Markov-switching state space models for uncovering musical interpretation
Daniel J. McDonald, Michael McBride, Yupeng Gu, Christopher Raphael
The Annals of Applied Statistics · 2021 · Volume 15 · Issue 3
Abstract
For concertgoers, musical interpretation is the most important factor in determining whether or not we enjoy a classical performance. Every performance includes mistakes—intonation issues, a lost note, an unpleasant sound—but these are all easily forgotten (or unnoticed) when a performer engages her audience, imbuing a piece with novel emotional content beyond the vague instructions inscribed on the printed page. In this research we use data from the CHARM Mazurka Project—46 professional recordings of Chopin’s Mazurka Op. 68 No. 3 by consummate artists—with the goal of elucidating musically interpretable performance decisions. We focus specifically on each performer’s use of tempo by examining the interonset intervals of the note attacks in the recording. To explain these tempo decisions, we develop a switching state space model and estimate it by maximum likelihood, combined with prior information gained from music theory and performance practice. We use the estimated parameters to quantitatively describe individual performance decisions and compare recordings. These comparisons suggest methods for informing music instruction, discovering listening preferences and analyzing performances.
Keywords
Classification and clustering, Hidden Markov model, Kalman filter
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