Fifive family - Revision history

FloraC: Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

2025-11-27T12:24:56Z

Text replacement - "Category:Temperament families↵Category:Pages with mostly numerical content" to "Category:Temperament families"

← Older revision		Revision as of 12:24, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Fifive family\| ]] <!-- main article -->		[[Category:Fifive family\| ]] <!-- main article -->
	[[Category:Fifive\| ]] <!-- key article -->		[[Category:Fifive\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

Lériendil: Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

2025-06-24T00:27:18Z

Text replacement - "Category:Temperament families" to "Category:Temperament families Category:Pages with mostly numerical content"

← Older revision		Revision as of 00:27, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Fifive family\| ]] <!-- main article -->		[[Category:Fifive family\| ]] <!-- main article -->
	[[Category:Fifive\| ]] <!-- key article -->		[[Category:Fifive\| ]] <!-- key article -->
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 05:20, 12 June 2025

2025-06-12T05:20:26Z

← Older revision		Revision as of 05:20, 12 June 2025
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	{{Mapping\|legend=1\| 2 2 3 4 \| 0 5 7 7 }}		{{Mapping\|legend=1\| 2 2 3 4 \| 0 5 7 7 }}

	~~{{Multival\|legend=1\| 10 14 14 -1 -6 -7 }}~~

	[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349		[[Optimal tuning]] ([[POTE]]): ~7/5 = 1\2, ~27/25 = 140.349

FloraC: Text replacement - "{{Technical data page}}

" to "{{Technical data page}}"

2025-04-13T13:41:12Z

Text replacement - "{{Technical data page}}<br><br>" to "{{Technical data page}}"

← Older revision		Revision as of 13:41, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''fifive family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[fifive comma]] ({{monzo\|legend=1\| -1 -14 10 }}, [[ratio]]: 9765625/9565938).		The '''fifive family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[fifive comma]] ({{monzo\|legend=1\| -1 -14 10 }}, [[ratio]]: 9765625/9565938).

BudjarnLambeth: {{Technical data page}}

2025-04-13T05:35:40Z

{{Technical data page}}<br><br>

← Older revision		Revision as of 05:35, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''fifive family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[fifive comma]] ({{monzo\|legend=1\| -1 -14 10 }}, [[ratio]]: 9765625/9565938).		The '''fifive family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[fifive comma]] ({{monzo\|legend=1\| -1 -14 10 }}, [[ratio]]: 9765625/9565938).

FloraC: +naming history

2025-04-01T11:56:38Z

+naming history

← Older revision		Revision as of 11:56, 1 April 2025
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	The '''fifive family''' tempers out the [[fifive comma]]~~, 9765625/9565938 =~~ {{monzo\| -1 -14 10 }}.		The '''fifive family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[fifive comma]] ({{monzo\|legend=1\| -1 -14 10 }}, [[ratio]]: 9765625/9565938).

			The name ''fifive'' was given by [[Petr Pařízek]] in 2011 for it splits the [[3/2\|perfect fifth]] in five.<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>

	Considered below are crepuscular, fifives, and fourfives.		Considered below are crepuscular, fifives, and fourfives.
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	Badness: 0.024796		Badness: 0.024796

			== Notes ==

	[[Category:Temperament families]]		[[Category:Temperament families]]

Lériendil: added fourfives

2024-08-27T04:01:39Z

added fourfives

@@ Line 1: / Line 1: @@
 The '''fifive family''' tempers out the [[fifive comma]], 9765625/9565938 = {{monzo| -1 -14 10 }}.
-Temperaments discussed elsewhere include:
+Considered below are crepuscular, fifives, and fourfives.
 == Fifive ==
@@ Line 170: / Line 167: @@
 Badness: 0.029429
 [[Category:Temperament families]]

FloraC: Review (restore POTE tuning since the replacement was based on a wrong assessment: CWE is ~140.629 not .623)

2024-04-19T02:47:20Z

Review (restore POTE tuning since the replacement was based on a wrong assessment: CWE is ~140.629 not .623)

← Older revision		Revision as of 02:47, 19 April 2024
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	: mapping generators: ~78125/50421, ~27/25		: mapping generators: ~78125/50421, ~27/25

	[[Optimal tuning]] ([[~~CWE~~]]): ~78125/50421 = 1\2, ~27/25 = 140.~~623~~		[[Optimal tuning]]s:
			* [[CTE]]: ~78125/50421 = 1\2, ~27/25 = 140.6349
			* [[POTE]]: ~78125/50421 = 1\2, ~27/25 = 140.624

	{{Optimal ET sequence\|legend=1\| 8, 26, 34, 94, 128 }}		{{Optimal ET sequence\|legend=1\| 8, 18bc, 26, 34, 94, 128 }}

	[[Badness]]: 0.205812		[[Badness]]:
			* Smith: 0.205812
	Dirichlet ~~badness~~: 4.828		* Dirichlet: 4.828

	=== 2.3.5.13 subgroup ===		=== 2.3.5.13 subgroup ===
			Subgroup: 2.3.5.13

	~~[[Subgroup]]~~: ~~2.3.5.13~~		Comma list: 325/324, 20000/19773

	~~[[Comma list]]~~: ~~9765625/9565938, 325/324~~		Mapping: {{mapping\| 2 2 3 6 \| 0 5 7 6 }}

	{{~~Mapping\|legend=1~~\| 2 2 3 6 \| 0 5 7 6 }}

	: mapping generators: ~351/250, ~13/12		: mapping generators: ~351/250, ~13/12

	[[Optimal ~~tuning]] ([[~~CWE~~]])~~: ~351/250 = 1\2, ~13/12 = 140.~~623~~		Optimal tunings:
			* CTE: ~351/250 = 1\2, ~13/12 = 140.5685
			* CWE: ~351/250 = 1\2, ~13/12 = 140.6232

	~~[[Patent val]] EDO tunings~~: 8, 26, 34~~, 60, 68~~, 94, 128		Optimal ET sequence: {{Optimal ET sequence\| 8, 18bcf, 26, 34, 94, 128 }}

	Dirichlet ~~badness~~: 0.800		Badness:
			* Smith: 0.0240
			* Dirichlet: 0.800

	=== 2.3.5.13.17 subgroup ===		=== 2.3.5.13.17 subgroup ===
			Subgroup: 2.3.5.13.17

	~~[[Subgroup]]: 2.3.5.13.17~~		Comma list: 170/169, 289/288, 325/324

	[[Comma list]]: ~~9765625~~/~~9565938~~, 325/324~~, 289/288~~

	{{~~Mapping\|legend=1~~\| 2 2 3 6 7 \| 0 5 7 6 5 }}		Mapping: {{mapping\| 2 2 3 6 7 \| 0 5 7 6 5 }}

	: mapping generators: ~17/12, ~13/12		: mapping generators: ~17/12, ~13/12

	[[Optimal ~~tuning]] ([[~~CWE~~]])~~: ~17/12 = 1\2, ~13/12 = 140.~~606~~		Optimal tunings:
			* CTE: ~17/12 = 1\2, ~13/12 = 140.5958
			* CWE: ~17/12 = 1\2, ~13/12 = 140.6057

	~~[[Patent val]] EDO tunings~~: 8, 26, 34~~, 60, 68~~, 94, 128		Optimal ET sequence: {{Optimal ET sequence\| 8, 18bcfg, 26, 34, 94, 128 }}

	Dirichlet ~~badness~~: 0.488		Badness:
			* Smith: 0.0110
			* Dirichlet: 0.488

	== Crepuscular ==		== Crepuscular ==

Godtone: restore old badness for reference

2024-04-19T01:19:40Z

restore old badness for reference

← Older revision		Revision as of 01:19, 19 April 2024
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	{{Optimal ET sequence\|legend=1\| 8, 26, 34, 94, 128 }}		{{Optimal ET sequence\|legend=1\| 8, 26, 34, 94, 128 }}

			[[Badness]]: 0.205812

	Dirichlet badness: 4.828		Dirichlet badness: 4.828

Godtone: clarify that these are using a different badness measure

2024-04-19T01:03:30Z

clarify that these are using a different badness measure

← Older revision		Revision as of 01:03, 19 April 2024
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	{{Optimal ET sequence\|legend=1\| 8, 26, 34, 94, 128 }}		{{Optimal ET sequence\|legend=1\| 8, 26, 34, 94, 128 }}

	~~[[Badness]]~~: 4.828		Dirichlet badness: 4.828

	=== 2.3.5.13 subgroup ===		=== 2.3.5.13 subgroup ===
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	[[Patent val]] EDO tunings: 8, 26, 34, 60, 68, 94, 128		[[Patent val]] EDO tunings: 8, 26, 34, 60, 68, 94, 128

	~~[[Badness]]~~: 0.800		Dirichlet badness: 0.800

	=== 2.3.5.13.17 subgroup ===		=== 2.3.5.13.17 subgroup ===
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	[[Patent val]] EDO tunings: 8, 26, 34, 60, 68, 94, 128		[[Patent val]] EDO tunings: 8, 26, 34, 60, 68, 94, 128

	~~[[Badness]]~~: 0.488		Dirichlet badness: 0.488

	== Crepuscular ==		== Crepuscular ==