Metodo

International Studies in Phenomenology and Philosophy

Series | Book | Chapter

226959

Geometry, iterated quantization and filtered voice-leading spaces

Clifton Callender

pp. 257-266

Abstract

A recent special issue of the Journal of Mathematics and Music on mathematical theories of voice leading focused on the intersections of geometrical voice-leading spaces (GVLS), filtered point-symmetry (FiPS) and iterated quantization, and signature transformations. In this paper I put forth a theoretical model that unifies all of these approaches. Beginning with the basic configuration of FiPS, allowing the n points of a filter or beacon to vary arbitrarily yields the continuous chord space of class="EmphasisTypeItalic ">n voices ((T^n/S_n)). Each point in the filter space induces a quantization or Voronoi diagram on the beacon space. The complete space of filter and beacon is a singular fiber bundle, combining the power and generalization of GVLS with the central FiPS insight of iterated filtering by harmonic context. Additionally, any of the sixteen types of generalized voice-leading spaces described by Callender, Quinn, and Tymoczko can be used as filters/beacons to model different contexts.

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: 257-266

DOI: 10.1007/978-3-319-20603-5_27

Full citation:

Callender Clifton (2015) „Geometry, iterated quantization and filtered voice-leading spaces“, In: T. Collins, D. Meredith & A. Volk (eds.), Mathematics and computation in music, Dordrecht, Springer, 257–266.