405/392: Difference between revisions

(5 intermediate revisions by 3 users not shown)

Line 1:

{{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]] [[~~medium~~ comma]]. Tempering it out, this leads to the [[~~greenwoodmic~~ temperaments]].

'''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 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 ==

=== 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:Commas with unknown etymology]]

~~{{Stub}}~~

@@ Line 1: / Line 1: @@
 {{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]] [[medium comma]]. Tempering it out, this leads to the [[greenwoodmic temperaments]].
+'''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 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| )/|\ }}.
 [[Category:Greenwoodmic]]
+[[Category:Commas with unknown etymology]]
-{{Stub}}