Garischisma: Difference between revisions

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The '''garischisma''' or '''septimal schisma''' is a very [[small comma|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It is ~~most well known as~~ the difference between the [[~~pythagorean~~ comma]] and the [[64/63|septimal ~~comma~~]]. It is also the difference the ~~difference between:~~

The '''garischisma''' or '''septimal schisma''' is a very [[small comma|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It can be considered the septimal counterpart of the [[schisma]]: whereas the schisma is the difference between the [[Pythagorean comma]] and the [[syntonic comma]], the garischisma is the difference between the [[septimal comma]] and the Pythagorean comma. Equivalently, it can be described as the amount by which a stack of two [[2187/2048|apotomes]] falls short of a [[8/7|septimal whole tone]]. It is also the difference between the [[aberschisma]] and the schisma in the full 7-limit.

* [[~~8/7]] and 2 [[2187/2048~~|~~apotomes]]~~

It factors into the following [[11-limit|11-]] and [[13-limit]] commas:

* The [[hemifamity comma]] and ~~the~~ [[~~schisma~~]]

* The [[19712/19683|symbiotic comma]] and [[131072/130977|olympia]];

* The [[wilschisma]] and the [[minisma]].

~~It also factors into the following higher limit~~ commas:

* The [[19712/19683|symbiotic comma]] and [[131072/130977|olympia]]

* The [[wilschisma]] and the [[minisma]]

== Temperaments ==

Tempering out this comma in the full 7-limit leads to the rank-3 '''garischismic ~~temperament~~''', or in the 2.3.7 subgroup, the rank-2 '''gary ~~temperament~~'''. See [[Garischismic family]] for the [[~~Temperament~~ families and clans|family]] of rank-3 temperaments where it is tempered out. See [[Garischismic clan]] for the [[~~Temperament~~ families and clans|clan]] of rank-2 temperaments where it is tempered out.

[[Tempering out]] this comma in the full 7-limit leads to the rank-3 '''garischismic''' temperament, or in the [[2.3.7 subgroup]], the rank-2 '''gary''' temperament. See [[Garischismic family]] for the [[temperament families and clans|family]] of rank-3 temperaments where it is tempered out. See [[Garischismic clan]] for the [[temperament families and clans|clan]] of rank-2 temperaments where it is tempered out.

== Etymology ==

Its name comes from the temperament [[garibaldi]] and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi.

[[Category:Garischismic]]

[[Category:Commas named by combining multiple temperament names]]

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-The '''garischisma''' or '''septimal schisma''' is a very [[small comma|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It is most well known as the difference between the [[pythagorean comma]] and the [[64/63|septimal comma]]. It is also the difference the difference between:
+The '''garischisma''' or '''septimal schisma''' is a very [[small comma|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It can be considered the septimal counterpart of the [[schisma]]: whereas the schisma is the difference between the [[Pythagorean comma]] and the [[syntonic comma]], the garischisma is the difference between the [[septimal comma]] and the Pythagorean comma. Equivalently, it can be described as the amount by which a stack of two [[2187/2048|apotomes]] falls short of a [[8/7|septimal whole tone]]. It is also the difference between the [[aberschisma]] and the schisma in the full 7-limit.
-* [[8/7]] and 2 [[2187/2048|apotomes]]
+It factors into the following [[11-limit|11-]] and [[13-limit]] commas:
-* The [[hemifamity comma]] and the [[schisma]]
+* The [[19712/19683|symbiotic comma]] and [[131072/130977|olympia]];
+* The [[wilschisma]] and the [[minisma]].
-It also factors into the following higher limit commas:
-* The [[19712/19683|symbiotic comma]] and [[131072/130977|olympia]]
-* The [[wilschisma]] and the [[minisma]]
 == Temperaments ==
-Tempering out this comma in the full 7-limit leads to the rank-3 '''garischismic temperament''', or in the 2.3.7 subgroup, the rank-2 '''gary temperament'''. See [[Garischismic family]] for the [[Temperament families and clans|family]] of rank-3 temperaments where it is tempered out. See [[Garischismic clan]] for the [[Temperament families and clans|clan]] of rank-2 temperaments where it is tempered out.
+[[Tempering out]] this comma in the full 7-limit leads to the rank-3 '''garischismic''' temperament, or in the [[2.3.7 subgroup]], the rank-2 '''gary''' temperament. See [[Garischismic family]] for the [[temperament families and clans|family]] of rank-3 temperaments where it is tempered out. See [[Garischismic clan]] for the [[temperament families and clans|clan]] of rank-2 temperaments where it is tempered out.
 == Etymology ==
 Its name comes from the temperament [[garibaldi]] and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi.
 [[Category:Garischismic]]
 [[Category:Commas named by combining multiple temperament names]]