Wilschisma: Difference between revisions

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| Ratio = 532480/531441

| Name = wilschisma

| Color name = s3oy2, sathoyo 2nd, Sathoyo comma

| Comma = yes

}}

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|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 [[7/1|7]] and [[11/1|11]], the wilschisma connects [[5/1|5]] and [[13/1|13]], and they differ by an [[ibnsinma]]. In addition, the wilschisma is the difference between the [[garischisma]] and the [[minisma]].

== 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'''.

[[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 ===

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[[Mapping]]:

[~~{{val~~| 1 0 0 0 0 -13 }}, ~~ ~~

{| class="right-all"

~~{{val~~| 0 1 0 0 0 12 }}, ~~ ~~

|-

~~{{val~~| 0 0 1 0 0 -1 }}, ~~ ~~

| [⟨ || 1 || 0 || 0 || 0 || 0 || -13 || ],

~~{{val~~| 0 0 0 1 0 0 }}, ~~ ~~

|-

~~{{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 ===

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[[Comma list]]: 532480/531441

~~[[Sval]] [[mapping]]: [~~{{~~val~~| 1 0 0 -13 ~~}}, {{val~~| 0 1 0 12 ~~}}, {{val~~| 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 × 10-3

== ~~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:Commas named for other reasons]]

@@ Line 2: / Line 2: @@
 | Ratio = 532480/531441
 | Name = wilschisma
+| Color name = s3oy2, sathoyo 2nd,<br>Sathoyo comma
 | Comma = yes
 }}
-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|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 [[7/1|7]] and [[11/1|11]], the wilschisma connects [[5/1|5]] and [[13/1|13]], and they differ by an [[ibnsinma]]. In addition, the wilschisma is the difference between the [[garischisma]] and the [[minisma]].
 == 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'''.
+[[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 ===
@@ Line 15: / Line 16: @@
 [[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 ===
@@ Line 30: / Line 38: @@
 [[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>
-== 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:Commas named for other reasons]]