(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]
|