180edo - Revision history

Francium: changed EDO intro to ED intro

2025-02-20T17:10:50Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:10, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|180~~}}		{{ED intro}}

	The equal temperament [[tempering out\|tempers out]] 531441/524288 ([[pythagorean comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli comma) and 274877906944/274658203125 (hemithirds comma); [[1029/1024]], [[3136/3125]], and 118098/117649 in the 7-limit.		The equal temperament [[tempering out\|tempers out]] 531441/524288 ([[pythagorean comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli comma) and 274877906944/274658203125 (hemithirds comma); [[1029/1024]], [[3136/3125]], and 118098/117649 in the 7-limit.

FloraC: Cleanup. +subsets. Its 2.5.13 subgroup is enfactored 90et.

2024-04-25T09:21:57Z

Cleanup. +subsets. Its 2.5.13 subgroup is enfactored 90et.

← Older revision		Revision as of 09:21, 25 April 2024
Line 2:		Line 2:
	{{EDO intro\|180}}		{{EDO intro\|180}}

	~~180edo~~ tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. ~~It is a strong 2.5~~.13 ~~subgroup system~~.		The equal temperament [[tempering out\|tempers out]] 531441/524288 ([[pythagorean comma]]) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli comma) and 274877906944/274658203125 (hemithirds comma); [[1029/1024]], [[3136/3125]], and 118098/117649 in the 7-limit.

			Using the [[patent val]], it tempers out [[540/539]], 2835/2816, [[4000/3993]], and 6912/6875 in the 11-limit; [[351/350]], [[364/363]], [[1001/1000]], and 1701/1690 in the 13-limit. Using the 180e val, it tempers out [[385/384]], [[441/440]], [[3388/3375]], and 216513/214375 in the 11-limit; 351/350, [[1188/1183]], [[1287/1280]], [[1573/1568]], and 3146/3125 in the 13-limit.

	Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.
	=== Odd harmonics ===		=== Odd harmonics ===
	{{harmonics in equal\|180}}		{{harmonics in equal\|180}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
			180edo is the 11th [[highly composite edo]]; its nontrivial subsets are: {{EDOs\| 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, and 90 }}.
	180edo is the 11th [[highly composite ~~EDO~~]].

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

Eliora: Adopt intro, cleanup

2023-10-22T15:06:27Z

Adopt intro, cleanup

← Older revision		Revision as of 15:06, 22 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''180edo''' is the [[~~EDO\|~~equal division of the octave]] into~~ 180 parts of 6.6667 cents each. It tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.		{{EDO intro\|180}}

	180edo is the 11th [[~~superabundant~~ EDO]].		180edo tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. It is a strong 2.5.13 subgroup system.

			Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.
			=== Odd harmonics ===
			{{harmonics in equal\|180}}

			=== Subsets and supersets ===

			180edo is the 11th [[highly composite EDO]].

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

Fredg999 category edits: Moving from Category:Highly melodic to Category:Highly composite using Cat-a-lot

2022-10-09T18:44:44Z

Moving from Category:Highly melodic to Category:Highly composite using Cat-a-lot

← Older revision		Revision as of 18:44, 9 October 2022
Line 5:		Line 5:

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

Plumtree: Infobox ET added

2022-10-04T21:15:04Z

Infobox ET added

← Older revision		Revision as of 21:15, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''180edo''' is the [[EDO\|equal division of the octave]] into 180 parts of 6.6667 cents each. It tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.		'''180edo''' is the [[EDO\|equal division of the octave]] into 180 parts of 6.6667 cents each. It tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.

Fredg999 category edits: Sort key

2022-07-02T21:22:23Z

Sort key

← Older revision		Revision as of 21:22, 2 July 2022
Line 3:		Line 3:
	180edo is the 11th [[superabundant EDO]].		180edo is the 11th [[superabundant EDO]].

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

Eliora: no

2022-01-20T12:55:33Z

← Older revision		Revision as of 12:55, 20 January 2022
Line 1:		Line 1:
	'''180edo''' is the [[EDO\|equal division of the octave]] into 180 parts of 6.6667 cents each. It tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.		'''180edo''' is the [[EDO\|equal division of the octave]] into 180 parts of 6.6667 cents each. It tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.

	180edo is the ~~12th~~ [[superabundant EDO]].		180edo is the 11th [[superabundant EDO]].

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

Eliora at 12:26, 5 January 2022

2022-01-05T12:26:19Z

← Older revision		Revision as of 12:26, 5 January 2022
Line 4:		Line 4:

	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]
	[[Category:~~Superabundant EDO~~]]		[[Category:Highly melodic]]

Eliora at 00:35, 4 January 2022

2022-01-04T00:35:40Z

← Older revision		Revision as of 00:35, 4 January 2022
Line 1:		Line 1:
	'''180edo''' is the [[EDO\|equal division of the octave]] into 180 parts of 6.6667 cents each. It tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.		'''180edo''' is the [[EDO\|equal division of the octave]] into 180 parts of 6.6667 cents each. It tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.

			180edo is the 12th [[superabundant EDO]].

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

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

2020-12-04T23:13:14Z

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:
	'''180edo''' is the [[EDO\|equal division of the octave]] into 180 parts of 6.6667 cents each. It tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.		'''180edo''' is the [[EDO\|equal division of the octave]] into 180 parts of 6.6667 cents each. It tempers out 531441/524288 (pythagorean comma) and 30958682112/30517578125 (trisedodge comma) in the 5-limit, as well as 31381059609/30517578125 (mowgli) and 274877906944/274658203125 (hemithirds comma); 1029/1024, 3136/3125, and 118098/117649 in the 7-limit. Using the patent val, it tempers out 540/539, 2835/2816, 4000/3993, and 6912/6875 in the 11-limit; 351/350, 364/363, 1001/1000, and 1701/1690 in the 13-limit. Using the 180e val, it tempers out 385/384, 441/440, 3388/3375, and 216513/214375 in the 11-limit; 351/350, 1188/1183, 1287/1280, 1573/1568, and 3146/3125 in the 13-limit.

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