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)]]. | ||
==Sagittal notation== | == 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. | |||
=== Greenwoodmic === | |||
[[Subgroup]]: 2.3.5.7 | |||
[[Comma list]]: 405/392 | |||
{{Mapping|legend=1| 1 0 1 -1 | 0 1 0 2 | 0 0 2 1 }} | |||
: mapping generators: ~2, ~3, ~14/9 | |||
[[Optimal tuning]]s: | |||
* [[CTE]]: ~2 = 1200.000, ~3/2 = 694.595, ~14/9 = 791.182 | |||
: [[error map]]: {{val| 0.000 -7.360 -3.949 +11.546 }} | |||
* [[CWE]]: ~2 = 1200.000, ~3/2 = 693.344, ~14/9 = 790.072 | |||
: [[error map]]: {{val| 0.000 -8.611 -6.169 +7.935 }} | |||
{{Optimal ET sequence|legend=1| 9, 12, 26, 38, 73bc }} | |||
[[Badness]] (Smith): 0.412 × 10<sup>-3</sup> | |||
== 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| )/|\ }}. | 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]] | [[Category:Commas with unknown etymology]] | ||