Dmitri Tymoczko — author of The Geometry of Music

  • how to make visual representations of music
  • (in paintings, video games, sculpture)
  • 5 constraints on a composition that are necessary (but not sufficient) for it to sound good
  • global statistical properties of songs
  • why 20th century classical music had little audience
  • a random painting is much less offensive to the eye than random notes are to the ear
  • “I came up with these 5 principles using my brain, which is a kind of crude statistical device”
  • the piano is essentially a line
  • [NB: linear ⊃ monotonic ⊃ totally ordered]
  • violin/voice musicians know that notes ⊂ continuous space, but the piano does us a favour by constraining us to a subset of those notes
  • line mod 13 = circle
  • (equivalence classes of octaves — A1=A2=A9 and E4=E7=E12 etc.)
  • directed segments, unordered tuples
  • musical translation = mathematical transposition, musical inversion = mathematical rotation
  • The fact that most people don’t have most perfect pitch (things sound the same in different keys) may be so that we can understand that, despite pitch differences in male/female adults’ speech and children’s speech, they are saying the same words.
  • “It’s as if we couldn’t tell the difference between red and blue, but we were highly sensitive to the-difference-between-red-and-orange and the-difference-between-blue-and-green.
  • [Also: this.]
  • Minor vs major is the other isometry of the circle (besides rotation): reflection.
  • “Harmonic progression is like zone defence”
  • Minute 26: Awesome. Watch how to move around in 2-chord space — seen on a circle and on Tymoczko’s grid
     
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