This paper explores the application of Bayesian probabilistic modeling to issues of music cognition and music theory. The main concern is with the problem of key-finding: the process of inferring the key from a pattern of notes. The Bayesian perspective leads to a simple, elegant, and highly effective model of this process; the same approach can also be extended to other aspects of music perception, such as metrical structure and melodic structure. Bayesian modeling also relates in interesting ways to a number of other musical issues, including musical tension, ambiguity, expectation, and the quantitative description of styles and stylistic differences.
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