223edo - Revision history

Lériendil at 16:34, 4 March 2025

2025-03-04T16:34:31Z

← Older revision		Revision as of 16:34, 4 March 2025
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|223\|columns=10}}		{{Harmonics in equal\|223\|columns=11}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	223edo is the 48th [[prime edo]].		223edo is the 48th [[prime edo]].

ArrowHead294 at 14:18, 20 February 2025

2025-02-20T14:18:50Z

← Older revision		Revision as of 14:18, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	223edo contains an excellent proportion of [[hornbostel]] temperament (via [[7L 2s]]), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is in[[consistent]] to the [[5-odd-limit]] and higher limit, with three mappings possible for the 5-limit:		223edo contains an excellent proportion of [[hornbostel]] temperament (via [[7L 2s]]), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is in[[consistent]] to the [[5-odd-limit]] and higher limit, with three mappings possible for the 5-limit:

FloraC: Cleanup; -number of lunar months (irrelevant)

2024-04-02T06:36:05Z

Cleanup; -number of lunar months (irrelevant)

← Older revision		Revision as of 06:36, 2 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''~~223edo~~''' is the [[EDO\|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It~~ contains an excellent proportion of [[hornbostel]] temperament (via ~~7L2s~~), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is ~~inconsistent~~ to the 5-limit and higher limit, with three mappings possible for the 5-limit:		{{EDO intro}}
	* {{val\| 223 353 518 }} (patent val),
			223edo contains an excellent proportion of [[hornbostel]] temperament (via [[7L 2s]]), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is in[[consistent]] to the [[5-odd-limit]] and higher limit, with three mappings possible for the 5-limit:
			* {{val\| 223 353 518 }} ([[patent val]]),
	* {{val\| 223 '''354''' 518 }} (223b),		* {{val\| 223 '''354''' 518 }} (223b),
	* {{val\| 223 353 '''517''' }} (223c).		* {{val\| 223 353 '''517''' }} (223c).
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	Using the patent val, it tempers out 393216/390625 ([[würschmidt comma]]) and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit; 243/242, 441/440, 5632/5625, and 1449459/1433600 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit.		Using the patent val, it tempers out 393216/390625 ([[würschmidt comma]]) and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit; 243/242, 441/440, 5632/5625, and 1449459/1433600 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit.

	Using the 223be val, it tempers out 15625/15552 ([[kleisma]]) and {{monzo\| 58 -38 1 }} in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit.		Using the 223be val, it tempers out 15625/15552 ([[kleisma]]) and {{monzo\| 58 -38 1 }} in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit. Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit.

	Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit.

	Using the 223c val, it tempers out the 129140163/128000000 ([[graviton]]) and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, and 4000/3993 in the 11-limit; 1188/1183, 1573/1568, 1625/1617, 1716/1715, and 3159/3136 in the 13-limit.		Using the 223c val, it tempers out the 129140163/128000000 ([[graviton]]) and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, and 4000/3993 in the 11-limit; 1188/1183, 1573/1568, 1625/1617, 1716/1715, and 3159/3136 in the 13-limit.
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	Using the 223e val, it tempers out 1944/1925, 2835/2816, and 4000/3993 in the 11-limit; 364/363, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.		Using the 223e val, it tempers out 1944/1925, 2835/2816, and 4000/3993 in the 11-limit; 364/363, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

	~~223edo is the 48th [[prime EDO]].~~		=== Odd harmonics ===

	~~223 is also the number of lunar months in an astronomical concept known as [[Wikipedia:Saros (astronomy)\|saros]].~~

	{{Harmonics in equal\|223\|columns=10}}		{{Harmonics in equal\|223\|columns=10}}

	~~[[Category:Equal divisions of~~ the ~~octave\|###]] <!-- 3-digit number -->~~		=== Subsets and supersets ===
	[[~~Category:Prime EDO~~]]		223edo is the 48th [[prime edo]].

Plumtree: Infobox ET added

2022-10-04T21:24:33Z

Infobox ET added

← Older revision		Revision as of 21:24, 4 October 2022
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			{{Infobox ET}}
	'''223edo''' is the [[EDO\|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It contains an excellent proportion of [[hornbostel]] temperament (via 7L2s), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit:		'''223edo''' is the [[EDO\|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It contains an excellent proportion of [[hornbostel]] temperament (via 7L2s), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit:
	* {{val\| 223 353 518 }} (patent val),		* {{val\| 223 353 518 }} (patent val),

Fredg999 category edits: Sort key

2022-07-03T18:35:14Z

Sort key

← Older revision		Revision as of 18:35, 3 July 2022
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	{{Harmonics in equal\|223\|columns=10}}		{{Harmonics in equal\|223\|columns=10}}
	[[Category:Equal divisions of the octave]]
			[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Prime EDO]]		[[Category:Prime EDO]]

Eliora at 11:10, 1 February 2022

2022-02-01T11:10:55Z

← Older revision		Revision as of 11:10, 1 February 2022
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	223 is also the number of lunar months in an astronomical concept known as [[Wikipedia:Saros (astronomy)\|saros]].		223 is also the number of lunar months in an astronomical concept known as [[Wikipedia:Saros (astronomy)\|saros]].

			{{Harmonics in equal\|223\|columns=10}}
	[[Category:Equal divisions of the octave]]		[[Category:Equal divisions of the octave]]
	[[Category:Prime EDO]]		[[Category:Prime EDO]]

Eliora at 20:42, 29 January 2022

2022-01-29T20:42:58Z

← Older revision		Revision as of 20:42, 29 January 2022
Line 15:		Line 15:

	223edo is the 48th [[prime EDO]].		223edo is the 48th [[prime EDO]].

			223 is also the number of lunar months in an astronomical concept known as [[Wikipedia:Saros (astronomy)\|saros]].

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

FloraC: Cleanup

2021-01-26T04:58:19Z

Cleanup

@@ Line 1: / Line 1: @@
-=<span style="color: #2230ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">223 equal divisions per octave</span>=
+'''223edo''' is the [[EDO|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It contains an excellent proportion of [[hornbostel]] temperament (via 7L2s), between square root of π (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit:
-'''223edo''' is the [[EDO|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It contains an excellent proportion of Hornbostel Temperament (via 7L2s), between Square root of Pi (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: &lt;223 353 518| (patent val), &lt;223 354 518| (223b), and &lt;223 353 517| (223c). Using the patent val, it tempers out the [[Würschmidt family|würschmidt comma]], 393216/390625 and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit; 243/242, 441/440, 5632/5625, and 1449459/1433600 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. Using the 223be val, it tempers out the [[Kleismic family|kleisma]], 15625/15552 and |58 -38 1&gt; in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit. Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit. Using the 223c val, it tempers out the [[Graviton|gravity comma]], 129140163/128000000 and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, and 4000/3993 in the 11-limit; 1188/1183, 1573/1568, 1625/1617, 1716/1715, and 3159/3136 in the 13-limit. Using the 223e val, it tempers out 1944/1925, 2835/2816, and 4000/3993 in the 11-limit; 364/363, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.
+* {{val| 223 353 518 }} (patent val),
 edo is the 48th [[prime EDO]].

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

2020-12-04T23:13:19Z

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
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	223edo is the 48th [[prime EDO]].		223edo is the 48th [[prime EDO]].

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

Xenllium at 23:04, 25 December 2018

2018-12-25T23:04:56Z

← Older revision		Revision as of 23:04, 25 December 2018
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	=<span style="color: #2230ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">223 equal divisions per octave</span>=		=<span style="color: #2230ff; font-family: 'Times New Roman',Times,serif; font-size: 113%;">223 equal divisions per octave</span>=
	'''223edo''' is the [[EDO\|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It contains an excellent proportion of Hornbostel Temperament (via 7L2s), between Square root of Pi (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <223 353 518\| (patent val), <223 354 518\| (223b), and <223 353 517\| (223c). Using the patent val, it tempers out the [[Würschmidt family\|würschmidt comma]], 393216/390625 and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit. Using the ~~223b~~ val, it tempers out the [[Kleismic family\|kleisma]], 15625/15552 and \|58 -38 1> in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit. Using the 223c val, it tempers out the [[Graviton\|gravity comma]], 129140163/128000000 and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit.		'''223edo''' is the [[EDO\|equal division of the octave]] into 223 parts of 5.38117 [[cent]]s each. It contains an excellent proportion of Hornbostel Temperament (via 7L2s), between Square root of Pi (184\223), Aureus interval (34/21 in 155\223) and the 6/5 interval (58\223). It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <223 353 518\| (patent val), <223 354 518\| (223b), and <223 353 517\| (223c). Using the patent val, it tempers out the [[Würschmidt family\|würschmidt comma]], 393216/390625 and 22876792454961/21990232555520 in the 5-limit; 2401/2400, 3136/3125, and 14348907/14000000 in the 7-limit; 243/242, 441/440, 5632/5625, and 1449459/1433600 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1573/1568 in the 13-limit. Using the 223be val, it tempers out the [[Kleismic family\|kleisma]], 15625/15552 and \|58 -38 1> in the 5-limit; 245/243, 3136/3125, and 67108864/66706983 in the 7-limit; 3025/3024, 3388/3375, 4375/4356, and 65536/65219 in the 11-limit; 352/351, 1001/1000, 2197/2178, and 2704/2695 in the 13-limit. Using the 223bef val, it tempers out 196/195, 325/324, 364/363, 625/624, and 49152/49049 in the 13-limit. Using the 223c val, it tempers out the [[Graviton\|gravity comma]], 129140163/128000000 and 35595703125/34359738368 in the 5-limit; 4375/4374, 33075/32768, and 78125/76832 in the 7-limit; 243/242, 385/384, and 4000/3993 in the 11-limit; 1188/1183, 1573/1568, 1625/1617, 1716/1715, and 3159/3136 in the 13-limit. Using the 223e val, it tempers out 1944/1925, 2835/2816, and 4000/3993 in the 11-limit; 364/363, 1001/1000, 1701/1690, and 1716/1715 in the 13-limit.

	223edo is the 48th [[prime EDO]].		223edo is the 48th [[prime EDO]].