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 [[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 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.

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 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~~ ==

== Etymology ==

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

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

* [[Small comma]]

[[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 [[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 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.
+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 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 ==
+== Etymology ==
-* [[Garischismic clan]], the rank-2 clan where it is tempered out
+Its name comes from the temperament [[garibaldi]] and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi.
-* [[Small comma]]
 [[Category:Garischismic]]
+[[Category:Commas named by combining multiple temperament names]]