3 ms·

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 w

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-script.md#chromatic-scale https://github.com/resource0x/concert0x/blob/master/doodle-s...

contravariant 8y ago
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.
- deleted 8y ago
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- resource0x 8y ago
  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.
  - hessenwolf 8y ago
    So rich, and sounds like a racket.
gowld 8y ago
Also: http://www.math.uwaterloo.ca/~mrubinst/tuning/12.html 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]
- resource0x 8y ago
  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.

contravariant 8y ago

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.

deleted 8y ago
[deleted]
resource0x 8y ago
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.
- hessenwolf 8y ago
  So rich, and sounds like a racket.

gowld 8y ago

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

resource0x 8y ago
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.