Canopus family - Revision history

Lériendil: Lériendil moved page Mirkwai family to Canopus family

2026-06-05T16:39:51Z

Lériendil moved page Mirkwai family to Canopus family

← Older revision	Revision as of 16:39, 5 June 2026
(No difference)

Lériendil at 16:39, 5 June 2026

2026-06-05T16:39:31Z

← Older revision		Revision as of 16:39, 5 June 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''~~mirkwai~~ family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.		The '''canopus family''' of [[planar temperament]]s tempers out the '''canopus''' or '''[[mirkwai comma]]''' ({{monzo\|legend=1\| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.

	== Mirkwai ==		== Canopic aka Mirkwai ==
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: 16875/16807 (~~mirkwai~~)		[[Comma list]]: 16875/16807 (canopus)

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

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

2025-11-27T12:31:44Z

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

← Older revision		Revision as of 12:31, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Mirkwai family]] <!-- main article -->		[[Category:Mirkwai family]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-06-24T00:28:45Z

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

← Older revision		Revision as of 00:28, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Mirkwai family]] <!-- main article -->		[[Category:Mirkwai family]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

" to "{{Technical data page}}"

2025-04-13T13:47:40Z

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 '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.		The '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.

BudjarnLambeth: {{Technical data page}}

2025-04-13T10:52:16Z

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

← Older revision		Revision as of 10:52, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.		The '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.

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

2023-05-07T16:28:51Z

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

Cmloegcmluin: unchanged interval → unchanged-interval

2023-05-05T23:40:37Z

unchanged interval → unchanged-interval

← Older revision		Revision as of 23:40, 5 May 2023
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	* [[7-odd-limit]]		* [[7-odd-limit]]
	: [{{monzo\| 1 0 0 0 }}, {{monzo\| 0 4/7 -4/7 5/7 }}, {{monzo\| 0 -3/7 3/7 5/7 }}, {{monzo\| 0 0 0 1 }}]		: [{{monzo\| 1 0 0 0 }}, {{monzo\| 0 4/7 -4/7 5/7 }}, {{monzo\| 0 -3/7 3/7 5/7 }}, {{monzo\| 0 0 0 1 }}]
	: [[Eigenmonzo]]s (unchanged intervals): 2, 8/7, 6/5		: [[Eigenmonzo]]s (unchanged-intervals): 2, 8/7, 6/5
	* [[9-odd-limit]]		* [[9-odd-limit]]
	: [{{monzo\| 1 0 0 0 }}, {{monzo\| 0 8/11 -4/11 5/11 }}, {{monzo\| 0 -6/11 3/11 10/11 }}, {{monzo\| 0 0 0 1 }}]		: [{{monzo\| 1 0 0 0 }}, {{monzo\| 0 8/11 -4/11 5/11 }}, {{monzo\| 0 -6/11 3/11 10/11 }}, {{monzo\| 0 0 0 1 }}]
	: [[Eigenmonzo]]s (unchanged intervals): 2, 10/9, 8/7		: [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 8/7

	{{Val list\|legend=1\| 31, 41, 72, 152, 224 }}		{{Val list\|legend=1\| 31, 41, 72, 152, 224 }}
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	* [[11-odd-limit]]		* [[11-odd-limit]]
	: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 10 10 -3 0 -5 }}, {{monzo\| 0 0 1 0 0 }}, {{monzo\| 6 6 -1 0 -3 }}, {{monzo\| 20 18 -6 0 -9 }}]		: [{{monzo\| 1 0 0 0 0 }}, {{monzo\| 10 10 -3 0 -5 }}, {{monzo\| 0 0 1 0 0 }}, {{monzo\| 6 6 -1 0 -3 }}, {{monzo\| 20 18 -6 0 -9 }}]
	: [[Eigenmonzo]]s (unchanged intervals): 2, 11/9, 5/4		: [[Eigenmonzo]]s (unchanged-intervals): 2, 11/9, 5/4

	{{Val list\|legend=1\| 31, 41, 72, 152, 224, 631d, 855d }}		{{Val list\|legend=1\| 31, 41, 72, 152, 224, 631d, 855d }}
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	* 13-odd-limit		* 13-odd-limit
	: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 4/5 6/5 -4/5 0 0 1/5 }}, {{monzo\| 8/5 2/5 -3/5 0 0 2/5 }}, {{monzo\| 44/25 26/25 -24/25 0 0 11/25 }}, {{monzo\| 62/25 48/25 -27/25 0 0 3/25 }}, {{monzo\| 8/5 2/5 -8/5 0 0 7/5 }}]		: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 4/5 6/5 -4/5 0 0 1/5 }}, {{monzo\| 8/5 2/5 -3/5 0 0 2/5 }}, {{monzo\| 44/25 26/25 -24/25 0 0 11/25 }}, {{monzo\| 62/25 48/25 -27/25 0 0 3/25 }}, {{monzo\| 8/5 2/5 -8/5 0 0 7/5 }}]
	: [[Eigenmonzo]]s (unchanged intervals): 2, 10/9, 13/10		: [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 13/10
	* 15-odd-limit minimax		* 15-odd-limit minimax
	: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 0 1 0 0 0 0 }}, {{monzo\| 5/4 1/2 0 -5/16 0 5/16 }}, {{monzo\| 1 1 0 -1/4 0 1/4 }}, {{monzo\| 5/4 3/2 0 3/16 0 -3/16 }}, {{monzo\| 1 1 0 -5/4 0 5/4 }}]		: [{{monzo\| 1 0 0 0 0 0 }}, {{monzo\| 0 1 0 0 0 0 }}, {{monzo\| 5/4 1/2 0 -5/16 0 5/16 }}, {{monzo\| 1 1 0 -1/4 0 1/4 }}, {{monzo\| 5/4 3/2 0 3/16 0 -3/16 }}, {{monzo\| 1 1 0 -5/4 0 5/4 }}]
	: [[Eigenmonzo]]s (unchanged intervals): 2, 14/13, 4/3		: [[Eigenmonzo]]s (unchanged-intervals): 2, 14/13, 4/3

	Optimal GPV sequence: {{Val list\| 31, 49f, 72, 103, 121, 152f, 193, 224 }}		Optimal GPV sequence: {{Val list\| 31, 49f, 72, 103, 121, 152f, 193, 224 }}

FloraC: Correct mapping and update keys and categories

2022-10-16T05:48:28Z

Correct mapping and update keys and categories

← Older revision		Revision as of 05:48, 16 October 2022
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	The '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.		The '''mirkwai family''' of [[planar temperament]]s tempers out the [[mirkwai comma]], 16875/16807.

	== Mirkwai ==		== Mirkwai ==
	Subgroup: 2.3.5.7		[[Subgroup]]: 2.3.5.7

	[[Comma list]]: 16875/16807 (mirkwai)		[[Comma list]]: 16875/16807 (mirkwai)
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	[[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5		[[Projection pair]]s: 5 84375/16807 7 16875/2401 to 2.3.7/5

	== Indra ==		== Indra ==
	Subgroup: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 540/539, 1375/1372		[[Comma list]]: 540/539, 1375/1372
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	Scales: [[indra31]]		Scales: [[indra31]]

	=== Shibi ===		=== Shibi ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: 540/539, 729/728, 1375/1372		Comma list: 540/539, 729/728, 1375/1372

	Mapping: [{{val\| 1 0 0 0 2 -4 -3 }}, {{val\| 0 1 3 3 0 11 3 }}, {{val\| 0 0 -5 -4 3 4 }}]		Mapping: [{{val\| 1 0 0 0 2 -3 }}, {{val\| 0 1 3 3 0 3 }}, {{val\| 0 0 -5 -4 4 }}]

	~~Vals~~: {{Val list\| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }}		Optimal GPV sequence: {{Val list\| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }}

	Badness: 0.721 × 10<sup>-3</sup>		Badness: 0.721 × 10<sup>-3</sup>

	=== Yajna ===		=== Yajna ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

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	: [[Eigenmonzo]]s (unchanged intervals): 2, 14/13, 4/3		: [[Eigenmonzo]]s (unchanged intervals): 2, 14/13, 4/3

	~~Vals~~: {{Val list\| 31, 49f, 72, 103, 121, 152f, 193, 224 }}		Optimal GPV sequence: {{Val list\| 31, 49f, 72, 103, 121, 152f, 193, 224 }}

	Badness: 0.700 × 10<sup>-3</sup>		Badness: 0.700 × 10<sup>-3</sup>

	=== Vibhu ===		=== Vibhu ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

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	Mapping: [{{val\| 1 0 0 0 2 1 }}, {{val\| 0 1 3 3 0 6 }}, {{val\| 0 0 -5 -4 3 -14 }}]		Mapping: [{{val\| 1 0 0 0 2 1 }}, {{val\| 0 1 3 3 0 6 }}, {{val\| 0 0 -5 -4 3 -14 }}]

	~~Vals~~: {{Val list\| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }}		Optimal GPV sequence: {{Val list\| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }}

	Badness: 0.826 × 10<sup>-3</sup>		Badness: 0.826 × 10<sup>-3</sup>

	=== Vish ===		=== Vish ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

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	Mapping: [{{val\| 1 0 0 0 2 2 }}, {{val\| 0 1 3 3 0 -2 }}, {{val\| 0 0 -5 -4 3 10 }}]		Mapping: [{{val\| 1 0 0 0 2 2 }}, {{val\| 0 1 3 3 0 -2 }}, {{val\| 0 0 -5 -4 3 10 }}]

	~~Vals~~: {{Val list\| 31f, 41, 72, 121, 193 }}		Optimal GPV sequence: {{Val list\| 31f, 41, 72, 121, 193 }}

	Badness: 0.930 × 10<sup>-3</sup>		Badness: 0.930 × 10<sup>-3</sup>

	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Mirkwai]]		[[Category:Mirkwai family]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

Fredg999 category edits: Removing from Category:Regular temperament theory using Cat-a-lot

2022-03-02T22:01:00Z

Removing from Category:Regular temperament theory using Cat-a-lot

← Older revision		Revision as of 22:01, 2 March 2022
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	Badness: 0.930 × 10<sup>-3</sup>		Badness: 0.930 × 10<sup>-3</sup>

	~~[[Category:Regular temperament theory]]~~
	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Mirkwai]]		[[Category:Mirkwai]]
	[[Category:Rank 3]]		[[Category:Rank 3]]

← Older revision		Revision as of 16:28, 7 May 2023
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	: [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 8/7		: [[Eigenmonzo]]s (unchanged-intervals): 2, 10/9, 8/7

	{{~~Val list~~\|legend=1\| 31, 41, 72, 152, 224 }}		{{Optimal ET sequence\|legend=1\| 31, 41, 72, 152, 224 }}

	[[Badness]]: 0.342 × 10<sup>-3</sup>		[[Badness]]: 0.342 × 10<sup>-3</sup>
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	: [[Eigenmonzo]]s (unchanged-intervals): 2, 11/9, 5/4		: [[Eigenmonzo]]s (unchanged-intervals): 2, 11/9, 5/4

	{{~~Val list~~\|legend=1\| 31, 41, 72, 152, 224, 631d, 855d }}		{{Optimal ET sequence\|legend=1\| 31, 41, 72, 152, 224, 631d, 855d }}

	[[Badness]]: 0.266 × 10<sup>-3</sup>		[[Badness]]: 0.266 × 10<sup>-3</sup>
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	Mapping: [{{val\| 1 0 0 0 2 -3 }}, {{val\| 0 1 3 3 0 3 }}, {{val\| 0 0 -5 -4 4 }}]		Mapping: [{{val\| 1 0 0 0 2 -3 }}, {{val\| 0 1 3 3 0 3 }}, {{val\| 0 0 -5 -4 4 }}]

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }}		{{Optimal ET sequence\|legend=1\| 31f, 39df, 41, 72, 111, 152f, 183, 224, 631d, 855d }}

	Badness: 0.721 × 10<sup>-3</sup>		Badness: 0.721 × 10<sup>-3</sup>
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	: [[Eigenmonzo]]s (unchanged-intervals): 2, 14/13, 4/3		: [[Eigenmonzo]]s (unchanged-intervals): 2, 14/13, 4/3

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 31, 49f, 72, 103, 121, 152f, 193, 224 }}		{{Optimal ET sequence\|legend=1\| 31, 49f, 72, 103, 121, 152f, 193, 224 }}

	Badness: 0.700 × 10<sup>-3</sup>		Badness: 0.700 × 10<sup>-3</sup>
Line 91:		Line 91:
	Mapping: [{{val\| 1 0 0 0 2 1 }}, {{val\| 0 1 3 3 0 6 }}, {{val\| 0 0 -5 -4 3 -14 }}]		Mapping: [{{val\| 1 0 0 0 2 1 }}, {{val\| 0 1 3 3 0 6 }}, {{val\| 0 0 -5 -4 3 -14 }}]

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }}		{{Optimal ET sequence\|legend=1\| 31, 64cdf, 72, 103, 111, 152, 175f, 183, 469f }}

	Badness: 0.826 × 10<sup>-3</sup>		Badness: 0.826 × 10<sup>-3</sup>
Line 102:		Line 102:
	Mapping: [{{val\| 1 0 0 0 2 2 }}, {{val\| 0 1 3 3 0 -2 }}, {{val\| 0 0 -5 -4 3 10 }}]		Mapping: [{{val\| 1 0 0 0 2 2 }}, {{val\| 0 1 3 3 0 -2 }}, {{val\| 0 0 -5 -4 3 10 }}]

	Optimal ~~GPV~~ sequence~~: {{Val list~~\| 31f, 41, 72, 121, 193 }}		{{Optimal ET sequence\|legend=1\| 31f, 41, 72, 121, 193 }}

	Badness: 0.930 × 10<sup>-3</sup>		Badness: 0.930 × 10<sup>-3</sup>