4096/4095
4096/4095, the schismina, is a 13-limit superparticular ratio of about 0.42 cents. It is the difference between:
- 64/63 and 65/64
- 27/26 and 8505/8192
- 36/35 and 1053/1024
- 35/32 and 128/117
- 39/32 and 128/105
- 45/32 and 128/91
- 13/8 and 512/315
| Interval information |
Sathurugu comma
reduced,
reduced subharmonic
It is also a Mersenne comma, and the smallest superparticular ratio in the 2.3.5.7.13 subgroup on which it is also a PIFE-like comma.
The name lends itself to the general interval size measure knowns as the mina. In Sagittal notation, 4096/4095 is the default comma represented by a mina or three tinas.
Temperaments
By tempering it out is defined the schisminic temperament, which enables the schisminic chords, the essentially tempered chords in the no-11 21-odd-limit. You may find a list of good equal temperaments that support this temperament below.
Subgroup: 2.3.5.7.13
| [⟨ | 1 | 0 | 0 | 0 | 0 | 12 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | -1 | ], |
- mapping generators: ~2, ~3, ~5, ~7
Optimal ET sequence: 22, 31, 41, 46, 53, 77, 84, 87, 118, 130, 183, 217, 224, 270, 494, 764, 935, 1012, 1236, 1506, 3236, 3323, 3817, 5323f, 9140cdf, 14463bcddfff, 17786bccddfff