Chord Proximity, Parsimony, and Analysis with Filtered Point-Symmetry

Abstract

Filtered Point-Symmetry (FiPS) is a tool for modeling relationships between iterated maximally even sets. Common musical relationships can be studied by using FiPS to model chords contained within a specific scalar context (such as C major or the 01-octatonic collection), and by capturing those relationships in a FiPS configuration space. In this work, many FiPS configuration spaces are presented; some are isomorphic to commonly referenced voice-leading spaces like the neo-Riemannian Tonnetz, and others show tonal networks that have not previously been explored. A displacement operation is introduced to codify the traversal of a configuration space, and a short music analysis is provided to demonstrate some benefits of the approach.