4096/4095
4096/4095, the minisma or minic comma, also described as the tridecimal schisma or tridecimal schismina[1], is an unnoticeable 13-limit superparticular comma of about 0.42 cents. It is the difference between the septimal comma (64/63) and the wilsorma (65/64), and between the septimal quartertone (36/35) and the tridecimal quartertone (1053/1024). It is also a Mersenne comma.
| Interval information |
minic comma
Sathurugu comma
reduced,
reduced subharmonic
It is also the smallest superparticular ratio in the 2.3.5.7.13 subgroup.
Temperaments
By tempering out this comma in the full 13-limit is defined the minismic temperament, which enables the minismic chords, the essentially tempered chords in the 21-odd-limit. You may find a list of good equal temperaments that support this temperament below.
Subgroup: 2.3.5.7.11.13
| [⟨ | 1 | 0 | 0 | 0 | 0 | 12 | ], |
| ⟨ | 0 | 1 | 0 | 0 | 0 | -2 | ], |
| ⟨ | 0 | 0 | 1 | 0 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 1 | 0 | -1 | ], |
| ⟨ | 0 | 0 | 0 | 0 | 1 | 0 | ]] |
- mapping generators: ~2, ~3, ~5, ~7, ~11
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, 9140cdef, 14463bcddeefff, 17786bccddeeefff
Etymology
The names minisma and minic comma were given by Flora Canou in 2026 after the general interval size measure knowns as the mina, because 4096/4095 is the default comma represented by a mina (or three tinas) in Sagittal notation. Mina is a clipping of schismina, which describes a range of commas in Sagittal notation, and in turn comes from schisma (the interval region) + -in (diminutive suffix). Eufalesio proposed trinyblisma, for the denominator is the largest integer that can be written in 3 nybbles (1.5 bytes).