Octagar family - Revision history

FloraC: + more intro to octagar

2026-03-13T16:28:14Z

+ more intro to octagar

← Older revision		Revision as of 16:28, 13 March 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''octagar family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the octagar comma, [[4000/3969]]. While many 7-limit rank-3 temperaments exhibit a tendency towards tuning flat, a slight sharp tendency is often preferred instead. Octagar provides this; for instance the [[7-odd-limit]] [[minimax tuning]] has [[3/1\|3]]'s and [[7/1\|7]]'s 2.245 cents sharp, with just [[5/1\|5]]'s.		The '''octagar family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the octagar comma, [[4000/3969]].

	For [[rank-2 temperament]]s that temper out the octagar comma, see [[Octagar temperaments]].		For [[rank-2 temperament]]s that temper out the octagar comma, see [[Octagar temperaments]].

	== Octagar ==		== Octagar ==
			Octagar is generated by a [[3/2\|perfect fifth]] and a minor sixth of [[~]][[63/40]], two of which make ~[[5/2]], and three make an interval short of two octaves by a [[64/63\|septimal comma]].

			While many 7-limit rank-3 temperaments exhibit a tendency towards tuning flat, a slight sharp tendency is often preferred instead. Octagar provides this; for instance the [[7-odd-limit]] [[minimax tuning]] has [[3/1\|3]]'s and [[7/1\|7]]'s 2.245 cents sharp, with just [[5/1\|5]]'s.

	This temperament is catalogued as ''octagari'' in [[Graham Breed]]'s [https://x31eq.com/temper/ Temperament Finder].		This temperament is catalogued as ''octagari'' in [[Graham Breed]]'s [https://x31eq.com/temper/ Temperament Finder].

FloraC: Wording

2026-03-13T14:20:43Z

Wording

← Older revision		Revision as of 14:20, 13 March 2026
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	{{Technical data page}}		{{Technical data page}}
	The '''octagar family''' of [[temperament]]~~s are~~ [[~~rank-3~~ temperament]]s [[tempering out]] the octagar comma, [[4000/3969]]. While ~~most~~ 7-limit ~~planar~~ temperaments exhibit a tendency towards tuning flat, ~~many people seem to prefer~~ a slight sharp tendency instead. Octagar provides this; for instance the 7-odd-limit minimax tuning has ~~fifths~~ and 7's 2.245 cents sharp, with just ~~major thirds~~.		The '''octagar family''' of [[rank-3 temperament\|rank-3]] [[regular temperament\|temperaments]] [[tempering out\|tempers out]] the octagar comma, [[4000/3969]]. While many 7-limit rank-3 temperaments exhibit a tendency towards tuning flat, a slight sharp tendency is often preferred instead. Octagar provides this; for instance the [[7-odd-limit]] [[minimax tuning]] has [[3/1\|3]]'s and [[7/1\|7]]'s 2.245 cents sharp, with just [[5/1\|5]]'s.

	[[~~Linear~~ temperament]]s that temper out the octagar comma ~~can be found in~~ [[~~octagar~~ temperaments]].		For [[rank-2 temperament]]s that temper out the octagar comma, see [[Octagar temperaments]].

	== Octagar ==		== Octagar ==
	This temperament is ~~also known~~ as ''octagari''.
			This temperament is catalogued as ''octagari'' in [[Graham Breed]]'s [https://x31eq.com/temper/ Temperament Finder].

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

FloraC: - POTE tunings

2026-03-13T14:09:30Z

- POTE tunings

← Older revision		Revision as of 14:09, 13 March 2026
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.3764{{c}}, ~63/40 = 792.6299{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.3764{{c}}, ~63/40 = 792.6299{{c}}
	: error map: {{val\| 0.000 +1.421 -1.054 +2.311 }}		: error map: {{val\| 0.000 +1.421 -1.054 +2.311 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.6224{{c}}, ~21/20 = 89.3227{{c}} -->~~

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.6783{{c}}, ~11/7 = 791.5168{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.6783{{c}}, ~11/7 = 791.5168{{c}}
	: error map: {{val\| 0.000 +1.723 -3.280 -1.632 +7.393 }}		: error map: {{val\| 0.000 +1.723 -3.280 -1.632 +7.393 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.8837{{c}}, ~21/20 = 87.8919{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 12, 15, 26, 27e, 41, 109e }}		{{Optimal ET sequence\|legend=1\| 12, 15, 26, 27e, 41, 109e }}
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	* WE: ~2 = 1200.5397{{c}}, ~3/2 = 702.2038{{c}}, ~11/7 = 789.6574{{c}}		* WE: ~2 = 1200.5397{{c}}, ~3/2 = 702.2038{{c}}, ~11/7 = 789.6574{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0977{{c}}, ~11/7 = 789.5686{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0977{{c}}, ~11/7 = 789.5686{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8881{{c}}, ~21/20 = 87.4143{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 12f, 14cf, 15, 26, 29, 41 }}		{{Optimal ET sequence\|legend=0\| 12f, 14cf, 15, 26, 29, 41 }}
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	* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.2662{{c}}, ~63/40 = 792.6212{{c}}		* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.2662{{c}}, ~63/40 = 792.6212{{c}}
	: error map: {{val\| 0.000 +1.311 -1.071 +2.505 +1.061 }}		: error map: {{val\| 0.000 +1.311 -1.071 +2.505 +1.061 }}
	~~<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.5501{{c}}, ~21/20 = 89.3956{{c}} -->~~

	{{Optimal ET sequence\|legend=1\| 27e, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d }}		{{Optimal ET sequence\|legend=1\| 27e, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d }}
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	* WE: ~2 = 1199.5112{{c}}, ~3/2 = 703.2823{{c}}, ~63/40 = 792.6491{{c}}		* WE: ~2 = 1199.5112{{c}}, ~3/2 = 703.2823{{c}}, ~63/40 = 792.6491{{c}}
	* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.3684{{c}}, ~63/40 = 792.7875{{c}}		* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.3684{{c}}, ~63/40 = 792.7875{{c}}
	~~<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 703.5688{{c}}, ~21/20 = 89.4032{{c}} -->~~

	{{Optimal ET sequence\|legend=0\| 27e, 41, 53, 80, 94, 121, 174d, 215, 295d, 336def }}		{{Optimal ET sequence\|legend=0\| 27e, 41, 53, 80, 94, 121, 174d, 215, 295d, 336def }}

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

2026-03-13T14:08:54Z

Switch to Sintel's badness, WE & CWE tunings

← Older revision		Revision as of 14:08, 13 March 2026
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	: Angle (63/50, 21/20) = 97.743 degrees		: Angle (63/50, 21/20) = 97.743 degrees

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.6224{{c}}, ~21/20 = 89.3227{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.5353{{c}}, ~3/2 = 703.3499{{c}}, ~63/40 = 792.6380{{c}}
			: [[error map]]: {{val\| -0.465 +0.930 -1.502 +1.459 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.3764{{c}}, ~63/40 = 792.6299{{c}}
			: error map: {{val\| 0.000 +1.421 -1.054 +2.311 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.6224{{c}}, ~21/20 = 89.3227{{c}} -->

	[[Minimax tuning]]:		[[Minimax tuning]]:
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	{{Optimal ET sequence\|legend=1\| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}		{{Optimal ET sequence\|legend=1\| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}

	[[Badness]] (~~Smith~~): 0.~~216 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.951

	[[Projection pair]]s: <code>5 3969/800 7 27783/4000</code> to 2.3.7/5		[[Projection pair]]s: <code>5 3969/800 7 27783/4000</code> to 2.3.7/5
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	: Angle (11/7, 22/21) = 97.747 degrees		: Angle (11/7, 22/21) = 97.747 degrees

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.8837{{c}}, ~21/20 = 87.8919{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.6137{{c}}, ~3/2 = 703.6571{{c}}, ~11/7 = 791.5207{{c}}
			: [[error map]]: {{val\| -0.386 +1.316 -3.659 -2.351 +6.678 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.6783{{c}}, ~11/7 = 791.5168{{c}}
			: error map: {{val\| 0.000 +1.723 -3.280 -1.632 +7.393 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.8837{{c}}, ~21/20 = 87.8919{{c}} -->

	{{Optimal ET sequence\|legend=1\| 12, 15, 26, 27e, 41, 109e }}		{{Optimal ET sequence\|legend=1\| 12, 15, 26, 27e, 41, 109e }}

	[[Badness]] (~~Smith~~): 0.~~539 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): 0.647

	[[Projection pair]]s: <code>5 242/49 7 21296/3087 11 234256/21609</code> to 2.3.11/7		[[Projection pair]]s: <code>5 242/49 7 21296/3087 11 234256/21609</code> to 2.3.11/7
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	Mapping: {{mapping\| 1 0 1 4 4 2 \| 0 1 0 -2 -2 -1 \| 0 0 2 3 4 5 }}		Mapping: {{mapping\| 1 0 1 4 4 2 \| 0 1 0 -2 -2 -1 \| 0 0 2 3 4 5 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.0000{{c}}, ~3/2 = 701.8881{{c}}, ~21/20 = 87.4143{{c}}		Optimal tunings:
			* WE: ~2 = 1200.5397{{c}}, ~3/2 = 702.2038{{c}}, ~11/7 = 789.6574{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0977{{c}}, ~11/7 = 789.5686{{c}}
			<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 701.8881{{c}}, ~21/20 = 87.4143{{c}} -->

	{{Optimal ET sequence\|legend=0\| 12f, 14cf, 15, 26, 29, 41 }}		{{Optimal ET sequence\|legend=0\| 12f, 14cf, 15, 26, 29, 41 }}

			Badness (Sintel): 0.832

	== Octasand ==		== Octasand ==
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	{{Mapping\|legend=1\| 1 0 1 4 -5 \| 0 1 0 -2 7 \| 0 0 2 3 -4 }}		{{Mapping\|legend=1\| 1 0 1 4 -5 \| 0 1 0 -2 7 \| 0 0 2 3 -4 }}

	[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.5501{{c}}, ~21/20 = 89.3956{{c}}		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.5255{{c}}, ~3/2 = 703.2719{{c}}, ~63/40 = 792.6321{{c}}
			: [[error map]]: {{val\| -0.475 +0.842 -1.524 +1.578 +0.108 }}
			* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.2662{{c}}, ~63/40 = 792.6212{{c}}
			: error map: {{val\| 0.000 +1.311 -1.071 +2.505 +1.061 }}
			<!-- * [[POTE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.5501{{c}}, ~21/20 = 89.3956{{c}} -->

	{{Optimal ET sequence\|legend=1\| ~~12e~~, ~~14c, 27e~~, 41, 53, 80, 94, 121 }}		{{Optimal ET sequence\|legend=1\| 27e, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d }}

			[[Badness]] (Sintel): 1.20

	=== 13-limit ===		=== 13-limit ===
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	Mapping: {{mapping\| 1 0 1 4 -5 0 \| 0 1 0 -2 7 4 \| 0 0 2 3 -4 -4 }}		Mapping: {{mapping\| 1 0 1 4 -5 0 \| 0 1 0 -2 7 4 \| 0 0 2 3 -4 -4 }}

	Optimal ~~tuning (~~POTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.5688{{c}}, ~21/20 = 89.4032{{c}}		Optimal tunings:
			* WE: ~2 = 1199.5112{{c}}, ~3/2 = 703.2823{{c}}, ~63/40 = 792.6491{{c}}
			* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 703.3684{{c}}, ~63/40 = 792.7875{{c}}
			<!-- * POTE: ~2 = 1200.0000{{c}}, ~3/2 = 703.5688{{c}}, ~21/20 = 89.4032{{c}} -->

			{{Optimal ET sequence\|legend=0\| 27e, 41, 53, 80, 94, 121, 174d, 215, 295d, 336def }}

	~~{{Optimal ET sequence\|legend=0\| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}~~		Badness (Sintel): 1.03

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

FloraC: Units & misc. cleanup. - redundant category

2026-03-13T10:48:05Z

Units & misc. cleanup. - redundant category

← Older revision		Revision as of 10:48, 13 March 2026
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	{{Mapping\|legend=1\| 1 0 1 4 \| 0 1 0 -2 \| 0 0 2 3 }}		{{Mapping\|legend=1\| 1 0 1 4 \| 0 1 0 -2 \| 0 0 2 3 }}

	: Mapping generators: ~2, ~3, ~63/40		: Mapping generators: ~2, ~3, ~63/40

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	: Angle (63/50, 21/20) = 97.743 degrees		: Angle (63/50, 21/20) = 97.743 degrees

	[[Optimal tuning]] (POTE): ~3/2 = 703.6224, ~21/20 = 89.3227		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.6224{{c}}, ~21/20 = 89.3227{{c}}

	[[Minimax tuning]]:		[[Minimax tuning]]:
	* [[7-odd-limit]]		* [[7-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 5/6 1/3 1/2 -1/3 \| 0 0 1 0 \| 5/6 -2/3 1/2 2/3 }}		: {{monzo list\| 1 0 0 0 \| 5/6 1/3 1/2 -1/3 \| 0 0 1 0 \| 5/6 -2/3 1/2 2/3 }}
	: [[~~Eigenmonzo~~ basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3		: [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3
	* [[9-odd-limit]]		* [[9-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 5/8 1/2 3/8 -1/4 \| 0 0 1 0 \| 5/4 -1 3/4 1/2 }}		: {{monzo list\| 1 0 0 0 \| 5/8 1/2 3/8 -1/4 \| 0 0 1 0 \| 5/4 -1 3/4 1/2 }}
	: [[~~Eigenmonzo~~ basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7		: [[eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7

	{{Optimal ET sequence\|legend=1\| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}		{{Optimal ET sequence\|legend=1\| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}

	[[Badness]]: 0.216 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.216 × 10<sup>-3</sup>

	[[Projection pair]]s: 5 - 3969/800, 7 - 27783/4000 to 2.3.7/5		[[Projection pair]]s: <code>5 3969/800 7 27783/4000</code> to 2.3.7/5

	{{Databox\|[[Hobbit\|Hobbit bases]]\|		{{Databox\|[[Hobbit\|Hobbit bases]]\|
Line 57:		Line 56:
	: Angle (11/7, 22/21) = 97.747 degrees		: Angle (11/7, 22/21) = 97.747 degrees

	[[Optimal tuning]] (POTE): ~3/2 = 703.8837, ~21/20 = 87.8919		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.8837{{c}}, ~21/20 = 87.8919{{c}}

	{{Optimal ET sequence\|legend=1\| 12, 15, 26, 27e, 41, 109e }}		{{Optimal ET sequence\|legend=1\| 12, 15, 26, 27e, 41, 109e }}

	[[Badness]]: 0.539 × 10<sup>-3</sup>		[[Badness]] (Smith): 0.539 × 10<sup>-3</sup>

	[[Projection pair]]s: 5 - 242/49, 7 - 21296/3087, 11 - 234256/21609 to 2.3.11/7		[[Projection pair]]s: <code>5 242/49 7 21296/3087 11 234256/21609</code> to 2.3.11/7

	[[Associated temperament]]: [[octacot]]		[[Associated temperament]]: [[octacot]]
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	Mapping: {{mapping\| 1 0 1 4 4 2 \| 0 1 0 -2 -2 -1 \| 0 0 2 3 4 5 }}		Mapping: {{mapping\| 1 0 1 4 4 2 \| 0 1 0 -2 -2 -1 \| 0 0 2 3 4 5 }}

	Optimal tuning (POTE): ~3/2 = 701.8881, ~21/20 = 87.4143		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 701.8881{{c}}, ~21/20 = 87.4143{{c}}

	~~Optimal ET sequence:~~ {{Optimal ET sequence\| 12f, 14cf, 15, 26, 29, 41 }}		{{Optimal ET sequence\|legend=0\| 12f, 14cf, 15, 26, 29, 41 }}

	== Octasand ==		== Octasand ==
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	{{Mapping\|legend=1\| 1 0 1 4 -5 \| 0 1 0 -2 7 \| 0 0 2 3 -4 }}		{{Mapping\|legend=1\| 1 0 1 4 -5 \| 0 1 0 -2 7 \| 0 0 2 3 -4 }}

	[[Optimal tuning]] (POTE): ~3/2 = 703.5501, ~21/20 = 89.3956		[[Optimal tuning]] ([[POTE]]): ~2 = 1200.0000{{c}}, ~3/2 = 703.5501{{c}}, ~21/20 = 89.3956{{c}}

	{{Optimal ET sequence\|legend=1\| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}		{{Optimal ET sequence\|legend=1\| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}
Line 98:		Line 97:
	Mapping: {{mapping\| 1 0 1 4 -5 0 \| 0 1 0 -2 7 4 \| 0 0 2 3 -4 -4 }}		Mapping: {{mapping\| 1 0 1 4 -5 0 \| 0 1 0 -2 7 4 \| 0 0 2 3 -4 -4 }}

	Optimal tuning (POTE): ~3/2 = 703.5688, ~21/20 = 89.4032		Optimal tuning (POTE): ~2 = 1200.0000{{c}}, ~3/2 = 703.5688{{c}}, ~21/20 = 89.4032{{c}}

	~~Optimal ET sequence:~~ {{Optimal ET sequence\| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}		{{Optimal ET sequence\|legend=0\| 12e, 14c, 27e, 41, 53, 80, 94, 121 }}

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

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

2025-11-27T12:18:01Z

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

← Older revision		Revision as of 12:18, 27 November 2025
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	[[Category:Temperament families]]		[[Category:Temperament families]]
	~~[[Category:Pages with mostly numerical content]]~~
	[[Category:Octagar family\| ]] <!-- main article -->		[[Category:Octagar family\| ]] <!-- main article -->
	[[Category:Octagar\| ]] <!-- key article -->		[[Category:Octagar\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-06-24T00:31:52Z

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

← Older revision		Revision as of 00:31, 24 June 2025
Line 103:		Line 103:

	[[Category:Temperament families]]		[[Category:Temperament families]]
			[[Category:Pages with mostly numerical content]]
	[[Category:Octagar family\| ]] <!-- main article -->		[[Category:Octagar family\| ]] <!-- main article -->
	[[Category:Octagar\| ]] <!-- key article -->		[[Category:Octagar\| ]] <!-- key article -->
	[[Category:Rank 3]]		[[Category:Rank 3]]

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

2025-06-21T06:58:43Z

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-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 5/6 1/3 1/2 -1/3 \| 0 0 1 0 \| 5/6 -2/3 1/2 2/3 }}		: {{monzo list\| 1 0 0 0 \| 5/6 1/3 1/2 -1/3 \| 0 0 1 0 \| 5/6 -2/3 1/2 2/3 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5.7/3		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3
	* [[9-odd-limit]]		* [[9-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 5/8 1/2 3/8 -1/4 \| 0 0 1 0 \| 5/4 -1 3/4 1/2 }}		: {{monzo list\| 1 0 0 0 \| 5/8 1/2 3/8 -1/4 \| 0 0 1 0 \| 5/4 -1 3/4 1/2 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5.9/7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7

	{{Optimal ET sequence\|legend=1\| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}		{{Optimal ET sequence\|legend=1\| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}

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

" to "{{Technical data page}}"

2025-04-13T13:49:42Z

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

← Older revision		Revision as of 13:49, 13 April 2025
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	{{Technical data page}}~~<br><br>~~		{{Technical data page}}
	The '''octagar family''' of [[temperament]]s are [[rank-3 temperament]]s [[tempering out]] the octagar comma, [[4000/3969]]. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7-odd-limit minimax tuning has fifths and 7's 2.245 cents sharp, with just major thirds.		The '''octagar family''' of [[temperament]]s are [[rank-3 temperament]]s [[tempering out]] the octagar comma, [[4000/3969]]. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7-odd-limit minimax tuning has fifths and 7's 2.245 cents sharp, with just major thirds.

BudjarnLambeth: {{Technical data page}}

2025-04-13T11:50:47Z

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

← Older revision		Revision as of 11:50, 13 April 2025
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			{{Technical data page}}<br><br>
	The '''octagar family''' of [[temperament]]s are [[rank-3 temperament]]s [[tempering out]] the octagar comma, [[4000/3969]]. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7-odd-limit minimax tuning has fifths and 7's 2.245 cents sharp, with just major thirds.		The '''octagar family''' of [[temperament]]s are [[rank-3 temperament]]s [[tempering out]] the octagar comma, [[4000/3969]]. While most 7-limit planar temperaments exhibit a tendency towards tuning flat, many people seem to prefer a slight sharp tendency instead. Octagar provides this; for instance the 7-odd-limit minimax tuning has fifths and 7's 2.245 cents sharp, with just major thirds.

← Older revision		Revision as of 06:58, 21 June 2025
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	* [[7-odd-limit]]		* [[7-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 5/6 1/3 1/2 -1/3 \| 0 0 1 0 \| 5/6 -2/3 1/2 2/3 }}		: {{monzo list\| 1 0 0 0 \| 5/6 1/3 1/2 -1/3 \| 0 0 1 0 \| 5/6 -2/3 1/2 2/3 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5.7/3		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.7/3
	* [[9-odd-limit]]		* [[9-odd-limit]]
	: {{monzo list\| 1 0 0 0 \| 5/8 1/2 3/8 -1/4 \| 0 0 1 0 \| 5/4 -1 3/4 1/2 }}		: {{monzo list\| 1 0 0 0 \| 5/8 1/2 3/8 -1/4 \| 0 0 1 0 \| 5/4 -1 3/4 1/2 }}
	: [[Eigenmonzo basis\|~~eigenmonzo (~~unchanged-interval) basis]]: 2.5.9/7		: [[Eigenmonzo basis\|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7

	{{Optimal ET sequence\|legend=1\| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}		{{Optimal ET sequence\|legend=1\| 12, 26, 27, 39d, 41, 53, 80, 94, 121, 174d, 215, 295d, 336d }}