Mint family - Revision history

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

2025-11-27T12:17:57Z

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

← Older revision		Revision as of 12:17, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Mint family\| ]] <!-- main article -->		[[Category:Mint family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: - POTE tunings

2025-11-19T13:13:49Z

- POTE tunings

← Older revision		Revision as of 13:13, 19 November 2025
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 695.2474{{c}}, ~5/4 = 401.1263{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 695.2474{{c}}, ~5/4 = 401.1263{{c}}
	: error map: {{val\| 0.000 -6.708 +14.813 +20.543 }}		: error map: {{val\| 0.000 -6.708 +14.813 +20.543 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 698.6351{{c}}, ~5/4 = 404.2809{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 4, 5, 7, 8d, 9, 12, 41cd, 53cdd }}		{{Optimal ET sequence\|legend=1\| 4, 5, 7, 8d, 9, 12, 41cd, 53cdd }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 687.9993{{c}}, ~5/4 = 391.2274{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 687.9993{{c}}, ~5/4 = 391.2274{{c}}
	: error map: {{val\| 0.000 -13.956 +4.914 +15.945 +15.908 }}		: error map: {{val\| 0.000 -13.956 +4.914 +15.945 +15.908 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 688.8370{{c}}, ~5/4 = 391.8801{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 7, 9, 12, 21, 28 }}		{{Optimal ET sequence\|legend=1\| 7, 9, 12, 21, 28 }}
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	* WE: ~2 = 1199.6174{{c}}, ~3/2 = 684.7864{{c}}, ~5/4 = 390.1319{{c}}		* WE: ~2 = 1199.6174{{c}}, ~3/2 = 684.7864{{c}}, ~5/4 = 390.1319{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 684.7716{{c}}, ~5/4 = 390.0622{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 684.7716{{c}}, ~5/4 = 390.0622{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 685.0048{{c}}, ~5/4 = 390.2563{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 7, 9, 12f, 16, 21, 28, 37b }}		{{Optimal ET sequence\|legend=0\| 7, 9, 12f, 16, 21, 28, 37b }}

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

2025-11-19T13:13:35Z

Switch to Sintel's badness, WE & CWE tunings, per community consensus

← Older revision		Revision as of 13:13, 19 November 2025
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	{{Mapping\|legend=1\| 1 0 0 2 \| 0 1 0 2 \| 0 0 1 -1 }}		{{Mapping\|legend=1\| 1 0 0 2 \| 0 1 0 2 \| 0 0 1 -1 }}
			: mapping generators: ~2, ~3, ~5

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 698.6351{{c}}, ~5/4 = 404.2809{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1196.3575{{c}}, ~3/2 = 696.5144{{c}}, ~5/4 = 403.0537{{c}}
			: [[error map]]: {{val\| -3.643 -9.083 +9.455 +13.864 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 695.2474{{c}}, ~5/4 = 401.1263{{c}}
			: error map: {{val\| 0.000 -6.708 +14.813 +20.543 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 698.6351{{c}}, ~5/4 = 404.2809{{c}} -->

	{{Optimal ET sequence\|legend=1\| 4, 5, 7, 8d, 9, 12 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 7, 8d, 9, 12, 41cd, 53cdd }}

	[[Badness]] (~~Smith~~): 0.~~0637 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.281

	== Nickel ==		== Nickel ==
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	{{Mapping\|legend=1\| 1 0 0 2 -2 \| 0 1 0 2 2 \| 0 0 1 -1 1 }}		{{Mapping\|legend=1\| 1 0 0 2 -2 \| 0 1 0 2 2 \| 0 0 1 -1 1 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 688.8370{{c}}, ~5/4 = 391.8801{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1198.7814{{c}}, ~3/2 = 688.1375{{c}}, ~5/4 = 391.4822{{c}}
			: [[error map]]: {{val\| -1.219 -15.036 +2.731 +13.530 +14.002 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 687.9993{{c}}, ~5/4 = 391.2274{{c}}
			: error map: {{val\| 0.000 -13.956 +4.914 +15.945 +15.908 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 688.8370{{c}}, ~5/4 = 391.8801{{c}} -->

	{{Optimal ET sequence\|legend=1\| 7, 9, 12, 21, 28 }}		{{Optimal ET sequence\|legend=1\| 7, 9, 12, 21, 28 }}

	[[Badness]] (~~Smith~~): 0.~~463 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.557

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

	Optimal ~~tuning (~~POTE): ~2 = 1200.0000{{c}}, ~3/2 = 685.0048{{c}}, ~5/4 = 390.2563{{c}}		Optimal tunings:
			* WE: ~2 = 1199.6174{{c}}, ~3/2 = 684.7864{{c}}, ~5/4 = 390.1319{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 684.7716{{c}}, ~5/4 = 390.0622{{c}}
			<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 685.0048{{c}}, ~5/4 = 390.2563{{c}} -->

	{{Optimal ET sequence\|legend=0\| 7, 9, 12f, 16, 21, 28 }}		{{Optimal ET sequence\|legend=0\| 7, 9, 12f, 16, 21, 28, 37b }}

	Badness (~~Smith~~): 0.~~647 × 10<sup>-3</sup>~~		Badness (Sintel): 0.605

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

FloraC: - redundant category

2025-11-19T13:03:02Z

- redundant category

← Older revision		Revision as of 13:03, 19 November 2025
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	Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 685.0048{{c}}, ~5/4 = 390.2563{{c}}		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 685.0048{{c}}, ~5/4 = 390.2563{{c}}

	{{Optimal ET sequence\|legend=1\| 7, 9, 12f, 16, 21, 28 }}		{{Optimal ET sequence\|legend=0\| 7, 9, 12f, 16, 21, 28 }}

	Badness (Smith): 0.647 × 10<sup>-3</sup>		Badness (Smith): 0.647 × 10<sup>-3</sup>
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	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:Mint family\| ]] <!-- main article -->		[[Category:Mint family\| ]] <!-- main article -->
	~~[[Category:Mint\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Units & misc. cleanup

2025-11-19T13:01:31Z

Units & misc. cleanup

← Older revision		Revision as of 13:01, 19 November 2025
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	{{Technical data page}}		{{Technical data page}}
	The '''mint family''' of [[rank-3 temperament]]s tempers out [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]].		The '''mint family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]].

	== Mint ==		== Mint ==
	[[Subgroup]]: 2.3.5.7		[[Subgroup]]: 2.3.5.7

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

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 698.6351, ~5/4 = 404.2809		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 698.6351{{c}}, ~5/4 = 404.2809{{c}}

	{{Optimal ET sequence\|legend=1\| 4, 5, 7, 8d, 9, 12 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 7, 8d, 9, 12 }}

	[[Badness]]: 0.0637 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.0637 × 10<sup>-3</sup>

	== Nickel ==		== Nickel ==
	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

	[[Comma list]]: 36/35, [[45/44]]		[[Comma list]]: 36/35, 45/44

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

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 688.8370, ~5/4 = 391.8801		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 688.8370{{c}}, ~5/4 = 391.8801{{c}}

	{{Optimal ET sequence\|legend=1\| 7, 9, 12, 21, 28 }}		{{Optimal ET sequence\|legend=1\| 7, 9, 12, 21, 28 }}

	[[Badness]]: 0.463 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.463 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: [[27/26]], 36/35, 45/44		Comma list: 27/26, 36/35, 45/44

	Mapping: {{mapping\| 1 0 0 2 -2 -1 \| 0 1 0 2 2 3 \| 0 0 1 -1 1 0 }}		Mapping: {{mapping\| 1 0 0 2 -2 -1 \| 0 1 0 2 2 3 \| 0 0 1 -1 1 0 }}

	Optimal tuning (POTE): ~2 = ~~1\1~~, ~3/2 = 685.0048, ~5/4 = 390.2563		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 685.0048{{c}}, ~5/4 = 390.2563{{c}}

	{{Optimal ET sequence\|legend=1\| 7, 9, 12f, 16, 21, 28 }}		{{Optimal ET sequence\|legend=1\| 7, 9, 12f, 16, 21, 28 }}

	Badness: 0.647 × 10<sup>-3</sup>		Badness (Smith): 0.647 × 10<sup>-3</sup>

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

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

2025-06-24T00:41:35Z

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

← Older revision		Revision as of 00:41, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Mint family\| ]] <!-- main article -->		[[Category:Mint family\| ]] <!-- main article -->
	[[Category:Mint\| ]] <!-- key article -->		[[Category:Mint\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

" to "{{Technical data page}}"

2025-04-13T13:45:14Z

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

← Older revision		Revision as of 13:45, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''mint family''' of [[rank-3 temperament]]s tempers out [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]].		The '''mint family''' of [[rank-3 temperament]]s tempers out [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]].

BudjarnLambeth: {{Technical data page}}

2025-04-13T11:48:57Z

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

← Older revision		Revision as of 11:48, 13 April 2025
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	The '''mint family''' of rank-3 ~~temperaments~~ tempers out [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]].		{{Technical data page}}<br><br>
			The '''mint family''' of [[rank-3 temperament]]s tempers out [[36/35]], identifying both [[7/6]] with [[6/5]] and [[5/4]] with [[9/7]].

	== Mint ==		== Mint ==

FloraC: Update keys

2023-08-05T05:58:15Z

Update keys

← Older revision		Revision as of 05:58, 5 August 2023
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	== Mint ==		== Mint ==
			[[Subgroup]]: 2.3.5.7
	Subgroup: 2.3.5.7

	[[Comma list]]: 36/35		[[Comma list]]: 36/35

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

	[[POTE ~~generator~~]]s: ~3/2 = 698.6351, ~5/4 = 404.2809		[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 698.6351, ~5/4 = 404.2809

	{{Optimal ET sequence\|legend=1\| 4, 5, 7, 8d, 9, 12 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 7, 8d, 9, 12 }}
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	== Nickel ==		== Nickel ==
			[[Subgroup]]: 2.3.5.7.11
	Subgroup: 2.3.5.7.11

	[[Comma list]]: 36/35, [[45/44]]		[[Comma list]]: 36/35, [[45/44]]

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

	[[POTE ~~generator~~]]s: ~3/2 = 688.8370, ~5/4 = 391.8801		[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 688.8370, ~5/4 = 391.8801

	{{Optimal ET sequence\|legend=1\| 7, 9, 12, 21, 28 }}		{{Optimal ET sequence\|legend=1\| 7, 9, 12, 21, 28 }}
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	=== 13-limit ===		=== 13-limit ===

	Subgroup: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	Comma list: [[27/26]], 36/35, 45/44		Comma list: [[27/26]], 36/35, 45/44

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

	POTE ~~generators~~: ~3/2 = 685.0048, ~5/4 = 390.2563		Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 685.0048, ~5/4 = 390.2563

	{{Optimal ET sequence\|legend=1\| 7, 9, 12f, 16, 21, 28 }}		{{Optimal ET sequence\|legend=1\| 7, 9, 12f, 16, 21, 28 }}
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	[[Category:Mint]]		[[Category:Mint family\| ]] <!-- main article -->
			[[Category:Mint\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2023-05-07T18:09:21Z

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

← Older revision		Revision as of 18:09, 7 May 2023
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	[[POTE generator]]s: ~3/2 = 698.6351, ~5/4 = 404.2809		[[POTE generator]]s: ~3/2 = 698.6351, ~5/4 = 404.2809

	{{~~Val list~~\|legend=1\| 4, 5, 7, 8d, 9, 12 }}		{{Optimal ET sequence\|legend=1\| 4, 5, 7, 8d, 9, 12 }}

	[[Badness]]: 0.0637 × 10<sup>-3</sup>		[[Badness]]: 0.0637 × 10<sup>-3</sup>
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	[[POTE generator]]s: ~3/2 = 688.8370, ~5/4 = 391.8801		[[POTE generator]]s: ~3/2 = 688.8370, ~5/4 = 391.8801

	{{~~Val list~~\|legend=1\| 7, 9, 12, 21, 28 }}		{{Optimal ET sequence\|legend=1\| 7, 9, 12, 21, 28 }}

	[[Badness]]: 0.463 × 10<sup>-3</sup>		[[Badness]]: 0.463 × 10<sup>-3</sup>
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	POTE generators: ~3/2 = 685.0048, ~5/4 = 390.2563		POTE generators: ~3/2 = 685.0048, ~5/4 = 390.2563

	{{~~Val list~~\|legend=1\| 7, 9, 12f, 16, 21, 28 }}		{{Optimal ET sequence\|legend=1\| 7, 9, 12f, 16, 21, 28 }}

	Badness: 0.647 × 10<sup>-3</sup>		Badness: 0.647 × 10<sup>-3</sup>