A Vocabulary-Free Infinity-Gram Model for Nonparametric Bayesian Chord Progression Analysis

This paper presents probabilistic n-gram models for symbolic chord sequences. To overcome the fundamental limitations in conventional models—that the model optimality is not guaranteed, that the value of n is fixed uniquely, and that a vocabulary of chord types (e.g., major, minor, · · · ) is defined in an arbitrary way—we propose a vocabulary-free infinity-gram model based on Bayesian nonparametrics. It accepts any combinations of notes as chord types and allows each chord appearing in a sequence to have an unbounded and variable-length context. All possibilities of n are taken into account when calculating the predictive probability of a next chord given a particular context, and when an unseen chord type emerges we can avoid out-of-vocabulary error by adaptively evaluating the 0-gram probability, i.e., the combinatorial probability of note components. Our experiments using Beatles songs showed that the predictive performance of the proposed model is better than that of the state-of-theart models and that we could find stochastically-coherent chord patterns by sorting variable-length n-grams in a line according to their generative probabilities.