Garischisma: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| JI glyph =
| Ratio = 33554432/33480783
| Ratio = 33554432/33480783
| Monzo = 25 -14 0 -1
| Name = garischisma, septimal schisma
| Cents = 3.8041
| Color name = ssr2, sasaru 2nd,<br>ssrM, sasaruma
| Name = garischisma, <br>septimal schisma
| Comma = yes
| Color name = ssr2, sasaru 2nd
| FJS name = d2<sub>7</sub>
| Sound =  
}}
}}


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]].  
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]].  


== Temperaments ==
== Temperaments ==
Tempering it out in the full 7-limit leads to the rank-3 '''garischismic temperament'''.
[[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.  
 
=== 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, 29, 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 ==
== Etymology ==
* [[Garischismic clan]], the rank-2 clan where it is tempered out
Its name comes from the temperament [[garibaldi]] and the schisma, as it is a similarly sized interval that alongside it, defines garibaldi.
* [[Small comma]]


[[Category:7-limit]]
[[Category:Small commas]]
[[Category:Unnoticeable comma]]
[[Category:Garischismic]]
[[Category:Garischismic]]
[[Category:Commas named by combining multiple temperament names]]

Latest revision as of 04:10, 29 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,
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 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:

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.