Mirwomo comma: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
|Ratio = 33075/32768 | | Ratio = 33075/32768 | ||
|Name = Mirwomo comma | | Name = Mirwomo comma | ||
|Color name = Lzzyy1, labizoyo unison | | Color name = Lzzyy1, labizoyo unison | ||
|Comma = yes | | Comma = yes | ||
}} | }} | ||
'''33075/32768''', the '''mirwomo comma''', is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 16.1 [[cent]]s. It is the difference between the Pythagorean apotome of [[2187/2048]] and a stack of two septimal quartertones of [[36/35]]. | |||
In terms of other commas, it is the difference between [[525/512]] and [[64/63]], or between [[81/80]] and [[6144/6125]]. It factors into simpler commas as ([[225/224]])⋅([[1029/1024]]), as well as (225/224)<sup>2</sup>⋅([[2401/2400]]). | |||
== | == 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)<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. | |||
== 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. | |||
[[Category:Mirwomo]] | [[Category:Mirwomo]] | ||
[[Category:Commas named by combining multiple temperament names]] | |||
Latest revision as of 07:32, 16 September 2026
| 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.
In terms of other commas, it is the difference between 525/512 and 64/63, or between 81/80 and 6144/6125. It factors into simpler commas as (225/224)⋅(1029/1024), as well as (225/224)2⋅(2401/2400).
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.