Tree-structured probabilistic model of monophonic written music based on the generative theory of tonal music

Abstract

This paper presents a probabilistic formulation of music language modelling based on the generative theory of tonal music (GTTM) named probabilistic GTTM (PGTTM). GTTM is a well-known music theory that describes the tree structure of written music in analogy with the phrase structure grammar of natural language. To develop a computational music language model incorporating GTTM and a machine-learning framework for data-driven music grammar induction, we construct a generative model of monophonic music based on probabilistic context-free grammar, in which the time-span tree proposed in GTTM corresponds to the parse tree. Applying the techniques of natural language processing, we also derive supervised and unsupervised learning algorithms based on the maximal-likelihood estimation, and a Bayesian inference algorithm based on the Gibbs sampling. Despite the conceptual simplicity of the model, we found that the model automatically acquires music grammar from data and reproduces time-span trees of written music as accurately as an analyser that required elaborate manual parameter tuning.