A group-theoretical classification of three-tone and four-tone harmonic chords
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- July 2020
- DOI:
- 10.48550/arXiv.2007.03134
- arXiv:
- arXiv:2007.03134
- Bibcode:
- 2020arXiv200703134P
- Keywords:
-
- Mathematics - Group Theory
- E-Print:
- 8 pages, comments welcome