A group-theoretical classification of three-tone and four-tone harmonic chords
Group Theory
2020-07-08 v1
Abstract
We classify three-tone and four-tone chords based on subgroups of the symmetric group acting on chords contained within a twelve-tone scale. The actions are inversion, major-minor duality, and augmented-diminished duality. These actions correspond to elements of symmetric groups, and also correspond directly to intuitive concepts in the harmony theory of music. We produce a graph of how these actions relate different seventh chords that suggests a concept of distance in the theory of harmony.
Keywords
Cite
@article{arxiv.2007.03134,
title = {A group-theoretical classification of three-tone and four-tone harmonic chords},
author = {Jason K. C. Polak},
journal= {arXiv preprint arXiv:2007.03134},
year = {2020}
}
Comments
8 pages, comments welcome