Corpus ID: 220381542

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

@inproceedings{Polak2020AGC,
  title={A group-theoretical classification of three-tone and four-tone harmonic chords},
  author={Jason K.C. Pol'ak},
  year={2020}
}
  • Jason K.C. Pol'ak
  • Published 2020
  • Mathematics
  • 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, majorminor 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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