Kleismic rank-3 family - Revision history

FloraC: Move catakleismoid here

2026-04-11T09:42:17Z

Move catakleismoid here

@@ Line 160: / Line 160: @@
 Badness (Sintel): 0.817
 [[Category:Temperament families]]
 [[Category:Kleismic rank-3 family| ]] <!-- main article -->
 [[Category:Rank 3]]

FloraC: - CTE tunings

2026-01-07T09:59:31Z

- CTE tunings

← Older revision		Revision as of 09:59, 7 January 2026
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 317.0308{{c}}, ~7/4 = 968.5773{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 317.0308{{c}}, ~7/4 = 968.5773{{c}}
	: error map: {{val\| 0.000 +0.230 -1.160 -0.249 }}		: error map: {{val\| 0.000 +0.230 -1.160 -0.249 }}
	~~<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~6/5 = 317.0586{{c}}, ~7/4 = 968.8259{{c}} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	* WE: ~2 = 1200.1210{{c}}, ~6/5 = 317.1076{{c}}, ~7/4 = 968.5830{{c}}		* WE: ~2 = 1200.1210{{c}}, ~6/5 = 317.1076{{c}}, ~7/4 = 968.5830{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0920{{c}}, ~7/4 = 968.6426{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0920{{c}}, ~7/4 = 968.6426{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~6/5 = 317.1110{{c}}, ~7/4 = 968.8259{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 15, 19, 34d, 49f, 53, 72, 121, 140, 333, 352f, 492f }}		{{Optimal ET sequence\|legend=0\| 15, 19, 34d, 49f, 53, 72, 121, 140, 333, 352f, 492f }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 316.9734{{c}}, ~7/4 = 967.4765{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 316.9734{{c}}, ~7/4 = 967.4765{{c}}
	: error map: {{val\| 0.000 -0.114 -1.447 -1.349 -1.821 }}		: error map: {{val\| 0.000 -0.114 -1.447 -1.349 -1.821 }}
	~~<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~6/5 = 317.0667{{c}}, ~7/4 = 967.6041{{c}} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	* WE: ~2 = 1200.3557{{c}}, ~6/5 = 317.1024{{c}}, ~7/4 = 967.7541{{c}}		* WE: ~2 = 1200.3557{{c}}, ~6/5 = 317.1024{{c}}, ~7/4 = 967.7541{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0355{{c}}, ~7/4 = 967.5068{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0355{{c}}, ~7/4 = 967.5068{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~6/5 = 317.1156{{c}}, ~7/4 = 967.6235{{c}} -->~~

	Minimax tuning:		Minimax tuning:
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 316.7598{{c}}, ~7/4 = 967.1919{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 316.7598{{c}}, ~7/4 = 967.1919{{c}}
	: error map: {{val\| 0.000 -1.396 -2.515 -1.634 -3.273 }}		: error map: {{val\| 0.000 -1.396 -2.515 -1.634 -3.273 }}
	~~<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~6/5 = 316.7584{{c}}, ~7/4 = 968.8259{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 19, 34e, …, 53, 72, 197e, 269ce, 341ce, 375cdee, 447cdee, 519bccddee }}		{{Optimal ET sequence\|legend=1\| 19, 34e, …, 53, 72, 197e, 269ce, 341ce, 375cdee, 447cdee, 519bccddee }}
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	* WE: ~2 = 1200.8711{{c}}, ~6/5 = 317.0291{{c}}, ~7/4 = 967.0809{{c}}		* WE: ~2 = 1200.8711{{c}}, ~6/5 = 317.0291{{c}}, ~7/4 = 967.0809{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 316.8070{{c}}, ~7/4 = 966.8000{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 316.8070{{c}}, ~7/4 = 966.8000{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~6/5 = 316.8446{{c}}, ~7/4 = 968.8259{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 19, 34e, …, 53, 72, 125f, 178def, 197ef, 231eef, 250deff, 303cdeefff }}		{{Optimal ET sequence\|legend=0\| 19, 34e, …, 53, 72, 125f, 178def, 197ef, 231eef, 250deff, 303cdeefff }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 317.0222{{c}}, ~33/25 = 484.1546{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~6/5 = 317.0222{{c}}, ~33/25 = 484.1546{{c}}
	: error map: {{val\| 0.000 +0.178 -1.203 -0.517 +0.925 }}		: error map: {{val\| 0.000 +0.178 -1.203 -0.517 +0.925 }}
	~~<!-- * [[CTE]]: ~2 = 1200.0000{{c}}, ~6/5 = 317.0396{{c}}, ~33/25 = 484.2358{{c}} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	* WE: ~2 = 1200.0373{{c}}, ~6/5 = 317.0967{{c}}, ~33/25 = 484.1601{{c}}		* WE: ~2 = 1200.0373{{c}}, ~6/5 = 317.0967{{c}}, ~33/25 = 484.1601{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0919{{c}}, ~33/25 = 484.1707{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~6/5 = 317.0919{{c}}, ~33/25 = 484.1707{{c}}
	~~<!-- * CTE: ~2 = 1200.0000{{c}}, ~6/5 = 317.1387{{c}}, ~33/25 = 483.3828{{c}} -->~~

	Minimax tuning:		Minimax tuning:

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

2026-01-07T09:59:03Z

Switch to Sintel's badness, WE & CWE tunings

Show changes

FloraC: Units & misc. cleanup

2026-01-07T09:33:57Z

Units & misc. cleanup

← Older revision		Revision as of 09:33, 7 January 2026
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	{{Mapping\|legend=1\| 1 0 1 0 \| 0 6 5 0 \| 0 0 0 1 }}		{{Mapping\|legend=1\| 1 0 1 0 \| 0 6 5 0 \| 0 0 0 1 }}

	: mapping generators: ~2, ~6/5, ~7		: mapping generators: ~2, ~6/5, ~7

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~6/5 = 317.0586, ~7/4 = 968.8259		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~6/5 = 317.0586{{c}}, ~7/4 = 968.8259{{c}}

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	{{Optimal ET sequence\|legend=1\| 15, 19, 34d, 49, 53, 72, 140, 212, 617c, 829c }}		{{Optimal ET sequence\|legend=1\| 15, 19, 34d, 49, 53, 72, 140, 212, 617c, 829c }}

	[[Badness]]: 0.363 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.363 × 10<sup>-3</sup>

	=== 2.3.5.7.13 subgroup ===		=== 2.3.5.7.13 subgroup ===
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	Comma list: 325/324, 625/624		Comma list: 325/324, 625/624

	~~Sval~~ mapping: {{mapping\| 1 0 1 0 0 \| 0 6 5 0 14 \| 0 0 0 1 0 }}		Subgroup-val mapping: {{mapping\| 1 0 1 0 0 \| 0 6 5 0 14 \| 0 0 0 1 0 }}

	Optimal tuning (CTE): ~2 = ~~1\1~~, ~6/5 = 317.1110, ~7/4 = 968.8259		Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~6/5 = 317.1110{{c}}, ~7/4 = 968.8259{{c}}

	{{Optimal ET sequence\|legend=1\| 15, 19, 34d, 49f, 53, 72, 121, 140, 333, 352f, 492f }}		{{Optimal ET sequence\|legend=0\| 15, 19, 34d, 49f, 53, 72, 121, 140, 333, 352f, 492f }}

	Badness: 0.290 × 10<sup>-3</sup>		Badness (Smith): 0.290 × 10<sup>-3</sup>

	== Enlil ==		== Enlil ==
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	{{Mapping\|legend=1\| 1 0 1 0 6 \| 0 6 5 0 1 \| 0 0 0 1 -1 }}		{{Mapping\|legend=1\| 1 0 1 0 6 \| 0 6 5 0 1 \| 0 0 0 1 -1 }}

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~6/5 = 317.0667, ~7/4 = 967.6041		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~6/5 = 317.0667{{c}}, ~7/4 = 967.6041{{c}}

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	{{Optimal ET sequence\|legend=1\| 15, 19, 34, 38, 53, 68, 72, 140, 159, 212, 284, 496ce, 583cde, 655cde, 867ccdee, 939ccddee }}		{{Optimal ET sequence\|legend=1\| 15, 19, 34, 38, 53, 68, 72, 140, 159, 212, 284, 496ce, 583cde, 655cde, 867ccdee, 939ccddee }}

	[[Badness]]: 0.798 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.798 × 10<sup>-3</sup>

	=== 13-limit (sumatra) ===		=== 13-limit (sumatra) ===
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	Mapping: {{mapping\| 1 0 1 0 6 0 \| 0 6 5 0 1 14 \| 0 0 0 1 -1 0 }}		Mapping: {{mapping\| 1 0 1 0 6 0 \| 0 6 5 0 1 14 \| 0 0 0 1 -1 0 }}

	Optimal tuning (CTE): ~2 = ~~1\1~~, ~6/5 = 317.1156, ~7/4 = 967.6235		Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~6/5 = 317.1156{{c}}, ~7/4 = 967.6235{{c}}

	Minimax tuning:		Minimax tuning:
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	: unchanged-interval (eigenmonzo) basis: 2.11/7.13/7		: unchanged-interval (eigenmonzo) basis: 2.11/7.13/7

	{{Optimal ET sequence\|legend=1\| 15, 19, 34, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 511cdef }}		{{Optimal ET sequence\|legend=0\| 15, 19, 34, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 511cdef }}

	Badness: 0.680 × 10<sup>-3</sup>		Badness (Smith): 0.680 × 10<sup>-3</sup>

	Complexity spectrum: 6/5, 18/13, 15/13, 5/4, 4/3, 10/9, 13/12, 13/10, 16/15, 9/8, 8/7, 11/8, 11/10, 7/5, 12/11, 7/6, 16/13, 15/11, 15/14, 11/9, 9/7, 13/11, 14/13, 14/11		Complexity spectrum: 6/5, 18/13, 15/13, 5/4, 4/3, 10/9, 13/12, 13/10, 16/15, 9/8, 8/7, 11/8, 11/10, 7/5, 12/11, 7/6, 16/13, 15/11, 15/14, 11/9, 9/7, 13/11, 14/13, 14/11
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	{{Mapping\|legend=1\| 1 0 1 0 9 \| 0 6 5 0 -21 \| 0 0 0 1 0 }}		{{Mapping\|legend=1\| 1 0 1 0 9 \| 0 6 5 0 -21 \| 0 0 0 1 0 }}

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~6/5 = 316.7584, ~7/4 = 968.8259		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~6/5 = 316.7584{{c}}, ~7/4 = 968.8259{{c}}

	{{Optimal ET sequence\|legend=1\| 19, 34e, 53, 72, 197e, 269ce, 341ce, 375cdee, 447cdee, 519bccddee }}		{{Optimal ET sequence\|legend=1\| 19, 34e, 53, 72, 197e, 269ce, 341ce, 375cdee, 447cdee, 519bccddee }}

	[[Badness]]: 3.690 × 10<sup>-3</sup>		[[Badness]] (Smith): 3.690 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 1 0 9 0 \| 0 6 5 0 -21 14 \| 0 0 0 1 0 0 }}		Mapping: {{mapping\| 1 0 1 0 9 0 \| 0 6 5 0 -21 14 \| 0 0 0 1 0 0 }}

	Optimal tuning (CTE): ~2 = ~~1\1~~, ~6/5 = 316.8446, ~7/4 = 968.8259		Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~6/5 = 316.8446{{c}}, ~7/4 = 968.8259{{c}}

	{{Optimal ET sequence\|legend=1\| 19, 34e, 53, 72, 125f, 178def, 197ef, 231eef, 250deff, 303cdeeff }}		{{Optimal ET sequence\|legend=0\| 19, 34e, 53, 72, 125f, 178def, 197ef, 231eef, 250deff, 303cdeeff }}

	Badness: 2.273 × 10<sup>-3</sup>		Badness (Smith): 2.273 × 10<sup>-3</sup>

	== Enki ==		== Enki ==
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	{{Mapping\|legend=1\| 1 0 1 0 1 \| 0 6 5 0 4 \| 0 0 0 2 1 }}		{{Mapping\|legend=1\| 1 0 1 0 1 \| 0 6 5 0 4 \| 0 0 0 2 1 }}

	: mapping generators: ~2, ~6/5, ~66/25		: mapping generators: ~2, ~6/5, ~66/25

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~6/5 = 317.0396, ~33/25 = 484.2358		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000{{c}}, ~6/5 = 317.0396{{c}}, ~33/25 = 484.2358{{c}}

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	{{Optimal ET sequence\|legend=1\| 15, 23de, 34d, 49, 72, 159, 193, 265, 352, 424 }}		{{Optimal ET sequence\|legend=1\| 15, 23de, 34d, 49, 72, 159, 193, 265, 352, 424 }}

	[[Badness]]: 1.09 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.09 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 1 0 1 0 \| 0 6 5 0 4 14 \| 0 0 0 2 1 0 }}		Mapping: {{mapping\| 1 0 1 0 1 0 \| 0 6 5 0 4 14 \| 0 0 0 2 1 0 }}

	Optimal tuning (CTE): ~2 = ~~1\1~~, ~6/5 = 317.1387, ~33/25 = 483.3828		Optimal tuning (CTE): ~2 = 1200.0000{{c}}, ~6/5 = 317.1387{{c}}, ~33/25 = 483.3828{{c}}

	Minimax tuning:		Minimax tuning:
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	: unchanged-interval (eigenmonzo) basis: 2.7.13/5		: unchanged-interval (eigenmonzo) basis: 2.7.13/5

	{{Optimal ET sequence\|legend=1\| 34d, 49f, 72, 87, 159, 193, 280 }}		{{Optimal ET sequence\|legend=0\| 34d, 49f, 72, 87, 159, 193, 280 }}

	Badness: 0.874 × 10<sup>-3</sup>		Badness (Smith): 0.874 × 10<sup>-3</sup>

	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Kleismic rank-3 family\| ]] <!-- main article -->		[[Category:Kleismic rank-3 family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-11-27T12:22:19Z

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

← Older revision		Revision as of 12:22, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Kleismic rank-3 family\| ]] <!-- main article -->		[[Category:Kleismic rank-3 family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: FloraC moved page Kleismic rank three family to Kleismic rank-3 family: For obvious reasons

2025-08-27T12:49:25Z

FloraC moved page Kleismic rank three family to Kleismic rank-3 family: For obvious reasons

← Older revision	Revision as of 12:49, 27 August 2025
(No difference)

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

2025-06-24T00:30:16Z

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

← Older revision		Revision as of 00:30, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Kleismic rank-3 family\| ]] <!-- main article -->		[[Category:Kleismic rank-3 family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-06-21T06:57:42Z

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

← Older revision		Revision as of 06:57, 21 June 2025
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	* [[7-odd-limit\|7-]] and [[9-odd-limit]]		* [[7-odd-limit\|7-]] and [[9-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| 1 5/6 0 0 \| 0 0 0 1 }}		: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| 1 5/6 0 0 \| 0 0 0 1 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.3.7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.7

	{{Optimal ET sequence\|legend=1\| 15, 19, 34d, 49, 53, 72, 140, 212, 617c, 829c }}		{{Optimal ET sequence\|legend=1\| 15, 19, 34d, 49, 53, 72, 140, 212, 617c, 829c }}
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 0 1 0 0 0 }}, {{monzo\| 1 5/6 0 0 0 }}, {{monzo\| 3 1/12 0 1/2 -1/2 }}, {{monzo\| 3 1/12 0 -1/2 1/2 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 0 1 0 0 0 }}, {{monzo\| 1 5/6 0 0 0 }}, {{monzo\| 3 1/12 0 1/2 -1/2 }}, {{monzo\| 3 1/12 0 -1/2 1/2 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.3.11/7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.11/7

	{{Optimal ET sequence\|legend=1\| 15, 19, 34, 38, 53, 68, 72, 140, 159, 212, 284, 496ce, 583cde, 655cde, 867ccdee, 939ccddee }}		{{Optimal ET sequence\|legend=1\| 15, 19, 34, 38, 53, 68, 72, 140, 159, 212, 284, 496ce, 583cde, 655cde, 867ccdee, 939ccddee }}
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	* 13- and 15-odd-limit		* 13- and 15-odd-limit
	: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 4/3 0 0 -2/9 -2/9 4/9 }}, {{monzo\| 19/9 0 0 -5/27 -5/27 10/27 }}, {{monzo\| 28/9 0 0 13/27 -14/27 1/27 }}, {{monzo\| 28/9 0 0 -14/27 13/27 1/27 }}, {{monzo\| 28/9 0 0 -14/27 -14/27 28/27 }}]		: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 4/3 0 0 -2/9 -2/9 4/9 }}, {{monzo\| 19/9 0 0 -5/27 -5/27 10/27 }}, {{monzo\| 28/9 0 0 13/27 -14/27 1/27 }}, {{monzo\| 28/9 0 0 -14/27 13/27 1/27 }}, {{monzo\| 28/9 0 0 -14/27 -14/27 28/27 }}]
	: ~~eigenmonzo (~~unchanged-interval) basis: 2.11/7.13/7		: unchanged-interval (eigenmonzo) basis: 2.11/7.13/7

	{{Optimal ET sequence\|legend=1\| 15, 19, 34, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 511cdef }}		{{Optimal ET sequence\|legend=1\| 15, 19, 34, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 511cdef }}
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| -18/13 0 6/13 -6/13 12/13 }}, {{monzo\| -2/13 0 5/13 -5/13 10/13 }}, {{monzo\| -2/13 0 -8/13 8/13 10/13 }}, {{monzo\| 0 0 0 0 1 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| -18/13 0 6/13 -6/13 12/13 }}, {{monzo\| -2/13 0 5/13 -5/13 10/13 }}, {{monzo\| -2/13 0 -8/13 8/13 10/13 }}, {{monzo\| 0 0 0 0 1 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.7/5.11		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11

	{{Optimal ET sequence\|legend=1\| 15, 23de, 34d, 49, 72, 159, 193, 265, 352, 424 }}		{{Optimal ET sequence\|legend=1\| 15, 23de, 34d, 49, 72, 159, 193, 265, 352, 424 }}
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	* 13- and 15-odd-limit		* 13- and 15-odd-limit
	: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 2/3 0 -2/3 0 0 2/3 }}, {{monzo\| 14/9 0 -5/9 0 0 5/9 }}, {{monzo\| 0 0 0 1 0 0 }}, {{monzo\| 13/9 0 -4/9 1/2 0 4/9 }}, {{monzo\| 14/9 0 -14/9 0 0 14/9 }}]		: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 2/3 0 -2/3 0 0 2/3 }}, {{monzo\| 14/9 0 -5/9 0 0 5/9 }}, {{monzo\| 0 0 0 1 0 0 }}, {{monzo\| 13/9 0 -4/9 1/2 0 4/9 }}, {{monzo\| 14/9 0 -14/9 0 0 14/9 }}]
	: ~~eigenmonzo (~~unchanged-interval) basis: 2.7.13/5		: unchanged-interval (eigenmonzo) basis: 2.7.13/5

	{{Optimal ET sequence\|legend=1\| 34d, 49f, 72, 87, 159, 193, 280 }}		{{Optimal ET sequence\|legend=1\| 34d, 49f, 72, 87, 159, 193, 280 }}

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

" to "{{Technical data page}}"

2025-04-13T13:49:58Z

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

← Older revision		Revision as of 13:49, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''kleismic rank-3 family''' of temperaments [[tempering out\|tempers out]] the kleisma, [[15625/15552]]. If nothing else is tempered out in the 7-limit, we have a [[planar temperament]]. With an 11-limit comma we get an 11-limit temperament, and so forth.		The '''kleismic rank-3 family''' of temperaments [[tempering out\|tempers out]] the kleisma, [[15625/15552]]. If nothing else is tempered out in the 7-limit, we have a [[planar temperament]]. With an 11-limit comma we get an 11-limit temperament, and so forth.

BudjarnLambeth: {{Technical data page}}

2025-04-13T11:47:36Z

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

← Older revision		Revision as of 11:47, 13 April 2025
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	The '''kleismic rank-3 family''' of temperaments tempers out the kleisma, [[15625/15552]]. If nothing else is tempered out in the 7-limit, we have a [[planar temperament]]. With an 11-limit comma we get an 11-limit temperament, and so forth.		{{Technical data page}}<br><br>
			The '''kleismic rank-3 family''' of temperaments [[tempering out\|tempers out]] the kleisma, [[15625/15552]]. If nothing else is tempered out in the 7-limit, we have a [[planar temperament]]. With an 11-limit comma we get an 11-limit temperament, and so forth.

	== Rank-3 kleismic ==		== Rank-3 kleismic ==

← Older revision		Revision as of 06:57, 21 June 2025
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	* [[7-odd-limit\|7-]] and [[9-odd-limit]]		* [[7-odd-limit\|7-]] and [[9-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| 1 5/6 0 0 \| 0 0 0 1 }}		: {{monzo list\| 1 0 0 0 \| 0 1 0 0 \| 1 5/6 0 0 \| 0 0 0 1 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.3.7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.7

	{{Optimal ET sequence\|legend=1\| 15, 19, 34d, 49, 53, 72, 140, 212, 617c, 829c }}		{{Optimal ET sequence\|legend=1\| 15, 19, 34d, 49, 53, 72, 140, 212, 617c, 829c }}
Line 47:		Line 47:
	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 0 1 0 0 0 }}, {{monzo\| 1 5/6 0 0 0 }}, {{monzo\| 3 1/12 0 1/2 -1/2 }}, {{monzo\| 3 1/12 0 -1/2 1/2 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 0 1 0 0 0 }}, {{monzo\| 1 5/6 0 0 0 }}, {{monzo\| 3 1/12 0 1/2 -1/2 }}, {{monzo\| 3 1/12 0 -1/2 1/2 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.3.11/7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.3.11/7

	{{Optimal ET sequence\|legend=1\| 15, 19, 34, 38, 53, 68, 72, 140, 159, 212, 284, 496ce, 583cde, 655cde, 867ccdee, 939ccddee }}		{{Optimal ET sequence\|legend=1\| 15, 19, 34, 38, 53, 68, 72, 140, 159, 212, 284, 496ce, 583cde, 655cde, 867ccdee, 939ccddee }}
Line 65:		Line 65:
	* 13- and 15-odd-limit		* 13- and 15-odd-limit
	: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 4/3 0 0 -2/9 -2/9 4/9 }}, {{monzo\| 19/9 0 0 -5/27 -5/27 10/27 }}, {{monzo\| 28/9 0 0 13/27 -14/27 1/27 }}, {{monzo\| 28/9 0 0 -14/27 13/27 1/27 }}, {{monzo\| 28/9 0 0 -14/27 -14/27 28/27 }}]		: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 4/3 0 0 -2/9 -2/9 4/9 }}, {{monzo\| 19/9 0 0 -5/27 -5/27 10/27 }}, {{monzo\| 28/9 0 0 13/27 -14/27 1/27 }}, {{monzo\| 28/9 0 0 -14/27 13/27 1/27 }}, {{monzo\| 28/9 0 0 -14/27 -14/27 28/27 }}]
	: ~~eigenmonzo (~~unchanged-interval) basis: 2.11/7.13/7		: unchanged-interval (eigenmonzo) basis: 2.11/7.13/7

	{{Optimal ET sequence\|legend=1\| 15, 19, 34, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 511cdef }}		{{Optimal ET sequence\|legend=1\| 15, 19, 34, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 511cdef }}
Line 115:		Line 115:
	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| -18/13 0 6/13 -6/13 12/13 }}, {{monzo\| -2/13 0 5/13 -5/13 10/13 }}, {{monzo\| -2/13 0 -8/13 8/13 10/13 }}, {{monzo\| 0 0 0 0 1 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| -18/13 0 6/13 -6/13 12/13 }}, {{monzo\| -2/13 0 5/13 -5/13 10/13 }}, {{monzo\| -2/13 0 -8/13 8/13 10/13 }}, {{monzo\| 0 0 0 0 1 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.7/5.11		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11

	{{Optimal ET sequence\|legend=1\| 15, 23de, 34d, 49, 72, 159, 193, 265, 352, 424 }}		{{Optimal ET sequence\|legend=1\| 15, 23de, 34d, 49, 72, 159, 193, 265, 352, 424 }}
Line 133:		Line 133:
	* 13- and 15-odd-limit		* 13- and 15-odd-limit
	: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 2/3 0 -2/3 0 0 2/3 }}, {{monzo\| 14/9 0 -5/9 0 0 5/9 }}, {{monzo\| 0 0 0 1 0 0 }}, {{monzo\| 13/9 0 -4/9 1/2 0 4/9 }}, {{monzo\| 14/9 0 -14/9 0 0 14/9 }}]		: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 2/3 0 -2/3 0 0 2/3 }}, {{monzo\| 14/9 0 -5/9 0 0 5/9 }}, {{monzo\| 0 0 0 1 0 0 }}, {{monzo\| 13/9 0 -4/9 1/2 0 4/9 }}, {{monzo\| 14/9 0 -14/9 0 0 14/9 }}]
	: ~~eigenmonzo (~~unchanged-interval) basis: 2.7.13/5		: unchanged-interval (eigenmonzo) basis: 2.7.13/5

	{{Optimal ET sequence\|legend=1\| 34d, 49f, 72, 87, 159, 193, 280 }}		{{Optimal ET sequence\|legend=1\| 34d, 49f, 72, 87, 159, 193, 280 }}