User:FloraC/Reasonable commas

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Thanks to @Dead Shaman.

Dead Shaman defines the reasonable comma as one such that there is not a number between the numerator and denominator which is in the subgroup.

My redefinition: a reasonable comma is one which cannot be factored into two simpler commas in a given subgroup.

List of 5-limit reasonable commas
Ratio Monzo Name
2/1 [1 Octave
3/2 [-1 1 Perfect fifth
4/3 [2 -1 Perfect fourth
5/4 [-2 0 1 Classic major third
6/5 [1 1 -1 Classic minor third
9/8 [-3 2 Major second
10/9 [1 -2 1 Classic major second
16/15 [4 -1 -1 Father comma
25/24 [-3 -1 2 Dicot comma
27/25 [0 -3 2 Bug comma
81/80 [-4 4 -1 Syntonic comma
128/125 [7 0 -3 Augmented comma
250/243 [1 -5 3 Porcupine comma
2048/2025 [11 -4 -2 Diaschisma
3125/3072 [-10 -1 5 Magic comma
15625/15552 [-6 -5 6 Kleisma
20000/19683 [5 -9 4 Tetracot comma
32805/32768 [-15 8 1 Schisma
78732/78125 [2 9 -7 Sensipent comma
393216/390625 [17 1 -8 Würschmidt comma
1600000/1594323 [9 -13 5 Amity comma
1224440064/1220703125 [8 14 -13 Parakleisma
4294967296/4271484375 [32 -7 -9 Escapade comma
6115295232/6103515625 [23 6 -14 Vishnuzma
10485760000/10460353203 [24 -21 4 Vulture comma
274877906944/274658203125 [38 -2 -15 Luna comma
7629394531250/7625597484987 [1 -27 18 Ennealimma
9010162353515625/9007199254740992 [-53 10 16 Kwazy comma
50031545098999707/50000000000000000 [-16 35 -17 Minortone comma
450359962737049600/450283905890997363 [54 -37 2 Monzisma
List of 7-limit reasonable commas
Ratio Monzo Name
2/1 [1 Octave
3/2 [-1 1 Perfect fifth
4/3 [2 -1 Perfect fourth
5/4 [-2 0 1 Classic major third
6/5 [1 1 -1 Classic minor third
7/6 [-1 -1 0 1 Septimal minor third
8/7 [3 0 0 -1 Septimal major second
9/8 [-3 2 Major second
10/9 [1 -2 1 Classic major second
15/14 [-1 1 1 -1 Septimal major semitone
16/15 [4 -1 -1 Father comma
21/20 [-2 1 -1 1 Septimal minor semitone
25/24 [-3 -1 2 Dicot comma
27/25 [0 -3 2 Bug comma
28/27 [2 -3 0 1 Trienstonic comma
36/35 [2 2 -1 -1 Mint comma
49/48 [-4 -1 0 2 Slendro diesis
50/49 [1 0 2 -2 Jubilisma
64/63 [6 -2 0 1 Septimal comma
81/80 [-4 4 -1 Syntonic comma
126/125 [1 2 -3 1 Starling comma
225/224 [-5 2 2 -1 Marvel comma
245/243 [0 -5 1 2 Sensamagic comma
1029/1024 [-10 1 0 3 Gamelisma
1728/1715 [6 3 -1 -3 Orwellisma
2048/2025 [11 -4 -2 Diaschisma
2401/2400 [-5 -1 -2 4 Breedsma
3125/3087 [0 -2 5 -3 Gariboh comma
3136/3125 [6 0 -5 2 Hemimean comma
4000/3969 [5 -4 3 -2 Octagar comma
4375/4374 [-1 -7 4 1 Ragisma
5120/5103 [10 -6 1 -1 Hemifamity comma
6144/6125 [11 1 -3 -2 Porwell comma
16875/16807 [0 3 4 -5 Mirkwai comma
19683/19600 [-4 9 -2 -2 Cataharry comma
32805/32768 [-15 8 1 Schisma
118098/117649 [1 10 0 -6 Stearnsma
250047/250000 [-4 6 -6 3 Landscape comma
589824/588245 [16 2 -1 -6 Hewuermera comma
703125/702464 [-11 2 7 -3 Meter comma
2460375/2458624 [-10 9 3 -4 Sesquiquartisma
14348907/14336000 [-14 15 -3 -1 Skeetsma
29360128/29296875 [22 -1 -10 1 Quasiorwellisma
33554432/33480783 [25 -14 0 -1 Garischisma
43046721/43025920 [-9 16 -1 -5 Trienstonisma
52734375/52706752 [-6 3 9 -7 Supermatertisma
67108864/66976875 [26 -7 -4 -2 Decovulture comma
78125000/78121827 [3 -13 10 -2 Euzenius comma