Wilschisma
| Interval information |
Sathoyo comma
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
The wilschisma (monzo: [13 -12 1 0 0 1⟩, ratio: 532480/531441) is an unnoticeable 13-limit (also 2.3.5.13-subgroup) 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
| [⟨ | 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): ~2 = 1200.0000, ~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
Etymology
This comma was named by Flora Canou in 2021 for its relationship with the wilsorma and Pythagorean comma.