405/392 - Revision history

FloraC: + factorization

2026-04-09T18:51:32Z

+ factorization

← Older revision		Revision as of 18:51, 9 April 2026
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	}}		}}
	'''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)]].		'''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 ==		== Temperaments ==

FloraC: Move data to a dedicated collection page

2025-12-24T13:34:08Z

Move data to a dedicated collection page

@@ Line 8: / Line 8: @@
 == 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.
 == Notation ==

FloraC: Update data

2025-12-24T13:32:59Z

Update data

← Older revision		Revision as of 13:32, 24 December 2025
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	{{Mapping\|legend=1\| 1 0 1 -1 \| 0 1 0 2 \| 0 0 2 1 }}		{{Mapping\|legend=1\| 1 0 1 -1 \| 0 1 0 2 \| 0 0 2 1 }}

	: mapping generators: ~2, ~3, ~14/9		: mapping generators: ~2, ~3, ~14/9

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	* [[~~CTE~~]]: ~2 = ~~1200~~.~~000~~, ~3/2 = ~~694~~.~~595~~, ~14/9 = ~~791~~.~~182~~		* [[WE]]: ~2 = 1201.9369{{c}}, ~3/2 = 693.3783{{c}}, ~14/9 = 790.3845{{c}}
	: [[error map]]: {{val\| 0.~~000~~ -7.~~360~~ -3.~~949~~ +11.~~546~~ }}		: [[error map]]: {{val\| +1.937 -6.640 -3.608 +10.252 }}
	* [[CWE]]: ~2 = 1200.~~000~~, ~3/2 = 693.~~344~~, ~14/9 = 790.~~072~~		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 693.3443{{c}}, ~14/9 = 790.0724{{c}}
	: [[error map]]: {{val\| 0.000 -8.611 -6.169 +7.935 }}		: error map: {{val\| 0.000 -8.611 -6.169 +7.935 }}

	{{Optimal ET sequence\|legend=1\| 9, 12, 26, 38, 73bc }}		{{Optimal ET sequence\|legend=1\| 9, 12, 26, 38, 73bc }}

	[[Badness]] (~~Smith~~): 0.~~412 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 1.82

	== Notation ==		== Notation ==

FloraC: Expand on the temperament

2025-01-06T11:58:00Z

Expand on the temperament

@@ Line 5: / Line 5: @@
 | Comma = yes
 }}
-'''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.
 == Notation ==
@@ Line 16: / Line 35: @@
 [[Category:Greenwoodmic]]
 [[Category:Commas with unknown etymology]]

FloraC: Note that it's the sum of 81/80 and 50/49

2025-01-06T11:46:34Z

Note that it's the sum of 81/80 and 50/49

← Older revision		Revision as of 11:46, 6 January 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''405/392''', the '''greenwoodma''', is a [[medium comma\|medium]] [[7-limit]] [[comma]].		'''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)]].

	== Temperaments ==		== Temperaments ==

FloraC: Cleanup

2025-01-06T11:41:40Z

Cleanup

← Older revision		Revision as of 11:41, 6 January 2025
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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]] [[~~medium~~ comma~~]]. Tempering it out, this leads to the [[greenwoodmic temperaments~~]].		'''405/392''', the '''greenwoodma''', is a [[medium comma\|medium]] [[7-limit]] [[comma]].

	==Sagittal notation==		== 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.

			== 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]]
	{{~~todo~~\|expand}}		{{Todo\| expand }}

BudjarnLambeth at 07:32, 3 November 2024

2024-11-03T07:32:14Z

← Older revision		Revision as of 07:32, 3 November 2024
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	[[Category:Greenwoodmic]]		[[Category:Greenwoodmic]]
			[[Category:Commas with unknown etymology]]
	{{todo\|expand}}		{{todo\|expand}}

Cmloegcmluin at 23:12, 14 October 2024

2024-10-14T23:12:33Z

← Older revision		Revision as of 23:12, 14 October 2024
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	}}		}}
	'''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 [[7-limit]] [[medium comma]]. Tempering it out, this leads to the [[greenwoodmic temperaments]].

			==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]]
	{{todo\|expand}}		{{todo\|expand}}

BudjarnLambeth: -stub +todo:expand

2024-01-30T07:21:11Z

-stub +todo:expand

← Older revision		Revision as of 07:21, 30 January 2024
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	[[Category:Greenwoodmic]]		[[Category:Greenwoodmic]]
			{{todo\|expand}}
	{{~~Stub~~}}

Francium: Created page with "{{Infobox Interval |Ratio = 405/392 |Name = greenwoodma |Color name = rry-2, ruruyo negative 2nd |Comma = yes }} '''405/392''', the '''greenwoodma''', is a 7-limit mediu..."

2023-09-07T08:32:00Z

Created page with "{{Infobox Interval |Ratio = 405/392 |Name = greenwoodma |Color name = rry-2, ruruyo negative 2nd |Comma = yes }} '''405/392''', the '''greenwoodma''', is a 7-limit mediu..."

New page

{{Infobox Interval
|Ratio = 405/392
|Name = greenwoodma
|Color name = rry-2, ruruyo negative 2nd
|Comma = yes
}}
'''405/392''', the '''greenwoodma''', is a [[7-limit]] [[medium comma]]. Tempering it out, this leads to the [[greenwoodmic temperaments]].

[[Category:Greenwoodmic]]

{{Stub}}