User:FloraC/Reasonable commas

Revision as of 13:05, 15 May 2022 by FloraC (talk | contribs) (Our defs are not equivalent... that's why the list is different :))

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 Classic minor second
25/24 [-3 -1 2 Classic chroma
27/25 [0 -3 2 Large limma
81/80 [-4 4 -1 Syntonic comma
128/125 [7 0 -3 Diesis
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