Beyond the Transition Matrix: A Language-Independent, String-Based Input Notation for Incomplete, Multiple-Order, Static Markov Transition Values

While Markov chain generators have been employed throughout the history of computer music as a tool for the creation of musical parameter values, input notations for Markov transition values are often cumbersome and opaque. Rejecting the transition matrix as an input notation, this paper offers a new language-independent, string-based input notation for incomplete, multiple-order, static Markov transition values. Transition values are given greater generality by accommodating multiple orders simultaneously, as well as the specification of transitions with the use of limited single-operator regular expressions. A complete Python implementation of this model is introduced, and high-level utilities and object interfaces are demonstrated in athenaCL.