405/392: Difference between revisions

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| Comma = yes

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'''405/392''', the '''greenwoodma''', is a [[medium comma|medium]] [[7-limit]] [[comma]]. It is the sum of the [[81/80|syntonic comma (81/80)]] and the [[50/49|jubilisma (50/49)]].

'''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)]].

== Temperaments ==

[[Tempering out]] this comma leads to the '''greenwoodmic temperament'''. 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.

=== Greenwoodmic ===

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 405/392

: 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 }}

[[Badness]] (Smith): 0.412 × 10<sup>-3</sup>

== Notation ==

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[[Category:Greenwoodmic]]

[[Category:Commas with unknown etymology]]

~~{{Todo| expand }}~~

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-'''405/392''', the '''greenwoodma''', is a [[medium comma|medium]] [[7-limit]] [[comma]]. It is the sum of the [[81/80|syntonic comma (81/80)]] and the [[50/49|jubilisma (50/49)]].
+'''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)]].
 == Temperaments ==
-[[Tempering out]] this comma leads to the '''greenwoodmic temperament'''. 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.
+=== 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 ==
@@ Line 16: / Line 35: @@
 [[Category:Greenwoodmic]]
 [[Category:Commas with unknown etymology]]
-{{Todo| expand }}