156edo - Revision history

Godtone: /* Prime harmonics */ good 41-limit system

2025-05-06T18:01:44Z

Prime harmonics: good 41-limit system

← Older revision		Revision as of 18:01, 6 May 2025
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|156\|intervals=prime}}		{{Harmonics in equal\|156\|intervals=prime\|columns=13}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

VectorGraphics at 18:06, 23 April 2025

2025-04-23T18:06:37Z

← Older revision		Revision as of 18:06, 23 April 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Sinece 156 factors into {{factorization\|156}}, 156edo has subset edos {{EDOs\| 2, 3, 4, 6, 12, 13, 26, 39, 52, and 78 }}. It is the smallest edo to contain both [[12edo]] and [[13edo]] as subsets.		Sinece 156 factors into {{factorization\|156}}, 156edo has subset edos {{EDOs\| 2, 3, 4, 6, 12, 13, 26, 39, 52, and 78 }}. It is the smallest edo to contain both [[12edo]] and [[13edo]] as subsets.

			== Intervals ==
			{{Interval table}}

ArrowHead294 at 18:24, 20 February 2025

2025-02-20T18:24:56Z

← Older revision		Revision as of 18:24, 20 February 2025
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	{{ED intro}}		{{ED intro}}

	~~The equal temperament~~ [[tempering out\|tempers out]] 531441/524288 ([[Pythagorean comma]]) and {{monzo\| -27 -2 13 }} (ditonmic comma) in the 5-limit, as well as {{monzo\| 8 14 -13 }} ([[parakleisma]]); [[225/224]], [[250047/250000]], and [[589824/588245]] in the 7-limit. Using the patent val, it tempers out [[441/440]], 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out [[385/384]], [[540/539]], 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, [[847/845]], and [[1001/1000]] in the 13-limit. It [[support]]s [[compton]] and gives a good tuning for the 5- and 7-limit version thereof.		It [[tempering out\|tempers out]] 531441/524288 ([[Pythagorean comma]]) and {{monzo\| -27 -2 13 }} (ditonmic comma) in the 5-limit, as well as {{monzo\| 8 14 -13 }} ([[parakleisma]]); [[225/224]], [[250047/250000]], and [[589824/588245]] in the 7-limit. Using the patent val, it tempers out [[441/440]], 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out [[385/384]], [[540/539]], 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, [[847/845]], and [[1001/1000]] in the 13-limit. It [[support]]s [[compton]] and gives a good tuning for the 5- and 7-limit version thereof.

	=== Prime harmonics ===		=== Prime harmonics ===

Francium: changed EDO intro to ED intro

2025-02-19T18:00:39Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:00, 19 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	The equal temperament [[tempering out\|tempers out]] 531441/524288 ([[Pythagorean comma]]) and {{monzo\| -27 -2 13 }} (ditonmic comma) in the 5-limit, as well as {{monzo\| 8 14 -13 }} ([[parakleisma]]); [[225/224]], [[250047/250000]], and [[589824/588245]] in the 7-limit. Using the patent val, it tempers out [[441/440]], 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out [[385/384]], [[540/539]], 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, [[847/845]], and [[1001/1000]] in the 13-limit. It [[support]]s [[compton]] and gives a good tuning for the 5- and 7-limit version thereof.		The equal temperament [[tempering out\|tempers out]] 531441/524288 ([[Pythagorean comma]]) and {{monzo\| -27 -2 13 }} (ditonmic comma) in the 5-limit, as well as {{monzo\| 8 14 -13 }} ([[parakleisma]]); [[225/224]], [[250047/250000]], and [[589824/588245]] in the 7-limit. Using the patent val, it tempers out [[441/440]], 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out [[385/384]], [[540/539]], 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, [[847/845]], and [[1001/1000]] in the 13-limit. It [[support]]s [[compton]] and gives a good tuning for the 5- and 7-limit version thereof.

FloraC: More rework and give more context

2024-05-11T09:10:46Z

More rework and give more context

← Older revision		Revision as of 09:10, 11 May 2024
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	{{EDO intro}}		{{EDO intro}}

	~~It supports [[compton]]. It is the smallest edo to contain both [[12edo]] and [[13edo]] as subsets.~~		The equal temperament [[tempering out\|tempers out]] 531441/524288 ([[Pythagorean comma]]) and {{monzo\| -27 -2 13 }} (ditonmic comma) in the 5-limit, as well as {{monzo\| 8 14 -13 }} ([[parakleisma]]); [[225/224]], [[250047/250000]], and [[589824/588245]] in the 7-limit. Using the patent val, it tempers out [[441/440]], 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out [[385/384]], [[540/539]], 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, [[847/845]], and [[1001/1000]] in the 13-limit. It [[support]]s [[compton]] and gives a good tuning for the 5- and 7-limit version thereof.

	The equal temperament [[tempering out\|tempers out]] 531441/524288 ([[Pythagorean comma]]) and ~~1220703125/1207959552~~ (ditonmic comma) in the 5-limit, as well as ~~1224440064/1220703125~~ ([[parakleisma]]); [[225/224]], [[250047/250000]], and [[589824/588245]] in the 7-limit. Using the patent val, it tempers out [[441/440]], 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out [[385/384]], [[540/539]], 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, [[847/845]], and [[1001/1000]] in the 13-limit.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|156\|intervals=prime}}		{{Harmonics in equal\|156\|intervals=prime}}

	{{~~stub~~}}		=== Subsets and supersets ===
	[[~~Category:Equal divisions of the octave\|###~~]] ~~<!-- 3-digit number -->~~		Sinece 156 factors into {{factorization\|156}}, 156edo has subset edos {{EDOs\| 2, 3, 4, 6, 12, 13, 26, 39, 52, and 78 }}. It is the smallest edo to contain both [[12edo]] and [[13edo]] as subsets.

FloraC: Linking; style; switch to prime harmonics since the odd harmonics table doesn't add much; -redundant categories

2024-05-11T09:06:55Z

Linking; style; switch to prime harmonics since the odd harmonics table doesn't add much; -redundant categories

← Older revision		Revision as of 09:06, 11 May 2024
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	{{EDO intro}}		{{EDO intro}}

	It supports [[compton]] ~~temperament~~. It is the smallest ~~EDO~~ to contain both [[12edo]] and [[13edo]] as subsets.		It supports [[compton]]. It is the smallest edo to contain both [[12edo]] and [[13edo]] as subsets.

	It tempers out 531441/524288 (~~pythagorean~~ comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.		The equal temperament [[tempering out\|tempers out]] 531441/524288 ([[Pythagorean comma]]) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 ([[parakleisma]]); [[225/224]], [[250047/250000]], and [[589824/588245]] in the 7-limit. Using the patent val, it tempers out [[441/440]], 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; [[351/350]], [[364/363]], [[625/624]], 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out [[385/384]], [[540/539]], 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, [[847/845]], and [[1001/1000]] in the 13-limit.

	== ~~Harmonics~~ ==		=== Prime harmonics ===
	{{Harmonics in equal\|156}}		{{Harmonics in equal\|156\|intervals=prime}}

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

BudjarnLambeth at 02:14, 30 January 2024

2024-01-30T02:14:30Z

← Older revision		Revision as of 02:14, 30 January 2024
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	{{EDO intro}}		{{EDO intro}}

	It supports [[compton]] temperament.		It supports [[compton]] temperament. It is the smallest EDO to contain both [[12edo]] and [[13edo]] as subsets.

	It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.		It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.

BudjarnLambeth: harmonics

2024-01-30T02:13:23Z

harmonics

← Older revision		Revision as of 02:13, 30 January 2024
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	It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.		It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.

			== Harmonics ==
			{{Harmonics in equal\|156}}

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

BudjarnLambeth: Added edo intro

2024-01-30T02:12:59Z

Added edo intro

← Older revision		Revision as of 02:12, 30 January 2024
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	{{Infobox ET}}		{{Infobox ET}}
	~~'''156edo''' is the~~ [[~~EDO\|equal division of the octave~~]] ~~into 156 parts of 7.6923 cents each~~. It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.		{{EDO intro}}

			It supports [[compton]] temperament.

			It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.
	{{stub}}		{{stub}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->

BudjarnLambeth: Marked as stub

2024-01-04T01:52:06Z

Marked as stub

← Older revision		Revision as of 01:52, 4 January 2024
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	{{Infobox ET}}		{{Infobox ET}}
	'''156edo''' is the [[EDO\|equal division of the octave]] into 156 parts of 7.6923 cents each. It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.		'''156edo''' is the [[EDO\|equal division of the octave]] into 156 parts of 7.6923 cents each. It tempers out 531441/524288 (pythagorean comma) and 1220703125/1207959552 (ditonmic comma) in the 5-limit, as well as 1224440064/1220703125 (parakleisma); 225/224, 250047/250000, and 589824/588245 in the 7-limit. Using the patent val, it tempers out 441/440, 1375/1372, 4375/4356, and 65536/65219 in the 11-limit; 351/350, 364/363, 625/624, 1625/1617, and 13122/13013 in the 13-limit. Using the 156e val, it tempers out 385/384, 540/539, 1331/1323, and 78408/78125 in the 11-limit; 351/350, 625/624, 847/845, and 1001/1000 in the 13-limit.
			{{stub}}
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->