Music and Probability

by Temperley, David

• ISBN13: 9780262515191
• ISBN10: 0262515199
• Format: Paperback
• Copyright: 2010-08-13
• Publisher: The MIT Press

Summary

In Music and Probability, David Temperley explores issues in music perception and cognition from a probabilistic perspective. The application of probabilistic ideas to music has been pursued only sporadically over the past four decades, but the time is ripe, Temperley argues, for a reconsideration of how probabilities shape music perception and even music itself. Recent advances in the application of probability theory to other domains of cognitive modeling, coupled with new evidence and theoretical insights about the working of the musical mind, have laid the groundwork for more fruitful investigations. Temperley proposes computational models for two basic cognitive processes, the perception of key and the perception of meter, using techniques of Bayesian probabilistic modeling. Drawing on his own research and surveying recent work by others, Temperley explores a range of further issues in music and probability, including transcription, phrase perception, pattern perception, harmony, improvisation, and musical styles. Music and Probability--the first full-length book to explore the application of probabilistic techniques to musical issues--includes a concise survey of probability theory, with simple examples and a discussion of its application in other domains. Temperley relies most heavily on a Bayesian approach, which not only allows him to model the perception of meter and tonality but also sheds light on such perceptual processes as error detection, expectation, and pitch identification. Bayesian techniques also provide insights into such subtle and advanced issues as musical ambiguity, tension, and "grammaticality," and lead to interesting and novel predictions about compositional practice and differences between musical styles.

Author Biography

David Temperley is Associate Professor of Music Theory at the Eastman School of Music, University of Rochester, and the author of The Cognition of Basic Musical Structures (MIT Press, 2001).

Table of Contents

Preface	p. ix
Introduction	p. 1
Probabilistic Foundations and Background	p. 7
Elementary Probability	p. 7
Conditional Probability and BayesÆ Rule	p. 8
Other Probabilistic Concepts	p. 14
Early Work on Music and Probability	p. 19
Melody I: The Rhythm Model	p. 23
Rhythm and Meter	p. 23
Previous Models of Meter Perception	p. 26
A Probabilistic Rhythm Model	p. 30
The Generative Process	p. 31
The Meter-Finding Process	p. 36
Testing the Model on Meter-Finding	p. 41
Problems and Possible Improvements	p. 43
Melody II: The Pitch Model	p. 49
Previous Models of Key-Finding	p. 50
The Pitch Model	p. 56
Testing the Model on Key-Finding	p. 62
Melody III: Expectation and Error Detection	p. 65
Calculating the Probability of a Melodic Surface	p. 65
Pitch Expectation	p. 66
Rhythmic Expectation	p. 71
Error Detection	p. 74
Further Issues	p. 76
A Polyphonic Key-Finding Model	p. 79
A Pitch-Class-Set Approach to Key-Finding	p. 79
The Generative Process	p. 83
The Key-Finding Process	p. 85
Comparing Distributional Models of Key-Finding	p. 89
Further Issues in Key-Finding	p. 92
Applications of the Polyphonic Key-Finding Model	p. 99
Key Relations	p. 99
Tonalness	p. 108
Tonal Ambiguity and Clarity	p. 116
Another Look at Major and Minor	p. 121
Ambiguous Pitch-Collections in Common-Practice Music	p. 125
Explaining Common Strategies of Tonal Harmony	p. 131
Bayesian Models of Other Aspects of Music	p. 139
Probabilistic Transcription Models	p. 139
Bod: The Perception of Phrase Structure	p. 143
Raphael and Stoddard: Harmonic Analysis	p. 147
Mavromatis: Modeling Greek Chant Improvisation	p. 151
Saffran et al.: Statistical Learning of Melodic Patterns	p. 156
Style and Composition	p. 159
Some Simple Cross-Entropy Experiments	p. 161
Modeling Stylistic Differences	p. 166
Testing Schenkerian Theory	p. 172
Communicative Pressure	p. 181
Communicative Pressure in Rules of Voice-Leading	p. 182
The Syncopation-Rubato Trade-Off	p. 184
Other Examples of Communicative Pressure in Rhythm	p. 191
öTrading Relationshipsö	p. 197
Low-Probability Events in Constrained Contexts	p. 202
Conclusions	p. 205
Notes	p. 209
References	p. 225
Author Index	p. 237
Subject Index	p. 241
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