1778edo - Revision history

ArrowHead294 at 23:05, 20 February 2025

2025-02-20T23:05:05Z

← Older revision		Revision as of 23:05, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1778~~}}		{{ED intro}}

	1778edo is [[consistent]] to the [[9-odd-limit]], but the errors of both [[harmonic]]s [[5/1\|5]] and [[7/1\|7]] are quite large. It is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[889edo]], [[tempering out\|tempering out]] {{monzo\| -29 -11 20 }} (gammic comma) and {{monzo\| -69 45 -1 }} ([[counterschisma]]). In the 7-limit, the equal temperament tempers out 2401/2400 ([[breedsma]]) and 48828125/48771072 (neptunisma). It provides the [[optimal patent val]] for the 7-limit [[neptune]] temperament.		1778edo is [[consistent]] to the [[9-odd-limit]], but the errors of both [[harmonic]]s [[5/1\|5]] and [[7/1\|7]] are quite large. It is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[889edo]], [[tempering out\|tempering out]] {{monzo\| -29 -11 20 }} (gammic comma) and {{monzo\| -69 45 -1 }} ([[counterschisma]]). In the 7-limit, the equal temperament tempers out 2401/2400 ([[breedsma]]) and 48828125/48771072 (neptunisma). It provides the [[optimal patent val]] for the 7-limit [[neptune]] temperament.

2023-10-30T13:20:31Z

Expand; +subsets and supersets

← Older revision		Revision as of 13:20, 30 October 2023
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	{{EDO intro\|1778}}		{{EDO intro\|1778}}

	~~Prime harmonics with less than~~ 1 ~~standard deviation~~ in ~~1778edo are: 2~~, 3, 11, ~~23, 43, 47, 61~~. ~~As such, it is best~~ for ~~use with~~ the ~~2.3.11.23.43.47.61~~ [[~~subgroup~~]].		1778edo is [[consistent]] to the [[9-odd-limit]], but the errors of both [[harmonic]]s [[5/1\|5]] and [[7/1\|7]] are quite large. It is [[enfactoring\|enfactored]] in the 5-limit, with the same tuning as [[889edo]], [[tempering out\|tempering out]] {{monzo\| -29 -11 20 }} (gammic comma) and {{monzo\| -69 45 -1 }} ([[counterschisma]]). In the 7-limit, the equal temperament tempers out 2401/2400 ([[breedsma]]) and 48828125/48771072 (neptunisma). It provides the [[optimal patent val]] for the 7-limit [[neptune]] temperament.

	~~In the 7-limit~~ it ~~provides the [[optimal patent val]]~~ for ~~the~~ [[~~neptune~~]] ~~temperament~~.		For higher harmonics, it is suitable for a 2.3.11.19.23.43.47.61 [[subgroup]] interpretation.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|1778}}		{{Harmonics in equal\|1778}}

			=== Subsets and supersets ===
			Since 1778 factors into {{factorization\|1778}}, 1778edo has subset edos {{EDOs\| 2, 7, 14, 127, 254, and 889 }}.

	[[Category:Neptune]]		[[Category:Neptune]]

2023-10-15T14:45:22Z

Cleanup and +categories

← Older revision		Revision as of 14:45, 15 October 2023
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	{{Infobox ET}}		{{Infobox ET}}
			{{EDO intro\|1778}}

			Prime harmonics with less than 1 standard deviation in 1778edo are: 2, 3, 11, 23, 43, 47, 61. As such, it is best for use with the 2.3.11.23.43.47.61 [[subgroup]].

	~~{{EDO intro\|1778}}~~		In the 7-limit it provides the [[optimal patent val]] for the [[neptune]] temperament.

	== ~~Theory~~ ==		=== Odd harmonics ===
	{{Harmonics in equal\|1778}}		{{Harmonics in equal\|1778}}
	~~Prime harmonics with less than 1 standard deviation in 1778edo are: 2, 3, 11, 23, 43, 47, 61. As such, it is best for use with the 2.3.11.23.43.47.61 subgroup.~~

	~~In the 7-limit, in which it is consistent, it provides the optimal patent val for the [[neptune]] temperament.~~

	[[Category:~~Equal divisions of the octave\|####~~]] ~~<!-- 4-digit number -->~~		[[Category:Neptune]]

2023-07-09T06:56:48Z

2023-07-09T04:53:40Z

2022-10-04T19:25:55Z

Infobox ET now computes most parameters automatically

2022-07-04T01:17:24Z

2022-05-04T11:17:47Z

2022-05-04T11:17:33Z

recalculated the consistency limit

← Older revision		Revision as of 11:17, 4 May 2022
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			{{Infobox ET\|
			\|Prime factorization = 2 × 7 × 127
			\|Step size = 0.6749¢
			\|Fifth=1040\1778 (520\889)
			\|Consistency limit=7
			}}

	{{EDO intro\|1778}}		{{EDO intro\|1778}}

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	Prime harmonics with less than 1 standard deviation in 1778edo are: 2, 3, 11, 23, 43, 47, 61. As such, it is best for use with the 2.3.11.23.43.47.61 subgroup.		Prime harmonics with less than 1 standard deviation in 1778edo are: 2, 3, 11, 23, 43, 47, 61. As such, it is best for use with the 2.3.11.23.43.47.61 subgroup.

	In the 7-limit, it provides the optimal patent val for the [[neptune]] temperament.		In the 7-limit, in which it is consistent, it provides the optimal patent val for the [[neptune]] temperament.

2022-05-03T23:07:49Z

Theory

← Older revision		Revision as of 23:07, 3 May 2022
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	{{Harmonics in equal\|1778}}		{{Harmonics in equal\|1778}}
	Prime harmonics with less than 1 standard deviation in 1778edo are: 2, 3, 11, 23, 43, 47, 61. As such, it is best for use with the 2.3.11.23.43.47.61 subgroup.		Prime harmonics with less than 1 standard deviation in 1778edo are: 2, 3, 11, 23, 43, 47, 61. As such, it is best for use with the 2.3.11.23.43.47.61 subgroup.

	~~Nonetheless, 1778edo is consistent in the 23-limit, and thus is open to simpler interpretations.~~

	In the 7-limit, it provides the optimal patent val for the [[neptune]] temperament.		In the 7-limit, it provides the optimal patent val for the [[neptune]] temperament.

← Older revision		Revision as of 01:17, 4 July 2022
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	In the 7-limit, in which it is consistent, it provides the optimal patent val for the [[neptune]] temperament.		In the 7-limit, in which it is consistent, it provides the optimal patent val for the [[neptune]] temperament.

			[[Category:Equal divisions of the octave\|####]] <!-- 4-digit number -->