The Perception of Rhythm in Non-Tonal Music: Rhythmic Contours in the Music of Edgard Varèse

Abstract

This paper develops a theory that models nonbeat-based rhythms as “rhythmic contours” of relative longs and shorts, drawing upon discussions of temporal spaces appearing in recent work of Robert Morris and David Lewin and upon various music-psychological investigations of rhythmic perception. A new type of temporal space is proposed: a duration space (d-space) analogous to Morris's contour space, in which elements are ordered sequentially from short to long. After developing equivalence relations for d-space segments, illustrated by excerpts from Edgard Varèse's Octandre, the paper concludes with an analysis of Density 21.5 that focuses upon relationships among rhythmic contours.