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Using fundamental groups and groupoids of chord spaces to model voice leading
pp. 267-278
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
Published in:
Collins Tom, Meredith David, Volk Anja (2015) Mathematics and computation in music: 5th international conference, MCM 2015, London, UK, June 22-25, 2015. Dordrecht, Springer.
Pages: 267-278
DOI: 10.1007/978-3-319-20603-5_28
Full citation:
Hughes James J. (2015) „Using fundamental groups and groupoids of chord spaces to model voice leading“, In: T. Collins, D. Meredith & A. Volk (eds.), Mathematics and computation in music, Dordrecht, Springer, 267–278.