271edo - Revision history

Francium: changed EDO intro to ED intro

2025-02-20T07:00:12Z

changed EDO intro to ED intro

← Older revision		Revision as of 07:00, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Rework

2024-03-08T06:48:15Z

Rework

← Older revision		Revision as of 06:48, 8 March 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	The '''271 equal divisions of the octave''' divides the [[octave]] into 271 [[equal]] intervals, each 4.428044 [[cent]]s in size. 271edo is the highest edo where the perfect fifth has greater absolute error than [[12edo]]. It is inconsistent in the 5-limit. Using the [[patent val]], it tempers out 4000/3969 and 65625/65536 in the 7-limit, [[896/891]] and 1375/1372 in the 11-limit, and [[352/351]], [[364/363]], [[676/675]], [[1575/1573]] and [[2200/2197]] in the 13-limit. It is an [[optimal patent val]] by some measures{{~~clarify~~}} ~~for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.~~		{{EDO intro}}

	~~271EDO~~ is the ~~58th~~ [[~~prime EDO~~]].		== Theory ==
			271edo is the highest edo where the [[3/2\|perfect fifth]] has greater absolute error than [[12edo]]. It is in[[consistent]] in the [[5-odd-limit]]. Using the [[patent val]] nonetheless, the equal temperament [[tempering out\|tempers out]] [[4000/3969]] and [[65625/65536]] in the 7-limit, [[896/891]] and 1375/1372 in the 11-limit, and [[352/351]], [[364/363]], [[676/675]], [[1575/1573]] and [[2200/2197]] in the 13-limit. It is the [[optimal patent val]] for the [[pepperoni]] temperament, tempering out 352/351 and 364/363 on the 2.3.11/7.13/7 [[subgroup]] of the 13-limit.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|271}}		{{Harmonics in equal\|271}}

			=== Subsets and supersets ===
			271edo is the 58th [[prime edo]].

	== Scales ==		== Scales ==
Line 12:		Line 16:
	* [[Cantonpenta]]		* [[Cantonpenta]]

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

BudjarnLambeth at 08:14, 25 January 2024

2024-01-25T08:14:44Z

← Older revision		Revision as of 08:14, 25 January 2024
Line 4:		Line 4:
	271EDO is the 58th [[prime EDO]].		271EDO is the 58th [[prime EDO]].

	=== ~~Prime~~ harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|271}}		{{Harmonics in equal\|271}}

BudjarnLambeth: Replaced deprecated template

2024-01-25T08:13:12Z

Replaced deprecated template

← Older revision		Revision as of 08:13, 25 January 2024
Line 5:		Line 5:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{~~Primes~~ in ~~edo~~\|~~edo=~~271~~\|columns=11\|prec=3~~}}		{{Harmonics in equal\|271}}

	== Scales ==		== Scales ==

Plumtree: Infobox ET added

2022-10-04T21:45:57Z

Infobox ET added

← Older revision		Revision as of 21:45, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	The '''271 equal divisions of the octave''' divides the [[octave]] into 271 [[equal]] intervals, each 4.428044 [[cent]]s in size. 271edo is the highest edo where the perfect fifth has greater absolute error than [[12edo]]. It is inconsistent in the 5-limit. Using the [[patent val]], it tempers out 4000/3969 and 65625/65536 in the 7-limit, [[896/891]] and 1375/1372 in the 11-limit, and [[352/351]], [[364/363]], [[676/675]], [[1575/1573]] and [[2200/2197]] in the 13-limit. It is an [[optimal patent val]] by some measures{{clarify}} for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.		The '''271 equal divisions of the octave''' divides the [[octave]] into 271 [[equal]] intervals, each 4.428044 [[cent]]s in size. 271edo is the highest edo where the perfect fifth has greater absolute error than [[12edo]]. It is inconsistent in the 5-limit. Using the [[patent val]], it tempers out 4000/3969 and 65625/65536 in the 7-limit, [[896/891]] and 1375/1372 in the 11-limit, and [[352/351]], [[364/363]], [[676/675]], [[1575/1573]] and [[2200/2197]] in the 13-limit. It is an [[optimal patent val]] by some measures{{clarify}} for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.

Fredg999 category edits: Sort key

2022-07-03T19:07:19Z

Sort key

← Older revision		Revision as of 19:07, 3 July 2022
Line 11:		Line 11:
	* [[Cantonpenta]]		* [[Cantonpenta]]

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

Yourmusic Productions: Add prime table to show just how high in relative error this one is.

2022-01-23T23:51:46Z

Add prime table to show just how high in relative error this one is.

← Older revision		Revision as of 23:51, 23 January 2022
Line 1:		Line 1:
	The '''271 equal divisions of the octave''' divides the [[octave]] into 271 [[equal]] intervals, each 4.428044 [[cent]]s in size. 271edo is the ~~last~~ edo ~~whose~~ perfect fifth ~~is tuned worse~~ than 12edo. It is inconsistent in the 5-limit. Using the [[patent val]], it tempers out 4000/3969 and 65625/65536 in the 7-limit, [[896/891]] and 1375/1372 in the 11-limit, and [[352/351]], [[364/363]], [[676/675]], [[1575/1573]] and [[2200/2197]] in the 13-limit. It is an [[optimal patent val]] by some measures{{clarify}} for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.		The '''271 equal divisions of the octave''' divides the [[octave]] into 271 [[equal]] intervals, each 4.428044 [[cent]]s in size. 271edo is the highest edo where the perfect fifth has greater absolute error than [[12edo]]. It is inconsistent in the 5-limit. Using the [[patent val]], it tempers out 4000/3969 and 65625/65536 in the 7-limit, [[896/891]] and 1375/1372 in the 11-limit, and [[352/351]], [[364/363]], [[676/675]], [[1575/1573]] and [[2200/2197]] in the 13-limit. It is an [[optimal patent val]] by some measures{{clarify}} for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.

	271EDO is the 58th [[prime EDO]].		271EDO is the 58th [[prime EDO]].

			=== Prime harmonics ===
			{{Primes in edo\|edo=271\|columns=11\|prec=3}}

	== Scales ==		== Scales ==

FloraC: Expansion

2021-08-09T13:16:44Z

Expansion

← Older revision		Revision as of 13:16, 9 August 2021
Line 1:		Line 1:
	'''271 ~~EDO~~''' divides the [[~~Octave\|~~octave]] into 271 [[~~Equal-step tuning\|~~equal]] intervals, each 4.428044 [[cent]]s in size. It tempers out 4000/3969 and 65625/65536 in the 7-limit, 896/891 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675, 1575/1573 and 2200/2197 in the 13-limit. It is an optimal patent val by some measures for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.		The '''271 equal divisions of the octave''' divides the [[octave]] into 271 [[equal]] intervals, each 4.428044 [[cent]]s in size. 271edo is the last edo whose perfect fifth is tuned worse than 12edo. It is inconsistent in the 5-limit. Using the [[patent val]], it tempers out 4000/3969 and 65625/65536 in the 7-limit, [[896/891]] and 1375/1372 in the 11-limit, and [[352/351]], [[364/363]], [[676/675]], [[1575/1573]] and [[2200/2197]] in the 13-limit. It is an [[optimal patent val]] by some measures{{clarify}} for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.

	271EDO is the 58th [[prime EDO]].		271EDO is the 58th [[prime EDO]].

	=Scales=		== Scales ==
	*[[Pepperoni7]]		* [[Pepperoni7]]
	*[[Pepperoni12]]		* [[Pepperoni12]]
	*[[Cantonpenta]]		* [[Cantonpenta]]

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]
	[[Category:Prime EDO]]		[[Category:Prime EDO]]

Keenan Pepper category edits: Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

2020-12-04T23:13:23Z

Moving from Category:Edo to Category:Equal divisions of the octave using Cat-a-lot

← Older revision		Revision as of 23:13, 4 December 2020
Line 8:		Line 8:
	*[[Cantonpenta]]		*[[Cantonpenta]]

	[[Category:~~Edo~~]]		[[Category:Equal divisions of the octave]]
	[[Category:Prime EDO]]		[[Category:Prime EDO]]

Xenllium at 06:26, 13 March 2019

2019-03-13T06:26:35Z

← Older revision		Revision as of 06:26, 13 March 2019
Line 1:		Line 1:
	'''271 EDO''' divides the [[Octave\|octave]] into 271 [[Equal\|equal]] intervals, each 4.~~428~~ [[~~cent\|~~cent]]s in size. It tempers out 4000/3969 and 65625/65536 in the 7-limit, 896/891 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675, 1575/1573 and 2200/2197 in the 13-limit. It is an optimal patent val by some measures for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.		'''271 EDO''' divides the [[Octave\|octave]] into 271 [[Equal-step tuning\|equal]] intervals, each 4.428044 [[cent]]s in size. It tempers out 4000/3969 and 65625/65536 in the 7-limit, 896/891 and 1375/1372 in the 11-limit, and 352/351, 364/363, 676/675, 1575/1573 and 2200/2197 in the 13-limit. It is an optimal patent val by some measures for the 13-limit pentacircle temperament, tempering out 352/351 and 364/363 on the 2.11/7.13/7 subgroup of the 13-limit.

			271EDO is the 58th [[prime EDO]].

	=Scales=		=Scales=
	[[~~pepperoni7\|pepperoni7~~]]		*[[Pepperoni7]]
			*[[Pepperoni12]]
	[[~~pepperoni12\|pepperoni12~~]]		*[[Cantonpenta]]

	~~[[cantonpenta\|cantonpenta]]~~ [[Category:~~271edo~~]]		[[Category:Edo]]
	[[Category:~~edo~~]]		[[Category:Prime EDO]]