by Dmitri Tymoczko

 A musical chord can be represented as a point in an orbifold. (An orbifold is a quotient manifold.)

Line segments join 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.

(via Artemy Kolchinsky)

book

149 notes

  1. clazzjassicalrockhop reblogged this from isomorphismes
  2. coffeenomics reblogged this from isomorphismes
  3. icaruscalling reblogged this from gusbritish and added:
    gusbritish is such a great blog/person
  4. gusbritish reblogged this from isomorphismes
  5. mohamed-ali-said reblogged this from isomorphismes
  6. frozenpride-old reblogged this from proofmathisbeautiful
  7. jubejoo reblogged this from proofmathisbeautiful
  8. nerdyfemmefatale reblogged this from isomorphismes and added:
    hoshit using this for science horizons
  9. alexlovesclay reblogged this from proofmathisbeautiful
  10. heabuh reblogged this from proofmathisbeautiful
  11. snowbubble reblogged this from anghella and added:
    Random fact #43829742: I am so incredibly jealous of music nerds. I can understand math and physics and obscure ass...
  12. iodizedsalt reblogged this from proofmathisbeautiful and added:
    Absolutely, utterly beautiful.
  13. toasttous reblogged this from isomorphismes
  14. triboluminiscencia reblogged this from proofmathisbeautiful
  15. applied-utility-knives reblogged this from cab1729
  16. minerva122 reblogged this from proofmathisbeautiful
  17. musicalmusing reblogged this from proofmathisbeautiful and added:
    Tweet
  18. innyouty reblogged this from proofmathisbeautiful
  19. objectsareevents reblogged this from proofmathisbeautiful
  20. diegueus9 reblogged this from proofmathisbeautiful
  21. orekane reblogged this from proofmathisbeautiful
  22. vwlsrmprtnt reblogged this from proofmathisbeautiful
  23. bakzamgai reblogged this from proofmathisbeautiful and added:
    Wow I want to understand this.