Generative statistical models of chord sequences play crucial roles in music processing. To capture syntactic similarities among certain chords (e.g. in C major key, between G and G7 and between F and Dm), we study hidden Markov models and probabilistic context-free grammar models with latent variables describing syntactic categories of chord symbols and their unsupervised learning techniques for inducing the latent grammar from data. Surprisingly, we find that these models often outperform conventional Markov models in predictive power, and the self-emergent categories often correspond to traditional harmonic functions. This implies the need for chord categories in harmony models from the informatics perspective.
In Ref. @cite_0 , unsupervised learning was applied to a variant of PCFG models for chord symbols in which nonterminals describe harmonic functions. In this study, the nonterminals and the production rules were manually determined in accordance with existing data of harmony analysis and only the probabilities were learned unsupervisedly. Our PCFG models can be considered as extensions of this model as we allow larger numbers of nonterminals and they have no prior labels or restricted production rules.
@cite_0
2550442014
While there is a growing body of work proposing grammars for music, there is little work testing analytical grammars in a generative setting. We explore the process of learning production probabilities for musical grammars from musical corpora and test the results using Kulitta, a recently developed framework for automated composition. To do this, we extend a well-known algorithm for learning production probabilities for context-free grammars (CFGs) to support various musical CFGs as well as an additional category of grammars called probabilistic temporal graph grammars.