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Publication details

Publisher: Springer

Place: Berlin

Year: 2015

Pages: 267-278

Series: Lecture Notes in Computer Science

ISBN (Hardback): 9783319206028

Full citation:

James J. Hughes, "Using fundamental groups and groupoids of chord spaces to model voice leading", in: Mathematics and computation in music, Berlin, Springer, 2015

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.

Publication details

Publisher: Springer

Place: Berlin

Year: 2015

Pages: 267-278

Series: Lecture Notes in Computer Science

ISBN (Hardback): 9783319206028

Full citation:

James J. Hughes, "Using fundamental groups and groupoids of chord spaces to model voice leading", in: Mathematics and computation in music, Berlin, Springer, 2015