405/392: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
|Ratio = 405/392 | | Ratio = 405/392 | ||
|Name = greenwoodma | | Name = greenwoodma | ||
|Color name = rry-2, ruruyo negative 2nd | | Color name = rry-2, ruruyo negative 2nd | ||
|Comma = yes | | Comma = yes | ||
}} | }} | ||
'''405/392''', the '''greenwoodma''', is a [[7-limit]] [[ | '''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 sum 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]]). | |||
== 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. | |||
== Notation == | |||
=== Sagittal notation === | |||
In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{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{{nbhsp}}{{sagittal | )\!/ }}. The upward version is called '''5/49M''' or '''49/5M up''' and is represented by {{sagittal| )/|\ }}. | |||
[[Category:Greenwoodmic]] | [[Category:Greenwoodmic]] | ||
[[Category:Commas with unknown etymology]] | |||
Latest revision as of 18:51, 9 April 2026
| Interval information |
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 sum 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.
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 .