139edo - Revision history

ArrowHead294 at 16:37, 20 February 2025

2025-02-20T16:37:18Z

← Older revision		Revision as of 16:37, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	139edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 139 220 323 }} ([[patent val]]), {{val\| 139 '''221''' 323 }} (139b), and {{val\| 139 220 '''322''' }} (139c).		139edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 139 220 323 }} ([[patent val]]), {{val\| 139 '''221''' 323 }} (139b), and {{val\| 139 220 '''322''' }} (139c).

FloraC: +subsets and supersets; misc. cleanup

2024-05-26T09:37:39Z

+subsets and supersets; misc. cleanup

← Older revision		Revision as of 09:37, 26 May 2024
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	{{EDO intro}}		{{EDO intro}}

	~~== Theory ==~~
	139edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 139 220 323 }} ([[patent val]]), {{val\| 139 '''221''' 323 }} (139b), and {{val\| 139 220 '''322''' }} (139c).		139edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 139 220 323 }} ([[patent val]]), {{val\| 139 '''221''' 323 }} (139b), and {{val\| 139 220 '''322''' }} (139c).

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	Using the 139df val, it tempers out [[225/224]], 51200/50421, and 157464/153125 in the 7-limit; [[99/98]], [[176/175]], and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments #Interpental\|interpental]] temperament; 144/143, 648/637, [[847/845]], [[1575/1573]], and 3159/3125 in the 13-limit.		Using the 139df val, it tempers out [[225/224]], 51200/50421, and 157464/153125 in the 7-limit; [[99/98]], [[176/175]], and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments #Interpental\|interpental]] temperament; 144/143, 648/637, [[847/845]], [[1575/1573]], and 3159/3125 in the 13-limit.

	Using the 139ce val, it tempers out 3125/3072 ([[magic comma]]) and ~~22876792454961/21990232555520~~ in the 5-limit; 1029/1024, [[3125/3087]], and [[19683/19600]] in the 7-limit, supporting the 7-limit [[trismegistus]] temperament; 540/539, 1331/1323, and 1815/1792 in the 11-limit; [[275/273]], [[325/324]], 847/845, 1287/1280, and 1575/1573 in the 13-limit.		Using the 139ce val, it tempers out 3125/3072 ([[magic comma]]) and {{monzo\| -42 28 -1 }} in the 5-limit; 1029/1024, [[3125/3087]], and [[19683/19600]] in the 7-limit, supporting the 7-limit [[trismegistus]] temperament; 540/539, 1331/1323, and 1815/1792 in the 11-limit; [[275/273]], [[325/324]], 847/845, 1287/1280, and 1575/1573 in the 13-limit.

	Using the 139bdf val, it tempers out 393216/390625 ([[würschmidt comma]]), and 409600000/387420489 in the 5-limit; [[245/243]], 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, [[512/507]], [[625/624]], 847/845, and 1625/1617 in the 13-limit.		Using the 139bdf val, it tempers out 393216/390625 ([[würschmidt comma]]), and 409600000/387420489 in the 5-limit; [[245/243]], 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, [[512/507]], [[625/624]], 847/845, and 1625/1617 in the 13-limit.
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|139}}		{{Harmonics in equal\|139}}

			=== Subsets and supersets ===
			139edo is the 34th [[prime edo]], following [[137edo]] and before [[149edo]].

FloraC: Adopt template: EDO intro; group the vals by similarity; -redundant categories; misc. cleanup

2024-05-26T09:33:19Z

Adopt template: EDO intro; group the vals by similarity; -redundant categories; misc. cleanup

← Older revision		Revision as of 09:33, 26 May 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''139edo''' is the [[~~EDO~~\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. 139edo is the 34th [[prime EDO]].~~		{{EDO intro}}

	It is ~~inconsistent~~ to the 5-limit and higher ~~limit~~, with three mappings possible for the 5-limit: ~~<~~139 220 323\| (patent val), ~~<~~139 221 323\| (139b), and ~~<~~139 220 322\| (139c).		== Theory ==
			139edo is in[[consistent]] to the [[5-odd-limit]] and higher limits, with three mappings possible for the 5-limit: {{val\| 139 220 323 }} ([[patent val]]), {{val\| 139 '''221''' 323 }} (139b), and {{val\| 139 220 '''322''' }} (139c).

	~~== Commas ==~~		Using the patent val, it [[tempering out\|tempers out]] 1990656/1953125 ([[valentine comma]]) and 43046721/41943040 ([[python comma]]) in the 5-limit; [[126/125]], [[1029/1024]], and 4782969/4705960 in the 7-limit, [[support]]ing the 7-limit [[valentine]] temperament; [[540/539]], 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; [[364/363]], [[676/675]], [[1287/1280]], 1701/1690, and [[1716/1715]] in the 13-limit. Using the alternative 139f val, it tempers out [[144/143]], [[196/195]], [[351/350]], [[4096/4095]], and 4455/4394 in the 13-limit.
	Using the patent val, it tempers out ~~the valentine comma,~~ 1990656/1953125 and ~~the lalagu comma,~~ 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit, ~~supporting~~ the 7-limit [[~~Starling temperaments\|~~valentine ~~temperament~~]]; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; 364/363, 676/675, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit.

	Using the ~~139bdf~~ val, it tempers out [[~~Würschmidt comma~~]], ~~393216~~/~~390625~~ and ~~409600000~~/~~387420489~~ in the 5-limit; ~~245~~/~~243~~, ~~3125~~/~~3087~~, and ~~131072~~/~~127575~~ in the 7-limit~~; 176/175, 1232/1215~~, ~~and 2560/2541 in~~ the 11-limit; ~~275~~/~~273~~, ~~512~~/~~507~~, ~~625~~/~~624~~, ~~847~~/~~845~~, and ~~1625~~/~~1617~~ in the 13-limit.		Using the 139df val, it tempers out [[225/224]], 51200/50421, and 157464/153125 in the 7-limit; [[99/98]], [[176/175]], and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments #Interpental\|interpental]] temperament; 144/143, 648/637, [[847/845]], [[1575/1573]], and 3159/3125 in the 13-limit.

	Using the 139ce val, it tempers out ~~the~~ [[~~Magic family\|small diesis~~]]~~, 3125/3072~~ and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit, supporting the 7-limit [[~~Magic family\|~~trismegistus ~~temperament~~]]; 540/539, 1331/1323, and 1815/1792 in the 11-limit; 275/273, 325/324, 847/845, 1287/1280, and 1575/1573 in the 13-limit.		Using the 139ce val, it tempers out 3125/3072 ([[magic comma]]) and 22876792454961/21990232555520 in the 5-limit; 1029/1024, [[3125/3087]], and [[19683/19600]] in the 7-limit, supporting the 7-limit [[trismegistus]] temperament; 540/539, 1331/1323, and 1815/1792 in the 11-limit; [[275/273]], [[325/324]], 847/845, 1287/1280, and 1575/1573 in the 13-limit.

	Using the ~~139df~~ val, it tempers out ~~225~~/~~224~~, ~~51200~~/~~50421~~, and ~~157464~~/~~153125~~ in the 7-limit; 99/98, ~~176~~/~~175~~, and ~~15309~~/~~15125~~ in the 11-limit, ~~supporting the 11-limit~~ [[~~Marvel temperaments\|interpental temperament~~]]~~; 144/143~~, ~~648~~/~~637~~, 847/845~~, 1575/1573~~, and ~~3159~~/~~3125~~ in the 13-limit.		Using the 139bdf val, it tempers out 393216/390625 ([[würschmidt comma]]), and 409600000/387420489 in the 5-limit; [[245/243]], 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, [[512/507]], [[625/624]], 847/845, and 1625/1617 in the 13-limit.

	~~Using 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.~~		=== Odd harmonics ===

	== ~~Harmonics~~ ==
	{{Harmonics in equal\|139}}		{{Harmonics in equal\|139}}
	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	~~[[Category:Prime EDO]]~~

BudjarnLambeth: Added "harmonics in equal" table; added subheadings

2023-06-24T07:17:55Z

Added "harmonics in equal" table; added subheadings

← Older revision		Revision as of 07:17, 24 June 2023
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	{{Infobox ET}}		{{Infobox ET}}
	'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is ~~inconsistent to~~ the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (patent val), <139 221 323\| (139b), and <139 220 322\| (139c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and the lalagu comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; 364/363, 676/675, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 139bdf val, it tempers out [[~~Würschmidt comma~~]], 393216/390625 and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, 512/507, 625/624, 847/845, and 1625/1617 in the 13-limit. Using the 139ce val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit, supporting the 7-limit [[Magic family\|trismegistus temperament]]; 540/539, 1331/1323, and 1815/1792 in the 11-limit; 275/273, 325/324, 847/845, 1287/1280, and 1575/1573 in the 13-limit. Using the 139df val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments\|interpental temperament]]; 144/143, 648/637, 847/845, 1575/1573, and 3159/3125 in the 13-limit. Using 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.		'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. 139edo is the 34th [[prime EDO]].

	~~139edo~~ is the ~~34th [[prime EDO]]~~.		It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (patent val), <139 221 323\| (139b), and <139 220 322\| (139c).

			== Commas ==
			Using the patent val, it tempers out the valentine comma, 1990656/1953125 and the lalagu comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; 364/363, 676/675, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit.

			Using the 139bdf val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, 512/507, 625/624, 847/845, and 1625/1617 in the 13-limit.

			Using the 139ce val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit, supporting the 7-limit [[Magic family\|trismegistus temperament]]; 540/539, 1331/1323, and 1815/1792 in the 11-limit; 275/273, 325/324, 847/845, 1287/1280, and 1575/1573 in the 13-limit.

			Using the 139df val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments\|interpental temperament]]; 144/143, 648/637, 847/845, 1575/1573, and 3159/3125 in the 13-limit.

			Using 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.

			== Harmonics ==
			{{Harmonics in equal\|139}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Prime EDO]]		[[Category:Prime EDO]]

Aura at 19:05, 4 October 2022

2022-10-04T19:05:55Z

← Older revision		Revision as of 19:05, 4 October 2022
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			{{Infobox ET}}
	'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (patent val), <139 221 323\| (139b), and <139 220 322\| (139c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and the lalagu comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; 364/363, 676/675, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 139bdf val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, 512/507, 625/624, 847/845, and 1625/1617 in the 13-limit. Using the 139ce val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit, supporting the 7-limit [[Magic family\|trismegistus temperament]]; 540/539, 1331/1323, and 1815/1792 in the 11-limit; 275/273, 325/324, 847/845, 1287/1280, and 1575/1573 in the 13-limit. Using the 139df val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments\|interpental temperament]]; 144/143, 648/637, 847/845, 1575/1573, and 3159/3125 in the 13-limit. Using 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.		'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (patent val), <139 221 323\| (139b), and <139 220 322\| (139c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and the lalagu comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; 364/363, 676/675, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 139bdf val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, 512/507, 625/624, 847/845, and 1625/1617 in the 13-limit. Using the 139ce val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit, supporting the 7-limit [[Magic family\|trismegistus temperament]]; 540/539, 1331/1323, and 1815/1792 in the 11-limit; 275/273, 325/324, 847/845, 1287/1280, and 1575/1573 in the 13-limit. Using the 139df val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments\|interpental temperament]]; 144/143, 648/637, 847/845, 1575/1573, and 3159/3125 in the 13-limit. Using 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.

Fredg999 category edits: Sort key

2022-07-02T16:35:13Z

Sort key

← Older revision		Revision as of 16:35, 2 July 2022
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	139edo is the 34th [[prime EDO]].		139edo is the 34th [[prime EDO]].

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

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

2020-12-04T23:13:08Z

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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	139edo is the 34th [[prime EDO]].		139edo is the 34th [[prime EDO]].

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

TallKite: updated the color names

2019-02-07T01:04:50Z

updated the color names

← Older revision		Revision as of 01:04, 7 February 2019
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	'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (patent val), <139 221 323\| (139b), and <139 220 322\| (139c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and the ~~double large green~~ comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; 364/363, 676/675, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 139bdf val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, 512/507, 625/624, 847/845, and 1625/1617 in the 13-limit. Using the 139ce val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit, supporting the 7-limit [[Magic family\|trismegistus temperament]]; 540/539, 1331/1323, and 1815/1792 in the 11-limit; 275/273, 325/324, 847/845, 1287/1280, and 1575/1573 in the 13-limit. Using the 139df val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments\|interpental temperament]]; 144/143, 648/637, 847/845, 1575/1573, and 3159/3125 in the 13-limit. Using 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.		'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (patent val), <139 221 323\| (139b), and <139 220 322\| (139c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and the lalagu comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; 364/363, 676/675, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 139bdf val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, 512/507, 625/624, 847/845, and 1625/1617 in the 13-limit. Using the 139ce val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit, supporting the 7-limit [[Magic family\|trismegistus temperament]]; 540/539, 1331/1323, and 1815/1792 in the 11-limit; 275/273, 325/324, 847/845, 1287/1280, and 1575/1573 in the 13-limit. Using the 139df val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments\|interpental temperament]]; 144/143, 648/637, 847/845, 1575/1573, and 3159/3125 in the 13-limit. Using 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.

	139edo is the 34th [[prime EDO]].		139edo is the 34th [[prime EDO]].

Xenllium at 12:38, 16 December 2018

2018-12-16T12:38:58Z

← Older revision		Revision as of 12:38, 16 December 2018
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	'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (~~optimal~~ patent val), <139 221 323\| (139b), and <139 220 322\| (139c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and the double large green comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit. Using the ~~139bd~~ val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit. Using the 139ce val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit; 540/539, 1331/1323, and 1815/1792 in the 11-limit. Using the ~~139d~~ val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit.		'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (patent val), <139 221 323\| (139b), and <139 220 322\| (139c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and the double large green comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit, supporting the 7-limit [[Starling temperaments\|valentine temperament]]; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit; 364/363, 676/675, 1287/1280, 1701/1690, and 1716/1715 in the 13-limit. Using the 139bdf val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit; 275/273, 512/507, 625/624, 847/845, and 1625/1617 in the 13-limit. Using the 139ce val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit, supporting the 7-limit [[Magic family\|trismegistus temperament]]; 540/539, 1331/1323, and 1815/1792 in the 11-limit; 275/273, 325/324, 847/845, 1287/1280, and 1575/1573 in the 13-limit. Using the 139df val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit, supporting the 11-limit [[Marvel temperaments\|interpental temperament]]; 144/143, 648/637, 847/845, 1575/1573, and 3159/3125 in the 13-limit. Using 139f val, it tempers out 144/143, 196/195, 351/350, 4096/4095, and 4455/4394 in the 13-limit.

	139edo is the 34th [[prime EDO]].		139edo is the 34th [[prime EDO]].

Xenllium at 22:51, 13 December 2018

2018-12-13T22:51:11Z

← Older revision		Revision as of 22:51, 13 December 2018
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	'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (optimal patent val), <139 221 323\| (139b), and <139 220 322\| (139c). Using the ~~optimal~~ patent val, it tempers out the valentine comma, 1990656/1953125 and the double large green comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit. Using the ~~139b~~ val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; ~~686~~/~~675~~ and ~~2240~~/~~2187~~ in the 7-limit. Using the ~~139c~~ val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit.		'''139edo''' is the [[EDO\|equal division of the octave]] into 139 parts of 8.6331 [[cent]]s each. It is inconsistent to the 5-limit and higher limit, with three mappings possible for the 5-limit: <139 220 323\| (optimal patent val), <139 221 323\| (139b), and <139 220 322\| (139c). Using the patent val, it tempers out the valentine comma, 1990656/1953125 and the double large green comma, 43046721/41943040 in the 5-limit; 126/125, 1029/1024, and 4782969/4705960 in the 7-limit; 540/539, 1944/1925, 2835/2816, and 12005/11979 in the 11-limit. Using the 139bd val, it tempers out [[Würschmidt comma]], 393216/390625 and 409600000/387420489 in the 5-limit; 245/243, 3125/3087, and 131072/127575 in the 7-limit; 176/175, 1232/1215, and 2560/2541 in the 11-limit. Using the 139ce val, it tempers out the [[Magic family\|small diesis]], 3125/3072 and 22876792454961/21990232555520 in the 5-limit; 1029/1024, 3125/3087, and 19683/19600 in the 7-limit; 540/539, 1331/1323, and 1815/1792 in the 11-limit. Using the 139d val, it tempers out 225/224, 51200/50421, and 157464/153125 in the 7-limit; 99/98, 176/175, and 15309/15125 in the 11-limit.

	139edo is the 34th [[prime EDO]].		139edo is the 34th [[prime EDO]].