275/273: Difference between revisions
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In [[just intonation]], '''275/273''', the '''gassorma''', is a [[small comma|small]] no-2's [[13-limit]] [[comma]] measuring about 12.6 [[cent]]s. It can be expressed as ([[5/3]])/(([[13/11]])⋅([[7/5]])), (5/3)/(([[14/11]])⋅([[13/10]])), ([[10/7]])/(([[13/11]])⋅([[6/5]])) and (10/7)/(([[12/11]])⋅(13/10)), among other expressions. | |||
In terms of commas, it is the difference between [[50/49]] and [[78/77]], between [[66/65]] and [[126/125]], between [[99/98]] and [[351/350]], between [[100/99]] and [[364/363]], and between [[121/120]] and [[1001/1000]]. It factors into ([[225/224]])⋅([[352/351]]). | |||
In terms of commas, it is the difference between [[50/49]] and [[78/77]], between [[66/65]] and [[126/125]], between [[99/98]] and [[351/350]], between [[100/99]] and [[364/363]], and between [[121/120]] and [[1001/1000]]. It factors into ([[225/224]])([[352/351]]). | |||
== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma in the 13-limit results in the rank-5 gassormic temperament and enables [[gassormic chords]]. Equal temperaments which temper out this comma include {{EDOs| 10, 15, 22, 26, 29, 31, 41, 53, 94}} and others; in such systems, 7/5 and [[55/39]] are equated. | [[Tempering out]] this comma in the 13-limit results in the rank-5 '''gassormic''' temperament and enables [[gassormic chords]]. Equal temperaments which temper out this comma include {{EDOs| 10, 15, 22, 26, 29, 31, 41, 53, 94 }} and others; in such systems, 7/5 and [[55/39]] are equated. | ||
94edo has a step size close to this, but it tempers it out by patent val. | 94edo has a step size close to this, but it tempers it out by patent val. | ||
[[Category:Gassormic]] | [[Category:Gassormic]] | ||
[[Category:Commas with unknown etymology]] | [[Category:Commas with unknown etymology]] | ||
Latest revision as of 05:18, 24 August 2026
| Interval information |
In just intonation, 275/273, the gassorma, is a small no-2's 13-limit comma measuring about 12.6 cents. It can be expressed as (5/3)/((13/11)⋅(7/5)), (5/3)/((14/11)⋅(13/10)), (10/7)/((13/11)⋅(6/5)) and (10/7)/((12/11)⋅(13/10)), among other expressions.
In terms of commas, it is the difference between 50/49 and 78/77, between 66/65 and 126/125, between 99/98 and 351/350, between 100/99 and 364/363, and between 121/120 and 1001/1000. It factors into (225/224)⋅(352/351).
Temperaments
Tempering out this comma in the 13-limit results in the rank-5 gassormic temperament and enables gassormic chords. Equal temperaments which temper out this comma include 10, 15, 22, 26, 29, 31, 41, 53, 94 and others; in such systems, 7/5 and 55/39 are equated.
94edo has a step size close to this, but it tempers it out by patent val.