206edo - Revision history

ArrowHead294 at 14:15, 20 February 2025

2025-02-20T14:15:04Z

← Older revision		Revision as of 14:15, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|206~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ ampersand -> ampersand comma to distinguish it from the temp

2025-01-18T09:03:53Z

Theory: ampersand -> ampersand comma to distinguish it from the temp

← Older revision		Revision as of 09:03, 18 January 2025
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	Using the patent val, it [[tempering out\|tempers out]] 48828125/47775744 ([[sycamore comma]]) and 32768000000/31381059609 in the 5-limit; 4000/3969, 84035/82944, and 458752/455625 in the 7-limit; [[385/384]], 2401/2376, 6875/6804, and 9375/9317 in the 11-limit; [[352/351]], [[1575/1573]], 1625/1617, 2197/2178, and [[4096/4095]] in the 13-limit; [[289/288]], [[375/374]], [[442/441]], [[715/714]], and 2000/1989 in the 17-limit; 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit.		Using the patent val, it [[tempering out\|tempers out]] 48828125/47775744 ([[sycamore comma]]) and 32768000000/31381059609 in the 5-limit; 4000/3969, 84035/82944, and 458752/455625 in the 7-limit; [[385/384]], 2401/2376, 6875/6804, and 9375/9317 in the 11-limit; [[352/351]], [[1575/1573]], 1625/1617, 2197/2178, and [[4096/4095]] in the 13-limit; [[289/288]], [[375/374]], [[442/441]], [[715/714]], and 2000/1989 in the 17-limit; 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit.

	Using the 206b val, it tempers out 78732/78125 ([[sensipent comma]]) and 34171875/33554432 ([[ampersand]]) in the 5-limit; [[225/224]], [[1029/1024]], and 177147/175000 in the 7-limit; 4375/4356, [[9801/9800]], 15309/15125, and 73728/73205 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1701/1690, and 31213/30976 in the 13-limit; [[273/272]], [[833/832]], 850/847, [[1089/1088]], [[1225/1224]], and 1458/1445 in the 17-limit; 210/209, 495/494, 729/722, 1235/1232, and [[1445/1444]] in the 19-limit.		Using the 206b val, it tempers out 78732/78125 ([[sensipent comma]]) and 34171875/33554432 ([[ampersand comma]]) in the 5-limit; [[225/224]], [[1029/1024]], and 177147/175000 in the 7-limit; 4375/4356, [[9801/9800]], 15309/15125, and 73728/73205 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1701/1690, and 31213/30976 in the 13-limit; [[273/272]], [[833/832]], 850/847, [[1089/1088]], [[1225/1224]], and 1458/1445 in the 17-limit; 210/209, 495/494, 729/722, 1235/1232, and [[1445/1444]] in the 19-limit.

	Using the 206be val, it tempers out [[243/242]], 385/384, 441/440, and 43923/43750 in the 11-limit; 351/350, 625/624, [[847/845]], [[1001/1000]], and [[1573/1568]] in the 13-limit; 273/272, 375/374, 561/560, 715/714, and 833/832 in the 17-limit; 363/361 and 729/722 in the 19-limit.		Using the 206be val, it tempers out [[243/242]], 385/384, 441/440, and 43923/43750 in the 11-limit; 351/350, 625/624, [[847/845]], [[1001/1000]], and [[1573/1568]] in the 13-limit; 273/272, 375/374, 561/560, 715/714, and 833/832 in the 17-limit; 363/361 and 729/722 in the 19-limit.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	206edo contains 2edo and 103edo as subsets. 412edo, which doubles it, provides an excellent correction to the approximation of harmonic 3.		206edo contains 2edo and 103edo as subsets. 412edo, which doubles it, provides an excellent correction to the approximation of harmonic 3.

	== Scales ==		== Scales ==

FloraC: Review

2024-04-13T11:53:22Z

Review

← Older revision		Revision as of 11:53, 13 April 2024
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	206edo is closely related to [[103edo]], but the [[patent val]]s differ on the mapping for 3, 11, and 19.		206edo is closely related to [[103edo]], but the [[patent val]]s differ on the mapping for 3, 11, and 19.

	It is in[[consistent]] to the 5-limit and higher ~~limit~~, with four mappings possible for the 19-limit:		It is in[[consistent]] to the [[5-odd-limit]] and higher limits, with four mappings possible for the 19-limit:
	* {{val\| 206 327 478 578 713 762 842 875 }} ([[patent val]])		* {{val\| 206 327 478 578 713 762 842 875 }} ([[patent val]])
	* {{val\| 206 '''326''' 478 578 713 762 842 875 }} (206b)		* {{val\| 206 '''326''' 478 578 713 762 842 875 }} (206b)
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	* {{val\| 206 327 '''479''' '''579''' 713 '''763''' 842 875 }} (206cdf)		* {{val\| 206 327 '''479''' '''579''' 713 '''763''' 842 875 }} (206cdf)

	Using the patent val, it tempers out 48828125/47775744 ([[sycamore comma]]) and 32768000000/31381059609 in the 5-limit; 4000/3969, 84035/82944, and 458752/455625 in the 7-limit; [[385/384]], 2401/2376, 6875/6804, and 9375/9317 in the 11-limit; [[352/351]], [[1575/1573]], 1625/1617, 2197/2178, and [[4096/4095]] in the 13-limit; [[289/288]], [[375/374]], [[442/441]], [[715/714]], and 2000/1989 in the 17-limit; 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit.		Using the patent val, it [[tempering out\|tempers out]] 48828125/47775744 ([[sycamore comma]]) and 32768000000/31381059609 in the 5-limit; 4000/3969, 84035/82944, and 458752/455625 in the 7-limit; [[385/384]], 2401/2376, 6875/6804, and 9375/9317 in the 11-limit; [[352/351]], [[1575/1573]], 1625/1617, 2197/2178, and [[4096/4095]] in the 13-limit; [[289/288]], [[375/374]], [[442/441]], [[715/714]], and 2000/1989 in the 17-limit; 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit.

	Using the 206b val, it tempers out 78732/78125 ([[sensipent comma]]) and 34171875/33554432 ([[ampersand]]) in the 5-limit; [[225/224]], [[1029/1024]], and 177147/175000 in the 7-limit; 4375/4356, [[9801/9800]], 15309/15125, and 73728/73205 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1701/1690, and 31213/30976 in the 13-limit; [[273/272]], [[833/832]], 850/847, [[1089/1088]], [[1225/1224]], and 1458/1445 in the 17-limit; 210/209, 495/494, 729/722, 1235/1232, and [[1445/1444]] in the 19-limit.		Using the 206b val, it tempers out 78732/78125 ([[sensipent comma]]) and 34171875/33554432 ([[ampersand]]) in the 5-limit; [[225/224]], [[1029/1024]], and 177147/175000 in the 7-limit; 4375/4356, [[9801/9800]], 15309/15125, and 73728/73205 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1701/1690, and 31213/30976 in the 13-limit; [[273/272]], [[833/832]], 850/847, [[1089/1088]], [[1225/1224]], and 1458/1445 in the 17-limit; 210/209, 495/494, 729/722, 1235/1232, and [[1445/1444]] in the 19-limit.

FloraC: Rework (2/2)

2023-07-09T14:21:32Z

Rework (2/2)

← Older revision		Revision as of 14:21, 9 July 2023
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	* {{val\| 206 327 '''479''' '''579''' 713 '''763''' 842 875 }} (206cdf)		* {{val\| 206 327 '''479''' '''579''' 713 '''763''' 842 875 }} (206cdf)

	Using the patent val, it tempers out		Using the patent val, it tempers out 48828125/47775744 ([[sycamore comma]]) and 32768000000/31381059609 in the 5-limit; 4000/3969, 84035/82944, and 458752/455625 in the 7-limit; [[385/384]], 2401/2376, 6875/6804, and 9375/9317 in the 11-limit; [[352/351]], [[1575/1573]], 1625/1617, 2197/2178, and [[4096/4095]] in the 13-limit; [[289/288]], [[375/374]], [[442/441]], [[715/714]], and 2000/1989 in the 17-limit; 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit.
	* 48828125/47775744 ([[sycamore comma]]) and 32768000000/31381059609 in the 5-limit
	* 4000/3969, 84035/82944, and 458752/455625 in the 7-limit
	* [[385/384]], 2401/2376, 6875/6804, and 9375/9317 in the 11-limit
	* [[352/351]], 1575/1573, 1625/1617, 2197/2178, and 4096/4095 in the 13-limit
	* 289/288, 375/374, 442/441, 715/714, and 2000/1989 in the 17-limit
	* 190/189, 361/360, 665/663, 969/968, 1235/1232, and 1375/1368 in the 19-limit

	Using the 206b val, it tempers out		Using the 206b val, it tempers out 78732/78125 ([[sensipent comma]]) and 34171875/33554432 ([[ampersand]]) in the 5-limit; [[225/224]], [[1029/1024]], and 177147/175000 in the 7-limit; 4375/4356, [[9801/9800]], 15309/15125, and 73728/73205 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1701/1690, and 31213/30976 in the 13-limit; [[273/272]], [[833/832]], 850/847, [[1089/1088]], [[1225/1224]], and 1458/1445 in the 17-limit; 210/209, 495/494, 729/722, 1235/1232, and [[1445/1444]] in the 19-limit.
	* 78732/78125 ([[sensipent comma]]) and 34171875/33554432 ([[ampersand]]) in the 5-limit
	* 225/224, 1029/1024, and 177147/175000 in the 7-limit
	* 4375/4356, [[9801/9800]], 15309/15125, and 73728/73205 in the 11-limit
	* 351/350, 364/363, 625/624, 1701/1690, and 31213/30976 in the 13-limit
	* 273/272, 833/832, 850/847, 1089/1088, 1225/1224, and 1458/1445 in the 17-limit
	* 210/209, 495/494, 729/722, 1235/1232, and 1445/1444 in the 19-limit

	Using the 206be val, it tempers out		Using the 206be val, it tempers out [[243/242]], 385/384, 441/440, and 43923/43750 in the 11-limit; 351/350, 625/624, [[847/845]], [[1001/1000]], and [[1573/1568]] in the 13-limit; 273/272, 375/374, 561/560, 715/714, and 833/832 in the 17-limit; 363/361 and 729/722 in the 19-limit.
	* [[243/242]], 385/384, 441/440, and 43923/43750 in the 11-limit
	* [[351/350~~]] (ratwolfsma)~~, 625/624, 847/845, 1001/1000, and 1573/1568 in the 13-limit
	* 273/272, 375/374, 561/560, 715/714, and 833/832 in the 17-limit
	* 363/361 and 729/722 in the 19-limit

	Using the 206cdf val, it tempers out		Using the 206cdf val, it tempers out 2048/2025 ([[diaschisma]]), and {{monzo\| 4 -45 29 }} in the 5-limit; [[4375/4374]], 110592/109375, and 235298/234375 in the 7-limit; [[176/175]], [[896/891]], and 1331/1323 in the 11-limit; 640/637, 847/845, 1001/1000, and [[2197/2187]] in the 13-limit; [[136/135]], [[256/255]], 561/560, and 1275/1274 in the 17-limit; 190/189, 476/475, 608/605, 836/833, and 969/968 in the 19-limit.
	* 2048/2025 ([[diaschisma]]), and {{monzo\| 4 -45 29 }}; in the 5-limit
	* 4375/4374, 110592/109375, and 235298/234375 in the 7-limit
	* [[176/175]], 896/891, and 1331/1323 in the 11-limit
	* 640/637, 847/845, 1001/1000, and 2197/2187 in the 13-limit
	* 136/135, 256/255, 561/560, and 1275/1274 in the 17-limit
	* 190/189, 476/475, 608/605, 836/833, and 969/968 in the 19-limit

	=== Odd harmonics ===		=== Odd harmonics ===

FloraC: Rework (1/2)

2023-07-09T14:17:35Z

Rework (1/2)

← Older revision		Revision as of 14:17, 9 July 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''206edo''' is the [[~~EDO\|~~equal division of the octave]] into~~ 206 ~~parts of 5.8252 [[cent]]s each. It~~ is closely related to [[103edo]], but the patent ~~vals~~ differ on the mapping for 3, 11, and 19.		{{EDO intro\|206}}
	~~{{Primes in edo\|206}}~~
			== Theory ==
			206edo is closely related to [[103edo]], but the [[patent val]]s differ on the mapping for 3, 11, and 19.

	~~== Mappings ==~~
	It is in[[consistent]] to the 5-limit and higher limit, with four mappings possible for the 19-limit:		It is in[[consistent]] to the 5-limit and higher limit, with four mappings possible for the 19-limit:
	* {{val\| 206 327 478 578 713 762 842 875 }} ([[patent val]])		* {{val\| 206 327 478 578 713 762 842 875 }} ([[patent val]])
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	* 136/135, 256/255, 561/560, and 1275/1274 in the 17-limit		* 136/135, 256/255, 561/560, and 1275/1274 in the 17-limit
	* 190/189, 476/475, 608/605, 836/833, and 969/968 in the 19-limit		* 190/189, 476/475, 608/605, 836/833, and 969/968 in the 19-limit

			=== Odd harmonics ===
			{{Harmonics in equal\|206}}

			=== Subsets and supersets ===
			206edo contains 2edo and 103edo as subsets. 412edo, which doubles it, provides an excellent correction to the approximation of harmonic 3.

	== Scales ==		== Scales ==

	* [[skwares8]]		* [[skwares8]]
	* [[skwares11]]		* [[skwares11]]
	* [[skwares14]]		* [[skwares14]]

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

BudjarnLambeth: Removed novelty tag for now. We can add it back later, but I think we should start with the biggest edos: 6000000, 4191814, 2901533… and work our way down. We should add the tag to bigger ones first.

2023-07-09T02:02:30Z

Removed novelty tag for now. We can add it back later, but I think we should start with the biggest edos: 6000000, 4191814, 2901533… and work our way down. We should add the tag to bigger ones first.

← Older revision		Revision as of 02:02, 9 July 2023
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	~~{{Novelty}}~~
	{{Infobox ET}}		{{Infobox ET}}
	'''206edo''' is the [[EDO\|equal division of the octave]] into 206 parts of 5.8252 [[cent]]s each. It is closely related to [[103edo]], but the patent vals differ on the mapping for 3, 11, and 19.		'''206edo''' is the [[EDO\|equal division of the octave]] into 206 parts of 5.8252 [[cent]]s each. It is closely related to [[103edo]], but the patent vals differ on the mapping for 3, 11, and 19.

Fredg999: Marked as novelty

2023-07-08T15:12:54Z

Marked as novelty

← Older revision		Revision as of 15:12, 8 July 2023
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			{{Novelty}}
	{{Infobox ET}}		{{Infobox ET}}
	'''206edo''' is the [[EDO\|equal division of the octave]] into 206 parts of 5.8252 [[cent]]s each. It is closely related to [[103edo]], but the patent vals differ on the mapping for 3, 11, and 19.		'''206edo''' is the [[EDO\|equal division of the octave]] into 206 parts of 5.8252 [[cent]]s each. It is closely related to [[103edo]], but the patent vals differ on the mapping for 3, 11, and 19.
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	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

	~~{{todo\|improve readability}}~~

BudjarnLambeth: Improved readability slightly

2023-07-07T02:28:35Z

Improved readability slightly

← Older revision		Revision as of 02:28, 7 July 2023
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	{{Primes in edo\|206}}		{{Primes in edo\|206}}

			== Mappings ==
	It is in[[consistent]] to the 5-limit and higher limit, with four mappings possible for the 19-limit:		It is in[[consistent]] to the 5-limit and higher limit, with four mappings possible for the 19-limit:
	* {{val\| 206 327 478 578 713 762 842 875 }} ([[patent val]])		* {{val\| 206 327 478 578 713 762 842 875 }} ([[patent val]])

Plumtree: Infobox ET added

2022-10-04T21:21:11Z

Infobox ET added

← Older revision		Revision as of 21:21, 4 October 2022
Line 1:		Line 1:
			{{Infobox ET}}
	'''206edo''' is the [[EDO\|equal division of the octave]] into 206 parts of 5.8252 [[cent]]s each. It is closely related to [[103edo]], but the patent vals differ on the mapping for 3, 11, and 19.		'''206edo''' is the [[EDO\|equal division of the octave]] into 206 parts of 5.8252 [[cent]]s each. It is closely related to [[103edo]], but the patent vals differ on the mapping for 3, 11, and 19.
	{{Primes in edo\|206}}		{{Primes in edo\|206}}

Fredg999 category edits: Sort key

2022-07-03T18:32:25Z

Sort key

← Older revision		Revision as of 18:32, 3 July 2022
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	* [[skwares14]]		* [[skwares14]]

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

	{{todo\|improve readability}}		{{todo\|improve readability}}