Mirwomo comma: Difference between revisions
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'''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]]. | '''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 == | == Temperaments == | ||
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.