456edo - Revision history

ArrowHead294 at 22:41, 20 February 2025

2025-02-20T22:41:36Z

← Older revision		Revision as of 22:41, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|456~~}}		{{ED intro}}

	456edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[152edo]], defined by [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 32 -7 -9 }} ([[escapade comma]]), as well as {{monzo\| 23 6 -14 }} ([[vishnuzma]]), {{monzo\| 41 -20 -4 }} (undim comma), and {{monzo\| -14 -19 19 }} ([[enneadeca]]). In the 7-limit, it tempers out [[10976/10935]], 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.		456edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[152edo]], defined by [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 32 -7 -9 }} ([[escapade comma]]), as well as {{monzo\| 23 6 -14 }} ([[vishnuzma]]), {{monzo\| 41 -20 -4 }} (undim comma), and {{monzo\| -14 -19 19 }} ([[enneadeca]]). In the 7-limit, it tempers out [[10976/10935]], 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.

FloraC: Rework

2023-11-03T07:20:52Z

Rework

← Older revision		Revision as of 07:20, 3 November 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''456edo''' is the [[~~EDO\|~~equal division of the octave]] into~~ 456 parts of 2.63158 cents each. It is [[contorted]] in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.		{{EDO intro\|456}}

	[[~~Category:Equal divisions of~~ the ~~octave~~\|~~###~~]] <!-- 3-~~digit number~~ -->		456edo is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[152edo]], defined by [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 32 -7 -9 }} ([[escapade comma]]), as well as {{monzo\| 23 6 -14 }} ([[vishnuzma]]), {{monzo\| 41 -20 -4 }} (undim comma), and {{monzo\| -14 -19 19 }} ([[enneadeca]]). In the 7-limit, it tempers out [[10976/10935]], 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.

			=== Odd harmonics ===
			{{Harmonics in equal\|456}}

			=== Subsets and supersets ===
			Since 456 factors into {{factorization\|456}}, 456edo has subset edos {{EDOs\| 2, 3, 4, 6, 8, 12, 19, 24, 38, 57, 76, 114, 152, and 228 }}.

			[[Category:Chromat]]

BudjarnLambeth at 06:35, 9 July 2023

2023-07-09T06:35:24Z

← Older revision		Revision as of 06:35, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is [[contorted]] in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.		'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is [[contorted]] in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.

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

BudjarnLambeth at 05:47, 9 July 2023

2023-07-09T05:47:52Z

← Older revision		Revision as of 05:47, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is [[contorted]] in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.		'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is [[contorted]] in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.

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

Plumtree: Infobox ET added

2022-10-04T21:56:30Z

Infobox ET added

← Older revision		Revision as of 21:56, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is [[contorted]] in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.		'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is [[contorted]] in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.

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

Fredg999 category edits: Sort key

2022-07-04T00:58:32Z

Sort key

← Older revision		Revision as of 00:58, 4 July 2022
Line 1:		Line 1:
	'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is [[contorted]] in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.		'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is [[contorted]] in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.

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

Cmloegcmluin: remove temporary link to defactoring

2021-11-12T23:10:43Z

remove temporary link to defactoring

← Older revision		Revision as of 23:10, 12 November 2021
Line 1:		Line 1:
	'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is [[contorted]] ~~(or [[enfactored]])~~ in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.		'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is [[contorted]] in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.

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

Cmloegcmluin: add link for defactoring

2021-09-29T19:44:25Z

add link for defactoring

← Older revision		Revision as of 19:44, 29 September 2021
Line 1:		Line 1:
	'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is contorted in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.		'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is [[contorted]] (or [[enfactored]]) in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.

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

Xenwolf: more direct link

2020-12-25T19:41:23Z

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

2020-12-04T23:13:54Z

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 1:		Line 1:
	'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is contorted in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[Hemimage temperaments\|chromat temperament]].		'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is contorted in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[Hemimage temperaments\|chromat temperament]].

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

← Older revision		Revision as of 19:41, 25 December 2020
Line 1:		Line 1:
	'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is contorted in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[~~Hemimage temperaments\|~~chromat ~~temperament~~]].		'''456edo''' is the [[EDO\|equal division of the octave]] into 456 parts of 2.63158 cents each. It is contorted in the 5-limit, tempering out 1600000/1594323 (amity comma) and 4294967296/4271484375 (escapade comma), as well as 6115295232/6103515625 (vishnuzma), 2199023255552/2179240250625 (undim comma), and 19073486328125/19042491875328 (enneadeca). In the 7-limit, it tempers out 10976/10935, 235298/234375, and 134217728/133984375, providing the [[optimal patent val]] for the [[chromat]] temperament.

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