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City Research Online City Research Online City, University of London Institutional Repository Citation: Cross, I. (1989). The cognitive organisation of musical pitch. (Unpublished Doctoral thesis, City University London) This is the accepted version of the paper. This version of the publication may differ from the final published version. Permanent repository link: https://openaccess.city.ac.uk/id/eprint/7663/ Link to published version: Copyright: City Research Online aims to make research outputs of City, University of London available to a wider audience. Copyright and Moral Rights remain with the author(s) and/or copyright holders. URLs from City Research Online may be freely distributed and linked to. Reuse: Copies of full items can be used for personal research or study, educational, or not-for-profit purposes without prior permission or charge. Provided that the authors, title and full bibliographic details are credited, a hyperlink and/or URL is given for the original metadata page and the content is not changed in any way. City Research Online: http://openaccess.city.ac.uk/ [email protected] The Cognitive Organisation of Musical Pitch A dissertation submitted in fulfilment of the requirements of the degree of Doctor of Philosophy in The City University, London by Ian Cross September1989 ABSTRACT This thesis takes as its initial Premise the idea that the rationales for the forms of pitch organisation employed within tonal music which have been adopted by music theorists have strongly affected those theorists` conceptions of music, and that it is of critical importance to music theory to investigate the potential origination of such rationales within the human sciences. Recent studies of musical pitch perception and cognition are examined, and an attempt is made to assess their capacity to provide sustainable rationales for pitch organisation in tonal music. Theoretical and experimental studies that focus on sensory processes are critically reviewed, and it is suggested that these do not adequately characterise important aspects of musical pitch organisation. Studies that examine more central cognitive constraints are discussed, and a detailed critique is made of recent cognitive-structural approaches to the representation of musical pitch. It is proposed that a significant aspect of tonal pitch organisation, diatonic structure, is neither adequately investigated nor provided with any compelling rationale by these studies. Three series of experiments on the perception and representation of diatonic structure are presented: it is suggested that the sensitivity to properties of diatonic structure shown by listeners in these and in other experiments implies that a representation of diatonic interval structure constitutes an important component of the cognitive organisation of musical pitch. A possible basis for this sensitivity is further explored, and a group-theoretic rationale for the musical use of diatonicism is proposed. The nature of the cognitive representation of diatonic interval structure is discussed. and relationships between diatonic structure. other western scale forms. tonality and (briefly) atonality are outlined. Ian Cross. September 1989 ACKNOWLEDGEMENTS In submitting this thesis. I wish to acknowledge the debt which I owe to a number of individuals who have assisted me in many ways. First of all, I wish to thank Natasha Spender; she introduced me to this area of research, and provided valuable and stimulating comment in the early stages of my research. Secondly, most of the experiments described in Chapters six, seven and eight were undertaken with the collaboration of Peter Howell and Robert West. They acted as my de facto "supervisors" in the psychological domain, at times in a personal as well as an intellectual sense. To Rob I owe thanks for his ability to offer succinct interpretations of some of my more deeply "nested" ideas, while to Pete in Particular I owe thanks for his tendency to instruct me to "go and do it" on those occasions when theory seemed more enticing than the corralling of experimental subjects. The exact nature of our collaboration - in terms of specifically who did what - is now a little difficult to disentangle. At one level, Pete and Rob were concerned to ensure the application of appropriate psychological method, and to ensure that any broad psychological implications of the design and results of the experiments were not overlooked. while my concern was directed more towards the elucidation of specifically musical and musico- cognitive problems. This is not to imply a simple split in responsibility for psychological and musical issues, however, for at a more detailed level I was directly responsible for the design and conduct of many of the experiments (including several not reported here which, through a process of attrition, helped to determine the forms and aims of subsequent experiments). Similarly. while I would claim responsibility for most of the ideas expounded in the course of describing the experiments, many of these were tested, or had their seeds in, discussions with Rob and Pete. Having claimed this responsibility, I am also obliged to claim sole responsibility for any errors or omissions in methodology or logic that remain. To many others I owe thanks for comments and encouragement. In particular. though. I would like to thank Malcolm Troup, for without the sheer and outrageous liveliness that he brought to Music at City University the act of musical discovery would not have been half so enjoyable. Lastly, most thanks to Jane, for understanding. CONTENTS Chaoter Subhead Pa e CHAPTER ONE 1 CHAPTER TWO The perception of pitch 8 Patterson's spiral detection of periodicity 10 The spiral processor and the organisation of 11 music pitch Terhardt's model of pitch perception 16 Terhardt's model and music 19 Parncutt and "pitch commonality" 24 Pitch categorisation 30 CHAPTER THREE Sound sources and auditory streams 34 Contour 40 Interval, scale and key 42 Scale, key" mode - music theory 49 Scale, key, mode - cognitive representation 55 CHAPTER FOUR Structural representations of musical pitch 63 The double helix representation of musical 67 pitch The cognitive-structural model - experiments 70 A cognitive-structural model for chords 74 and keys - experiments Cross-cultural evidence for the 79 cognitive-structural model The cognitive-structural model - implications 83 for perception CHAPTER FIVE Problems with the cognitive-structural model 90 Experimental results - lack of fit with 91 theory Experimental materials and their relation 94 to theory Tonal hierarchy - acquired by learning or 97 acculturation ? Separability of syntax and duration 99 The "representativeness" of contexts 100 The "informational" approach - objections 104 The neglect of scale structure 106 Problems with experimental approaches to 110 musical pitch cognition The group-theoretic representation of 113 musical pitch The unexplored question 118 CHAPTER SIX Experimental Series 1 121 Procedures for generating experimental 126 sequences Experiment 1.1 129 Experiment 1.2 135 Experiment 1.3 137 Structural bases for first-order preference 139 Experiment 1.4 144 Experiment 1.5 148 CHAPTER SEVEN Experimental Series 2 154 Experiment 2.1 157 Experiments 2.2 and 2.3 169 CHAPTER EIGHT Rarity and ubiquity - Browne and the 179 diatonic set Experimental Series 3 186 Experiment 3.1 189 Experiment 3.2 191 Multiplicity and equivalence relations 195 Experiments 3.3 and 3.4 198 Experiment 3.5 205 Experiment 3.6 210 CHAPTER NINE Conclusions 214 Diatonic subset representativeness and 215 interval vector similarity Diatonic rarity and the attribution of 224 tonal centre Group-theoretic rationale for 226 diatonic structure Diatonicism, major and minor 228 Scales as theories 230 Tonality and the diatonic set 233 Diatonicism and atonality 240 REFERENCES 243 CHAPTER ONE Pitch has generally been regarded as the dominant structural dimension of western music: the way that pitch is organised within that music is complex and idiosyncratic. As musical styles have changed it has changed, with changes in pitch organisation often constituting the principle feature of style change; however, certain constancies appear to remain even through these style changes. The constancies of pitch organisation in western music over the last four hundred years are usually referred to as the principles of tonality. exemplified in the employment of successions of triadic chords within major and minor keys to articulate musical structure. In attempting to codify the principles of tonality (whether for ontological, aesthetic or pedagogical purposes) theorists have continually sought or advanced rationales for the particular forms of pitch organisation - triads, triadic successions and keys - employed within tonal music. These rationales have often come to play significant roles in shaping ideas about what constitutes the "stuff" of music. I The importance and influence of these rationales can be seen most clearly in musical analysis. The structure of a piece of music as revealed in analysis can often be related directly to the particular rationales for pitch organisation - or even to the nature or phenomenal locus of those rationales - that an analyst chooses to employ. That is. the criteria that are used in an analysis for expressing the actual pitches of a piece of music in terms of the representation peculiar to the analytic method applied can be directly referable to the rationales for the structure of triads or keys that have been incorporated into that (1) analytic method. Hence the claims made by analysts as to what facets of music or musical experience an analysis represents - and the controversies that may arise around these claims - can be determined at least in part by the analyst's adoption of specific rationales for pitch organisation in tonal music. The point is perhaps best made by providing a concrete example. influential Currently, the most and widely applied method of musical analysis of western tonal music is that developed by Schenker. It is Heinrich possible to see, in the structures that Schenkerian analyses-reveal. the importance of the rationale for the structure of triads and keys that is used within that analytic system.
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