Ragismic family - Revision history

FloraC: /* Vidar */ note the relation with lux

2026-04-22T10:32:40Z

Vidar: note the relation with lux

← Older revision		Revision as of 10:32, 22 April 2026
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	== Vidar ==		== Vidar ==
			Vidar tempers out the [[luxma]] and shares the same generators with [[lux]], from which it only differs in the mapping of [[prime interval\|prime]] [[7/1\|7]].

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

FloraC: Oops

2026-04-22T10:26:33Z

Oops

← Older revision		Revision as of 10:26, 22 April 2026
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	: Angle (10/9, 6/5) = 105.299°		: Angle (10/9, 6/5) = 105.299°

	[[Optimal ~~tunings~~]]:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1200.0018{{c}}, ~3/2 = 701.9851{{c}}, ~5/4 = 386.2710{{c}}		* [[WE]]: ~2 = 1200.0018{{c}}, ~3/2 = 701.9851{{c}}, ~5/4 = 386.2710{{c}}
	: [[error map]]: {{val\| +0.002 +0.032 -0.039 -0.014 }}		: [[error map]]: {{val\| +0.002 +0.032 -0.039 -0.014 }}
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	{{Mapping\|legend=1\| 1 0 0 1 6 \| 0 1 0 7 -6 \| 0 0 1 -4 3 }}		{{Mapping\|legend=1\| 1 0 0 1 6 \| 0 1 0 7 -6 \| 0 0 1 -4 3 }}

	[[Optimal ~~tunings~~]]:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1200.4709{{c}}, ~3/2 = 701.3876{{c}}, ~5/4 = 385.3287{{c}}		* [[WE]]: ~2 = 1200.4709{{c}}, ~3/2 = 701.3876{{c}}, ~5/4 = 385.3287{{c}}
	: [[error map]]: {{val\| +0.471 -0.097 -0.043 -0.427 -0.833 }}		: [[error map]]: {{val\| +0.471 -0.097 -0.043 -0.427 -0.833 }}
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	{{Mapping\|legend=1\| 1 0 0 1 -3 \| 0 1 0 7 7 \| 0 0 1 -4 -2 }}		{{Mapping\|legend=1\| 1 0 0 1 -3 \| 0 1 0 7 7 \| 0 0 1 -4 -2 }}

	[[Optimal ~~tunings~~]]:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1199.1423{{c}}, ~3/2 = 703.8558{{c}}, ~5/4 = 389.2089{{c}}		* [[WE]]: ~2 = 1199.1423{{c}}, ~3/2 = 703.8558{{c}}, ~5/4 = 389.2089{{c}}
	: [[error map]]: {{val\| -0.858 +1.043 +1.180 +1.329 -2.745 }}		: [[error map]]: {{val\| -0.858 +1.043 +1.180 +1.329 -2.745 }}
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	: mapping generators: ~99/70, ~3, ~5		: mapping generators: ~99/70, ~3, ~5

	[[Optimal ~~tunings~~]]:		[[Optimal tuning]]s:
	* [[WE]]: ~99/70 = 600.0103{{c}}, ~3/2 = 701.9669{{c}}, ~5/4 = 386.2245{{c}}		* [[WE]]: ~99/70 = 600.0103{{c}}, ~3/2 = 701.9669{{c}}, ~5/4 = 386.2245{{c}}
	: [[error map]]: {{val\| +0.021 +0.033 -0.048 +0.045 -0.126 }}		: [[error map]]: {{val\| +0.021 +0.033 -0.048 +0.045 -0.126 }}
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	: mapping generators: ~2, ~343/198, ~5		: mapping generators: ~2, ~343/198, ~5

	[[Optimal ~~tunings~~]]:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1200.0031{{c}}, ~343/198 = 950.9942{{c}}, ~5/4 = 386.2812{{c}}		* [[WE]]: ~2 = 1200.0031{{c}}, ~343/198 = 950.9942{{c}}, ~5/4 = 386.2812{{c}}
	: [[error map]]: {{val\| +0.021 +0.033 -0.048 +0.045 -0.126 }}		: [[error map]]: {{val\| +0.021 +0.033 -0.048 +0.045 -0.126 }}
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	: mapping generators: ~2, ~3, ~320/297		: mapping generators: ~2, ~3, ~320/297

	[[Optimal ~~tunings~~]]:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1199.9750{{c}}, ~3/2 = 702.0222{{c}}, ~320/297 = 128.7779{{c}}		* [[WE]]: ~2 = 1199.9750{{c}}, ~3/2 = 702.0222{{c}}, ~320/297 = 128.7779{{c}}
	: [[error map]]: {{val\| -0.025 +0.042 -0.030 -0.006 +0.046 }}		: [[error map]]: {{val\| -0.025 +0.042 -0.030 -0.006 +0.046 }}
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	: mapping generators: ~2, ~3, ~55/48		: mapping generators: ~2, ~3, ~55/48

	[[Optimal ~~tunings~~]]:		[[Optimal tuning]]s:
	* [[WE]]: ~2 = 1199.9928{{c}}, ~3/2 = 701.9969{{c}}, ~55/48 = 235.6566{{c}}		* [[WE]]: ~2 = 1199.9928{{c}}, ~3/2 = 701.9969{{c}}, ~55/48 = 235.6566{{c}}
	: [[error map]]: {{val\| -0.007 +0.035 -0.036 -0.016 +0.022 }}		: [[error map]]: {{val\| -0.007 +0.035 -0.036 -0.016 +0.022 }}

FloraC: Switch to Sintel's badness, WE & CWE tunings

2026-04-22T10:25:31Z

Switch to Sintel's badness, WE & CWE tunings

Show changes

FloraC: Update

2026-04-11T10:06:40Z

Update

← Older revision		Revision as of 10:06, 11 April 2026
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	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
	* ''[[Sensigh]]'' → [[~~Sensamagic~~ family #Sensigh\|~~Sensamagic~~ family]]		* ''[[Sensigh]]'' → [[Sengic family #Sensigh\|Sengic family]]
	* ''[[Catakleismoid]]'' → [[~~Marvel~~ family #Catakleismoid\|~~Marvel~~ family]]		* ''[[Catakleismoid]]'' → [[Kleismic rank-3 family #Catakleismoid\|Kleismic rank-3 family]]
	* ''[[Ennealimmic]]'' → [[Breed family #Ennealimmic\|Breed family]]		* ''[[Ennealimmic]]'' → [[Breed family #Ennealimmic\|Breed family]]

FloraC: Units & misc. cleanup. - redundant category

2026-03-25T15:56:11Z

Units & misc. cleanup. - redundant category

← Older revision		Revision as of 15:56, 25 March 2026
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	{{Mapping\|legend=1\| 1 0 0 1 \| 0 1 0 7 \| 0 0 1 -4 }}		{{Mapping\|legend=1\| 1 0 0 1 \| 0 1 0 7 \| 0 0 1 -4 }}

	: mapping generators: ~2, ~3, ~5		: mapping generators: ~2, ~3, ~5

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	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[7-odd-limit]] [[~~Eigenmonzo~~ basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7		* [[7-odd-limit]] [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7
	* [[9-odd-limit]] [[~~Eigenmonzo~~ basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5		* [[9-odd-limit]] [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

	{{Optimal ET sequence\|legend=1\| 19, 27, 45, 46, 53, 72, 99, 171, 441, 612, 935, 1106, 1277, 1547, 1718, 4983, 6701, 8419, 17279c }}		{{Optimal ET sequence\|legend=1\| 19, 27, 45, 46, 53, 72, 99, 171, 441, 612, 935, 1106, 1277, 1547, 1718, 4983, 6701, 8419, 17279c }}

	[[Projection pair]]: ~7 = ~4374/625		[[Projection pair]]: <code>7 ~4374/625</code>

	Scales: [[Ragismic19]], [[Ragismic chromatic]]		Scales: [[Ragismic19]], [[Ragismic chromatic]]
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	{{Optimal ET sequence\|legend=1\| 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee }}		{{Optimal ET sequence\|legend=1\| 7, 19, 26, 45, 46, 53, 72, 118, 190, 315e, 361e, 433de, 623cdee }}

	[[Badness]]: 0.721 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.721 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 0 1 6 2 \| 0 1 0 7 -6 4 \| 0 0 1 -4 3 -2 }}		Mapping: {{mapping\| 1 0 0 1 6 2 \| 0 1 0 7 -6 4 \| 0 0 1 -4 3 -2 }}

	{{Optimal ET sequence\|legend=1\| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}		{{Optimal ET sequence\|legend=0\| 7, 19, 26, 46, 53, 72, 118f, 125f, 171ef, 190ff, 197ef, 243eff }}

	Badness: 0.840 × 10<sup>-3</sup>		Badness (Smith): 0.840 × 10<sup>-3</sup>

	== Ulmo ==		== Ulmo ==
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	{{Optimal ET sequence\|legend=1\| 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd }}		{{Optimal ET sequence\|legend=1\| 7, 39, 46, 53, 80, 126, 179, 259cd, 385bcd }}

	[[Badness]]: 1.23 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.23 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 0 1 -3 2 \| 0 1 0 7 7 4 \| 0 0 1 -4 -2 -2 }}		Mapping: {{mapping\| 1 0 0 1 -3 2 \| 0 1 0 7 7 4 \| 0 0 1 -4 -2 -2 }}

	{{Optimal ET sequence\|legend=1\| 7, 39, 46, 53, 80, 133d, 179, 312cdf }}		{{Optimal ET sequence\|legend=0\| 7, 39, 46, 53, 80, 133d, 179, 312cdf }}

	Badness: 0.932 × 10<sup>-3</sup>		Badness (Smith): 0.932 × 10<sup>-3</sup>

	== Thor ==		== Thor ==
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	{{Mapping\|legend=1\| 2 0 0 2 5 \| 0 1 0 7 5 \| 0 0 1 -4 -3 }}		{{Mapping\|legend=1\| 2 0 0 2 5 \| 0 1 0 7 5 \| 0 0 1 -4 -3 }}

	: mapping generators: ~99/70, ~3, ~5		: mapping generators: ~99/70, ~3, ~5

	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[11-odd-limit]] [[~~Eigenmonzo~~ basis\|unchanged-interval (eigenmonzo) basis]]: 2.7.11/5		* [[11-odd-limit]] [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.7.11/5

	{{Optimal ET sequence\|legend=1\| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}		{{Optimal ET sequence\|legend=1\| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}

	[[Badness]]: 0.0888 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.0888 × 10<sup>-3</sup>

	[[Projection pair]]s: 2 ~~= ~~~9801/4900, ~7 ~~= ~~~21434787/3062500, ~11 ~~= ~~~2310905821257/210087500000 to 3.5.14/11		[[Projection pair]]s: <code>2 9801/4900, 7 21434787/3062500, 11 2310905821257/210087500000</code> to 3.5.14/11

	=== Thunor ===		=== Thunor ===
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	* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13		* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13

	{{Optimal ET sequence\|legend=1\| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}		{{Optimal ET sequence\|legend=0\| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}

	Badness: 0.341 × 10<sup>-3</sup>		Badness (Smith): 0.341 × 10<sup>-3</sup>

	Scales: [[Thunor46]]		Scales: [[Thunor46]]
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	Mapping: {{mapping\| 2 0 0 2 5 22 \| 0 1 0 7 5 -9 \| 0 0 1 -4 -3 3 }}		Mapping: {{mapping\| 2 0 0 2 5 22 \| 0 1 0 7 5 -9 \| 0 0 1 -4 -3 3 }}

	{{Optimal ET sequence\|legend=1\| 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 }}		{{Optimal ET sequence\|legend=0\| 46, 72f, 106, 118, 152, 224, 270, 494, 764, 1106, 1376, 1870 }}

	Badness: 0.549 × 10<sup>-3</sup>		Badness (Smith): 0.549 × 10<sup>-3</sup>

	=== Donar ===		=== Donar ===
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	* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11		* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11

	{{Optimal ET sequence\|legend=1\| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}		{{Optimal ET sequence\|legend=0\| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}

	Badness: 0.322 × 10<sup>-3</sup>		Badness (Smith): 0.322 × 10<sup>-3</sup>

	Scales: [[Donar46]]		Scales: [[Donar46]]
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	{{Mapping\|legend=1\| 1 0 0 1 2 \| 0 2 0 14 37 \| 0 0 1 -4 -12 }}		{{Mapping\|legend=1\| 1 0 0 1 2 \| 0 2 0 14 37 \| 0 0 1 -4 -12 }}

	: mapping generators: ~2, ~343/198, ~5		: mapping generators: ~2, ~343/198, ~5

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	Mapping: {{mapping\| 1 0 2 -7 8 -6 \| 0 1 0 7 -3 7 \| 0 0 3 -12 2 -13 }}		Mapping: {{mapping\| 1 0 2 -7 8 -6 \| 0 1 0 7 -3 7 \| 0 0 3 -12 2 -13 }}

	{{Optimal ET sequence\|legend=1\| 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f }}		{{Optimal ET sequence\|legend=0\| 46, 111df, 159df, 178, 205, 224, 270, 494, 764, 1258, 1771, 2041f, 2265, 2535f }}

	== Vidar ==		== Vidar ==
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	{{Mapping\|legend=1\| 1 0 0 1 5 \| 0 1 4 -9 -3 \| 0 0 -5 20 4 }}		{{Mapping\|legend=1\| 1 0 0 1 5 \| 0 1 4 -9 -3 \| 0 0 -5 20 4 }}

	: mapping generators: ~2, ~3, ~96/55		: mapping generators: ~2, ~3, ~96/55

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	Mapping: {{mapping\| 1 0 0 1 5 6 \| 0 1 4 -9 -3 -5 \| 0 0 -5 20 4 7 }}		Mapping: {{mapping\| 1 0 0 1 5 6 \| 0 1 4 -9 -3 -5 \| 0 0 -5 20 4 7 }}

	{{Optimal ET sequence\|legend=1\| 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f }}		{{Optimal ET sequence\|legend=0\| 46, 87d, 91, 133d, 137d, 178, 224, 270, 494, 764, 1125, 1395, 1619, 1665, 1889, 4048, 4542, 6431f }}

	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Ragismic family\| ]] <!-- main article -->		[[Category:Ragismic family\| ]] <!-- main article -->
	~~[[Category:Ragismic\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

Overthink: /* Thunor */ + scale

2025-12-06T21:52:31Z

Thunor: + scale

← Older revision		Revision as of 21:52, 6 December 2025
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	Badness: 0.341 × 10<sup>-3</sup>		Badness: 0.341 × 10<sup>-3</sup>

			Scales: [[Thunor46]]

	=== Rym ===		=== Rym ===

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

2025-11-27T12:28:39Z

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

← Older revision		Revision as of 12:28, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Ragismic family\| ]] <!-- main article -->		[[Category:Ragismic family\| ]] <!-- main article -->
	[[Category:Ragismic\| ]] <!-- key article -->		[[Category:Ragismic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-06-24T00:32:09Z

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

← Older revision		Revision as of 00:32, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Ragismic family\| ]] <!-- main article -->		[[Category:Ragismic family\| ]] <!-- main article -->
	[[Category:Ragismic\| ]] <!-- key article -->		[[Category:Ragismic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

Lériendil: Text replacement - "eigenmonzo (unchanged-interval) " to "unchanged-interval (eigenmonzo) "

2025-06-21T06:58:12Z

Text replacement - "eigenmonzo (unchanged-interval) " to "unchanged-interval (eigenmonzo) "

← Older revision		Revision as of 06:58, 21 June 2025
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	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[7-odd-limit]] [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5.7		* [[7-odd-limit]] [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7
	* [[9-odd-limit]] [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.3.7/5		* [[9-odd-limit]] [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.7/5

	{{Optimal ET sequence\|legend=1\| 19, 27, 45, 46, 53, 72, 99, 171, 441, 612, 935, 1106, 1277, 1547, 1718, 4983, 6701, 8419, 17279c }}		{{Optimal ET sequence\|legend=1\| 19, 27, 45, 46, 53, 72, 99, 171, 441, 612, 935, 1106, 1277, 1547, 1718, 4983, 6701, 8419, 17279c }}
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	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[11-odd-limit]] [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.7.11/5		* [[11-odd-limit]] [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.7.11/5

	{{Optimal ET sequence\|legend=1\| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}		{{Optimal ET sequence\|legend=1\| 26, 34d, 46, 72, 118, 152, 224, 270, 342, 494, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}
Line 110:		Line 110:

	Minimax tuning:		Minimax tuning:
	* 13- and 15-odd-limit ~~eigenmonzo (~~unchanged-interval) basis: 2.9/7.13		* 13- and 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.9/7.13

	{{Optimal ET sequence\|legend=1\| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}		{{Optimal ET sequence\|legend=1\| 26, 46, 72, 152f, 198, 224, 270, 494, 764, 1258 }}
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	Minimax tuning:		Minimax tuning:
	* 13-odd-limit ~~eigenmonzo (~~unchanged-interval) basis: 2.7.11/5		* 13-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.11/5
	* 15-odd-limit ~~eigenmonzo (~~unchanged-interval) basis: 2.7.15/11		* 15-odd-limit unchanged-interval (eigenmonzo) basis: 2.7.15/11

	{{Optimal ET sequence\|legend=1\| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}		{{Optimal ET sequence\|legend=1\| 34d, 46, 80, 144, 178, 190, 224, 494, 684, 764, 954, 1178, 1448, 6970ceeff, 8418ceeff }}

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

" to "{{Technical data page}}"

2025-04-13T13:43:18Z

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

← Older revision		Revision as of 13:43, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''ragismic family''' of temperaments are rank-3 microtemperaments which temper out [[4375/4374]].		The '''ragismic family''' of temperaments are rank-3 microtemperaments which temper out [[4375/4374]].