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arXiv · 2007.03134

A group-theoretical classification of three-tone and four-tone harmonic chords

Jason K. C. Polak
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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.

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Jason K. C. Polak. 2020-07-06. A group-theoretical classification of three-tone and four-tone harmonic chords. https://arxiv.org/abs/2007.03134

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