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City University of New York (CUNY) CUNY Academic Works All Dissertations, Theses, and Capstone Projects Dissertations, Theses, and Capstone Projects 10-2014 A Derivation of the Tonal Hierarchy from Basic Perceptual Processes David Smey Graduate Center, City University of New York How does access to this work benefit ou?y Let us know! More information about this work at: https://academicworks.cuny.edu/gc_etds/312 Discover additional works at: https://academicworks.cuny.edu This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] A DERIVATION OF THE TONAL HIERARCHY FROM BASIC PERCEPTUAL PROCESSES by David Smey A dissertation submitted to the Graduate Faculty in Music in partial fulfillment of the requirements for the degree of Doctor of Philosophy, The City University of New York 2014 ii © DAVID SMEY 2014 All rights reserved iii This manuscript has been read and accepted for the Graduate Faculty in Music in satisfaction of the dissertation requirement for the degree of Doctor of Philosophy ________________ _______________________________ Date Stephen Blum Chair of Examining Committee ________________ _______________________________ Date Norman Carey Executive Officer Supervisory Committee Joseph N. Straus, advisor Philip Rupprecht, first reader Stephen Blum Fred Lerdahl THE CITY UNIVERSITY OF NEW YORK iv Abstract A DERIVATION OF THE TONAL HIERARCHY FROM BASIC PERCEPTUAL PROCESSES by David Smey Advisor: Professor Joseph N. Straus In recent decades music psychologists have explained the functioning of tonal music in terms of the tonal hierarchy, a stable schema of relative structural importance that helps us interpret the events in a passage of tonal music. This idea has been most influentially disseminated by Carol Krumhansl in her 1990 monograph Cognitive Foundations of Musical Pitch. Krumhansl hypothesized that this sense of the importance or centrality of certain tones of a key is learned through exposure to tonal music, in particular by learning the relative frequency of appearance of the various pitch classes in tonal passages. The correlation of pitch-class quantity and structural status has been the subject of a number of successful studies, leading to the general acceptance of the pitch-distributional account of tonal hierarchy in the field of music psychology. This study argues that the correlation of pitch-class quantity with structural status is a byproduct of other, more fundamental perceptual properties, all of which are derived from aspects of everyday listening. Individual chapters consider the phenomena of consonance and dissonance, intervallic rootedness, the short-term memory for pitch collection, and the interaction of temporal ordering and voice-leading that Jamshed Bharucha calls melodic anchoring. The study concludes with an elaborate self-experiment that observes the interaction of these v properties in a pool of 275 stimuli, each of which is constructed from a single dyad plus one subsequent tone. vi Acknowledgements This project is the result of a rather extended period of introspection and exploration, and I am grateful to the faculty of the CUNY Graduate Center for the generous patience, scholarly latitude and unflagging encouragement that allowed me to undertake such a journey. In particular I am deeply indebted to my advisors Philip Rupprecht and Joseph Straus, who have provided incisive feedback and moral support over the years. I would also like to express my gratitude for the many scholars who have done groundbreaking work in the area of music psychology and perceptually-oriented music theory over the last few decades – specific works by Albert Bregman, Christopher Hasty, David Huron, Ray Jackendoff, Carol Krumhansl, Fred Lerdahl, and David Lewin were particularly energizing and inspirational for me and I cannot imagine working in this field without these invaluable precedents. The influence of some of these figures on the current study will be rather obvious to an informed reader, and there are, of course, many other individuals who have contributed work that has proven essential to what follows. Finally I must thank my wonderful wife, Melissa Smey, for her love and support during this rather long and occasionally difficult process. I could not have completed this work without her, and I hope that it lays the foundation for a long and fruitful partnership in the field of music. vii Contents Abstract .............................................................................................................................. iv Acknowledgements ............................................................................................................ vi Multimedia and Computer Programs ................................................................................. ix List of Examples ................................................................................................................ x I. Introduction and Overview .............................................................................................. 1 General principles for a perceptual model of tonality ........................................... 2 Recent theories of the tonal hierarchy ................................................................... 5 Carol Krumhansl’s Cognitive Foundations of Musical Pitch .................... 7 Fred Lerdahl’s Tonal Pitch Space .............................................................. 17 Other suggestive precedents ...................................................................... 27 The overall approach .............................................................................................. 28 II. Vertical Relations, Part One: Consonance and Dissonance .......................................... 32 The overtone series ................................................................................................ 32 The overtone series and tonality – historical precedents ....................................... 34 Consonance and dissonance ................................................................................... 36 Is the triad the "most consonant" sonority? ........................................................... 44 Relative consonance as tonic-making .................................................................... 48 The problem of defining consonance ..................................................................... 49 III. Vertical Relations, Part Two: Intervallic Rootedness .................................................. 58 The residue pitch .................................................................................................... 59 A precedent: Hindemith’s Craft of Musical Composition ..................................... 63 First thesis: Applying Terhardt’s pitch-finding algorithm to rooted intervals ....... 65 Second thesis: Rootedness as "next-best" fit ......................................................... 69 Third thesis: Rootedness in pitch-class space ........................................................ 71 The acoustic root in context ................................................................................... 89 viii Non-tonic harmonies as a shift in perspective ....................................................... 95 The global significance of tonic tones ................................................................... 98 Can any sonority serve as the center of the tonal hierarchy? ................................. 100 IV. The Underlying Scale .................................................................................................. 102 Annabel Cohen's Well-Tempered Clavier experiment ........................................... 104 Pitch-location memory: The trace .......................................................................... 105 Scales consist of steps ............................................................................................ 113 The consecutive semitone constraint ..................................................................... 119 The "deep scale" property ...................................................................................... 122 The diatonic collection and consonance ................................................................ 124 Non-traditional scales and scalar perception: The Ondine experiment ................. 127 The scalar vs. chromatic distinction and musical experience ................................ 136 V. Simple Diachronic Relations ........................................................................................ 155 The hierarchical structure of a single tone ............................................................. 155 Two events ............................................................................................................. 160 Beginners’ advantage ............................................................................................. 163 Arpeggiations ......................................................................................................... 164 The power of voice leading and the finality effect ................................................ 167 VI. The Dyad Plus Monad Experiment .............................................................................. 176 Designing the experiment ...................................................................................... 181 Presenting the data ................................................................................................. 189 Findings..................................................................................................................
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