The Markov Process as a Compositional Model: A Survey and Tutorial

The author combines a survey of Markov-based efforts in automated composition with a tutorial demonstrating how various theoretical properties associated with Markov processes can be put to practical use. The historical background is traced from A. A. Markov’s original formulation through to the present. A digression into Markov-chain theory introduces ‘waiting counts’ and ‘stationary probabilities’. The author’s Demonstration 4 for solo clarinet illustrates how these properties affect the behavior of a melody composed using Markov chains. This simple example becomes a point of departure for increasingly general interpretations of the Markov process. The interpretation of ‘states’ is reevaluated in the light of recent musical efforts that employ Markov chains of higher-level objects and in the light of other efforts that incorporate relative attributes into the possible interpretations. Other efforts expand Markov’s original definition to embrace ‘Nth-order’ transitions, evolving transition matrices and chains of chains. The remainder of this article contrasts Markov processes with alternative compositional strategies.