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]]. Tempering it out leads to the rank-3 [[~~Garischismic_family~~|~~garischismic temperament~~]].

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]].

== Temperaments ==

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

=== 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, 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 ~~family~~]]

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

* [[Garischismic clan]]

* [[Small comma]]

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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]]. Tempering it out leads to the rank-3 [[Garischismic_family|garischismic temperament]].
+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]].
+== Temperaments ==
+Tempering it out in the full 7-limit leads to the rank-3 '''garischismic temperament'''.
+=== 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, 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 family]]
+* [[Garischismic clan]], the rank-2 clan where it is tempered out
-* [[Garischismic clan]]
 * [[Small comma]]