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 n voices (Tn/Sn). 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.
CITATION STYLE
Callender, C. (2015). Geometry, iterated quantization and filtered voice-leading spaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9110, pp. 257–266). Springer Verlag. https://doi.org/10.1007/978-3-319-20603-5_27
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