Markov-Switching State Space Models for Uncovering Musical Interpretation

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—forty-six 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 musical tempo by examining the inter-onset 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.

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About Daniel J. McDonald

Daniel is Associate Professor of Statistics at the University of British Columbia in Vancouver. Before moving North, Daniel spent 8 years on the faculty at Indiana University, Bloomington. His research interests involve the estimation and quantification of prediction risk, especially developing methods for evaluating the predictive abilities of complex dependent data. This includes the application of statistical learning techniques to time series prediction problems in the context of economic forecasting, as well as investigations of cross-validation and the bootstrap for risk estimation.

Daniel did his undergraduate studies at Indiana University where he received two bachelor’s degrees: a Bachelor of Science in Music with a concentration in cello performance from the Jacobs School of Music and a Bachelor of Arts in economics and mathematics. Prior to graduate school, he worked as a Research Associate at the Federal Reserve Bank of St. Louis. He received his Ph.D. from Carnegie Mellon University in statistics where he was named graduate student of the year for 2012 and received the Umesh Gavasakar Memorial Thesis Award for his dissertation “Generalization Error Bounds for State Space Models.” In 2017, he was a recipient of the Indiana University Trustees Teaching Award. In 2018, he received an NSF CAREER award. His work has also been supported by grants from the Institute for New Economic Thinking, the Canadian Statistical Sciences Institute, and the National Sciences and Engineering Research Council of Canada.

Since the beginning of the COVID-19 pandemic, much of Daniel’s applied work has focused on methods for understanding and modelling epidemiological data. He is a core member of the BC COVID-19 Modelling Group and works on research, forecasting, nowcasting, and software development with Carnegie Mellon University’s Delphi Research Group.