Ditonmic family - Revision history

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

2025-11-27T12:16:56Z

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

← Older revision		Revision as of 12:16, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Ditonmic family\| ]] <!-- main article -->		[[Category:Ditonmic family\| ]] <!-- main article -->
	[[Category:Ditonmic]]		[[Category:Ditonmic]]
	[[Category:Rank 2]]		[[Category:Rank 2]]

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

2025-06-24T00:29:41Z

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

← Older revision		Revision as of 00:29, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Ditonmic family\| ]] <!-- main article -->		[[Category:Ditonmic family\| ]] <!-- main article -->
	[[Category:Ditonmic]]		[[Category:Ditonmic]]
	[[Category:Rank 2]]		[[Category:Rank 2]]

VectorGraphics at 04:46, 12 June 2025

2025-06-12T04:46:16Z

← Older revision		Revision as of 04:46, 12 June 2025
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	{{Mapping\|legend=1\| 1 6 3 13 \| 0 -13 -2 -30 }}		{{Mapping\|legend=1\| 1 6 3 13 \| 0 -13 -2 -30 }}

	~~{{Multival\|legend=1\| 13 2 30 -27 11 64 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:
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	{{Mapping\|legend=1\| 1 6 3 -4 \| 0 -13 -2 20 }}		{{Mapping\|legend=1\| 1 6 3 -4 \| 0 -13 -2 20 }}

	~~{{Multival\|legend=1\| 13 2 -20 -27 -68 -52 }}~~

	[[Optimal tuning]]s:		[[Optimal tuning]]s:

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

" to "{{Technical data page}}"

2025-04-13T13:42:55Z

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

← Older revision		Revision as of 13:42, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''ditonmic family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[ditonma]] ([[ratio]]: 1220703125/1207959552, {{monzo\|legend=1\| -27 -2 13 }}).		The '''ditonmic family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[ditonma]] ([[ratio]]: 1220703125/1207959552, {{monzo\|legend=1\| -27 -2 13 }}).

BudjarnLambeth: {{Technical data page}}

2025-04-13T07:09:50Z

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

← Older revision		Revision as of 07:09, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''ditonmic family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[ditonma]] ([[ratio]]: 1220703125/1207959552, {{monzo\|legend=1\| -27 -2 13 }}).		The '''ditonmic family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[ditonma]] ([[ratio]]: 1220703125/1207959552, {{monzo\|legend=1\| -27 -2 13 }}).

FloraC: +CTE tunings and error maps

2025-03-13T09:18:18Z

+CTE tunings and error maps

← Older revision		Revision as of 09:18, 13 March 2025
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	{{Mapping\|legend=1\| 1 6 3 \| 0 -13 -2 }}		{{Mapping\|legend=1\| 1 6 3 \| 0 -13 -2 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~15625/12288 = 407.574		[[Optimal tuning]]s:
			* [[CTE]]: ~2 = 1200.000, ~15625/12288 = 407.534
			: [[error map]]: {{val\| 0.000 +0.099 -1.382 }}
			* [[POTE]]: ~2 = 1200.000, ~15625/12288 = 407.574
			: error map: {{val\| 0.000 -0.416 -1.462 }}

	{{Optimal ET sequence\|legend=1\| 3, 47, 50, 53, 474c, 527c, 580c, 633c, 686c, 739c, 792c, 845cc }}		{{Optimal ET sequence\|legend=1\| 3, …, 47, 50, 53, 474c, 527c, 580c, 633c, 686c, 739c, 792c, 845cc }}

	[[Badness]] (Smith): 0.167086		[[Badness]] (Smith): 0.167086
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	{{Multival\|legend=1\| 13 2 30 -27 11 64 }}		{{Multival\|legend=1\| 13 2 30 -27 11 64 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~1225/972 = 407.690		[[Optimal tuning]]s:
			* [[CTE]]: ~2 = 1200.000, ~1225/972 = 407.642
			: [[error map]]: {{val\| 0.000 -1.298 -1.597 +1.921 }}
			* [[POTE]]: ~2 = 1200.000, ~1225/972 = 407.690
			: error map: {{val\| 0.000 -1.921 -1.693 +0.483 }}

	{{Optimal ET sequence\|legend=1\| 3d, 50, 53, 103, 156 }}		{{Optimal ET sequence\|legend=1\| 3d, 50, 53, 103, 156 }}
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	Mapping: {{mapping\| 1 6 3 13 -3 \| 0 -13 -2 -30 19 }}		Mapping: {{mapping\| 1 6 3 13 -3 \| 0 -13 -2 -30 19 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.000, ~1225/972 = 407.741		Optimal tunings:
			* CTE: ~2 = 1200.000, ~1225/972 = 407.688
			* POTE: ~2 = 1200.000, ~1225/972 = 407.741

	{{Optimal ET sequence\|legend=0\| 50, 53, 103 }}		{{Optimal ET sequence\|legend=0\| 50, 53, 103 }}
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	Mapping: {{mapping\| 1 6 3 13 -3 2 \| 0 -13 -2 -30 19 5 }}		Mapping: {{mapping\| 1 6 3 13 -3 2 \| 0 -13 -2 -30 19 5 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.000, ~325/256 = 407.736		Optimal tunings:
			* CTE: ~2 = 1200.000, ~325/256 = 407.691
			* POTE: ~2 = 1200.000, ~325/256 = 407.736

	{{Optimal ET sequence\|legend=0\| 50, 53, 103 }}		{{Optimal ET sequence\|legend=0\| 50, 53, 103 }}
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	Mapping: {{mapping\| 1 6 3 13 15 \| 0 -13 -2 -30 -34 }}		Mapping: {{mapping\| 1 6 3 13 15 \| 0 -13 -2 -30 -34 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.000, ~242/189 = 407.567		Optimal tunings:
			* CTE: ~2 = 1200.000, ~242/189 = 407.528
			* POTE: ~2 = 1200.000, ~242/189 = 407.567

	{{Optimal ET sequence\|legend=0\| 3de, 50e, 53 }}		{{Optimal ET sequence\|legend=0\| 3de, 50e, 53 }}
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	Mapping: {{mapping\| 1 6 3 13 15 20 \| 0 -13 -2 -30 -34 -48 }}		Mapping: {{mapping\| 1 6 3 13 15 20 \| 0 -13 -2 -30 -34 -48 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.000, ~33/26 = 407.541		Optimal tunings:
			* CTE: ~2 = 1200.000, ~242/189 = 407.514
			* POTE: ~2 = 1200.000, ~33/26 = 407.541

	{{Optimal ET sequence\|legend=0\| 3def, 53 }}		{{Optimal ET sequence\|legend=0\| 3def, 50eff, 53 }}

	Badness (Smith): 0.043989		Badness (Smith): 0.043989
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	{{Multival\|legend=1\| 13 2 -20 -27 -68 -52 }}		{{Multival\|legend=1\| 13 2 -20 -27 -68 -52 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~2625/2048 = 407.954		[[Optimal tuning]]s:
			* [[CTE]]: ~2 = 1200.000, ~2625/2048 = 407.922
			: [[error map]]: {{val\| 0.000 -4.939 -2.157 -10.388 }}
			* [[POTE]]: ~2 = 1200.000, ~2625/2048 = 407.954
			: error map: {{val\| 0.000 -5.353 -2.221 -9.751 }}

	{{Optimal ET sequence\|legend=1\| 3, 47, 50 }}		{{Optimal ET sequence\|legend=1\| 3, 47, 50 }}
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	Mapping: {{mapping\| 1 6 3 -4 -3 \| 0 -13 -2 20 19 }}		Mapping: {{mapping\| 1 6 3 -4 -3 \| 0 -13 -2 20 19 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.000, ~14/11 = 407.892		Optimal tunings:
			* CTE: ~2 = 1200.000, ~14/11 = 407.930
			* POTE: ~2 = 1200.000, ~14/11 = 407.892

	{{Optimal ET sequence\|legend=0\| 3, 47, 50~~, 53d~~ }}		{{Optimal ET sequence\|legend=0\| 3, 47, 50 }}

	Badness (Smith): 0.100884		Badness (Smith): 0.100884
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	Mapping: {{mapping\| 1 6 3 -4 -3 2 \| 0 -13 -2 20 19 5 }}		Mapping: {{mapping\| 1 6 3 -4 -3 2 \| 0 -13 -2 20 19 5 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.000, ~14/11 = 407.887		Optimal tunings:
			* CTE: ~2 = 1200.000, ~14/11 = 407.933
			* POTE: ~2 = 1200.000, ~14/11 = 407.887

	{{Optimal ET sequence\|legend=0\| 3, 47, 50~~, 53d~~ }}		{{Optimal ET sequence\|legend=0\| 3, 47, 50 }}

	Badness (Smith): 0.054997		Badness (Smith): 0.054997

FloraC: Spell 1\1 in decimal, note the badness metric being used, and misc. cleanup

2025-03-13T09:05:12Z

Spell 1\1 in decimal, note the badness metric being used, and misc. cleanup

← Older revision		Revision as of 09:05, 13 March 2025
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	{{Mapping\|legend=1\| 1 6 3 \| 0 -13 -2 }}		{{Mapping\|legend=1\| 1 6 3 \| 0 -13 -2 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~15625/12288 = 407.574		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~15625/12288 = 407.574

	{{Optimal ET sequence\|legend=1\| 3, 47, 50, 53, 474c, 527c, 580c, 633c, 686c, 739c, 792c, 845cc }}		{{Optimal ET sequence\|legend=1\| 3, 47, 50, 53, 474c, 527c, 580c, 633c, 686c, 739c, 792c, 845cc }}

	[[Badness]]: 0.167086		[[Badness]] (Smith): 0.167086

	== Coditone ==		== Coditone ==
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	{{Multival\|legend=1\| 13 2 30 -27 11 64 }}		{{Multival\|legend=1\| 13 2 30 -27 11 64 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~1225/972 = 407.690		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~1225/972 = 407.690

	{{Optimal ET sequence\|legend=1\| 3d, 50, 53, 103, 156 }}		{{Optimal ET sequence\|legend=1\| 3d, 50, 53, 103, 156 }}

	[[Badness]]: 0.064356		[[Badness]] (Smith): 0.064356

	=== 11-limit ===		=== 11-limit ===
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	Mapping: {{mapping\| 1 6 3 13 -3 \| 0 -13 -2 -30 19 }}		Mapping: {{mapping\| 1 6 3 13 -3 \| 0 -13 -2 -30 19 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~1225/972 = 407.741		Optimal tuning (POTE): ~2 = 1200.000, ~1225/972 = 407.741

	~~Optimal ET sequence:~~ {{~~optimal~~ ET sequence\| 50, 53, 103 }}		{{Optimal ET sequence\|legend=0\| 50, 53, 103 }}

	Badness: 0.044329		Badness (Smith): 0.044329

	==== 13-limit ====		==== 13-limit ====
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	Mapping: {{mapping\| 1 6 3 13 -3 2 \| 0 -13 -2 -30 19 5 }}		Mapping: {{mapping\| 1 6 3 13 -3 2 \| 0 -13 -2 -30 19 5 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~325/256 = 407.736		Optimal tuning (POTE): ~2 = 1200.000, ~325/256 = 407.736

	~~Optimal ET sequence:~~ {{~~optimal~~ ET sequence\| 50, 53, 103 }}		{{Optimal ET sequence\|legend=0\| 50, 53, 103 }}

	Badness: 0.024352		Badness (Smith): 0.024352

	=== Coditonic ===		=== Coditonic ===
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	Mapping: {{mapping\| 1 6 3 13 15 \| 0 -13 -2 -30 -34 }}		Mapping: {{mapping\| 1 6 3 13 15 \| 0 -13 -2 -30 -34 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~242/189 = 407.567		Optimal tuning (POTE): ~2 = 1200.000, ~242/189 = 407.567

	~~Optimal ET sequence:~~ {{~~optimal~~ ET sequence\| 3de, 50e, 53 }}		{{Optimal ET sequence\|legend=0\| 3de, 50e, 53 }}

	Badness: 0.063876		Badness (Smith): 0.063876

	==== 13-limit ====		==== 13-limit ====
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	Mapping: {{mapping\| 1 6 3 13 15 20 \| 0 -13 -2 -30 -34 -48 }}		Mapping: {{mapping\| 1 6 3 13 15 20 \| 0 -13 -2 -30 -34 -48 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~33/26 = 407.541		Optimal tuning (POTE): ~2 = 1200.000, ~33/26 = 407.541

	~~Optimal ET sequence:~~ {{~~optimal~~ ET sequence\| 3def, 53 }}		{{Optimal ET sequence\|legend=0\| 3def, 53 }}

	Badness: 0.043989		Badness (Smith): 0.043989

	== Diton ==		== Diton ==
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	{{Multival\|legend=1\| 13 2 -20 -27 -68 -52 }}		{{Multival\|legend=1\| 13 2 -20 -27 -68 -52 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~2625/2048 = 407.954		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~2625/2048 = 407.954

	{{Optimal ET sequence\|legend=1\| 3, 47, 50 }}		{{Optimal ET sequence\|legend=1\| 3, 47, 50 }}

	[[Badness]]: 0.242101		[[Badness]] (Smith): 0.242101

	=== 11-limit ===		=== 11-limit ===
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	Mapping: {{mapping\| 1 6 3 -4 -3 \| 0 -13 -2 20 19 }}		Mapping: {{mapping\| 1 6 3 -4 -3 \| 0 -13 -2 20 19 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~14/11 = 407.892		Optimal tuning (POTE): ~2 = 1200.000, ~14/11 = 407.892

	~~Optimal ET sequence:~~ {{~~optimal~~ ET sequence\| 3, 47, 50, 53d }}		{{Optimal ET sequence\|legend=0\| 3, 47, 50, 53d }}

	Badness: 0.100884		Badness (Smith): 0.100884

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 6 3 -4 -3 2 \| 0 -13 -2 20 19 5 }}		Mapping: {{mapping\| 1 6 3 -4 -3 2 \| 0 -13 -2 20 19 5 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~14/11 = 407.887		Optimal tuning (POTE): ~2 = 1200.000, ~14/11 = 407.887

	~~Optimal ET sequence:~~ {{~~optimal~~ ET sequence\| 3, 47, 50, 53d }}		{{Optimal ET sequence\|legend=0\| 3, 47, 50, 53d }}

	Badness: 0.054997		Badness (Smith): 0.054997

	== Notes ==		== Notes ==

FloraC: Sorting: move the bad extension below coditone

2025-03-13T09:02:49Z

Sorting: move the bad extension below coditone

@@ Line 15: / Line 15: @@
 [[Badness]]: 0.167086
 == Coditone ==
@@ Line 125: / Line 82: @@
 Badness: 0.043989
 == Notes ==

FloraC: De-canonicalize septimal ditonic. Note where the true ditone is

2025-03-13T09:02:09Z

De-canonicalize septimal ditonic. Note where the true ditone is

← Older revision		Revision as of 09:02, 13 March 2025
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	The '''ditonmic family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[ditonma]], 1220703125/1207959552 = {{monzo\| -27 -2 13 }}.		The '''ditonmic family''' of [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the [[ditonma]] ([[ratio]]: 1220703125/1207959552, {{monzo\|legend=1\| -27 -2 13 }}).

	== Ditonic ==		== Ditonic ==
	Named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>, ditonic can be described as the 50 & 53 temperament. It splits [[~]][[8/5]] in two for a generator, which happens to be an interval very close to the [[ditone]].		Named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>, ditonic can be described as the 50 & 53 temperament. It splits [[~]][[8/5]] in two for a generator, which happens to be an interval very close in size to the [[ditone]], ~81/64. Note that the ditone itself is 52 generator steps away.

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5
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	[[Badness]]: 0.167086		[[Badness]]: 0.167086

	== ~~Septimal ditonic~~ ==		== Diton ==
			This extension is known as ''ditonic'' in [[Graham Breed]]'s temperament finder.

	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

FloraC: +description

2024-11-04T16:18:18Z

+description

← Older revision		Revision as of 16:18, 4 November 2024
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	== Ditonic ==		== Ditonic ==
			Named by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group \| ''Suggested names for the unclasified temperaments'']</ref>, ditonic can be described as the 50 & 53 temperament. It splits [[~]][[8/5]] in two for a generator, which happens to be an interval very close to the [[ditone]].

	[[Subgroup]]: 2.3.5		[[Subgroup]]: 2.3.5

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	Badness: 0.043989		Badness: 0.043989

			== Notes ==

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