A Calculus of Accent

Author: Roeder, John

Publication details: Journal of Music Theory 39, no. 1 (Spring, 1995): 1-46

Weblink: http://www.jstor.org

Abstract: Writings by Wallace Berry and William Benjamin describe musical accent not simply as the momentary emphasis of a time-point in relation to its context, but as the “the intensity peak of a shaped pattern of activity,” and “a point from which reactive events recede and toward which preparatory events incline.” It follows that our perception of the weight of an accent-which bears crucially on analysis-depends both upon its musical context and upon what moment we are at in the piece. This paper formalizes the concept of accents of climax in a model of musical streams related formally to the constructs of Tenney and Lewin. The algebraic definition of accent in this model does not correspond to traditional notions of pitch or durational accent, but it precisely captures the “peaking” process that Berry and Benjamin discuss. It specifies the weight of an accent within a given musical stream, and quantifies how our evaluation of an accent varies over time. The discrete version of the theory is applied to excerpts from works by Berio, Carter, Bartók, and Schoenberg. It reveals patterns of increasing or decreasing weight which establish a direction, or progression, independent of “a priori” pitch-structural functions. It also uncovers similarities of accentual pattern which help to associate different timepoints in a composition, that is, to create musical form. The algebraic expressions of the theory generalize naturally using the differential calculus to describe the formation of accent when pitch, dynamics, or other musical properties are changing continuously, as in some electroacoustic music. This continuous version of the theory is applied in analyses of Xenakis’s “Diamorphoses II” and Carter’s Woodwind Etude No. 7.