Garischisma: Difference between revisions

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| Ratio = 33554432/33480783

| Name = garischisma, septimal schisma

| Color name = ssr2, sasaru 2nd,<br>~~Sasaru comma~~

| Color name = ssr2, sasaru 2nd,<br>ssrM, sasaruma

| Comma = yes

}}

The '''garischisma''' or '''septimal schisma''' is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. ~~While~~ the [[schisma]] is the difference between the [[Pythagorean comma]] and the [[~~81/80|~~syntonic comma]], the garischisma~~, in contrast,~~ is the difference between ~~the Pythagorean comma and~~ the [[~~64/63|~~septimal comma]]. It can ~~also~~ be described as the ~~difference between the~~ [[8/7|septimal whole tone]] ~~and a stack of two~~ [[~~2187/2048|apotomes~~]].

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.

In the 11-limit~~, it factors into simpler~~ commas ~~as (~~[[19712/19683]])([[131072/130977]]).

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

@@ Line 2: / Line 2: @@
 | Ratio = 33554432/33480783
 | Name = garischisma, septimal schisma
-| Color name = ssr2, sasaru 2nd,<br>Sasaru comma
+| Color name = ssr2, sasaru 2nd,<br>ssrM, sasaruma
 | Comma = yes
 }}
-The '''garischisma''' or '''septimal schisma''' is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. While the [[schisma]] is the difference between the [[Pythagorean comma]] and the [[81/80|syntonic comma]], the garischisma, in contrast, is the difference between the Pythagorean comma and the [[64/63|septimal comma]]. It can also be described as the difference between the [[8/7|septimal whole tone]] and a stack of two [[2187/2048|apotomes]].
+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.
-In the 11-limit, it factors into simpler commas as ([[19712/19683]])([[131072/130977]]).
+It factors into the following [[11-limit|11-]] and [[13-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]]