275/273: Difference between revisions

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{{Infobox Interval

~~| Ratio = 275/273~~

~~| Monzo = 0 -1 2 -1 1 -1~~

~~| Cents = 12.63680~~

| Name = gassorma

| Color name = ~~thuloruyoyo negative 2nd~~

| Color name = 3u1oryy-2, Thuloruyoyo comma

| ~~FJS name~~ = ~~d-2<sup>5, 5, 11</sup><sub>7, 13</sub>~~

| Comma = yes

}}

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]].

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 {{~~Vals~~| 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:Rational intervals]]~~

~~[[Category:13-limit]]~~

~~[[Category:Small comma]]~~

[[Category:Gassormic]]

[[Category:Commas with unknown etymology]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Ratio = 275/273
-| Monzo = 0 -1 2 -1 1 -1
-| Cents = 12.63680
 | Name = gassorma
-| Color name = thuloruyoyo negative 2nd
+| Color name = 3u1oryy-2, Thuloruyoyo comma
-| FJS name = d-2<sup>5, 5, 11</sup><sub>7, 13</sub>
+| Comma = yes
 }}
+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]].
+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 {{Vals| 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:Rational intervals]]
-[[Category:13-limit]]
-[[Category:Small comma]]
 [[Category:Gassormic]]
+[[Category:Commas with unknown etymology]]