Garischisma: Difference between revisions

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The '''garischisma''' or '''septimal schisma''' is a [[7-limit]] [[comma]] measuring about 3.80 ~~cents~~. 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 two [[2187/2048|apotomes]].

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]].

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

== Temperaments ==

Tempering it out in the full 7-limit leads to the rank-3 '''garischismic temperament'''.

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.

~~=== Garischismic (41 & 53 & 270) ===~~

~~Subgroup:~~ 2.3.5.7

[[~~Comma list~~]]~~: 33554432/33480783~~

[[~~Mapping~~]]~~: [{{val| 1 0 0 25 }}, {{val| 0 1 0~~ -~~14 }}, {{val| 0 0 1 0 }}]~~

~~[[POTE generator]]s: ~~~3~~/2 = 702~~.~~2079, ~5/4 = 386.5100~~

~~{{Val list|legend=1| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}~~

[[~~Badness~~]]~~: 1.313 × 10<sup>-3</sup>~~

~~== See also ==~~

* [[~~Garischismic~~ clan]]~~, the~~ rank-2 ~~clan~~ where it is tempered out

* [[Small comma]]

[[Category:Garischismic]]

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

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-The '''garischisma''' or '''septimal schisma''' is a [[7-limit]] [[comma]] measuring about 3.80 cents. 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 two [[2187/2048|apotomes]].
+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]].
+In the 11-limit, it factors into simpler commas as ([[19712/19683]])([[131072/130977]]).
 == Temperaments ==
-Tempering it out in the full 7-limit leads to the rank-3 '''garischismic temperament'''.
+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.
-=== Garischismic (41 & 53 & 270) ===
-Subgroup: 2.3.5.7
-[[Comma list]]: 33554432/33480783
-[[Mapping]]: [{{val| 1 0 0 25 }}, {{val| 0 1 0 -14 }}, {{val| 0 0 1 0 }}]
-[[POTE generator]]s: ~3/2 = 702.2079, ~5/4 = 386.5100
-{{Val list|legend=1| 12, 29, 41, 53, 94, 164, 176, 217, 229, 270, 593, 863, 1133, 1996d, 2037, 2307, 2900bd, 3170bd, 4303bcd }}
-[[Badness]]: 1.313 × 10<sup>-3</sup>
-== See also ==
-* [[Garischismic clan]], the rank-2 clan where it is tempered out
-* [[Small comma]]
 [[Category:Garischismic]]
+[[Category:Commas named by combining multiple temperament names]]