165edo - Revision history

Francium: changed EDO intro to ED intro

2025-02-19T18:04:21Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:04, 19 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	165edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 5-limit: {{val\| 165 262 383 }} ([[patent val]]) and {{val\| 165 '''261''' 383 }} (165b).		165edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 5-limit: {{val\| 165 262 383 }} ([[patent val]]) and {{val\| 165 '''261''' 383 }} (165b).

FloraC: Ampersand -> ampersand comma to distinguish it from the temp

2025-01-18T09:16:25Z

Ampersand -> ampersand comma to distinguish it from the temp

← Older revision		Revision as of 09:16, 18 January 2025
Line 4:		Line 4:
	165edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 5-limit: {{val\| 165 262 383 }} ([[patent val]]) and {{val\| 165 '''261''' 383 }} (165b).		165edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 5-limit: {{val\| 165 262 383 }} ([[patent val]]) and {{val\| 165 '''261''' 383 }} (165b).

	Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 ([[immunity comma]]) and {{monzo\| -27 -2 13 }} (ditonma) in the 5-limit; [[4000/3969]], [[65625/65536]], and 84035/82944 in the 7-limit; [[385/384]], 2401/2376, [[3388/3375]], and 6655/6561 in the 11-limit; [[196/195]], [[364/363]], [[676/675]], 3185/3168, and 3200/3159 in the 13-limit.		Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 ([[immunity comma]]) and {{monzo\| -27 -2 13 }} ([[ditonma]]) in the 5-limit; [[4000/3969]], [[65625/65536]], and 84035/82944 in the 7-limit; [[385/384]], 2401/2376, [[3388/3375]], and 6655/6561 in the 11-limit; [[196/195]], [[364/363]], [[676/675]], 3185/3168, and 3200/3159 in the 13-limit.

	Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 ([[ampersand]]) and 129140163/125000000 in the 5-limit; [[225/224]], [[1029/1024]], and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, [[4000/3993]], and 12005/11979 in the 11-limit; [[144/143]], [[351/350]], [[625/624]], [[847/845]], and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, [[1001/1000]], 1701/1690, and [[1716/1715]] in the 13-limit.		Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 ([[ampersand comma]]) and 129140163/125000000 in the 5-limit; [[225/224]], [[1029/1024]], and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, [[4000/3993]], and [[12005/11979]] in the 11-limit; [[144/143]], [[351/350]], [[625/624]], [[847/845]], and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, [[1001/1000]], 1701/1690, and [[1716/1715]] in the 13-limit.

	=== Odd harmonics ===		=== Odd harmonics ===
Line 12:		Line 12:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 165 factors into ~~{{factorization\|165}}~~, 165edo has subset edos {{EDOs\| 3, 5, 11, 15, 33, and 55 }}. [[330edo]], which doubles it, provides good correction for the approximation of harmonic 3.		Since 165 factors into 3 × 5 × 11, 165edo has subset edos {{EDOs\| 3, 5, 11, 15, 33, and 55 }}. [[330edo]], which doubles it, provides good correction for the approximation of harmonic 3.

FloraC: +subsets and supersets

2024-05-05T08:58:09Z

+subsets and supersets

← Older revision		Revision as of 08:58, 5 May 2024
Line 10:		Line 10:
	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|165}}		{{Harmonics in equal\|165}}

			=== Subsets and supersets ===
			Since 165 factors into {{factorization\|165}}, 165edo has subset edos {{EDOs\| 3, 5, 11, 15, 33, and 55 }}. [[330edo]], which doubles it, provides good correction for the approximation of harmonic 3.

FloraC: Cleanup

2024-05-05T08:55:54Z

Cleanup

← Older revision		Revision as of 08:55, 5 May 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	~~'''165edo''' is the [[~~EDO~~\|equal division of the octave]] into 165 parts of 7.2727 [[cent]]s each.~~		{{EDO intro}}

	It is ~~inconsistent~~ to the 5-limit and higher ~~limit~~, with two mappings possible for the 5-limit: ~~<~~165 262 383\| (patent val) and ~~<~~165 261 383\| (165b).		165edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with two mappings possible for the 5-limit: {{val\| 165 262 383 }} ([[patent val]]) and {{val\| 165 '''261''' 383 }} (165b).

	Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and ~~1220703125/1207959552~~ (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit.		Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 ([[immunity comma]]) and {{monzo\| -27 -2 13 }} (ditonma) in the 5-limit; [[4000/3969]], [[65625/65536]], and 84035/82944 in the 7-limit; [[385/384]], 2401/2376, [[3388/3375]], and 6655/6561 in the 11-limit; [[196/195]], [[364/363]], [[676/675]], 3185/3168, and 3200/3159 in the 13-limit.

	Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (~~Ampersand's comma~~) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.		Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 ([[ampersand]]) and 129140163/125000000 in the 5-limit; [[225/224]], [[1029/1024]], and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, [[4000/3993]], and 12005/11979 in the 11-limit; [[144/143]], [[351/350]], [[625/624]], [[847/845]], and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, [[1001/1000]], 1701/1690, and [[1716/1715]] in the 13-limit.

			=== Odd harmonics ===
	{{Harmonics in equal\|165}}		{{Harmonics in equal\|165}}
	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~

BudjarnLambeth: Added "harmonics in equal" table

2023-06-24T07:10:41Z

Added "harmonics in equal" table

← Older revision		Revision as of 07:10, 24 June 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	'''165edo''' is the [[EDO\|equal division of the octave]] into 165 parts of 7.2727 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <165 262 383\| (patent val) and <165 261 383\| (165b). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.		'''165edo''' is the [[EDO\|equal division of the octave]] into 165 parts of 7.2727 [[cent]]s each.

			It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <165 262 383\| (patent val) and <165 261 383\| (165b).

			Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit.

			Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

			{{Harmonics in equal\|165}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

Aura at 19:11, 4 October 2022

2022-10-04T19:11:13Z

← Older revision		Revision as of 19:11, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''165edo''' is the [[EDO\|equal division of the octave]] into 165 parts of 7.2727 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <165 262 383\| (patent val) and <165 261 383\| (165b). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.		'''165edo''' is the [[EDO\|equal division of the octave]] into 165 parts of 7.2727 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <165 262 383\| (patent val) and <165 261 383\| (165b). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

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

Fredg999 category edits: Sort key

2022-07-02T21:15:20Z

Sort key

← Older revision		Revision as of 21:15, 2 July 2022
Line 1:		Line 1:
	'''165edo''' is the [[EDO\|equal division of the octave]] into 165 parts of 7.2727 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <165 262 383\| (patent val) and <165 261 383\| (165b). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.		'''165edo''' is the [[EDO\|equal division of the octave]] into 165 parts of 7.2727 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <165 262 383\| (patent val) and <165 261 383\| (165b). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

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

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

2020-12-04T23:13:11Z

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:
	'''165edo''' is the [[EDO\|equal division of the octave]] into 165 parts of 7.2727 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <165 262 383\| (patent val) and <165 261 383\| (165b). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.		'''165edo''' is the [[EDO\|equal division of the octave]] into 165 parts of 7.2727 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <165 262 383\| (patent val) and <165 261 383\| (165b). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

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

Xenwolf: Reverted edits by The55edoEht (talk) to last revision by Xenllium

2020-07-17T19:36:26Z

Reverted edits by The55edoEht (talk) to last revision by Xenllium

← Older revision		Revision as of 19:36, 17 July 2020
Line 1:		Line 1:
	~~[[{{PAGENAME}}]]~~ is the [[EDO\|equal division of the octave]] into 165 parts of ~~{{#expr: 1200/165}}~~ [[cent]]s each. ~~That's the triple of [[55edo]]!!!~~ It is inconsistent to the 5-limit and higher limit, with~~, like in any [[Equal-step Tuning]] (ET), infinitely many~~ mappings possible for the 5-limit~~, including, but not limited to~~: <165 262 383\| (patent val) and <165 261 383\| (165b~~) and <165 261 384\| ([[K/N\|165/3]] generic meantone val~~). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.		'''165edo''' is the [[EDO\|equal division of the octave]] into 165 parts of 7.2727 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with two mappings possible for the 5-limit: <165 262 383\| (patent val) and <165 261 383\| (165b). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

	[[Category:Edo]]		[[Category:Edo]]

The55edoEht at 18:04, 17 July 2020

2020-07-17T18:04:53Z

← Older revision		Revision as of 18:04, 17 July 2020
Line 1:		Line 1:
	[[{{PAGENAME}}]] is the [[EDO\|equal division of the octave]] into 165 parts of {{#expr: 1200/165}} [[cent]]s each. That's the triple of [[55edo]]!!! It is inconsistent to the 5-limit and higher limit, with ~~three~~ mappings possible for the 5-limit: <165 262 383\| (patent val) and <165 261 383\| (165b) and <165 261 ~~381~~\| ([[K/N\|165/3]] generic meantone val). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.		[[{{PAGENAME}}]] is the [[EDO\|equal division of the octave]] into 165 parts of {{#expr: 1200/165}} [[cent]]s each. That's the triple of [[55edo]]!!! It is inconsistent to the 5-limit and higher limit, with, like in any [[Equal-step Tuning]] (ET), infinitely many mappings possible for the 5-limit, including, but not limited to: <165 262 383\| (patent val) and <165 261 383\| (165b) and <165 261 384\| ([[K/N\|165/3]] generic meantone val). Using the patent val (with a sharp fifth), it tempers out 1638400/1594323 (immunity comma) and 1220703125/1207959552 (ditonma) in the 5-limit; 4000/3969, 65625/65536, and 84035/82944 in the 7-limit; 385/384, 2401/2376, 3388/3375, and 6655/6561 in the 11-limit; 196/195, 364/363, 676/675, 3185/3168, and 3200/3159 in the 13-limit. Using the 165b val (with a flat fifth), it tempers out 34171875/33554432 (Ampersand's comma) and 129140163/125000000 in the 5-limit; 225/224, 1029/1024, and 100442349/97656250 in the 7-limit; 1944/1925, 2187/2156, 4000/3993, and 12005/11979 in the 11-limit; 144/143, 351/350, 625/624, 847/845, and 9261/9152 in the 13-limit. Using the 165bf val, it tempers out 364/363, 975/968, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

	[[Category:Edo]]		[[Category:Edo]]