85/84: Difference between revisions
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'''85/84''', the '''monk comma''', is a [[17-limit]] [[superparticular | '''85/84''', the '''monk comma''', is a [[small comma|small]] [[17-limit]] [[superparticular]] [[comma]] measuring about 20.5 [[cent]]s. It is the difference between [[6/5]] and [[17/14]], as well as [[7/5]] and [[17/12]]. | ||
== Notation == | == Notation == | ||
This comma can be represented as a secondary comma for 5C ({{Sagittal|\!}}) in Sagittal. | This comma can be represented as a secondary comma for 5C ({{Sagittal|\!}}) in [[Sagittal]]. | ||
== Temperaments == | == Temperaments == | ||
It can be [[tempering out|tempered out]] in the [[17-limit]], leading to a rank-6 temperament, or in the 2.3.5.7.17-subgroup, leading to a rank-4 temperament. However, 85/84 factors as [[225/224]] | It can be [[tempering out|tempered out]] in the [[17-limit]], leading to a rank-6 temperament, or in the 2.3.5.7.17-subgroup, leading to a rank-4 temperament. However, 85/84 factors as ([[225/224]])⋅([[256/255]])⋅([[289/288]]), i.e. ({{S|15}})⋅({{S|16}})⋅({{S|17}}), so that it is natural to temper out all of them, leading to the 2.3.5.7.17 version of [[pajara]] temperament, which also tempers out [[50/49]]. From there we can see that 50/49 = ([[99/98]])⋅([[100/99]]), and tempering both out leads to the 2.3.5.7.11.17-subgroup version of pajara. | ||
== Etymology == | |||
The word ''monk'' for this comma was introduced by [[Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:san-serif" lang="ja">僧侶</span> (<span style="font-family:san-serif" lang="ja">そうりょ</span>, sōryo), a play of its [[Kite's color notation|color name]], ''soruyo'' (as resembling pronunciation). | |||
== See also == | == See also == | ||
* [[List of superparticular intervals]] | * [[List of superparticular intervals]] | ||
[[Category:Commas named after their color name]] | [[Category:Commas named after their color name]] | ||
[[Category:Commas named by translating something into another language]] | [[Category:Commas named by translating something into another language]] | ||
Revision as of 05:37, 17 May 2026
| Interval information |
Soruyo comma
reduced
85/84, the monk comma, is a small 17-limit superparticular comma measuring about 20.5 cents. It is the difference between 6/5 and 17/14, as well as 7/5 and 17/12.
Notation
This comma can be represented as a secondary comma for 5C () in Sagittal.
Temperaments
It can be tempered out in the 17-limit, leading to a rank-6 temperament, or in the 2.3.5.7.17-subgroup, leading to a rank-4 temperament. However, 85/84 factors as (225/224)⋅(256/255)⋅(289/288), i.e. (S15)⋅(S16)⋅(S17), so that it is natural to temper out all of them, leading to the 2.3.5.7.17 version of pajara temperament, which also tempers out 50/49. From there we can see that 50/49 = (99/98)⋅(100/99), and tempering both out leads to the 2.3.5.7.11.17-subgroup version of pajara.
Etymology
The word monk for this comma was introduced by Xenllium in 2023. It was translated from Japanese word 僧侶 (そうりょ, sōryo), a play of its color name, soruyo (as resembling pronunciation).