**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