “dominant” instrument: Oboe (right side), trumpet (left front), and saxophone (far rear corner). These subjects were nonmusic majors; we have found that music major results produce a similar graph, with even a tighter clustering of dyads. In order to interpret dimensions, we conducted extensive verbal rating experiments (Kendall & Carterette, In Press, a, b). As far as we know, this was the first study to obtain verbal ratings using adjectives derived from a musical source (Piston, 1955), rather than simply relying on nonmusician’s intuition. Contrary to previous research which has emphasized “sharpness” (Bismarck, 1974) “acuteness” (Slawson, 1985), or “brightness” (Bismarck, 1974; Risset & Wessel, 1982) we found the principle dimension to be one of “nasality”: (Figure 2) (D1=nasal (negative, −2) vs. non-nasal (positive, +1). Note that OF (oboe-flute) was the most nasal sounding instrument combination; SC (saxophoneclarinet) was the least nasal. Dimension 2 represents “brilliant” (−1) vs. “rich” (=1), which generally separates trumpet from saxophone. The FC dyad surprisingly is rated as relatively “brilliant,” a finding which holds across contexts. Dimension 3 relates to “strong” and “complex” (+1) vs. “weak” and “simple” (−1). For ease in observing twodimensional pairs, the points are projected as diamonds on the floor and walls of the figure. For example, D1 vs. D2 is the floor; D1 vs. D3 is the rear wall; D2 vs. D3 is the left side wall. We were struck by the fact that “nasal” and “rich” were first used by Helmholtz (1863/1888/1954, p. 118) to describe the relationship between instrument timbres and vowels.


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Figure 3 Two-dimensional INDSCAL solution summarizing wind instrument dyad distances across contexts. Left to right is “nasal” to “not nasal”; top to bottom is “rich” to “brilliant.” From Kendall & Carterette (1991).


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Figure 4 Two-dimensional configuration of single instruments positioned by a professor of musicology on the basis of mental image of timbre (Bb4). Dimension 1 (left to right) was “nasal” to “not nasal” and dimension 2 (top to bottom) was “rich” to “brilliant.” From Kendall & Carterette (1991). We submitted the entire set of scalings over all contexts to INDSCAL (INdividual Differences SCALing), which provided a summary solution. The two dimensions gave essentially as good a fit as three; we present the two-dimensional solution here (Figure 3). The result was a circumplex with a notable gap on both sides of the oboe dyads. Other well-known circumplexes are those for pitch chroma (Shepard, 1964) and visual colors (Shepard, 1962). In terms of verbal attributes, left to right along dimension 1 (Figure 3) is “nasal” to “not nasal”; top to bottom is “rich” to “brilliant.” A circumplex like Figure 3 might arise from the vector sum of the positions of single instruments arranged in two dimensions (Figure 4): Nasal-not nasal and brilliant-rich. In fact, the results of


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positioning single instruments in such a space by a professor of musicology generated a quasi-circumplex similar to Figure 3 (Kendall & Carterette, In Press, a, b).

Experiments in identification and blend We report here new work designed to complement and extend the results of our previous research. We wanted to know the relationship between our verbal and perceptual scaling data and the degree of identifiability of the constituent instruments of a dyad as well as the rated “blend.” In our study, we operationalize “blend” in terms of the extent of “oneness” versus “twoness.” Orchestration treatises differ regarding the degree of emphasis placed upon blend. Indeed, most monographs lightly treat sound combinations, instead focusing on the characteristics of instruments and their uses as soloists within the orchestra. Piston (1955) distinguishes between “instrumentation” and “orchestration” in order to emphasize the fact that orchestration involves more than memorization of instrument properties, and devotes several chapters to instruments in combination—yet blend does not appear as an overriding concern. Rimsky-Korsakov (1913), on the other hand, seems preoccupied with the concept. Some authors suggest that instrument combinations which “blend well” are more desirable than those which do not. However, even a cursory examination of orchestral music leads to the conclusion that the degree of blend is a variable being manipulated by the composer according the demands of the musical context. Therefore it is as useful to know what does not blend as well as what does. The present study investigated blend with two experimental approaches: 1. Ratings, where a subject indicates the degree of “oneness” to “twoness” of wind instrument combinations; 2. Identification, where a subject must name the constituent instruments of a dyad.

Experiment 1: Ratings of perceived blend Methods and materials The aim of this experiment was to discover the degree to which a pair of simultaneously playing natural instruments blended, or fused, perceptually. The stimuli were all possible combinations of flute, clarinet, oboe, trumpet, and alto saxophone, performing the six contexts outlined above. Stimuli were digitally recorded in stereo on stage in a moderately reverberant concert hall (without audience, reverberation time=ca. 1.6 sec). The recordings were sampled in stereo directly to hard disk (35714 samples/sec per channel) with five-pole Butterworth anti-aliasing filters with a cut-off frequency set to 10 Khz.2 Playback and control of experiments was handled by an IBM 80386-based computer and custom software3 (Kendall, 1988). The method required the listener to make a simple response along a 12.7 cm bar displayed on a graphics screen. At the left end of the bar the word “one” was displayed, and at the right end of the bar the word “two.” The subject’s task was to move the pointer


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from its initial, randomly set position along the bar to the position which the subject felt best described his feeling of “oneness” or “twoness”. The subject set the position of the pointer by moving a mouse on a pad. Subjects knew that every sound was played by a pair of wind instruments. There were 9 subjects all of whom were music majors with at least ten years of formal instruction. Each subject heard six blocks of stimuli, grouped by context, in a random order; the six blocks were presented twice and data were averaged. Results and discussion Subject ratings were converted to blend by taking the complement: High scores indicating “twoness” became low scores for blend; low scores indicating “oneness” became high scores for blend. Analysis of Variance (ANOVA) on repeated measures indicated that the mean values for blend across contexts were statistically significantly different (df=5,40; F=3.7p; p

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