A Unified Probabilistic Model for Polyphonic Music Analysis

Abstract

This article presents a probabilistic model of polyphonic music analysis. Taking a note pattern as input, the model combines three aspects of symbolic music analysis—metrical analysis, harmonic analysis, and stream segregation—into a single process, allowing it to capture the complex interactions between these structures. The model also yields an estimate of the probability of the note pattern itself; this has implications for the modelling of music transcription. I begin by describing the generative process that is assumed and the analytical process that is used to infer metrical, harmonic, and stream structures from a note pattern. I then present some tests of the model on metrical analysis and harmonic analysis, and discuss ongoing work to integrate the model into a transcription system.

Notes

¹The source code for the implementation of the model, which is written in C, can be downloaded at www.theory.esm.rochester.edu/temperley/melisma2.

²The analytical procedure presented here has much in common with the stream analysis model presented in Temperley (2001), and could (roughly speaking) be regarded as a probabilistic version of that model.

³Let us assume that the ‘correct’ model is the one in which the probabilities of all structures are raised by the same proportion to make up for the loss of mass in the way just suggested. The most probable structure will be the same one with or without this adjustment, as the probabilities of all structures are adjusted equally.

⁴For this purpose, any offset that occurs after tactus beat T_n and before or at beat T _n + 1 is assumed to occur at T _n + 1; following the logic of the generative model, we do not recognize offsets at non-tactus positions, unless the offset coincides with a note-onset.

⁵At the beginning of the piece, we allow the first tactus beat to be anywhere within a range of pips before and including the first note-onset, thus allowing that the first onset may not be on a tactus beat; at the end of the piece, similarly, we consider a range of possible positions for the last tactus.