Garischisma: Difference between revisions
Expansion |
mNo edit summary |
||
| (10 intermediate revisions by 5 users not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 33554432/33480783 | | Ratio = 33554432/33480783 | ||
| Name = garischisma, septimal schisma | |||
| Color name = ssr2, sasaru 2nd,<br>Sasaru comma | |||
| Name = garischisma, | | Comma = yes | ||
| Color name = | |||
| | |||
}} | }} | ||
The '''garischisma''' or '''septimal schisma''' is a [[7-limit]] [[comma]] measuring about 3.80 | 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]]. | ||
== | In the 11-limit, it factors into simpler commas as ([[19712/19683]])([[131072/130977]]). | ||
== 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. | |||
[[Category:Garischismic]] | [[Category:Garischismic]] | ||
[[Category:Commas named by combining multiple temperament names]] | |||
Latest revision as of 12:37, 21 March 2025
| Interval information |
septimal schisma
Sasaru comma
reduced subharmonic
The garischisma or septimal schisma is a small 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 a stack of two apotomes.
In the 11-limit, it factors into simpler commas as (19712/19683)(131072/130977).
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.