Wilschisma: Difference between revisions

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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~~]].

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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-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]].
+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 ===