Gariboh family - Revision history

FloraC: Text replacement - "rank-3 temperament" to "rank-3 temperament"

2026-06-08T08:36:20Z

Text replacement - "rank-3 temperament" to "rank-3 temperament"

← Older revision		Revision as of 08:36, 8 June 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''gariboh family''' of [[rank-3 ~~temperament\|rank-3]] [[regular temperament\|~~temperament]]s [[tempering out\|tempers out]] the gariboh comma, [[3125/3087]].		The '''gariboh family''' of [[rank-3 temperament]]s [[tempering out\|tempers out]] the gariboh comma, [[3125/3087]].

	== Gariboh ==		== Gariboh ==

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

2025-11-27T12:23:10Z

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

← Older revision		Revision as of 12:23, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Gariboh family\| ]] <!-- main article -->		[[Category:Gariboh family\| ]] <!-- main article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

FloraC: Note 94edo as a recommended tuning

2025-11-09T11:48:51Z

Note 94edo as a recommended tuning

← Older revision		Revision as of 11:48, 9 November 2025
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	== Gariboh ==		== Gariboh ==
	Gariboh is generated by a perfect fifth and a narrow minor third of ~25/21, ~~two of which~~ make ~7/5.		Gariboh is generated by a perfect fifth and a narrow minor third of ~25/21, three make ~5/3 and five make ~7/3. [[94edo]] makes for an excellent tuning for it.

	A notable tuning ~~of gariboh~~ is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 702.4482{{c}}, 293.7397{{c}} with pure octaves since prime 2 is not involved in the comma to begin with, though its difference from [[CWE]] is practically unnoticeable.		Another notable tuning is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 702.4482{{c}}, 293.7397{{c}} with pure octaves since prime 2 is not involved in the comma to begin with, though its difference from [[CWE]] is practically unnoticeable.

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

FloraC: + intro to gariboh and note its TE/CTE/POTE tuning

2025-11-08T17:28:41Z

+ intro to gariboh and note its TE/CTE/POTE tuning

← Older revision		Revision as of 17:28, 8 November 2025
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	== Gariboh ==		== Gariboh ==
			Gariboh is generated by a perfect fifth and a narrow minor third of ~25/21, two of which make ~7/5.

			A notable tuning of gariboh is given by [[TE]], [[CTE]] and [[POTE]], all coinciding at 702.4482{{c}}, 293.7397{{c}} with pure octaves since prime 2 is not involved in the comma to begin with, though its difference from [[CWE]] is practically unnoticeable.

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

FloraC: - CTE & POTE tunings

2025-11-08T17:27:39Z

- CTE & POTE tunings

← Older revision		Revision as of 17:27, 8 November 2025
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.4468{{c}}, ~25/21 = 293.7395{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.4468{{c}}, ~25/21 = 293.7395{{c}}
	: error map: {{val\| 0.000 +0.492 -2.648 +2.319 }}		: error map: {{val\| 0.000 +0.492 -2.648 +2.319 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.4482{{c}}, ~25/21 = 293.7397{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 53, 94 }}		{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 53, 94 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.7792{{c}}, ~25/21 = 293.5634{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.7792{{c}}, ~25/21 = 293.5634{{c}}
	: error map: {{val\| 0.000 +0.824 -2.844 +1.770 -0.703 }}		: error map: {{val\| 0.000 +0.824 -2.844 +1.770 -0.703 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.7001{{c}}, ~25/21 = 293.5587{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 90e, 94, 229c }}		{{Optimal ET sequence\|legend=1\| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 90e, 94, 229c }}
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	* WE: ~2 = 1199.9929{{c}}, ~3/2 = 702.5339{{c}}, ~13/11 = 293.6861{{c}}		* WE: ~2 = 1199.9929{{c}}, ~3/2 = 702.5339{{c}}, ~13/11 = 293.6861{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5314{{c}}, ~13/11 = 293.6875{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5314{{c}}, ~13/11 = 293.6875{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5381{{c}}, ~13/11 = 293.6878{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 8d, 12e, 25bccddf, 33cd, 41, 53, 94 }}		{{Optimal ET sequence\|legend=0\| 8d, 12e, 25bccddf, 33cd, 41, 53, 94 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5845{{c}}, ~25/21 = 292.9597{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5845{{c}}, ~25/21 = 292.9597{{c}}
	: error map: {{val\| 0.000 +2.630 -2.850 +0.557 +6.440 }}		: error map: {{val\| 0.000 +2.630 -2.850 +0.557 +6.440 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3 = 705.0554{{c}}, ~25/21 = 293.1102{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 90e, 131e }} *		{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 90e, 131e }} *
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1698{{c}}, ~12/11 = 146.9960{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1698{{c}}, ~12/11 = 146.9960{{c}}
	: error map: {{val\| 0.000 +0.215 -2.168 +3.304 +3.856 }}		: error map: {{val\| 0.000 +0.215 -2.168 +3.304 +3.856 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.5559{{c}}, ~12/11 = 147.0103{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 8d, 16, 24d, 33cd, 41, 65d, 90e, 106, 147 }}		{{Optimal ET sequence\|legend=1\| 8d, 16, 24d, 33cd, 41, 65d, 90e, 106, 147 }}
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	* WE: ~2 = 1198.9833{{c}}, ~3/2 = 702.3448{{c}}, ~12/11 = 146.9886{{c}}		* WE: ~2 = 1198.9833{{c}}, ~3/2 = 702.3448{{c}}, ~12/11 = 146.9886{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0567{{c}}, ~12/11 = 147.0902{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0567{{c}}, ~12/11 = 147.0902{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9404{{c}}, ~12/11 = 147.1132{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 8d, 16, 24d, 33cd, 41, 65d, 106f }}		{{Optimal ET sequence\|legend=0\| 8d, 16, 24d, 33cd, 41, 65d, 106f }}
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	* WE: ~2 = 1198.6534{{c}}, ~3/2 = 702.2909{{c}}, ~12/11 = 147.0794{{c}}		* WE: ~2 = 1198.6534{{c}}, ~3/2 = 702.2909{{c}}, ~12/11 = 147.0794{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8744{{c}}, ~12/11 = 147.2433{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8744{{c}}, ~12/11 = 147.2433{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 703.0799{{c}}, ~12/11 = 147.2446{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 8d, 16, 24d, 33cd, 41, 49fg, 65d, 106fg }}		{{Optimal ET sequence\|legend=0\| 8d, 16, 24d, 33cd, 41, 49fg, 65d, 106fg }}

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

2025-11-08T17:23:21Z

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

← Older revision		Revision as of 17:23, 8 November 2025
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	: mapping generators: ~2, ~3, ~25/21		: mapping generators: ~2, ~3, ~25/21

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3 = 702.4482{{c}}, ~25/21 = 293.7397{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.9983{{c}}, ~3/2 = 702.4472{{c}}, ~25/21 = 293.7393{{c}}
			: [[error map]]: {{val\| -0.002 +0.490 -2.650 +2.316 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.4468{{c}}, ~25/21 = 293.7395{{c}}
			: error map: {{val\| 0.000 +0.492 -2.648 +2.319 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.4482{{c}}, ~25/21 = 293.7397{{c}} -->

	{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 53, 94 }}		{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 53, 94 }}

	[[Badness]] (~~Smith~~): 0.~~614 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 2.71

	[[Projection pair]]s: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7		[[Projection pair]]s: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7
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	{{Mapping\|legend=1\| 1 0 0 0 2 \| 0 1 1 1 2 \| 0 0 3 5 -7 }}		{{Mapping\|legend=1\| 1 0 0 0 2 \| 0 1 1 1 2 \| 0 0 3 5 -7 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3 = 702.7001{{c}}, ~25/21 = 293.5587{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.9983{{c}}, ~3/2 = 702.4472{{c}}, ~25/21 = 293.7393{{c}}
			: [[error map]]: {{val\| +0.086 +0.881 -2.738 +1.909 -0.531 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.7792{{c}}, ~25/21 = 293.5634{{c}}
			: error map: {{val\| 0.000 +0.824 -2.844 +1.770 -0.703 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.7001{{c}}, ~25/21 = 293.5587{{c}} -->

	{{Optimal ET sequence\|legend=1\| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c }}		{{Optimal ET sequence\|legend=1\| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 90e, 94, 229c }}

	[[Badness]] (~~Smith~~): 1.~~75 ×~~ 10~~<sup>-3</sup>~~		[[Badness]] (Sintel): 2.10

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 0 0 2 2 \| 0 1 1 1 2 2 \| 0 0 3 5 -7 -6 }}		Mapping: {{mapping\| 1 0 0 0 2 2 \| 0 1 1 1 2 2 \| 0 0 3 5 -7 -6 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.0000{{c}}, ~3 = 702.5381{{c}}, ~13/11 = 293.6878{{c}}		Optimal tunings:
			* WE: ~2 = 1199.9929{{c}}, ~3/2 = 702.5339{{c}}, ~13/11 = 293.6861{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5314{{c}}, ~13/11 = 293.6875{{c}}
			<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.5381{{c}}, ~13/11 = 293.6878{{c}} -->

	{{Optimal ET sequence\|legend=0\| 8d, 12e, 33cd, 41, 53, 94 }}		{{Optimal ET sequence\|legend=0\| 8d, 12e, 25bccddf, 33cd, 41, 53, 94 }}

			Badness (Sintel): 1.22

	== Androboh ==		== Androboh ==
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	{{Mapping\|legend=1\| 1 0 0 0 2 \| 0 1 1 1 0 \| 0 0 3 5 6 }}		{{Mapping\|legend=1\| 1 0 0 0 2 \| 0 1 1 1 0 \| 0 0 3 5 6 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3 = 705.0554{{c}}, ~25/21 = 293.1102{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.2176{{c}}, ~3/2 = 704.5957{{c}}, ~25/21 = 292.9191{{c}}
			: [[error map]]: {{val\| -0.782 +1.858 -3.743 -0.417 +4.632 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.5845{{c}}, ~25/21 = 292.9597{{c}}
			: error map: {{val\| 0.000 +2.630 -2.850 +0.557 +6.440 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3 = 705.0554{{c}}, ~25/21 = 293.1102{{c}} -->

	{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 90e, 131e }} *		{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 90e, 131e }} *
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	<nowiki>*</nowiki> [[optimal patent val]]: [[119edo\|119]]		<nowiki>*</nowiki> [[optimal patent val]]: [[119edo\|119]]

	[[Badness]] (~~Smith~~): 1.~~20 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 1.44

	== Trismegiboh ==		== Trismegiboh ==
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	: mapping generators: ~2, ~3, ~12/11		: mapping generators: ~2, ~3, ~12/11

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.5559{{c}}, ~12/11 = 147.0103{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.5499{{c}}, ~3/2 = 702.2924{{c}}, ~12/11 = 146.9551{{c}}
			: [[error map]]: {{val\| -0.450 -0.113 -2.741 +2.568 +2.669 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1698{{c}}, ~12/11 = 146.9960{{c}}
			: error map: {{val\| 0.000 +0.215 -2.168 +3.304 +3.856 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.5559{{c}}, ~12/11 = 147.0103{{c}} -->

			{{Optimal ET sequence\|legend=1\| 8d, 16, 24d, 33cd, 41, 65d, 90e, 106, 147 }}

	~~{{Optimal ET sequence\|legend=1\| 8d, 16, 33cd, 41, 49 }}~~		[[Badness]] (Sintel): 3.38

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 0 0 2 2 \| 0 1 1 1 1 1 \| 0 0 6 10 -1 1 }}		Mapping: {{mapping\| 1 0 0 0 2 2 \| 0 1 1 1 1 1 \| 0 0 6 10 -1 1 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.9404{{c}}, ~12/11 = 147.1132{{c}}		Optimal tunings:
			* WE: ~2 = 1198.9833{{c}}, ~3/2 = 702.3448{{c}}, ~12/11 = 146.9886{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0567{{c}}, ~12/11 = 147.0902{{c}}
			<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9404{{c}}, ~12/11 = 147.1132{{c}} -->

			{{Optimal ET sequence\|legend=0\| 8d, 16, 24d, 33cd, 41, 65d, 106f }}

	~~{{Optimal ET sequence\|legend=0\| 8d, 16, 33cd, 41, 49f }}~~		Badness (Sintel): 1.83

	=== 17-limit ===		=== 17-limit ===
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	Mapping: {{mapping\| 1 0 0 0 2 2 3 \| 0 1 1 1 1 1 1 \| 0 0 6 10 -1 1 -4 }}		Mapping: {{mapping\| 1 0 0 0 2 2 3 \| 0 1 1 1 1 1 1 \| 0 0 6 10 -1 1 -4 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.0799{{c}}, ~12/11 = 147.2446{{c}}		Optimal tunings:
			* WE: ~2 = 1198.6534{{c}}, ~3/2 = 702.2909{{c}}, ~12/11 = 147.0794{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8744{{c}}, ~12/11 = 147.2433{{c}}
			<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 703.0799{{c}}, ~12/11 = 147.2446{{c}} -->

			{{Optimal ET sequence\|legend=0\| 8d, 16, 24d, 33cd, 41, 49fg, 65d, 106fg }}

	~~{{Optimal ET sequence\|legend=0\| 8d, 16, 33cd, 41, 49fg }}~~		Badness (Sintel): 1.55

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

FloraC: Units & misc. cleanup

2025-11-08T13:14:20Z

Units & misc. cleanup

← Older revision		Revision as of 13:14, 8 November 2025
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	{{Technical data page}}		{{Technical data page}}
	The '''gariboh family''' of [[~~Rank~~-3 temperament\|rank-3]] [[temperament]]s [[~~Tempering~~ out\|tempers out]] the gariboh comma, [[3125/3087]].		The '''gariboh family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperament]]s [[tempering out\|tempers out]] the gariboh comma, [[3125/3087]].

	== Gariboh ==		== Gariboh ==
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	{{Mapping\|legend=1\| 1 0 0 0 \| 0 1 1 1 \| 0 0 3 5 }}		{{Mapping\|legend=1\| 1 0 0 0 \| 0 1 1 1 \| 0 0 3 5 }}
			: mapping generators: ~2, ~3, ~25/21

	~~: Mapping generators: ~2, ~3, ~25/21~~		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3 = 702.4482{{c}}, ~25/21 = 293.7397{{c}}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3 = 702.4482, ~25/21 = 293.7397

	{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 53, 94 }}		{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 53, 94 }}

	[[Badness]]: 0.614 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.614 × 10<sup>-3</sup>

	[[Projection pair]]s: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7		[[Projection pair]]s: 5 – 15625/3087, 7 – 9765625/1361367 to 2.3.25/7
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	{{Mapping\|legend=1\| 1 0 0 0 2 \| 0 1 1 1 2 \| 0 0 3 5 -7 }}		{{Mapping\|legend=1\| 1 0 0 0 2 \| 0 1 1 1 2 \| 0 0 3 5 -7 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3 = 702.7001, ~25/21 = 293.5587		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3 = 702.7001{{c}}, ~25/21 = 293.5587{{c}}

	{{Optimal ET sequence\|legend=1\| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c }}		{{Optimal ET sequence\|legend=1\| 8d, 12e, 25bccdd, 33cd, 37ee, 41, 53, 94, 229c }}

	[[Badness]]: 1.75 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.75 × 10<sup>-3</sup>

	=== 13-limit ===		=== 13-limit ===
	[[Subgroup]]: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 275/273, 325/324, 540/539		Comma list: 275/273, 325/324, 540/539

	{{~~Mapping\|legend=1~~\| 1 0 0 0 2 2 \| 0 1 1 1 2 2 \| 0 0 3 5 -7 -6 }}		Mapping: {{mapping\| 1 0 0 0 2 2 \| 0 1 1 1 2 2 \| 0 0 3 5 -7 -6 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3 = 702.5381, ~13/11 = 293.6878		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3 = 702.5381{{c}}, ~13/11 = 293.6878{{c}}

	{{Optimal ET sequence\|legend=1\| 8d, 12e, 33cd, 41, 53, 94 }}		{{Optimal ET sequence\|legend=0\| 8d, 12e, 33cd, 41, 53, 94 }}

	== Androboh ==		== Androboh ==
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	{{Mapping\|legend=1\| 1 0 0 0 2 \| 0 1 1 1 0 \| 0 0 3 5 6 }}		{{Mapping\|legend=1\| 1 0 0 0 2 \| 0 1 1 1 0 \| 0 0 3 5 6 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3 = 705.0554, ~25/21 = 293.1102		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3 = 705.0554{{c}}, ~25/21 = 293.1102{{c}}

	{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 90e, 131e }} *		{{Optimal ET sequence\|legend=1\| 8d, 12, 29, 37, 41, 90e, 131e }} *
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	<nowiki>*</nowiki> [[optimal patent val]]: [[119edo\|119]]		<nowiki>*</nowiki> [[optimal patent val]]: [[119edo\|119]]

	[[Badness]]: 1.20 × 10<sup>-3</sup>		[[Badness]] (Smith): 1.20 × 10<sup>-3</sup>

	== Trismegiboh ==		== Trismegiboh ==
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	{{Mapping\|legend=1\| 1 0 0 0 2 \| 0 1 1 1 1 \| 0 0 6 10 -1 }}		{{Mapping\|legend=1\| 1 0 0 0 2 \| 0 1 1 1 1 \| 0 0 6 10 -1 }}
			: mapping generators: ~2, ~3, ~12/11

	~~: Mapping generators: ~2, ~3, ~12/11~~		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 702.5559{{c}}, ~12/11 = 147.0103{{c}}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 702.5559, ~12/11 = 147.0103

	{{Optimal ET sequence\|legend=1\| 8d, 16, 33cd, 41, 49 }}		{{Optimal ET sequence\|legend=1\| 8d, 16, 33cd, 41, 49 }}

	=== 13-limit ===		=== 13-limit ===
	[[Subgroup]]: 2.3.5.7.11.13		Subgroup: 2.3.5.7.11.13

	[[Comma list]]: 144/143, 275/273, 847/845		Comma list: 144/143, 275/273, 847/845

	{{~~Mapping\|legend=1~~\| 1 0 0 0 2 2 \| 0 1 1 1 1 1 \| 0 0 6 10 -1 1 }}		Mapping: {{mapping\| 1 0 0 0 2 2 \| 0 1 1 1 1 1 \| 0 0 6 10 -1 1 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 702.9404, ~12/11 = 147.1132		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 702.9404{{c}}, ~12/11 = 147.1132{{c}}

	{{Optimal ET sequence\|legend=1\| 8d, 16, 33cd, 41, 49f }}		{{Optimal ET sequence\|legend=0\| 8d, 16, 33cd, 41, 49f }}

	=== 17-limit ===		=== 17-limit ===
	[[Subgroup]]: 2.3.5.7.11.13.17		Subgroup: 2.3.5.7.11.13.17

	[[Comma list]]: 120/119, 144/143, 170/169, 847/845		Comma list: 120/119, 144/143, 170/169, 847/845

	{{~~Mapping\|legend=1~~\| 1 0 0 0 2 2 3 \| 0 1 1 1 1 1 1 \| 0 0 6 10 -1 1 -4 }}		Mapping: {{mapping\| 1 0 0 0 2 2 3 \| 0 1 1 1 1 1 1 \| 0 0 6 10 -1 1 -4 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = ~~1\1~~, ~3/2 = 703.0799, ~12/11 = 147.2446		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.0799{{c}}, ~12/11 = 147.2446{{c}}

	{{Optimal ET sequence\|legend=1\| 8d, 16, 33cd, 41, 49fg }}		{{Optimal ET sequence\|legend=0\| 8d, 16, 33cd, 41, 49fg }}

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

FloraC: - redundant category

2025-11-08T12:15:52Z

- redundant category

← Older revision		Revision as of 12:15, 8 November 2025
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	[[Category:Pages with mostly numerical content]]		[[Category:Pages with mostly numerical content]]
	[[Category:Gariboh family\| ]] <!-- main article -->		[[Category:Gariboh family\| ]] <!-- main article -->
	~~[[Category:Gariboh\| ]] <!-- key article -->~~
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-06-24T00:34:22Z

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

← Older revision		Revision as of 00:34, 24 June 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Gariboh family\| ]] <!-- main article -->		[[Category:Gariboh family\| ]] <!-- main article -->
	[[Category:Gariboh\| ]] <!-- key article -->		[[Category:Gariboh\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

" to "{{Technical data page}}"

2025-04-13T13:43:20Z

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 '''gariboh family''' of [[Rank-3 temperament\|rank-3]] [[temperament]]s [[Tempering out\|tempers out]] the gariboh comma, [[3125/3087]].		The '''gariboh family''' of [[Rank-3 temperament\|rank-3]] [[temperament]]s [[Tempering out\|tempers out]] the gariboh comma, [[3125/3087]].