Visualizing and Interpreting Rhythmic Patterns Using Phase Space Plots

Abstract

Structure in musical rhythm can be measured using a number of analytical techniques. While some techniques—like circular statistics or grammar induction—rely on strong top-down assumptions, assumption-free techniques can only provide limited insights on higher-order rhythmic structure. I suggest that research in music perception and performance can benefit from systematically adopting phase space plots, a visualization technique originally developed in mathematical physics that overcomes the aforementioned limitations. By jointly plotting adjacent interonset intervals (IOI), the motivic rhythmic structure of musical phrases, if present, is visualized geometrically without making any a priori assumptions concerning isochrony, beat induction, or metrical hierarchies. I provide visual examples and describe how particular features of rhythmic patterns correspond to geometrical shapes in phase space plots. I argue that research on music perception and systematic musicology stands to benefit from this descriptive tool, particularly in comparative analyses of rhythm production. Phase space plots can be employed as an initial assumption-free diagnostic to find higher order structures (i.e., beyond distributional regularities) before proceeding to more specific, theory-driven analyses.