129edo - Revision history

Lériendil: /* Subsets and supersets */

2025-07-13T22:57:23Z

Subsets and supersets

← Older revision		Revision as of 22:57, 13 July 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 129 factors into {{factorization\|129}}, 129edo contains [[3edo]] and [[43edo]] as its subsets.		Since 129 factors into {{factorization\|129}}, 129edo contains [[3edo]] and [[43edo]] as its subsets. [[258edo]], which doubles it, provides a good correction for the 3rd and 5th harmonics.

	== Instruments ==		== Instruments ==

Yourmusic Productions: Add lumatone mapping link.

2025-07-13T17:21:26Z

Add lumatone mapping link.

← Older revision		Revision as of 17:21, 13 July 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 129 factors into {{factorization\|129}}, 129edo contains [[3edo]] and [[43edo]] as its subsets.		Since 129 factors into {{factorization\|129}}, 129edo contains [[3edo]] and [[43edo]] as its subsets.

			== Instruments ==
			* [[Lumatone mapping for 129edo]]

	[[Category:Clio]]		[[Category:Clio]]

ArrowHead294 at 17:00, 18 February 2025

2025-02-18T17:00:48Z

← Older revision		Revision as of 17:00, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|129~~}}		{{ED intro}}

	129edo is in[[consistent]] to the [[5-odd-limit]] and both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are about halfway between its steps. The [[patent val]] is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[43edo]]. It is the last patent val that [[tempering out\|tempers out]] [[81/80]] so as to [[support]] [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]]. It provides the [[optimal patent val]] for the 11-limit rank-3 [[clio]] temperament.		129edo is in[[consistent]] to the [[5-odd-limit]] and both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are about halfway between its steps. The [[patent val]] is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[43edo]]. It is the last patent val that [[tempering out\|tempers out]] [[81/80]] so as to [[support]] [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]]. It provides the [[optimal patent val]] for the 11-limit rank-3 [[clio]] temperament.

FloraC: Note its patent val is the same as 43et

2024-05-27T17:26:29Z

Note its patent val is the same as 43et

← Older revision		Revision as of 17:26, 27 May 2024
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	{{EDO intro\|129}}		{{EDO intro\|129}}

	129edo is in[[consistent]] to the [[5-odd-limit]] and both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are about halfway between its steps. It is the last [[patent val]] that [[tempering out\|tempers out]] [[81/80]] so as to [[support]] [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]]. It provides the [[optimal patent val]] for the 11-limit rank-3 [[clio]] temperament.		129edo is in[[consistent]] to the [[5-odd-limit]] and both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are about halfway between its steps. The [[patent val]] is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[43edo]]. It is the last patent val that [[tempering out\|tempers out]] [[81/80]] so as to [[support]] [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]]. It provides the [[optimal patent val]] for the 11-limit rank-3 [[clio]] temperament.

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: +overview to its harmonic quality, before going on to talk about the patent val. Misc. cleanup

2024-05-27T17:23:02Z

+overview to its harmonic quality, before going on to talk about the patent val. Misc. cleanup

← Older revision		Revision as of 17:23, 27 May 2024
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	{{EDO intro\|129}}		{{EDO intro\|129}}

	129edo ~~provides the~~ [[~~optimal patent val~~]] ~~for~~ the 11-limit ~~rank-~~3 [[~~clio~~]] ~~temperament~~. It is the last [[patent val]] that [[tempering out\|tempers out]] 81/80 so as to support [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]].		129edo is in[[consistent]] to the [[5-odd-limit]] and both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are about halfway between its steps. It is the last [[patent val]] that [[tempering out\|tempers out]] [[81/80]] so as to [[support]] [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]]. It provides the [[optimal patent val]] for the 11-limit rank-3 [[clio]] temperament.

	~~The factorization of 129 is~~ [[~~3edo\|3~~]] ~~and~~ [[~~43edo\|43~~]].

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|129}}		{{Harmonics in equal\|129}}

	[[~~Category:Equal divisions of the octave\|###~~]] ~~<!-- 3-digit number -->~~		=== Subsets and supersets ===
			Since 129 factors into {{factorization\|129}}, 129edo contains [[3edo]] and [[43edo]] as its subsets.

	[[Category:Clio]]		[[Category:Clio]]

BudjarnLambeth: Edo intro

2024-01-25T09:55:57Z

Edo intro

← Older revision		Revision as of 09:55, 25 January 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''~~129edo~~''' is the [[equal division of the octave]] into 129 parts of 9.302 [[cent]]s each. It~~ provides the [[optimal patent val]] for the 11-limit rank-3 [[clio]] temperament. It is the last [[patent val]] that [[tempering out\|tempers out]] 81/80 so as to support [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]].		{{EDO intro\|129}}

			129edo provides the [[optimal patent val]] for the 11-limit rank-3 [[clio]] temperament. It is the last [[patent val]] that [[tempering out\|tempers out]] 81/80 so as to support [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]].

			The factorization of 129 is [[3edo\|3]] and [[43edo\|43]].

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|129}}		{{Harmonics in equal\|129}}

	~~=== Miscellany ===~~
	~~The factorization of 129 is [[3edo\|3]] and [[43edo\|43]].~~

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Clio]]		[[Category:Clio]]

FloraC: This is the last meantone pval edo, not 105edo

2022-11-27T13:01:05Z

This is the last meantone pval edo, not 105edo

← Older revision		Revision as of 13:01, 27 November 2022
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	{{Infobox ET}}		{{Infobox ET}}
	'''129edo''' is the [[~~Equal_division_of_the_octave\|~~equal division of the octave]] into 129 parts of 9.302 [[~~cent\|~~cent]]s each. It provides the [[~~Optimal_patent_val\|~~optimal patent val]] for the 11-limit rank ~~three~~ [[~~Didymus_rank_three_family\|~~clio ~~temperament~~]]. It [[~~tempering_out~~\|tempers out]] 81/80 ~~in the~~ [[5-limit~~\|5-limit]];~~ 1029/1024 and 1728/1715 in the [[~~7-limit\|~~7-limit]]; 176/175 and 540/539 in the [[~~11-limit\|~~11-limit]]; 507/500, 676/675 and 847/845 in the [[~~13-limit\|~~13-limit]]; 221/220 in the [[~~17-limit\|~~17-limit]]; 171/170 and 286/285 in the [[~~19-limit\|~~19-limit]].		'''129edo''' is the [[equal division of the octave]] into 129 parts of 9.302 [[cent]]s each. It provides the [[optimal patent val]] for the 11-limit rank-3 [[clio]] temperament. It is the last [[patent val]] that [[tempering out\|tempers out]] 81/80 so as to support [[meantone]] and its higher-limit expansions. It also tempers out [[1029/1024]] and [[1728/1715]] in the [[7-limit]]; [[176/175]] and [[540/539]] in the [[11-limit]]; [[507/500]], [[676/675]] and [[847/845]] in the [[13-limit]]; [[221/220]] in the [[17-limit]]; [[171/170]] and [[286/285]] in the [[19-limit]].

	The factorization of 129 is [[3edo\|3]] and [[43edo\|43]]		=== Odd harmonics ===
			{{Harmonics in equal\|129}}

			=== Miscellany ===
			The factorization of 129 is [[3edo\|3]] and [[43edo\|43]].

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Clio]]		[[Category:Clio]]

Aura at 18:55, 4 October 2022

2022-10-04T18:55:29Z

← Older revision		Revision as of 18:55, 4 October 2022
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			{{Infobox ET}}
	'''129edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 129 parts of 9.302 [[cent\|cent]]s each. It provides the [[Optimal_patent_val\|optimal patent val]] for the 11-limit rank three [[Didymus_rank_three_family\|clio temperament]]. It [[tempering_out\|tempers out]] 81/80 in the [[5-limit\|5-limit]]; 1029/1024 and 1728/1715 in the [[7-limit\|7-limit]]; 176/175 and 540/539 in the [[11-limit\|11-limit]]; 507/500, 676/675 and 847/845 in the [[13-limit\|13-limit]]; 221/220 in the [[17-limit\|17-limit]]; 171/170 and 286/285 in the [[19-limit\|19-limit]].		'''129edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 129 parts of 9.302 [[cent\|cent]]s each. It provides the [[Optimal_patent_val\|optimal patent val]] for the 11-limit rank three [[Didymus_rank_three_family\|clio temperament]]. It [[tempering_out\|tempers out]] 81/80 in the [[5-limit\|5-limit]]; 1029/1024 and 1728/1715 in the [[7-limit\|7-limit]]; 176/175 and 540/539 in the [[11-limit\|11-limit]]; 507/500, 676/675 and 847/845 in the [[13-limit\|13-limit]]; 221/220 in the [[17-limit\|17-limit]]; 171/170 and 286/285 in the [[19-limit\|19-limit]].

Fredg999 category edits: Sort key

2022-07-02T16:27:38Z

Sort key

← Older revision		Revision as of 16:27, 2 July 2022
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	'''129edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 129 parts of 9.302 [[cent\|cent]]s each. It provides the [[Optimal_patent_val\|optimal patent val]] for the 11-limit rank three [[Didymus_rank_three_family\|clio temperament]]. It [[tempering_out\|tempers out]] 81/80 in the [[5-limit\|5-limit]]; 1029/1024 and 1728/1715 in the [[7-limit\|7-limit]]; 176/175 and 540/539 in the [[11-limit\|11-limit]]; 507/500, 676/675 and 847/845 in the [[13-limit\|13-limit]]; 221/220 in the [[17-limit\|17-limit]]; 171/170 and 286/285 in the [[19-limit\|19-limit]].		'''129edo''' is the [[Equal_division_of_the_octave\|equal division of the octave]] into 129 parts of 9.302 [[cent\|cent]]s each. It provides the [[Optimal_patent_val\|optimal patent val]] for the 11-limit rank three [[Didymus_rank_three_family\|clio temperament]]. It [[tempering_out\|tempers out]] 81/80 in the [[5-limit\|5-limit]]; 1029/1024 and 1728/1715 in the [[7-limit\|7-limit]]; 176/175 and 540/539 in the [[11-limit\|11-limit]]; 507/500, 676/675 and 847/845 in the [[13-limit\|13-limit]]; 221/220 in the [[17-limit\|17-limit]]; 171/170 and 286/285 in the [[19-limit\|19-limit]].

	The factorization of 129 is [[3edo\|3]] and [[43edo\|43]] [[Category:~~clio~~]]		The factorization of 129 is [[3edo\|3]] and [[43edo\|43]]
	[[Category:~~Equal divisions of the octave~~]]
			[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
			[[Category:Clio]]

Fredg999 category edits: Removing from Category:Theory using Cat-a-lot

2022-02-26T16:48:49Z

Removing from Category:Theory using Cat-a-lot

← Older revision		Revision as of 16:48, 26 February 2022
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	The factorization of 129 is [[3edo\|3]] and [[43edo\|43]] [[Category:clio]]		The factorization of 129 is [[3edo\|3]] and [[43edo\|43]] [[Category:clio]]
	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]
	~~[[Category:theory]]~~