ABSTRACT
Musical events can often be classified into a finite or countable number of categories that occur in a temporal sequence. A natural question is then whether the transition between different categories can be characterized by probabilities. In particular, a successful model may be able to reproduce formally a listener’s expectation of “what happens next”, by giving appropriate conditional probabilities. Markov chains are simple models in discrete time that are defined by conditioning on the immediate past only. The theory of Markov chains is well developed and many beautiful results are available. More complicated, but very flexible, are hidden Markov processes. For these models, the probability distribution itself changes dynamically according to a Markov process. Many of the developments on hidden Markov models have been stimulated by problems in speech recognition. It is therefore not surprising that these models are also very useful for analyzing musical signals. Here, a very brief introduction to Markov chains and hidden Markov models is given. For an extended discussion see, for instance, Chung (1967), Isaacson and Madsen (1976), Kemey et al. (1976), Billingsley (1986), Elliott et al. (1995), MacDonald and Zucchini (1997), Norris (1998), Bremaud (1999).
