Review of David Temperley,Music and Probability(MIT Press, 2007)

Abstract

[1] In Music and Probability, David Temperley presents a meaningful analysis of the cognitive resources implied in music perception, providing a sound and coherent series of models based on a probabilistic perspective.[2] Cognitive sciences aim at understanding how our minds-and perhaps even artificial ones-are able to combine information about the external world with internal mental representations, in order to perform certain actions and achieve specific goals. Cognition gives us a more or less realistic, accurate perspective of the existence and behavior of the outside world. By processing this information we are able to plan our actions, solve problems, and obtain desired results (Von Eckardt 1993).[3] Originally, cognitive sciences employed a symbolic approach. According to this paradigm, minds are viewed as symbolic processors, and syntactic rules-rules that correlate with the form of information only, not its contents-were enough in principle to represent knowledge and the way humans think and solve problems (Gardner 1985). Since computers were particularly well suited to perform syntactic analysis, it seemed conceivable that one could turn them into cognitive agents (Turing 1950).[4] Due to its formal structure, music was one of the early targets in cognitive research. Several researchers and experimental musicians were convinced that music could be analyzed mathematically as some sort of code, and could therefore be artificially generated (Meyer 1967). Avant-garde artists dreamed of ensembles of humans and computers improvising in jam sessions. Those interested in cognitive processes and music believed we could understand those processes better by assimilating them into the way computers and humans processed syntax (Jackendoff 1983).[5] When this paradigm proved to be too limiting (Dreyfus 1992, Varela 1991), emphasis was directed towards statistical and probabilistic approaches, the same as in Music and Probability. The older models, however, were black box approaches to mathematical generation of music. There was no attempt to give any psychological reality to models, despite the fact that this has been one of the main aims of the cognitive sciences since their inception (Johnson-Laird 1983).[6] Much of this earlier research mirrored cognitive science's understanding of neural networks at the time (Rumelhart 1989). Neural networks were trained to recognize certain patterns and structures, and they did astonishing things that symbolic AI (Artificial Intelligence) could not. For example, they could recognize faces and speech, and they could play backgammon better than humans. Yet cognitive scientists could not explain how these networks worked. They found it very difficult to extract useful information, which would help them to better understand how humans perceive or generate music. An early appreciation of such difficulties within a probabilistic study of music can be found in Cohen (1962).[7] Early statistical and probabilistic approaches only showed that, when humans recognize a musical passage, some sort of statistical process occurred in their neurons. Although the process was thought to be equivalent in some sense to that of neural networks, it was impossible to develop an algorithm that could predict what the cognitive processes would be like. This is a general problem that most probabilistic and neural networks models share, as stated in Clark (1989).[8] Music and Probability is different from earlier probabilistic studies of music cognition. Temperley clearly understands mathematics, music, and cognitive sciences, and he successfully and convincingly combines them in his book. He leads the reader into a deeper interaction with cognitive processes. The reader learns how the brain uses the mathematical nature of music to perceive and create music.Music and Probability? Main Contents[9] This book serves as an introductory and systematic course on the probabilistic analysis of music, and on how to use that approach in music theory as well as in the cognitive sciences. …