85/84: Difference between revisions
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== 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 == | |||
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]] ({{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. | |||
== See also == | == See also == | ||
Revision as of 17:45, 16 May 2026
| Interval information |
Soruyo comma
reduced
85/84, the monk comma, is a 17-limit superparticular interval. It is the difference between 6/5 and 17/14, as well as 7/5 and 17/12.
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).
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 (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.