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(2015) Mathematics and computation in music, Dordrecht, Springer.
Using fundamental groups and groupoids of chord spaces to model voice leading
James J. Hughes
pp. 267-278
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
DOI: 10.1007/978-3-319-20603-5_28
Full citation:
Hughes, J. 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, pp. 267-278.
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