4096/4095
Ratio | 4096/4095 |
Factorization | 2^{12} × 3^{-2} × 5^{-1} × 7^{-1} × 13^{-1} |
Monzo | [12 -2 -1 -1 0 -1⟩ |
Size in cents | 0.42271617¢ |
Name | schismina |
Color name | s3urg1, sathurugu 1sn, Sathurugu comma |
FJS name | [math]\text{P1}_{5,7,13}[/math] |
Special properties | square superparticular, reduced, reduced subharmonic |
Tenney height (log_{2} nd) | 23.9996 |
Weil height (log_{2} max(n, d)) | 24 |
Wilson height (sopfr (nd)) | 55 |
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math]) |
~1.20076 bits |
Comma size | unnoticeable |
S-expression | S64 |
open this interval in xen-calc |
4096/4095, the schismina, is a 13-limit superparticular ratio 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 a Mersenne 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 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