Music and Probability

by David Temperley

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.

Genres: Music, Mathematics, Reference

256 pages, Hardcover

First published December 15, 2006

Reviews

[AJ Kerrigan · Rating 4 out of 5]

David Temperley explores applications of probabilistic models to music, including:

* Music analysis: Identifying rhythm, melody and key
* Composition: How probabilistic analysis can help explain or inform composition style
* Perception: Using insights from computational models to better understand how our brains perceive music

Overall this was a good read covering a lot of ground. I found some sections pretty dry and some absolutely fascinating. Some of my favorite passages come near the end of the book, in the "Style and Composition" and "Communicative Pressure" chapters.

"Thus successful musical communication depends on shared knowledge about the style. I will argue here, however, that it depends also on the nature of the style itself."

"The function of any communication system, linguistic or musical, is to convey certain types of information: for example, syntactic relations in the case of language. If the source of this information is lost (e.g., case endings in Middle English), some other means must be found of conveying it (fixed word order).

Another causal pattern may occur as well: if a kind of information, already present in the language in one form, is introduced in another form as well, the initial form of the information becomes redundant and may drop out."

The discussion of "trading relationships" reminded me of tradeoffs in computer programming choices (such as static vs. dynamic typing).

[Mehmet · Rating 5 out of 5]

What a wonderful book! It brings together two of my greatest loves. And does a really good job of explaining why they are related.

[Plamen · Rating 4 out of 5]

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.

### Review

"Temperley has made a seminal contribution to the emerging fields of empirical and cognitive musicology. Probabilistic reasoning provides the glue that attaches theory to data. Temperley, an accomplished and imaginative music theorist, knows the data of music to which he lucidly applies probabilistic modeling techniques. The emphasis is on Bayesian methods and the result is a firm empirical grounding for music theory."--David Wessel, Professor of Music, University of California, Berkeley

"As he did in *The Cognition of Basic Musical Structures*, Temperley here challenges the frontiers of the definition of music theory and cognition." **J. Rubin ** *Choice*

### About the Author

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).

[Eric · Rating 3 out of 5]

Ultimately I had higher hopes for this book, which would be best utilized by either someone writing music analysis software (for, say, a Pandora-like application) or someone interested in the current state of the same.

The tantalizing prospect is that the analyses that Mr. Temperley conducts could say a lot about music composition that traditional analysis does not. So, for example, even studying Hindemith you might find yourself wondering how chromaticism evolved from Beethoven to Brahms to the Beatles to Bratmobile. There is a gulf between theory (or 'analysis') and practice. The author only takes the first tentative steps in this direction, posing the questions as to whether the methodology might shine some light on Schenkerian theory and why jazz infrequently inverts chords.

To my taste, this feels like it should be the first volume in a multi-volume set. Now that there is a methodology, let's see some informed speculation... that makes for good reading.

[Scott Miles · Rating 4 out of 5]

Temperley presents a pretty strong case for his Bayesian probabilistic approach to the modeling of music perception, cognition, and composition. This field is ripe, and Temperley has tilled the soil of it here.