Video on Human Mathematics

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
   

(Source: http://www.youtube.com/)