Wilschisma: Difference between revisions

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The '''wilschisma''' (monzo: {{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 [[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]].  
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 ==
Line 16: Line 16:


[[Mapping]]: <br>
[[Mapping]]: <br>
[{{val| 1 0 0 0 0 -13 }}, <br>
{| class="right-all"
{{val| 0 1 0 0 0 12 }}, <br>
|-
{{val| 0 0 1 0 0 -1 }}, <br>
| [⟨ || 1 || 0 || 0 || 0 || 0 || -13 || ],
{{val| 0 0 0 1 0 0 }}, <br>
|-
{{val| 0 0 0 0 1 0 }}]
| ⟨ || 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
: mapping generators: ~2, ~3, ~5, ~7, ~11


{{Val list|legend=1| 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 2599bdef, 2869bde, 3450bde, 3872bbdeef }}
{{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 ===
=== Will ===
Line 31: Line 38:
[[Comma list]]: 532480/531441
[[Comma list]]: 532480/531441


[[Sval]] [[mapping]]: [{{val| 1 0 0 -13 }}, {{val| 0 1 0 12 }}, {{val| 0 0 1 -1 }}]
{{Mapping|legend=2| 1 0 0 -13 | 0 1 0 12 | 0 0 1 -1 }}


[[Optimal tuning]] ([[CTE]]): ~3/2 = 702.2227, ~5/4 = 386.2658
[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 702.2227, ~5/4 = 386.2658


{{Val list|legend=1| 41, 53, 164, 217, 270, 422, 475, 528, 745, 798, 1273, 1326, 2071b, 3397bf }}
{{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>
[[Badness]]: 0.132 × 10<sup>-3</sup>


== See also ==
== Etymology ==
* [[Unnoticeable comma]]
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
Ratio 532480/531441
Factorization 213 × 3-12 × 5 × 13
Monzo [13 -12 1 0 0 1⟩
Size in cents 3.381365¢
Name wilschisma
Color name s3oy2, sathoyo 2nd,
Sathoyo comma
FJS name [math]\displaystyle{ \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
Comma size unnoticeable
Open this interval in xen-calc

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

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): ~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.

Retrieved from "https://en.xen.wiki/index.php?title=Wilschisma&oldid=164221"