Wilschisma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 532480/531441 | | Ratio = 532480/531441 | ||
| Name = wilschisma | | Name = wilschisma | ||
| Color name = | | Color name = s3oy2, sathoyo 2nd,<br>Sathoyo comma | ||
| | | Comma = yes | ||
}} | }} | ||
The '''wilschisma''' ( | The '''wilschisma''' ({{monzo|legend=1| 13 -12 1 0 0 1 }}, [[ratio]]: 532480/531441) is an [[unnoticeable comma|unnoticeable]] [[13-limit]] (also 2.3.5.13-[[subgroup]]) [[comma]] measuring about 3.38 [[cent]]s. 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 == | == Temperaments == | ||
Tempering out this comma in the full 13-limit results in the rank-5 wilschismic temperament. | 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]]: <br> | |||
{| class="right-all" | |||
|- | |||
| [⟨ || 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|legend=1| 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 | |||
{{Mapping|legend=2| 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|legend=1| 41, 53, 164, 217, 270, 422, 475, 528, 745, 798, 1273, 1326, 2071b, 3397bf }} | |||
[[Badness]]: 0.132 × 10<sup>-3</sup> | |||
== Etymology == | |||
This comma was named by [[Flora Canou]] in 2021 for its relationship with the wilsorma and Pythagorean comma. | |||
[[Category:Wilschismic]] | [[Category:Wilschismic]] | ||
[[Category:Commas named for other reasons]] | |||
Latest revision as of 16:44, 4 November 2024
| Interval information |
Sathoyo comma
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.