Mirwomo comma: Difference between revisions
Update |
m Formatting (this was dumb) |
||
| Line 8: | Line 8: | ||
== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma results in the 7-limit version of the [[mirwomo]] temperament. Mirwomo has a canonical [[11-limit]] [[extension]] that tempers out [[243/242]] and [[385/384]], as | [[Tempering out]] this comma results in the 7-limit version of the [[mirwomo]] temperament. Mirwomo has a canonical [[11-limit]] [[extension]] that tempers out [[243/242]] and [[385/384]], as 33075/32768 = (243/242)⋅(385/384)<sup>2</sup> (→ [[Rastmic rank-3 clan #Mirwomo]]). | ||
Mirwomo is tempered out in rank-2 temperaments such as [[miracle]], [[worschmidt]], and [[mohajira]]. See [[Mirwomo temperaments]] for a collection of rank-2 temperaments in which the comma gets tempered out. | Mirwomo is tempered out in rank-2 temperaments such as [[miracle]], [[worschmidt]], and [[mohajira]]. See [[Mirwomo temperaments]] for a collection of rank-2 temperaments in which the comma gets tempered out. | ||
Latest revision as of 16:40, 27 November 2025
| Interval information |
reduced harmonic
33075/32768, the mirwomo comma, is a small 7-limit comma measuring about 16.1 cents. It is the difference between the Pythagorean apotome of 2187/2048 and a stack of two septimal quartertones of 36/35.
Temperaments
Tempering out this comma results in the 7-limit version of the mirwomo temperament. Mirwomo has a canonical 11-limit extension that tempers out 243/242 and 385/384, as 33075/32768 = (243/242)⋅(385/384)2 (→ Rastmic rank-3 clan #Mirwomo).
Mirwomo is tempered out in rank-2 temperaments such as miracle, worschmidt, and mohajira. See Mirwomo temperaments for a collection of rank-2 temperaments in which the comma gets tempered out.
Etymology
As is noted above, the mirwomo comma is tempered out in miracle, worschmidt, and mohajira, and so the name is probably a contraction of these three names.