Using fundamental groups and groupoids of chord spaces to model voice leading

James J. Hughes

pp. 267-278

in: Tom Collins, David Mérédith, Anja Volk (eds), Mathematics and computation in music, Berlin, Springer, 2015

Abstract

We model voice leading using tools from algebraic topology, principally the fundamental group, the orbifold fundamental group, and related groupoids. Doing so is a natural extension of modeling voice leading by continuous paths in chord spaces. The resulting algebraic precision in the representation of voice leadings and their concatenations allows for new distinctions between voice crossing cases, and enhanced connections with other approaches to voice leading.