User:CompactStar/JI notation
(This may be moved to mainspace when it is more fleshed out)
The naturals CDEFGAB correspond to Pythagorean intervals. Sharp and flat accidentals raise/lower by 2187/2048, and half-sharp and half-flat accidentals raise/lower by 33/32. To represent non-2.3.11 subgroup intervals, a list of primes, each of which multiplies the basic note by a comma, is added (e.g. 5/4 = E[-5], 13/10 = Fd[+13, -5]).
Commas
| Prime | Comma | Notation of harmonic |
|---|---|---|
| 5 | 81/80 | 5/4 = E[-5] |
| 7 | 896/891 | 7/4 = At[+7] |
| 13 | 352/351 | 13/8 = Abt[-13] |
| 17 | 2187/2176 | 17/16 = C#[-17] |
| 19 | 513/512 | 19/16 = Eb[+19] |
| 23 | 736/729 | 23/16 = F#[+23] |
| 29 | 88/87 | 29/16 = Bbt[-29] |
| 31 | 1024/1023 | 31/16 = Cd[-31] |
| 37 | 37/32 = |