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 [[ | 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 == | == See also == | ||
* [[Garischismic | * [[Garischismic clan]], the rank-2 clan where it is tempered out | ||
* [[Small comma]] | * [[Small comma]] | ||
Revision as of 18:26, 7 May 2021
| Interval information |
septimal schisma
reduced subharmonic
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 syntonic comma, the garischisma, in contrast, is the difference between the Pythagorean comma and the septimal comma. It can also be described as the difference between the septimal whole tone and two 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: [⟨1 0 0 25], ⟨0 1 0 -14], ⟨0 0 1 0]]
POTE generators: ~3/2 = 702.2079, ~5/4 = 386.5100
Badness: 1.313 × 10-3
See also
- Garischismic clan, the rank-2 clan where it is tempered out
- Small comma