User:CompactStar/JI notation

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(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 comma-seperated 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]
13 144/143 13/8 = Ad[-13]
17 2187/2176 17/16 = C#[-17]
19 513/512 19/16 = Eb[+19]
23 736/729 23/16 = F#[+23]
29 261/256 29/16 = Bb[+29]
31 1024/1023 31/16 = Cd[-31]
37 297/296 37/32 = Dt[-37]
41 82/81 41/32 = E[+41]
43 129/128 43/32 = F[+43]
47 517/512 47/32 = Gd[+47]
53 583/576 53/32 = Ad[+53]

15-odd-limit

Interval Notation
16/15 Db[+5]
15/14 Dd[-5, -7]
14/13 Ctt[+7, +13]
13/12 Dd[-13]
12/11 Dd
11/10 Dbt[+5]
10/9 D[-5]
9/8 D
8/7 Ebd[-7]
15/13 Dt[-5, +13]
7/6 Dt[+7]
13/11 Edd[-13]
6/5 Eb[+5]