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Comment by resource0x | Hacker News Reader

Only tangentially related, but it's fascinating how number 12 emerges in music naturally. And the fact that 12 has many divisors is a big coincidence without which Western music as we know it would be impossible. I have a short write-up on this: https://github.com/resource0x/concert0x/blob/master/doodle-s...

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To the best of my knowledge the divisibility of 12 is rarely used in music. Most chords consist use several different intervals.

The popularity of pentatonic music also suggests divisibility isn't unmissable.

It's very important in jazz. Diminished scale is all over. Augmented scale, too (e.g T. Monk's tunes). Tritone substitution is the basis of reharmonization (due to 12=6*2). Jazz uses everything (including pentatonic), that's why it's so rich.

So rich, and sounds like a racket.

Also: http://www.math.uwaterloo.ca/~mrubinst/tuning/12.html

Why do the divisors of 12 matter in music? I'm not aware of anything using the divisors of 12.

12 is mainly important in music because the (3/2)^12 is a power of 2. We divide up the octave into fractions of frequencies, not multiple os steps (a.k.a. fractions of number-of-steps-per-octave). The harmonious way of stepping through the 12 notes is in steps of size [2,2,1,2,2,2,1], which is importantly not by divisors of 12. (Stepping strictly in any arithmetic progression hits at least one low-harmony tone and misses high-harmony tones.).

Stepping in the sequence [2,2,1,2,2,2,1] leads to frequency ratios in these low-complexity (==harmonious) fractions: [1 9/8 5/4 4/3 3/2 5/3 15/8 2]

divisibility by 3 is important because it leads to diminished scale, and it serves as a universal glue. Divisibility by 4 is important because it leads to augmented scale. (This is not all) This all sounds vague without piano demonstration anyway, sorry.

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