A Geometric Framework for Analyzing Drum Groove: Coupled Timing-Amplitude Vector Representations

Abstract

Musicians and listeners alike experience the rhythmic quality "groove." Often described as "the subjective experience of wanting to move rhythmically when listening to music," the phenomenon continues to resist precise definition. Prior research has found long-range temporal correlations in drum performances, and inspires a complimentary question: What quanitifiable short-range patterns in timing and amplitude give drum performances their characteristic feel? This research proposes a framework for analyzing groove by representing each drum hit as a two dimensional vector that couples timing deviation with amplitude. While previous studies treat these dimensions independently, this approach enables geometric analysis of how drummers navigate timing-amplitude space from hit to hit. The central hypothesis is that groove may be characterized by measureable patterns that exist within microtiming deviations, that these patterns are present in remarkably brief periods of music, and that timing deviations cannot be meaningfully analyzed in isolation from their associated amplitudes.