Temperley's Models

PROBABILITY theory and Bayesian reasoning have been used widely and successfully for modelling perception and cognition in recent times (e.g. Chater et al., 2006, and Chater and Manning, 2006) but, for some reason, application of these approaches in musical research has been rather sporadic, even though many scholars since Leonard Meyer (1957) have noted that many concepts in music might lend themselves naturally to a formulation in probability theory. So, David Temperley is right to say, in the introduction to his new book, that “the time is ripe, then, for a reconsideration of music and probability” (p. 1). With Music and Probability, Temperley sets out to fulfill two main tasks: to give an introduction to Bayesian reasoning and probabilistic models; and to present actual research that demonstrates the strengths of this approach when employed for modelling musical phenomena. For the latter, the book not only covers his own probabilistic models but also summarises very concisely and thoroughly related work by other researchers (this is one of his strengths as a writer). At the very beginning, three basic principles are proposed: that “perception is an inferential, multileveled, uncertain process”; that “our knowledge of probabilities comes, in large part, from regularities in the environment”; and that “producers of communication are sensitive to, and affected by, its probabilistic nature” (p. 3). These axiomatic statements provide the motivation for Temperley’s engagement with probabilistic models, and lead into an introduction to probability theory sufficient to provide an intuitive understanding of the concepts required to understand later material. Conditional probability is introduced and followed through to Bayes’ rule, used throughout in the book, most often in the form: