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 [[just intonation]], '''275/273''' is a no-twos 13-limit comma, '''gassorma''', measuring about 12.6¢. 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 ==

[[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 }} 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.

~~== See also ==~~

94edo has a step size close to this, but it tempers it out by patent val.

* [[Small comma]]

* [[Gassormic chords]]

[[Category:Gassormic]]

[[Category:Commas with unknown etymology]]

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 | Comma = yes
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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 [[just intonation]], '''275/273''' is a no-twos 13-limit comma, '''gassorma''', measuring about 12.6¢. 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 ==
-[[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 }} 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.
-== See also ==
+edo has a step size close to this, but it tempers it out by patent val.
-* [[Small comma]]
-* [[Gassormic chords]]
 [[Category:Gassormic]]
+[[Category:Commas with unknown etymology]]