405/392: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 405/392 | | Ratio = 405/392 | ||
| Name = greenwoodma | | Name = greenwoodma, smaller breedsmic half-apotome | ||
| Color name = rry-2, ruruyo negative 2nd | | Color name = rry-2, ruruyo negative 2nd | ||
| Comma = yes | | Comma = yes | ||
}} | }} | ||
'''405/392''', the '''greenwoodma''', is a [[medium comma|medium]] [[7-limit]] [[comma]]. It is the difference between [[8/5]] and a stack of two [[9/7]]'s. In terms of commas, it is the | '''405/392''', the '''greenwoodma''', is a [[medium comma|medium]] [[7-limit]] [[comma]]. It is the difference between [[8/5]] and a stack of two [[9/7]]'s. In terms of commas, it is the product of the [[81/80|syntonic comma (81/80)]] and the [[50/49|jubilisma (50/49)]]. | ||
In the 11-limit, it factors into simpler commas as ([[45/44]])⋅([[99/98]]). | In the 11-limit, it factors into simpler commas as ([[45/44]])⋅([[99/98]]). | ||
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== Temperaments == | == Temperaments == | ||
[[Tempering out]] this comma leads to the rank-3 [[greenwoodmic]] temperament. This temperament splits a [[~]][[5/2]] in two, each representing ~[[14/9]]. See [[Greenwoodmic temperaments]] for a collection of rank-2 temperaments where it is tempered out. | [[Tempering out]] this comma leads to the rank-3 [[greenwoodmic]] temperament. This temperament splits a [[~]][[5/2]] in two, each representing ~[[14/9]]. See [[Greenwoodmic temperaments]] for a collection of rank-2 temperaments where it is tempered out. | ||
Tempering out instead [[2401/2400]] equates this with [[1323/1280]] and sets both equal to [[sqrt(2187/2048)]]. | |||
== Notation == | == Notation == | ||
Latest revision as of 17:11, 3 October 2026
| Interval information |
smaller breedsmic half-apotome
405/392, the greenwoodma, is a medium 7-limit comma. It is the difference between 8/5 and a stack of two 9/7's. In terms of commas, it is the product of the syntonic comma (81/80) and the jubilisma (50/49).
In the 11-limit, it factors into simpler commas as (45/44)⋅(99/98).
Temperaments
Tempering out this comma leads to the rank-3 greenwoodmic temperament. This temperament splits a ~5/2 in two, each representing ~14/9. See Greenwoodmic temperaments for a collection of rank-2 temperaments where it is tempered out.
Tempering out instead 2401/2400 equates this with 1323/1280 and sets both equal to sqrt(2187/2048).
Notation
Sagittal notation
In the Sagittal system, the downward version of this comma (possibly tempered) is represented by the sagittal and is called the 49/5 medium diesis, or 49/5M for short, because the simplest interval it notates is 49/5 = 7×7/5 (equiv. 49/40), as for example in C-E . The upward version is called 5/49M or 49/5M up and is represented by .