127edo - Revision history

Yourmusic Productions: Add lumatone mapping link.

2025-07-30T06:51:04Z

Add lumatone mapping link.

← Older revision		Revision as of 06:51, 30 July 2025
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	=== MOS scales ===		=== MOS scales ===
	See [[List of MOS scales in 127edo]].		See [[List of MOS scales in 127edo]].

			== Instruments ==
			* [[Lumatone mapping for 127edo]]

	[[Category:Würschmidt]]		[[Category:Würschmidt]]
	[[Category:Hemiwürschmidt]]		[[Category:Hemiwürschmidt]]
	[[Category:Minerva]]		[[Category:Minerva]]

ArrowHead294 at 17:00, 18 February 2025

2025-02-18T17:00:09Z

← Older revision		Revision as of 17:00, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|127~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup and link to previous and next prime edos

2024-05-29T05:33:35Z

Theory: cleanup and link to previous and next prime edos

← Older revision		Revision as of 05:33, 29 May 2024
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	== Theory ==		== Theory ==
	127edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering out\|tempers out]]:		127edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering out\|tempers out]]:
			* In the [[5-limit]], it tempers out 393216/390625 ([[würschmidt comma]]) and hence [[support]]s the [[würschmidt]] temperament.
	* In the [[5-limit]], it tempers out ~~the würschmidt comma,~~ 393216/390625 and hence [[support]]s [[~~Würschmidt_family\|~~würschmidt ~~temperament~~]].		* In the [[7-limit]], it also tempers out [[225/224]], and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.
	* In the [[7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.		* In the [[11-limit]], it tempers out [[99/98]], [[176/175]] and [[243/242]], and is an excellent tuning for the 11-limit version of würschmidt, as well as [[minerva]], the [[rank-3 temperament]] tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank-4 temperament tempering out 99/98, for which it also provides the optimal patent val.
	* In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank ~~three~~ temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank ~~four~~ temperament tempering out 99/98, for which it also provides the optimal patent val.

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	127edo is the 31st [[prime edo]].		127edo is the 31st [[prime edo]], following [[113edo]] and before [[131edo]].

	== Scales ==		== Scales ==

FloraC: Cleanup

2024-05-29T05:31:12Z

Cleanup

← Older revision		Revision as of 05:31, 29 May 2024
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	{{EDO intro\|127}}		{{EDO intro\|127}}

	127edo is interesting because of its approximations, defined by the [[comma]]s it [[~~tempering_out~~\|tempers out]]:		== Theory ==
			127edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering out\|tempers out]]:

	* In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family\|würschmidt temperament]].		* In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family\|würschmidt temperament]].
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	* In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.		* In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

	~~127edo is the 31st [[prime_numbers~~\|~~prime]] edo.~~		=== Odd harmonics ===
			{{Harmonics in equal\|127}}

	=== ~~Harmonics~~ ===		=== Subsets and supersets ===
	~~{{Harmonics in equal\|127}}~~		127edo is the 31st [[prime edo]].

	=== MOS ~~Scales~~ ===		== Scales ==
	[[~~MOS_Scales_of_127edo\|~~MOS ~~Scales of~~ 127edo]]		=== MOS scales ===
			See [[List of MOS scales in 127edo]].

	[[Category:~~Equal divisions of the octave\|###~~]] ~~<!-- 3-digit number -->~~		[[Category:Würschmidt]]
	[[Category:Hemiwürschmidt]]		[[Category:Hemiwürschmidt]]
	[[Category:Minerva]]		[[Category:Minerva]]
	~~[[Category:Prime EDO]]~~
	~~[[Category:Würschmidt]]~~

BudjarnLambeth: EDO intro

2024-01-25T09:53:09Z

EDO intro

← Older revision		Revision as of 09:53, 25 January 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''127edo''', which divides the [[Octave~~\|~~octave]] into~~ 127 ~~parts of 9.45 [[cents\|cents]] each,~~ is ~~an equal division~~ interesting because of its approximations, defined by the [[comma]]s it [[tempering_out\|tempers out]]:		{{EDO intro\|127}}

			127edo is interesting because of its approximations, defined by the [[comma]]s it [[tempering_out\|tempers out]]:

	* In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family\|würschmidt temperament]].		* In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family\|würschmidt temperament]].

BudjarnLambeth: Added subheadings, turned paragraph into dot point list, added table of harmonics

2023-06-24T02:58:23Z

Added subheadings, turned paragraph into dot point list, added table of harmonics

← Older revision		Revision as of 02:58, 24 June 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''127edo''', which divides the [[Octave\|octave]] into 127 parts of 9.45 [[cents\|cents]] each, is ~~another~~ equal division interesting because of its approximations, defined by the [[~~Comma\|~~comma]]s it [[tempering_out\|tempers out]]. In the [[~~5-limit\|~~5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family\|würschmidt temperament]]. In the [[~~7-limit\|~~7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the [[~~11-limit\|~~11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[~~Optimal_patent_val\|~~optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.		'''127edo''', which divides the [[Octave\|octave]] into 127 parts of 9.45 [[cents\|cents]] each, is an equal division interesting because of its approximations, defined by the [[comma]]s it [[tempering_out\|tempers out]]:

			* In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family\|würschmidt temperament]].
			* In the [[7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.
			* In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

	127edo is the 31st [[prime_numbers\|prime]] edo.		127edo is the 31st [[prime_numbers\|prime]] edo.

			=== Harmonics ===
			{{Harmonics in equal\|127}}

			=== MOS Scales ===
	[[MOS_Scales_of_127edo\|MOS Scales of 127edo]]		[[MOS_Scales_of_127edo\|MOS Scales of 127edo]]

Aura at 18:54, 4 October 2022

2022-10-04T18:54:32Z

← Older revision		Revision as of 18:54, 4 October 2022
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			{{Infobox ET}}
	'''127edo''', which divides the [[Octave\|octave]] into 127 parts of 9.45 [[cents\|cents]] each, is another equal division interesting because of its approximations, defined by the [[Comma\|comma]]s it [[tempering_out\|tempers out]]. In the [[5-limit\|5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family\|würschmidt temperament]]. In the [[7-limit\|7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the [[11-limit\|11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[Optimal_patent_val\|optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.		'''127edo''', which divides the [[Octave\|octave]] into 127 parts of 9.45 [[cents\|cents]] each, is another equal division interesting because of its approximations, defined by the [[Comma\|comma]]s it [[tempering_out\|tempers out]]. In the [[5-limit\|5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family\|würschmidt temperament]]. In the [[7-limit\|7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the [[11-limit\|11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[Optimal_patent_val\|optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

Fredg999 category edits: Sort key

2022-07-02T16:26:32Z

Sort key

← Older revision		Revision as of 16:26, 2 July 2022
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	[[MOS_Scales_of_127edo\|MOS Scales of 127edo]]		[[MOS_Scales_of_127edo\|MOS Scales of 127edo]]

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Hemiwürschmidt]]		[[Category:Hemiwürschmidt]]
	[[Category:Minerva]]		[[Category:Minerva]]
	[[Category:Prime EDO]]		[[Category:Prime EDO]]
	[[Category:Würschmidt]]		[[Category:Würschmidt]]

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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	[[Category:Minerva]]		[[Category:Minerva]]
	[[Category:Prime EDO]]		[[Category:Prime EDO]]
	~~[[Category:Theory]]~~
	[[Category:Würschmidt]]		[[Category:Würschmidt]]

Cmloegcmluin: link to new page for Supports

2022-01-25T18:35:09Z

link to new page for Supports

← Older revision		Revision as of 18:35, 25 January 2022
Line 1:		Line 1:
	'''127edo''', which divides the [[Octave\|octave]] into 127 parts of 9.45 [[cents\|cents]] each, is another equal division interesting because of its approximations, defined by the [[Comma\|comma]]s it [[tempering_out\|tempers out]]. In the [[5-limit\|5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence ~~supports~~ [[Würschmidt_family\|würschmidt temperament]]. In the [[7-limit\|7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the [[11-limit\|11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[Optimal_patent_val\|optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.		'''127edo''', which divides the [[Octave\|octave]] into 127 parts of 9.45 [[cents\|cents]] each, is another equal division interesting because of its approximations, defined by the [[Comma\|comma]]s it [[tempering_out\|tempers out]]. In the [[5-limit\|5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family\|würschmidt temperament]]. In the [[7-limit\|7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the [[11-limit\|11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[Optimal_patent_val\|optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

	127edo is the 31st [[prime_numbers\|prime]] edo.		127edo is the 31st [[prime_numbers\|prime]] edo.