Diatonic Voice-Leading Transformations

Abstract

Abstract This article draws on the mathematical approaches of Tymoczko (2011) and Hook (2008) to construct a transformational space of closed-position diatonic triads. The group acts on a set of twenty-one objects: the seven diatonic triads differentiated by the three closed-position inversions. After constructing the transformation group as an abstract voice-leading space, I interpret the system as an instrumental space (De Souza 2017) that captures the chord shapes required to play triadic progressions on a keyboard. This emphasis on the space’s ability to capture such chord shapes leads to generalizations of the system that explore interactions between voice leading and chord spacing using geometric and diatonic theory.