Wilschisma
| Ratio | 532480/531441 |
| Factorization | 213 × 3-12 × 5 × 13 |
| Monzo | [13 -12 1 0 0 1⟩ |
| Size in cents | 3.3813652¢ |
| Name | wilschisma |
| Color name | s3oy2, sathoyo 2nd, Sathoyo comma |
| FJS name | [math]\text{d2}^{5,13}[/math] |
| Special properties | reduced |
| Tenney height (log2 nd) | 38.0419 |
| Weil height (log2 max(n, d)) | 38.0447 |
| Wilson height (sopfr (nd)) | 80 |
| Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.44821 bits |
| Comma size | unnoticeable |
| open this interval in xen-calc | |
The wilschisma (monzo: [13 -12 1 0 0 1⟩, ratio: 532480/531441) is a 13-limit (also 2.3.5.13 subgroup) unnoticeable comma measuring about 3.38 cents. It is the difference between the wilsorma (65/64) and the Pythagorean comma, hence the name. The wilschisma can be viewed as a counterpart of the symbiotic comma – while the symbiotic comma connects 7 and 11, the wilschisma connects 5 and 13, and they differ by an ibnsinma. In addition, the wilschisma is the difference between the garischisma and the schismina.
Temperaments
Tempering out this comma in the full 13-limit results in the rank-5 wilschismic temperament. You may find a list of good equal temperaments that support this temperament below. Adding the ibnsinma and thus the symbiotic comma to the comma list gives symbiotic (→ Rank-4 temperament #Symbiotic (19712/19683)), with virtually no additional error, so it is highly recommendable. Otherwise, retracting it to the 2.3.5.13 subgroup gives the rank-3 will temperament.
Wilschismic
Subgroup: 2.3.5.7.11.13
Comma list: 532480/531441
Mapping:
[⟨1 0 0 0 0 -13],
⟨0 1 0 0 0 12],
⟨0 0 1 0 0 -1],
⟨0 0 0 1 0 0],
⟨0 0 0 0 1 0]]
Mapping generators: ~2, ~3, ~5, ~7, ~11
Optimal ET sequence: 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 2599bdef, 2869bde, 3450bde, 3872bbdeef
Will
Subgroup: 2.3.5.13
Comma list: 532480/531441
Sval mapping: [⟨1 0 0 -13], ⟨0 1 0 12], ⟨0 0 1 -1]]
Optimal tuning (CTE): ~3/2 = 702.2227, ~5/4 = 386.2658
Optimal ET sequence: 41, 53, 164, 217, 270, 422, 475, 528, 745, 798, 1273, 1326, 2071b, 3397bf
Badness: 0.132 × 10-3