578edo - Revision history

ArrowHead294 at 15:36, 20 February 2025

2025-02-20T15:36:25Z

← Older revision		Revision as of 15:36, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|578~~}}		{{ED intro}}

	578edo is [[enfactoring\|enfactored]] in the [[5-limit]], [[tempering out]] [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 118098/117649 (stearnsma) which together with the schisma gives 7-limit [[pogo]] temperament, the 224 & 354 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.		578edo is [[enfactoring\|enfactored]] in the [[5-limit]], [[tempering out]] [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 118098/117649 (stearnsma) which together with the schisma gives 7-limit [[pogo]] temperament, the 224 & 354 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.

Godtone at 17:39, 8 April 2024

2024-04-08T17:39:04Z

← Older revision		Revision as of 17:39, 8 April 2024
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	{{EDO intro\|578}}		{{EDO intro\|578}}

	578edo is [[enfactoring\|enfactored]] in the [[5-limit]], [[tempering out]] [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out ~~119098~~/117649 (stearnsma) which together with the schisma gives 7-limit [[pogo]] temperament, the 224 & 354 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.		578edo is [[enfactoring\|enfactored]] in the [[5-limit]], [[tempering out]] [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 118098/117649 (stearnsma) which together with the schisma gives 7-limit [[pogo]] temperament, the 224 & 354 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.

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

FloraC: Adopt template: Factorization

2023-11-02T13:39:27Z

Adopt template: Factorization

← Older revision		Revision as of 13:39, 2 November 2023
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	578 factors as ~~2 × 17<sup>2</sup>~~, with divisors 2, 17, 34, and 289.		578 factors as {{factorization\|578}}, with divisors {{EDOs\| 2, 17, 34, and 289 }}.

	[[Category:Swetismic]]		[[Category:Swetismic]]
	[[Category:Hades]]		[[Category:Hades]]
	[[Category:Pogo]]		[[Category:Pogo]]

FloraC: Correction (it doesn't support bisupermajor); sectioning; -redundant categories

2023-10-25T09:56:38Z

Correction (it doesn't support bisupermajor); sectioning; -redundant categories

← Older revision		Revision as of 09:56, 25 October 2023
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	{{EDO intro\|578}}		{{EDO intro\|578}}

	578edo is [[~~contorted~~]] in the [[5-limit]], tempering out [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out ~~10976~~/~~10935 ([[hemimage comma]]) and 65625/65536~~ (~~[[horwell comma]]~~) ~~in the [[7-limit]], supporting [[bisupermajor]], the 22 & 118 temperament, and 119098/117649~~ which together with the schisma gives 7-limit [[pogo]] temperament, the 94 & ~~130~~ temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.		578edo is [[enfactoring\|enfactored]] in the [[5-limit]], [[tempering out]] [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 119098/117649 (stearnsma) which together with the schisma gives 7-limit [[pogo]] temperament, the 224 & 354 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.

			=== Prime harmonics ===
			{{Harmonics in equal\|578\|columns=11}}

			=== Subsets and supersets ===
	578 factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289.		578 factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289.

	~~{{Harmonics in equal\|578\|columns=11}}~~

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

BudjarnLambeth at 06:40, 9 July 2023

2023-07-09T06:40:07Z

← Older revision		Revision as of 06:40, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|578}}		{{EDO intro\|578}}

BudjarnLambeth at 05:40, 9 July 2023

2023-07-09T05:40:04Z

← Older revision		Revision as of 05:40, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|578}}		{{EDO intro\|578}}

Plumtree: Infobox ET added

2022-10-04T21:59:31Z

Infobox ET added

← Older revision		Revision as of 21:59, 4 October 2022
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			{{Infobox ET}}
	{{EDO intro\|578}}		{{EDO intro\|578}}

FloraC: Cleanup; +prime error table

2022-08-17T18:45:33Z

Cleanup; +prime error table

← Older revision		Revision as of 18:45, 17 August 2022
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	~~The '''578 equal division''' divides the octave into~~ 578 ~~equal parts of 2.076 cents each. It~~ is [[contorted]] in the [[5-limit]], tempering out [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 10976/10935 ([[hemimage comma]]) and 65625/65536 ([[horwell comma]]) in the [[7-limit]], supporting [[~~Hemimage temperaments #Bisupermajor\|~~bisupermajor]], the 22&118 temperament, and 119098/117649 which together with the schisma gives 7-limit [[~~Schismatic family #Pogo\|~~pogo ~~temperament~~]], the 94&130 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[~~Swetismic temperaments #Hades\|~~hades]], as well as other temperaments tempering out 540/539, the rank ~~four~~ temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.		{{EDO intro\|578}}

			578edo is [[contorted]] in the [[5-limit]], tempering out [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 10976/10935 ([[hemimage comma]]) and 65625/65536 ([[horwell comma]]) in the [[7-limit]], supporting [[bisupermajor]], the 22 & 118 temperament, and 119098/117649 which together with the schisma gives 7-limit [[pogo]] temperament, the 94 & 130 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[hades]], as well as other temperaments tempering out 540/539, the rank-4 temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.

	578 factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289.		578 factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289.

			{{Harmonics in equal\|578\|columns=11}}

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

Fredg999 category edits: Sort key

2022-07-04T01:02:42Z

Sort key

← Older revision		Revision as of 01:02, 4 July 2022
Line 3:		Line 3:
	578 factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289.		578 factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289.

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

Cmloegcmluin: remove temporary link to defactoring

2021-11-12T23:08:12Z

remove temporary link to defactoring

← Older revision		Revision as of 23:08, 12 November 2021
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	The '''578 equal division''' divides the octave into 578 equal parts of 2.076 cents each. It is [[contorted]] ~~(or [[enfactored]])~~ in the [[5-limit]], tempering out [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 10976/10935 ([[hemimage comma]]) and 65625/65536 ([[horwell comma]]) in the [[7-limit]], supporting [[Hemimage temperaments #Bisupermajor\|bisupermajor]], the 22&118 temperament, and 119098/117649 which together with the schisma gives 7-limit [[Schismatic family #Pogo\|pogo temperament]], the 94&130 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[Swetismic temperaments #Hades\|hades]], as well as other temperaments tempering out 540/539, the rank four temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.		The '''578 equal division''' divides the octave into 578 equal parts of 2.076 cents each. It is [[contorted]] in the [[5-limit]], tempering out [[32805/32768]] (schisma) with the same tuning as [[289edo]]. It tempers out 10976/10935 ([[hemimage comma]]) and 65625/65536 ([[horwell comma]]) in the [[7-limit]], supporting [[Hemimage temperaments #Bisupermajor\|bisupermajor]], the 22&118 temperament, and 119098/117649 which together with the schisma gives 7-limit [[Schismatic family #Pogo\|pogo temperament]], the 94&130 temperament. In the [[11-limit]] it tempers out [[540/539]] and [[4000/3993]] and provides the [[optimal patent val]] for 11-limit pogo and the planar temperament [[Swetismic temperaments #Hades\|hades]], as well as other temperaments tempering out 540/539, the rank four temperament for which it also provides the optimal patent val. In the 13-limit, it tempers out [[729/728]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], and provides the optimal patent val for 13-limit pogo.

	578 factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289.		578 factors as 2 × 17<sup>2</sup>, with divisors 2, 17, 34, and 289.