Cataharry family - Revision history

FloraC: + intro to cataharry

2026-07-07T10:33:08Z

+ intro to cataharry

← Older revision		Revision as of 10:33, 7 July 2026
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	{{Technical data page}}		{{Technical data page}}

	The '''cataharry family''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the [[cataharry comma]] ({{monzo\| -4 9 -2 -2 }}, [[ratio]]: 19683/19600).		The '''cataharry family''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the [[cataharry comma]] ({{monzo\|legend=1\| -4 9 -2 -2 }}, [[ratio]]: 19683/19600).

	== Cataharry ==		== Cataharry ==
			Cataharry splits the [[3/1\|3rd harmonic]] into two semitwelfths. Bending the semitwelfth up by a [[syntonic comma]] results in ~[[7/4]], and down results in ~[[12/7]].

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

FloraC: Switch to Sintel's badness; + optimal tunings

2026-07-07T10:25:58Z

Switch to Sintel's badness; + optimal tunings

Show changes

FloraC: Units, misc. cleanup, - redundant category

2026-07-07T09:54:51Z

Units, misc. cleanup, - redundant category

← Older revision		Revision as of 09:54, 7 July 2026
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	{{Technical data page}}		{{Technical data page}}

	The '''cataharry family''' of [[~~Rank-3 temperament\|~~rank-3~~]] [[~~temperament]]s [[~~Tempering~~ out\|tempers out]] the [[cataharry comma]], 19683/19600.		The '''cataharry family''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the [[cataharry comma]] ({{monzo\| -4 9 -2 -2 }}, [[ratio]]: 19683/19600).

	== Cataharry ==		== Cataharry ==
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	{{Mapping\|legend=1\| 1 0 0 -2 \| 0 2 0 9 \| 0 0 1 -1 }}		{{Mapping\|legend=1\| 1 0 0 -2 \| 0 2 0 9 \| 0 0 1 -1 }}

	: mapping generators: ~2, ~140/81, ~5		: mapping generators: ~2, ~140/81, ~5

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	{{Optimal ET sequence\|legend=1\| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}		{{Optimal ET sequence\|legend=1\| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}

	[[Badness]]: 0.301 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.301 × 10<sup>-3</sup>

	[[Projection pair]]s: 3 19600/6561 7 1033052339200000000/150094635296999121 to 2.5.81/7		[[Projection pair]]s: <code>3 19600/6561 7 1033052339200000000/150094635296999121</code> to 2.5.81/7

	== Albus ==		== Albus ==
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	{{Mapping\|legend=1\| 1 0 0 -2 6 \| 0 2 0 9 -12 \| 0 0 1 -1 3 }}		{{Mapping\|legend=1\| 1 0 0 -2 6 \| 0 2 0 9 -12 \| 0 0 1 -1 3 }}

	: mapping generators: ~2, ~140/81, ~5		: mapping generators: ~2, ~140/81, ~5

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	{{Optimal ET sequence\|legend=1\| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}		{{Optimal ET sequence\|legend=1\| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}

	[[Badness]]: 0.621 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.621 × 10<sup>-3</sup>

	=== Madagascar ===		=== Madagascar ===
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	: unchanged-interval (eigenmonzo) basis: 2.7/5.11/5		: unchanged-interval (eigenmonzo) basis: 2.7/5.11/5

	{{Optimal ET sequence\|legend=1\| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}		{{Optimal ET sequence\|legend=0\| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}

	Badness: 0.560 × 10<sup>-3</sup>		Badness (Smith): 0.560 × 10<sup>-3</sup>

	Complexity spectrum: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11		Complexity spectrum: 15/13, 4/3, 13/10, 10/9, 6/5, 9/7, 18/13, 9/8, 5/4, 7/6, 13/12, 15/14, 16/15, 14/13, 8/7, 7/5, 16/13, 11/10, 15/11, 11/8, 12/11, 13/11, 11/9, 14/11
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	{{Optimal ET sequence\|legend=1\| 19e, 33cdee, 39dee, 53e, 58, 72, 130, 202, 351, 423d, 481, 553 }}		{{Optimal ET sequence\|legend=1\| 19e, 33cdee, 39dee, 53e, 58, 72, 130, 202, 351, 423d, 481, 553 }}

	[[Badness]]: 0.988 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.988 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 0 -2 -7 -1 \| 0 2 0 9 22 3 \| 0 0 1 -1 -3 1 }}		Mapping: {{mapping\| 1 0 0 -2 -7 -1 \| 0 2 0 9 22 3 \| 0 0 1 -1 -3 1 }}

	{{Optimal ET sequence\|legend=1\| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }}		{{Optimal ET sequence\|legend=0\| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }}

	Badness: 0.786 × 10<sup>-3</sup>		Badness (Smith): 0.786 × 10<sup>-3</sup>

	== Hagrid ==		== Hagrid ==
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	{{Mapping\|legend=1\| 2 0 0 -4 -1 \| 0 2 0 9 5 \| 0 0 1 -1 0 }}		{{Mapping\|legend=1\| 2 0 0 -4 -1 \| 0 2 0 9 5 \| 0 0 1 -1 0 }}

	: mapping generators: ~99/70, ~140/81, ~5		: mapping generators: ~99/70, ~140/81, ~5

	{{Optimal ET sequence\|legend=1\| 24, 34d, 48, 58, 72, 130, 202 }}		{{Optimal ET sequence\|legend=1\| 24, 34d, 48, 58, 72, 130, 202 }}

	[[Badness]]: 1.116 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.116 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 2 0 0 -4 -1 -2 \| 0 2 0 9 5 3 \| 0 0 1 -1 0 1 }}		Mapping: {{mapping\| 2 0 0 -4 -1 -2 \| 0 2 0 9 5 3 \| 0 0 1 -1 0 1 }}

	: mapping generators: ~99/70, ~26/15, ~5		: mapping generators: ~99/70, ~26/15, ~5

	{{Optimal ET sequence\|legend=1\| 24, 34d, 58, 72, 130 }}		{{Optimal ET sequence\|legend=0\| 24, 34d, 58, 72, 130 }}

	Badness: 0.876 × 10<sup>-3</sup>		Badness (Smith): 0.876 × 10<sup>-3</sup>

	== Draco ==		== Draco ==
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	{{Optimal ET sequence\|legend=1\| 19e, 24, 34d, 53, 58, 111, 280cd }}		{{Optimal ET sequence\|legend=1\| 19e, 24, 34d, 53, 58, 111, 280cd }}

	[[Badness]]: 1.934 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.934 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 0 -2 -6 -1 \| 0 2 0 9 9 3 \| 0 0 1 -1 1 1 }}		Mapping: {{mapping\| 1 0 0 -2 -6 -1 \| 0 2 0 9 9 3 \| 0 0 1 -1 1 1 }}

	{{Optimal ET sequence\|legend=1\| 19e, 24, 34d, 53, 58, 111, 280cdf }}		{{Optimal ET sequence\|legend=0\| 19e, 24, 34d, 53, 58, 111, 280cdf }}

	Badness: 0.999 × 10<sup>-3</sup>		Badness (Smith): 0.999 × 10<sup>-3</sup>

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

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

2025-11-27T12:25:00Z

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

← Older revision		Revision as of 12:25, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Cataharry family\| ]] <!-- main article -->		[[Category:Cataharry family\| ]] <!-- main article -->
	[[Category:Cataharry\| ]] <!-- key article -->		[[Category:Cataharry\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-06-24T00:39:29Z

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

← Older revision		Revision as of 00:39, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Cataharry family\| ]] <!-- main article -->		[[Category:Cataharry family\| ]] <!-- main article -->
	[[Category:Cataharry\| ]] <!-- key article -->		[[Category:Cataharry\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-06-21T06:58:36Z

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

← Older revision		Revision as of 06:58, 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 \| 4/9 0 2/9 2/9 \| 0 0 1 0 \| 0 0 0 1 }}		: {{monzo list\| 1 0 0 0 \| 4/9 0 2/9 2/9 \| 0 0 1 0 \| 0 0 0 1 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5.7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7

	{{Optimal ET sequence\|legend=1\| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}		{{Optimal ET sequence\|legend=1\| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo\| 5 0 7/2 -2 -3/2 }}, {{monzo\| 5 0 5/2 -1 -3/2 }}, {{monzo\| 5 0 5/2 -2 -1/2 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo\| 5 0 7/2 -2 -3/2 }}, {{monzo\| 5 0 5/2 -1 -3/2 }}, {{monzo\| 5 0 5/2 -2 -1/2 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.7/5.11/5		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/5

	{{Optimal ET sequence\|legend=1\| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}		{{Optimal ET sequence\|legend=1\| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}
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	* 13- and 15-odd-limit		* 13- and 15-odd-limit
	: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo\| 5 0 7/2 -2 -3/2 0 }}, {{monzo\| 5 0 5/2 -1 -3/2 0 }}, {{monzo\| 5 0 5/2 -2 -1/2 0 }}, {{monzo\| 8 0 11/2 -3 -5/2 0 }}]		: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo\| 5 0 7/2 -2 -3/2 0 }}, {{monzo\| 5 0 5/2 -1 -3/2 0 }}, {{monzo\| 5 0 5/2 -2 -1/2 0 }}, {{monzo\| 8 0 11/2 -3 -5/2 0 }}]
	: ~~eigenmonzo (~~unchanged-interval) basis: 2.7/5.11/5		: unchanged-interval (eigenmonzo) basis: 2.7/5.11/5

	{{Optimal ET sequence\|legend=1\| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}		{{Optimal ET sequence\|legend=1\| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}

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

" to "{{Technical data page}}"

2025-04-13T13:47:11Z

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

← Older revision		Revision as of 13:47, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}

	The '''cataharry family''' of [[Rank-3 temperament\|rank-3]] [[temperament]]s [[Tempering out\|tempers out]] the [[cataharry comma]], 19683/19600.		The '''cataharry family''' of [[Rank-3 temperament\|rank-3]] [[temperament]]s [[Tempering out\|tempers out]] the [[cataharry comma]], 19683/19600.

BudjarnLambeth: {{Technical data page}}

2025-04-13T11:02:28Z

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

← Older revision		Revision as of 11:02, 13 April 2025
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			{{Technical data page}}<br><br>

	The '''cataharry family''' of [[Rank-3 temperament\|rank-3]] [[temperament]]s [[Tempering out\|tempers out]] the [[cataharry comma]], 19683/19600.		The '''cataharry family''' of [[Rank-3 temperament\|rank-3]] [[temperament]]s [[Tempering out\|tempers out]] the [[cataharry comma]], 19683/19600.

FloraC: Update keys

2023-09-14T08:50:22Z

Update keys

← Older revision		Revision as of 08:50, 14 September 2023
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	The '''cataharry family''' of rank-3 ~~temperaments~~ tempers out the [[cataharry comma]], 19683/19600.		The '''cataharry family''' of [[Rank-3 temperament\|rank-3]] [[temperament]]s [[Tempering out\|tempers out]] the [[cataharry comma]], 19683/19600.

	== Cataharry ==		== Cataharry ==
	Subgroup: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: [[19683/19600]]		[[Comma list]]: [[19683/19600]]

	~~[[Mapping]]: [~~{{~~val~~\| 1 0 0 -2 ~~}}, {{val~~\| 0 2 0 9 ~~}}, {{val~~\| 0 0 1 -1 }}]		{{Mapping\|legend=1\| 1 0 0 -2 \| 0 2 0 9 \| 0 0 1 -1 }}

	~~Mapping~~ generators: ~2, ~140/81, ~5		: mapping generators: ~2, ~140/81, ~5

	[[Minimax tuning]]:		[[Minimax tuning]]:
	* 7- and [[9-odd-limit]]:		* [[7-odd-limit\|7-]] and [[9-odd-limit]]:
	: [{{monzo\| 1 0 0 0 ~~}}, {{monzo~~\| 4/9 0 2/9 2/9 ~~}}, {{monzo~~\| 0 0 1 0 ~~}}, {{monzo~~\| 0 0 0 1 }}]		: {{monzo list\| 1 0 0 0 \| 4/9 0 2/9 2/9 \| 0 0 1 0 \| 0 0 0 1 }}
	: ~~Eigenmonzos~~: 2~~, 8/~~7~~, 5/4~~		: [[Eigenmonzo basis\|eigenmonzo (unchanged-interval) basis]]: 2.5.7

	{{Optimal ET sequence\|legend=1\| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}		{{Optimal ET sequence\|legend=1\| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}
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	== Albus ==		== Albus ==
	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 540/539, 8019/8000		[[Comma list]]: 540/539, 8019/8000

	~~[[Mapping]]: [~~{{~~val~~\| 1 0 0 -2 6 ~~}}, {{val~~\| 0 2 0 9 -12 ~~}}, {{val~~\| 0 0 1 -1 3 }}]		{{Mapping\|legend=1\| 1 0 0 -2 6 \| 0 2 0 9 -12 \| 0 0 1 -1 3 }}

	~~Mapping~~ generators: ~2, ~140/81, ~5		: mapping generators: ~2, ~140/81, ~5

	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo\| 5 0 7/2 -2 -3/2 }}, {{monzo\| 5 0 5/2 -1 -3/2 }}, {{monzo\| 5 0 5/2 -2 -1/2 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo\| 5 0 7/2 -2 -3/2 }}, {{monzo\| 5 0 5/2 -1 -3/2 }}, {{monzo\| 5 0 5/2 -2 -1/2 }}]
	: ~~Eigenmonzos~~: 2, 11~~/10, 7~~/5		: [[Eigenmonzo basis\|eigenmonzo (unchanged-interval) basis]]: 2.7/5.11/5

	{{Optimal ET sequence\|legend=1\| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}		{{Optimal ET sequence\|legend=1\| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}
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	Comma list: 351/350, 540/539, 676/675		Comma list: 351/350, 540/539, 676/675

	Mapping: [{{~~val~~\| 1 0 0 -2 6 -1 ~~}}, {{val~~\| 0 2 0 9 -12 3 ~~}}, {{val~~\| 0 0 1 -1 3 1 }}]		Mapping: {{mapping\| 1 0 0 -2 6 -1 \| 0 2 0 9 -12 3 \| 0 0 1 -1 3 1 }}

	~~Mapping generators: ~2, ~26/15, ~5~~

	[[Mapping to lattice]]: [{{val\| 0 -2 -3 -6 3 -6 }}, {{val\| 0 0 -1 1 -3 -1 }}]		[[Mapping to lattice]]: [{{val\| 0 -2 -3 -6 3 -6 }}, {{val\| 0 0 -1 1 -3 -1 }}]
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	* 13- and 15-odd-limit		* 13- and 15-odd-limit
	: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo\| 5 0 7/2 -2 -3/2 0 }}, {{monzo\| 5 0 5/2 -1 -3/2 0 }}, {{monzo\| 5 0 5/2 -2 -1/2 0 }}, {{monzo\| 8 0 11/2 -3 -5/2 0 }}]		: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo\| 5 0 7/2 -2 -3/2 0 }}, {{monzo\| 5 0 5/2 -1 -3/2 0 }}, {{monzo\| 5 0 5/2 -2 -1/2 0 }}, {{monzo\| 8 0 11/2 -3 -5/2 0 }}]
	: ~~Eigenmonzos~~: 2, 11~~/10, 7~~/5		: eigenmonzo (unchanged-interval) basis: 2.7/5.11/5

	{{Optimal ET sequence\|legend=1\| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}		{{Optimal ET sequence\|legend=1\| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}
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	== Snape ==		== Snape ==
	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 441/440, 19683/19600		[[Comma list]]: 441/440, 19683/19600

	~~[[Mapping]]: [~~{{~~val~~\| 1 0 0 -2 -7 ~~}}, {{val~~\| 0 2 0 9 22 ~~}}, {{val~~\| 0 0 1 -1 -3 }}]		{{Mapping\|legend=1\| 1 0 0 -2 -7 \| 0 2 0 9 22 \| 0 0 1 -1 -3 }}

	~~Mapping generators: ~2, ~140/81, ~5~~

	{{Optimal ET sequence\|legend=1\| 19e, 33cdee, 39dee, 53e, 58, 72, 130, 202, 351, 423d, 481, 553 }}		{{Optimal ET sequence\|legend=1\| 19e, 33cdee, 39dee, 53e, 58, 72, 130, 202, 351, 423d, 481, 553 }}
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	Comma list: 351/350, 441/440, 676/675		Comma list: 351/350, 441/440, 676/675

	Mapping: [{{~~val~~\| 1 0 0 -2 -7 -1 ~~}}, {{val~~\| 0 2 0 9 22 3 ~~}}, {{val~~\| 0 0 1 -1 -3 1 }}]		Mapping: {{mapping\| 1 0 0 -2 -7 -1 \| 0 2 0 9 22 3 \| 0 0 1 -1 -3 1 }}

	~~Mapping generators: ~2, ~26/15, ~5~~

	{{Optimal ET sequence\|legend=1\| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }}		{{Optimal ET sequence\|legend=1\| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }}
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	== Hagrid ==		== Hagrid ==
	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 243/242, 9801/9800		[[Comma list]]: 243/242, 9801/9800

	~~[[Mapping]]: [~~{{~~val~~\| 2 0 0 -4 -1 ~~}}, {{val~~\| 0 2 0 9 5 ~~}}, {{val~~\| 0 0 1 -1 0 }}]		{{Mapping\|legend=1\| 2 0 0 -4 -1 \| 0 2 0 9 5 \| 0 0 1 -1 0 }}

	~~Mapping~~ generators: ~99/70, ~140/81, ~5		: mapping generators: ~99/70, ~140/81, ~5

	{{Optimal ET sequence\|legend=1\| 24, 34d, 48, 58, 72, 130, 202 }}		{{Optimal ET sequence\|legend=1\| 24, 34d, 48, 58, 72, 130, 202 }}
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	Comma list: 243/242, 351/350, 364/363		Comma list: 243/242, 351/350, 364/363

	Mapping: [{{~~val~~\| 2 0 0 -4 -1 -2 ~~}}, {{val~~\| 0 2 0 9 5 3 ~~}}, {{val~~\| 0 0 1 -1 0 1 }}]		Mapping: {{mapping\| 2 0 0 -4 -1 -2 \| 0 2 0 9 5 3 \| 0 0 1 -1 0 1 }}

	~~Mapping~~ generators: ~99/70, ~26/15, ~5		: mapping generators: ~99/70, ~26/15, ~5

	{{Optimal ET sequence\|legend=1\| 24, 34d, 58, 72, 130 }}		{{Optimal ET sequence\|legend=1\| 24, 34d, 58, 72, 130 }}
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	== Draco ==		== Draco ==
	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 176/175, 19683/19600		[[Comma list]]: 176/175, 19683/19600

	~~[[Mapping]]: [~~{{~~val~~\| 1 0 0 -2 -6 ~~}}, {{val~~\| 0 2 0 9 9 ~~}}, {{val~~\| 0 0 1 -1 1 }}]		{{Mapping\|legend=1\| 1 0 0 -2 -6 \| 0 2 0 9 9 \| 0 0 1 -1 1 }}

	{{Optimal ET sequence\|legend=1\| 19e, 24, 34d, 53, 58, 111, 280cd }}		{{Optimal ET sequence\|legend=1\| 19e, 24, 34d, 53, 58, 111, 280cd }}
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	Comma list: 176/175, 351/350, 676/675		Comma list: 176/175, 351/350, 676/675

	Mapping: [{{~~val~~\| 1 0 0 -2 -6 -1 ~~}}, {{val~~\| 0 2 0 9 9 3 ~~}}, {{val~~\| 0 0 1 -1 1 1 }}]		Mapping: {{mapping\| 1 0 0 -2 -6 -1 \| 0 2 0 9 9 3 \| 0 0 1 -1 1 1 }}

	{{Optimal ET sequence\|legend=1\| 19e, 24, 34d, 53, 58, 111, 280cdf }}		{{Optimal ET sequence\|legend=1\| 19e, 24, 34d, 53, 58, 111, 280cdf }}
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Cataharry family\| ]] <!-- main article -->		[[Category:Cataharry family\| ]] <!-- main article -->
			[[Category:Cataharry\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T18:23:59Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

← Older revision		Revision as of 18:23, 7 May 2023
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	: Eigenmonzos: 2, 8/7, 5/4		: Eigenmonzos: 2, 8/7, 5/4

	{{~~Val list~~\|legend=1\| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}		{{Optimal ET sequence\|legend=1\| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}

	[[Badness]]: 0.301 × 10<sup>-3</sup>		[[Badness]]: 0.301 × 10<sup>-3</sup>
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	: Eigenmonzos: 2, 11/10, 7/5		: Eigenmonzos: 2, 11/10, 7/5

	{{~~Val list~~\|legend=1\| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}		{{Optimal ET sequence\|legend=1\| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}

	[[Badness]]: 0.621 × 10<sup>-3</sup>		[[Badness]]: 0.621 × 10<sup>-3</sup>
Line 59:		Line 59:
	: Eigenmonzos: 2, 11/10, 7/5		: Eigenmonzos: 2, 11/10, 7/5

	~~Vals:~~ {{~~Val list~~\| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}		{{Optimal ET sequence\|legend=1\| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}

	Badness: 0.560 × 10<sup>-3</sup>		Badness: 0.560 × 10<sup>-3</sup>
Line 78:		Line 78:
	Mapping generators: ~2, ~140/81, ~5		Mapping generators: ~2, ~140/81, ~5

	{{~~Val list~~\|legend=1\| 19e, 33cdee, 39dee, 53e, 58, 72, 130, 202, 351, 423d, 481, 553 }}		{{Optimal ET sequence\|legend=1\| 19e, 33cdee, 39dee, 53e, 58, 72, 130, 202, 351, 423d, 481, 553 }}

	[[Badness]]: 0.988 × 10<sup>-3</sup>		[[Badness]]: 0.988 × 10<sup>-3</sup>
Line 91:		Line 91:
	Mapping generators: ~2, ~26/15, ~5		Mapping generators: ~2, ~26/15, ~5

	~~Vals:~~ {{~~Val list~~\| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }}		{{Optimal ET sequence\|legend=1\| 19e, 33cdeeff, 39deef, 53e, 58, 72, 130, 279, 409 }}

	Badness: 0.786 × 10<sup>-3</sup>		Badness: 0.786 × 10<sup>-3</sup>
Line 104:		Line 104:
	Mapping generators: ~99/70, ~140/81, ~5		Mapping generators: ~99/70, ~140/81, ~5

	{{~~Val list~~\|legend=1\| 24, 34d, 48, 58, 72, 130, 202 }}		{{Optimal ET sequence\|legend=1\| 24, 34d, 48, 58, 72, 130, 202 }}

	[[Badness]]: 1.116 × 10<sup>-3</sup>		[[Badness]]: 1.116 × 10<sup>-3</sup>
Line 117:		Line 117:
	Mapping generators: ~99/70, ~26/15, ~5		Mapping generators: ~99/70, ~26/15, ~5

	~~Vals:~~ {{~~Val list~~\| 24, 34d, 58, 72, 130 }}		{{Optimal ET sequence\|legend=1\| 24, 34d, 58, 72, 130 }}

	Badness: 0.876 × 10<sup>-3</sup>		Badness: 0.876 × 10<sup>-3</sup>
Line 128:		Line 128:
	[[Mapping]]: [{{val\| 1 0 0 -2 -6 }}, {{val\| 0 2 0 9 9 }}, {{val\| 0 0 1 -1 1 }}]		[[Mapping]]: [{{val\| 1 0 0 -2 -6 }}, {{val\| 0 2 0 9 9 }}, {{val\| 0 0 1 -1 1 }}]

	{{~~Val list~~\|legend=1\| 19e, 24, 34d, 53, 58, 111, 280cd }}		{{Optimal ET sequence\|legend=1\| 19e, 24, 34d, 53, 58, 111, 280cd }}

	[[Badness]]: 1.934 × 10<sup>-3</sup>		[[Badness]]: 1.934 × 10<sup>-3</sup>
Line 139:		Line 139:
	Mapping: [{{val\| 1 0 0 -2 -6 -1 }}, {{val\| 0 2 0 9 9 3 }}, {{val\| 0 0 1 -1 1 1 }}]		Mapping: [{{val\| 1 0 0 -2 -6 -1 }}, {{val\| 0 2 0 9 9 3 }}, {{val\| 0 0 1 -1 1 1 }}]

	~~Vals:~~ {{~~Val list~~\| 19e, 24, 34d, 53, 58, 111, 280cdf }}		{{Optimal ET sequence\|legend=1\| 19e, 24, 34d, 53, 58, 111, 280cdf }}

	Badness: 0.999 × 10<sup>-3</sup>		Badness: 0.999 × 10<sup>-3</sup>

← Older revision		Revision as of 06:58, 21 June 2025
Line 15:		Line 15:
	* [[7-odd-limit\|7-]] and [[9-odd-limit]]:		* [[7-odd-limit\|7-]] and [[9-odd-limit]]:
	: {{monzo list\| 1 0 0 0 \| 4/9 0 2/9 2/9 \| 0 0 1 0 \| 0 0 0 1 }}		: {{monzo list\| 1 0 0 0 \| 4/9 0 2/9 2/9 \| 0 0 1 0 \| 0 0 0 1 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5.7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7

	{{Optimal ET sequence\|legend=1\| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}		{{Optimal ET sequence\|legend=1\| 19, 34d, 39d, 53, 72, 130, 183, 202, 385, 587 }}
Line 35:		Line 35:
	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo\| 5 0 7/2 -2 -3/2 }}, {{monzo\| 5 0 5/2 -1 -3/2 }}, {{monzo\| 5 0 5/2 -2 -1/2 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 }}, {{monzo\| 5 0 7/2 -2 -3/2 }}, {{monzo\| 5 0 5/2 -1 -3/2 }}, {{monzo\| 5 0 5/2 -2 -1/2 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.7/5.11/5		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.7/5.11/5

	{{Optimal ET sequence\|legend=1\| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}		{{Optimal ET sequence\|legend=1\| 19, 33cd, 39d, 53, 58, 72, 130, 183, 255, 385, 640 }}
Line 57:		Line 57:
	* 13- and 15-odd-limit		* 13- and 15-odd-limit
	: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo\| 5 0 7/2 -2 -3/2 0 }}, {{monzo\| 5 0 5/2 -1 -3/2 0 }}, {{monzo\| 5 0 5/2 -2 -1/2 0 }}, {{monzo\| 8 0 11/2 -3 -5/2 0 }}]		: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 8/3 0 4/3 -2/3 -2/3 0 }}, {{monzo\| 5 0 7/2 -2 -3/2 0 }}, {{monzo\| 5 0 5/2 -1 -3/2 0 }}, {{monzo\| 5 0 5/2 -2 -1/2 0 }}, {{monzo\| 8 0 11/2 -3 -5/2 0 }}]
	: ~~eigenmonzo (~~unchanged-interval) basis: 2.7/5.11/5		: unchanged-interval (eigenmonzo) basis: 2.7/5.11/5

	{{Optimal ET sequence\|legend=1\| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}		{{Optimal ET sequence\|legend=1\| 19, 33cdff, 39df, 53, 58, 72, 111, 130, 183, 313 }}