Diaschismic rank-3 family - Revision history

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

2025-11-27T12:21:48Z

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

← Older revision		Revision as of 12:21, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Diaschismic rank-3 family\| ]] <!-- main article -->		[[Category:Diaschismic rank-3 family\| ]] <!-- main article -->
	[[Category:Diaschismic\| ]] <!-- key article -->		[[Category:Diaschismic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Make varda the standard name in the 11-limit

2025-08-29T14:09:36Z

Make varda the standard name in the 11-limit

← Older revision		Revision as of 14:09, 29 August 2025
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	[[Badness]] (Sintel): 1.95		[[Badness]] (Sintel): 1.95

	== ~~Julius a~~.k.a. ~~varda ==~~		== Varda ==
			Varda tempers out 176/175, 896/891 as well as 9801/9800, and is the main extension of rank-3 diaschismic to the 11-limit. Notice the identity {{nowrap\| 2048/2025 {{=}} (176/175)⋅(896/891) }}. In the natural 13-limit extension, 351/350, 352/351 and 364/363 are further tempered out, and in the 17-limit, 136/135, 256/255 and 289/288.

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

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	; Scales		; Scales
	* ~~Julius~~[22] [[hobbit]] [[transversal]]:		* Varda[22] [[hobbit]] [[transversal]]:
	: 28/27, 16/15, 11/10, 9/8, 32/27, 6/5, 5/4, 9/7, 4/3, 15/11, 45/32, 22/15, 3/2, 14/9, 8/5, 5/3, 27/16, 16/9, 20/11, 15/8, 27/14, 2		: 28/27, 16/15, 11/10, 9/8, 32/27, 6/5, 5/4, 9/7, 4/3, 15/11, 45/32, 22/15, 3/2, 14/9, 8/5, 5/3, 27/16, 16/9, 20/11, 15/8, 27/14, 2
	* ~~Julius~~[24] hobbit transversal		* Varda[24] hobbit transversal
	: 28/27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2		: 28/27, 16/15, 11/10, 9/8, 7/6, 6/5, 40/33, 5/4, 9/7, 4/3, 15/11, 45/32, 16/11, 3/2, 14/9, 8/5, 33/20, 27/16, 7/4, 16/9, 20/11, 15/8, 27/14, 2

	=== ~~Varda~~ ===		=== 13-limit ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

FloraC: - POTE tunings

2025-08-29T13:53:42Z

- POTE tunings

← Older revision		Revision as of 13:53, 29 August 2025
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	* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.9585{{c}}, ~7/4 = 971.2952{{c}}		* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.9585{{c}}, ~7/4 = 971.2952{{c}}
	: error map: {{val\| 0.000 +3.003 +3.769 +2.469 }}		: error map: {{val\| 0.000 +3.003 +3.769 +2.469 }}
	~~<!-- * [[POTE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.8982{{c}}, ~7/4 = 972.1330{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 10, 12, 22, 34d, 46, 58, 68, 80, 126, 206cd, 332bccd }}		{{Optimal ET sequence\|legend=1\| 10, 12, 22, 34d, 46, 58, 68, 80, 126, 206cd, 332bccd }}
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	* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.6576{{c}}, ~7/4 = 971.9790{{c}}		* [[CWE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.6576{{c}}, ~7/4 = 971.9790{{c}}
	: error map: {{val\| 0.000 +2.703 +4.371 +3.153 +2.031 }}		: error map: {{val\| 0.000 +2.703 +4.371 +3.153 +2.031 }}
	~~<!-- * [[POTE]]: ~45/32 = 600.0000{{c}}, ~3/2 = 704.8982{{c}}, ~7/4 = 972.1330{{c}} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:

FloraC: + missing tunings and badnesses

2025-08-29T13:53:22Z

+ missing tunings and badnesses

Show changes

FloraC: Units & stuff

2025-08-29T13:20:58Z

Units & stuff

← Older revision		Revision as of 13:20, 29 August 2025
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	{{Technical data page}}		{{Technical data page}}
	The '''diaschismic rank-3 family''' of [[temperament]]s [[tempering out\|tempers out]] the diaschisma, [[2048/2025]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.		The '''diaschismic rank-3 family''' of [[rank-3 temperament\|rank-3]] [[temperament]]s [[tempering out\|tempers out]] the diaschisma, [[2048/2025]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

	== Rank-3 diaschismic ==		== Rank-3 diaschismic ==
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	: mapping generators: ~45/32, ~3, ~7		: mapping generators: ~45/32, ~3, ~7

	[[Optimal tuning]] ([[POTE]]): ~3/2 = 704.8982, ~7/4 = 972.1330		[[Optimal tuning]] ([[POTE]]): ~3/2 = 704.8982{{c}}, ~7/4 = 972.1330{{c}}

	{{Optimal ET sequence\|legend=1\| 10, 12, 22, 34d, 46, 58, 68, 80, 126, 206cd, 332bccd }}		{{Optimal ET sequence\|legend=1\| 10, 12, 22, 34d, 46, 58, 68, 80, 126, 206cd, 332bccd }}

	[[Badness]]: 0.442 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.442 × 10<sup>-3</sup>

	== Julius ~~aka~~ varda ==		== Julius a.k.a. varda ==
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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	{{Optimal ET sequence\|legend=1\| 12, 22, 34d, 46, 58, 68, 80, 126, 184c, 206cd, 264bccde }}		{{Optimal ET sequence\|legend=1\| 12, 22, 34d, 46, 58, 68, 80, 126, 184c, 206cd, 264bccde }}

	[[Badness]]: 0.728 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.728 × 10<sup>-3</sup>

	Julius[22] [[hobbit]] [[transversal]]:		Julius[22] [[hobbit]] [[transversal]]:
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	Mapping: {{mapping\| 2 0 11 0 14 24 \| 0 1 -2 0 -4 -7 \| 0 0 0 1 1 1 }}		Mapping: {{mapping\| 2 0 11 0 14 24 \| 0 1 -2 0 -4 -7 \| 0 0 0 1 1 1 }}

	{{Optimal ET sequence\|legend=1\| 12f, 22, 34d, 46, 58, 80, 138cde, 242cde, 322bcde }}		{{Optimal ET sequence\|legend=0\| 12f, 22, 34d, 46, 58, 80, 138cde, 242cde, 322bcde }}

	Badness: 0.970 × 10<sup>-3</sup>		Badness (Smith): 0.970 × 10<sup>-3</sup>

	===== 17-limit =====		===== 17-limit =====
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	Mapping: {{mapping\| 2 0 11 0 14 24 5 \| 0 1 -2 0 -4 -7 1 \| 0 0 0 1 1 1 0 }}		Mapping: {{mapping\| 2 0 11 0 14 24 5 \| 0 1 -2 0 -4 -7 1 \| 0 0 0 1 1 1 0 }}

	{{Optimal ET sequence\|legend=1\| 12f, 22, 34d, 46, 58, 80, 126, 138cde }}		{{Optimal ET sequence\|legend=0\| 12f, 22, 34d, 46, 58, 80, 126, 138cde }}

	=== Julius ===		=== Julius ===
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	Mapping: {{mapping\| 2 0 11 0 14 -18 \| 0 1 -2 0 -4 8 \| 0 0 0 1 1 0 }}		Mapping: {{mapping\| 2 0 11 0 14 -18 \| 0 1 -2 0 -4 8 \| 0 0 0 1 1 0 }}

	{{Optimal ET sequence\|legend=1\| 12, 22f, 34d, 46, 68, 80, 148d, 228bcd }}		{{Optimal ET sequence\|legend=0\| 12, 22f, 34d, 46, 68, 80, 148d, 228bcd }}

	Badness: 1.78 × 10<sup>-3</sup>		Badness (Smith): 1.78 × 10<sup>-3</sup>

	===== 17-limit =====		===== 17-limit =====
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	Mapping: {{mapping\| 2 0 11 0 14 -18 5 \| 0 1 -2 0 -4 8 1 \| 0 0 0 1 1 0 0 }}		Mapping: {{mapping\| 2 0 11 0 14 -18 5 \| 0 1 -2 0 -4 8 1 \| 0 0 0 1 1 0 0 }}

	{{Optimal ET sequence\|legend=1\| 12, 22f, 34d, 46, 68, 80, 148d, 228bcd }}		{{Optimal ET sequence\|legend=0\| 12, 22f, 34d, 46, 68, 80, 148d, 228bcd }}

	===== 19-limit =====		===== 19-limit =====
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	Mapping: {{mapping\| 2 0 11 0 14 -18 5 -13 \| 0 1 -2 0 -4 8 1 5 \| 0 0 0 1 1 0 0 1 }}		Mapping: {{mapping\| 2 0 11 0 14 -18 5 -13 \| 0 1 -2 0 -4 8 1 5 \| 0 0 0 1 1 0 0 1 }}

	{{Optimal ET sequence\|legend=1\| 12, 22fh, 34dh, 46, 68, 80, 148d, 228bcd }}		{{Optimal ET sequence\|legend=0\| 12, 22fh, 34dh, 46, 68, 80, 148d, 228bcd }}

	== Augustus ==		== Augustus ==
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	{{Optimal ET sequence\|legend=1\| 10, 12e, 22, 46, 68, 114, 170b }}		{{Optimal ET sequence\|legend=1\| 10, 12e, 22, 46, 68, 114, 170b }}

	[[Badness]]: 1.58 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.58 × 10<sup>-3</sup>

	== Tiberius ==		== Tiberius ==
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	{{Optimal ET sequence\|legend=1\| 46, 58, 104c, 160, 162ce, 172ce, 218ce }}		{{Optimal ET sequence\|legend=1\| 46, 58, 104c, 160, 162ce, 172ce, 218ce }}

	[[Badness]]: 1.71 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.71 × 10<sup>-3</sup>

	== Claudius ==		== Claudius ==
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	{{Optimal ET sequence\|legend=1\| 22, 46e, 48c, 58, 80, 138cde, 218cde, 286bcddeee, 366bccdddeee }}		{{Optimal ET sequence\|legend=1\| 22, 46e, 48c, 58, 80, 138cde, 218cde, 286bcddeee, 366bccdddeee }}

	[[Badness]]: 1.97 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.97 × 10<sup>-3</sup>

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

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

2025-08-27T12:49:08Z

FloraC moved page Diaschismic rank three family to Diaschismic 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"

2025-06-24T00:35:59Z

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

← Older revision		Revision as of 00:35, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Diaschismic rank-3 family\| ]] <!-- main article -->		[[Category:Diaschismic rank-3 family\| ]] <!-- main article -->
	[[Category:Diaschismic\| ]] <!-- key article -->		[[Category:Diaschismic\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-06-21T06:58:25Z

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

← Older revision		Revision as of 06:58, 21 June 2025
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| -1/8 3/2 -5/4 0 1 }}, {{monzo\| 11/8 -1/2 -1/4 0 1 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| -1/8 3/2 -5/4 0 1 }}, {{monzo\| 11/8 -1/2 -1/4 0 1 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.9/5.11/3		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11/3

	{{Optimal ET sequence\|legend=1\| 12, 22, 34d, 46, 58, 68, 80, 126, 184c, 206cd, 264bccde }}		{{Optimal ET sequence\|legend=1\| 12, 22, 34d, 46, 58, 68, 80, 126, 184c, 206cd, 264bccde }}
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| 45/16 3/4 -3/8 1/2 -1/2 }}, {{monzo\| 45/16 3/4 -3/8 -1/2 1/2 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| 45/16 3/4 -3/8 1/2 -1/2 }}, {{monzo\| 45/16 3/4 -3/8 -1/2 1/2 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.9/5.11/7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11/7

	{{Optimal ET sequence\|legend=1\| 10, 12e, 22, 46, 68, 114, 170b }}		{{Optimal ET sequence\|legend=1\| 10, 12e, 22, 46, 68, 114, 170b }}
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| 0 0 0 1 0 }}, {{monzo\| -3 2 -1 2 0 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| 0 0 0 1 0 }}, {{monzo\| -3 2 -1 2 0 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.9/5.7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.9/5.7

	{{Optimal ET sequence\|legend=1\| 46, 58, 104c, 160, 162ce, 172ce, 218ce }}		{{Optimal ET sequence\|legend=1\| 46, 58, 104c, 160, 162ce, 172ce, 218ce }}
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 9/7 0 -3/7 2/7 1/7 }}, {{monzo\| 41/14 0 6/7 -4/7 -2/7 }}, {{monzo\| 41/14 0 -1/7 3/7 -2/7 }}, {{monzo\| 41/14 0 -1/7 -4/7 5/7 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 9/7 0 -3/7 2/7 1/7 }}, {{monzo\| 41/14 0 6/7 -4/7 -2/7 }}, {{monzo\| 41/14 0 -1/7 3/7 -2/7 }}, {{monzo\| 41/14 0 -1/7 -4/7 5/7 }}]
	: [[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\| 22, 46e, 48c, 58, 80, 138cde, 218cde, 286bcddeee, 366bccdddeee }}		{{Optimal ET sequence\|legend=1\| 22, 46e, 48c, 58, 80, 138cde, 218cde, 286bcddeee, 366bccdddeee }}

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

" to "{{Technical data page}}"

2025-04-13T13:43:17Z

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 '''diaschismic rank-3 family''' of [[temperament]]s [[tempering out\|tempers out]] the diaschisma, [[2048/2025]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.		The '''diaschismic rank-3 family''' of [[temperament]]s [[tempering out\|tempers out]] the diaschisma, [[2048/2025]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

BudjarnLambeth: {{Technical data page}}

2025-04-13T11:36:30Z

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

← Older revision		Revision as of 11:36, 13 April 2025
Line 1:		Line 1:
			{{Technical data page}}<br><br>
	The '''diaschismic rank-3 family''' of [[temperament]]s [[tempering out\|tempers out]] the diaschisma, [[2048/2025]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.		The '''diaschismic rank-3 family''' of [[temperament]]s [[tempering out\|tempers out]] the diaschisma, [[2048/2025]]. If nothing else is tempered out we have a 7-limit planar temperament, with an 11-limit comma we get an 11-limit temperament, and so forth.

← Older revision		Revision as of 06:58, 21 June 2025
Line 33:		Line 33:
	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| -1/8 3/2 -5/4 0 1 }}, {{monzo\| 11/8 -1/2 -1/4 0 1 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| -1/8 3/2 -5/4 0 1 }}, {{monzo\| 11/8 -1/2 -1/4 0 1 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.9/5.11/3		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11/3

	{{Optimal ET sequence\|legend=1\| 12, 22, 34d, 46, 58, 68, 80, 126, 184c, 206cd, 264bccde }}		{{Optimal ET sequence\|legend=1\| 12, 22, 34d, 46, 58, 68, 80, 126, 184c, 206cd, 264bccde }}
Line 104:		Line 104:
	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| 45/16 3/4 -3/8 1/2 -1/2 }}, {{monzo\| 45/16 3/4 -3/8 -1/2 1/2 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| 45/16 3/4 -3/8 1/2 -1/2 }}, {{monzo\| 45/16 3/4 -3/8 -1/2 1/2 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.9/5.11/7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.9/5.11/7

	{{Optimal ET sequence\|legend=1\| 10, 12e, 22, 46, 68, 114, 170b }}		{{Optimal ET sequence\|legend=1\| 10, 12e, 22, 46, 68, 114, 170b }}
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| 0 0 0 1 0 }}, {{monzo\| -3 2 -1 2 0 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 11/8 1/2 -1/4 0 0 }}, {{monzo\| 11/4 -1 1/2 0 0 }}, {{monzo\| 0 0 0 1 0 }}, {{monzo\| -3 2 -1 2 0 }}]
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.9/5.7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.9/5.7

	{{Optimal ET sequence\|legend=1\| 46, 58, 104c, 160, 162ce, 172ce, 218ce }}		{{Optimal ET sequence\|legend=1\| 46, 58, 104c, 160, 162ce, 172ce, 218ce }}
Line 136:		Line 136:
	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 9/7 0 -3/7 2/7 1/7 }}, {{monzo\| 41/14 0 6/7 -4/7 -2/7 }}, {{monzo\| 41/14 0 -1/7 3/7 -2/7 }}, {{monzo\| 41/14 0 -1/7 -4/7 5/7 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 9/7 0 -3/7 2/7 1/7 }}, {{monzo\| 41/14 0 6/7 -4/7 -2/7 }}, {{monzo\| 41/14 0 -1/7 3/7 -2/7 }}, {{monzo\| 41/14 0 -1/7 -4/7 5/7 }}]
	: [[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\| 22, 46e, 48c, 58, 80, 138cde, 218cde, 286bcddeee, 366bccdddeee }}		{{Optimal ET sequence\|legend=1\| 22, 46e, 48c, 58, 80, 138cde, 218cde, 286bcddeee, 366bccdddeee }}