Beats that Commute: Algebraic and Kinesthetic Models for Math-Rock Grooves - Brad Osborn (Gamut: Online Journal of the Music Theory Society of the Mid-Atlantic, 2012)
Math rock’s most salient compositional facet is its cyclical repetition of grooves featuring changing and odd-cardinality meter. These unconventional grooves deform the conventional rhythmic structures of rock, such as backbeat and steady pulse, in such a way that a listener’s sense of metric organization is initially thwarted. Using transcriptions from math-rock artists such as Radiohead, The Mars Volta, and The Chariot, the author demonstrates a new analytical apparatus aimed at making sense of the ways listeners and performers process these changing pulse levels: the pivot pulse. The pivot pulse is defined as the slowest temporal level preserved in a given meter change. The author suggests that the preservation or disruption of the primary pulse level (that is, the temporal level at which a listener’s or performer’s primary kinesthetic involvement happens, such as dancing or foot-tapping) is of paramount importance. For example, a change from 4/4 to 3/4, which preserves the quarter-note pulse, will be less disruptive to a listener’s metric entrainment than a change from 4/4 to 7/8 or 7/8 to 15/16, both of which split the primary pulse in half. In order to formalize pivot-pulse methodology, the author presents an algebraic model based on the commutative operations greatest common denominator and lowest common multiple. Pivot-pulse methodology is also applied metaphorically to the kinesthetic interpretations of performers and listeners to better understand the complex movements incited by math-rock grooves.