#orbifold

[imfbsl]

Animated slices of the three-dimensional orbifold T3/S3

(from wikipedia)

[hensa]

What tumblr theme do you use? I love how organized the sidebar is!

http://themes.dronz.co/post/116070752672/theme-08-install-another-clean-and-superThis one here, I just use a little html linking with my own images for a navsidebar

[isomorphismes]

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