275/273: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = gassorma | | Name = gassorma | ||
| Color name = | | Color name = 3u1oryy-2, Thuloruyoyo comma | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
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]] | 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]]). | |||
== 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 {{ | [[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. | ||
== See also == | == See also == | ||
| Line 15: | Line 17: | ||
[[Category:Gassormic]] | [[Category:Gassormic]] | ||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 23:14, 15 November 2024
| Interval information |
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).
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 and others; in such systems, 7/5 and 55/39 are equated.