Septischisma: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Ratio = 33554432/33480783
| Ratio = 33554432/33480783
| Name = garischisma, septimal schisma
| Name = septischisma, garysma
| Color name = ssr2, sasaru 2nd,<br>ssrM, sasaruma
| Color name = ssr2, sasaru 2nd,<br>ssrM, sasaruma
| Comma = yes
| Comma = yes
}}
}}


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.  
The '''septischisma''' or '''garysma''' 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:  
It factors into the following [[11-limit|11-]] and [[13-limit]] commas:  
Line 13: Line 13:


== Temperaments ==
== 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 [[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.  
[[Tempering out]] this comma in the full 7-limit leads to the rank-3 '''septischismic''' 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 used to be ''garischisma'', which comes from the temperament [[garibaldi]] and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi. This etymology partly lingers in the subgroup temperament gary. The current name is trivial.


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

Revision as of 12:44, 15 August 2026

Interval information
Ratio 33554432/33480783
Factorization 225 × 3-14 × 7-1
Monzo [25 -14 0 -1
Size in cents 3.804081¢
Names septischisma,
garysma
Color name ssr2, sasaru 2nd,
ssrM, sasaruma
FJS name [math]\displaystyle{ \text{d2}_{7} }[/math]
Special properties reduced,
reduced subharmonic
Tenney norm (log2 nd) 49.9968
Weil norm (log2 max(n, d)) 50
Wilson norm (sopfr(nd)) 99
Comma size small
Open this interval in xen-calc

The septischisma or garysma 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:

Temperaments

Tempering out this comma in the full 7-limit leads to the rank-3 septischismic 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 used to be garischisma, which comes from the temperament garibaldi and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi. This etymology partly lingers in the subgroup temperament gary. The current name is trivial.