Garischisma: Difference between revisions

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The '''garischisma''' or '''septimal schisma''' is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 3.80 [[cent]]s. 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 a stack of 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 is most well known as the difference between the Pythagorean comma and the [[64/63|septimal comma]]. It is also the difference the difference between: 


In the 11-limit, it factors into simpler commas as ([[19712/19683]])([[131072/130977]]).
* [[8/7]] and 2 [[2187/2048|apotomes]]
* The [[hemifamity comma]] and the [[schisma]]
 
It also factors into the following higher limit commas:
 
* 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 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 '''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 ==
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]]

Revision as of 20:13, 11 April 2026

Interval information
Ratio 33554432/33480783
Factorization 225 × 3-14 × 7-1
Monzo [25 -14 0 -1⟩
Size in cents 3.804081¢
Names garischisma,
septimal schisma
Color name ssr2, sasaru 2nd,
Sasaru comma
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 garischisma or septimal schisma is a very small 7-limit comma measuring about 3.80 cents. It is most well known as the difference between the Pythagorean comma and the septimal comma. It is also the difference the difference between:

It also factors into the following higher limit commas:

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.

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