189edo - Revision history

ArrowHead294 at 19:30, 20 February 2025

2025-02-20T19:30:35Z

← Older revision		Revision as of 19:30, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	189edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]]s [[3/1\|3]] and [[7/1\|7]] are about halfway between its steps. It has good approximations to [[5/1\|5]], [[9/1\|9]], [[11/1\|11]], [[19/1\|19]], and [[21/1\|21]], making it suitable for a 2.9.5.21.11.19 [[subgroup]] interpretation.		189edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]]s [[3/1\|3]] and [[7/1\|7]] are about halfway between its steps. It has good approximations to [[5/1\|5]], [[9/1\|9]], [[11/1\|11]], [[19/1\|19]], and [[21/1\|21]], making it suitable for a 2.9.5.21.11.19 [[subgroup]] interpretation.

FloraC: Expand

2024-04-22T15:45:33Z

Expand

← Older revision		Revision as of 15:45, 22 April 2024
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	{{EDO intro}}		{{EDO intro}}

	~~The~~ equal temperament [[tempering out\|tempers out]] 15625/15552 (kleisma) and ~~9007199254740992/8578797170610375~~ in the 5-limit; [[4000/3969]], [[6144/6125]], and 537824/531441 in the 7-limit, supporting the [[hemikleismic]] temperament. ~~Using the [[patent val]], it~~ tempers out [[896/891]], 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1001/1000]] in the 13-limit.		189edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]]s [[3/1\|3]] and [[7/1\|7]] are about halfway between its steps. It has good approximations to [[5/1\|5]], [[9/1\|9]], [[11/1\|11]], [[19/1\|19]], and [[21/1\|21]], making it suitable for a 2.9.5.21.11.19 [[subgroup]] interpretation.

			Using the full 13-limit [[patent val]] nonetheless, the equal temperament [[tempering out\|tempers out]] 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| 53 -29 -3 }} in the 5-limit; [[4000/3969]], [[6144/6125]], and 537824/531441 in the 7-limit, supporting the [[hemikleismic]] temperament. It tempers out [[896/891]], 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1001/1000]] in the 13-limit.

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 189 factors into {{factorization\|189}}, 189edo contains {{EDOs\| 3, 7, 9, 21, 27, and 63 }} as its subsets.		Since 189 factors into {{factorization\|189}}, 189edo contains {{EDOs\| 3, 7, 9, 21, 27, and 63 }} as its subsets. [[378edo]], which doubles it, provides a good correction for the approximation of 3 and 7.

FloraC: Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories

2024-04-22T15:38:08Z

Adopt template: EDO intro; +prime error table; +subsets and supersets; -redundant categories

← Older revision		Revision as of 15:38, 22 April 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''189edo''' is the [[~~EDO\|equal division of the octave]] into 189 parts of 6.3492 cents each. It tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the [[Kleismic family\|hemikleismic temperament]]. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 in the 13-limit.		{{EDO intro}}

	[[~~Category:Equal divisions of the octave~~\|~~###~~]] <!-- 3-~~digit number~~ -->		The equal temperament [[tempering out\|tempers out]] 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; [[4000/3969]], [[6144/6125]], and 537824/531441 in the 7-limit, supporting the [[hemikleismic]] temperament. Using the [[patent val]], it tempers out [[896/891]], 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; [[169/168]], [[352/351]], [[364/363]], and [[1001/1000]] in the 13-limit.

			=== Odd harmonics ===
			{{Harmonics in equal\|189}}

			=== Subsets and supersets ===
			Since 189 factors into {{factorization\|189}}, 189edo contains {{EDOs\| 3, 7, 9, 21, 27, and 63 }} as its subsets.

Plumtree: Infobox ET added

2022-10-04T21:17:09Z

Infobox ET added

← Older revision		Revision as of 21:17, 4 October 2022
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			{{Infobox ET}}
	'''189edo''' is the [[EDO\|equal division of the octave]] into 189 parts of 6.3492 cents each. It tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the [[Kleismic family\|hemikleismic temperament]]. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 in the 13-limit.		'''189edo''' is the [[EDO\|equal division of the octave]] into 189 parts of 6.3492 cents each. It tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the [[Kleismic family\|hemikleismic temperament]]. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 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

2022-07-02T21:23:36Z

Sort key

← Older revision		Revision as of 21:23, 2 July 2022
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	'''189edo''' is the [[EDO\|equal division of the octave]] into 189 parts of 6.3492 cents each. It tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the [[Kleismic family\|hemikleismic temperament]]. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 in the 13-limit.		'''189edo''' is the [[EDO\|equal division of the octave]] into 189 parts of 6.3492 cents each. It tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the [[Kleismic family\|hemikleismic temperament]]. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 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

2020-12-04T23:13:14Z

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
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	'''189edo''' is the [[EDO\|equal division of the octave]] into 189 parts of 6.3492 cents each. It tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the [[Kleismic family\|hemikleismic temperament]]. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 in the 13-limit.		'''189edo''' is the [[EDO\|equal division of the octave]] into 189 parts of 6.3492 cents each. It tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the [[Kleismic family\|hemikleismic temperament]]. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 in the 13-limit.

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

Xenllium: Created page with "'''189edo''' is the equal division of the octave into 189 parts of 6.3492 cents each. It tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the..."

2019-03-17T00:10:57Z

Created page with "'''189edo''' is the equal division of the octave into 189 parts of 6.3492 cents each. It tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the..."

New page

'''189edo''' is the [[EDO|equal division of the octave]] into 189 parts of 6.3492 cents each. It tempers out 15625/15552 (kleisma) and 9007199254740992/8578797170610375 in the 5-limit; 4000/3969, 6144/6125, and 537824/531441 in the 7-limit, supporting the [[Kleismic family|hemikleismic temperament]]. Using the patent val, it tempers out 896/891, 1331/1323, 1375/1372, and 16896/16807 in the 11-limit; 169/168, 352/351, 364/363, and 1001/1000 in the 13-limit.

[[Category:Edo]]