Garischisma: Difference between revisions
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| Ratio = 33554432/33480783 | | Ratio = 33554432/33480783 | ||
| Name = garischisma, septimal schisma | | Name = garischisma, septimal schisma | ||
| Color name = ssr2, sasaru 2nd,<br> | | Color name = ssr2, sasaru 2nd,<br>ssrM, sasaruma | ||
| Comma = yes | | Comma = yes | ||
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The '''garischisma''' or '''septimal schisma''' is a very [[small comma|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. It is | 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]]. | |||
* The [[19712/19683|symbiotic comma]] and [[131072/130977|olympia]] | |||
* The [[wilschisma]] and the [[minisma]] | |||
== Temperaments == | == Temperaments == | ||
Tempering out this comma in the full 7-limit leads to the rank-3 '''garischismic | [[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 == | == Etymology == | ||
Its name comes from the temperament [[garibaldi]] and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi. | 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:Garischismic]] | ||
[[Category:Commas named by combining multiple temperament names]] | [[Category:Commas named by combining multiple temperament names]] | ||
Latest revision as of 04:10, 29 April 2026
| Interval information |
septimal schisma
ssrM, sasaruma
reduced subharmonic
The garischisma or septimal schisma is a very small 7-limit comma measuring about 3.80 cents. 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 apotomes falls short of a 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- and 13-limit commas:
- The symbiotic comma and 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 family of rank-3 temperaments where it is tempered out. See Garischismic clan for the 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.