A Generalized Parsing Framework for Generative Models of Harmonic Syntax
Daniel Harasim, Martin Rohrmeier, Timothy J. O’Donnell · Zenodo (CERN European Organization for Nuclear Research) · 2018
Modeling the structure of musical pieces constitutes a central research problem for music information retrieval, music generation, and musicology. At the present, models of harmonic syntax face challenges on the tasks of detecting local and higher-level modulations (most previous models assume a priori knowledge of key), computing connected parse trees for long sequences, and parsing sequences that do not end with tonic chords, but in turnarounds. This paper addresses those problems by proposing a new generative formalism Probabilistic Abstract Context-Free Grammars (PACFGs) to address these issues, and presents variants of standard parsing algorithms that efficiently enumerate all possible parses of long chord sequences and to estimate their probabilities. PACFGs specifically allow for structured non-terminal symbols in rich and highly flexible feature spaces. The inference procedure moreover takes advantage of these abstractions by sharing probability mass between grammar rules over joint features. The paper presents a model of the harmonic syntax of Jazz using this formalism together with stochastic variational inference to learn the probabilistic parameters of a grammar from a corpus of Jazz-standards. The PACFG model outperforms the standard context-free approach while reducing the number of free parameters and performing key finding on the fly.