Analysing musical performance through functional data analysis: rhythmic structure in Schumann's Träumerei

Functional Data Analysis is a relatively new branch of Statistics devoted to describing and modelling data that are complete functions. Many relevant aspects of musical performance and perception can be understood and quantified as dynamic processes evolving as functions of time. In this paper, we show that Functional Data Analysis is a statistical methodology well-suited for research into the field of quantitative musical performance analysis. To demonstrate this suitability, we consider tempo data for 28 performances of Schumann’s Träumerei and analyse them by means of functional principal component analysis (one of the most powerful descriptive tools included in Functional Data Analysis). Specifically, we investigate the commonalities and differences between different performances regarding (expressive) timing, and we cluster similar performances together. We conclude that musical data considered as functional data reveals performance structures that otherwise might go unnoticed.