The Geometry of Musical Chords

@article{Tymoczko2006TheGO,
  title={The Geometry of Musical Chords},
  author={Dmitri Tymoczko},
  journal={Science},
  year={2006},
  volume={313},
  pages={72 - 74}
}
A musical chord can be represented as a point in a geometrical space called an orbifold. Line segments represent mappings from the notes of one chord to those of another. Composers in a wide range of styles have exploited the non-Euclidean geometry of these spaces, typically by using short line segments between structurally similar chords. Such line segments exist only when chords are nearly symmetrical under translation, reflection, or permutation. Paradigmatically consonant and dissonant… 
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