410edo - Revision history

FloraC: Update

2026-08-10T13:09:39Z

Update

← Older revision		Revision as of 13:09, 10 August 2026
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	== Theory ==		== Theory ==
	410edo is [[enfactored]] in the [[5-limit]], with the same tuning as [[205edo]] characterized by [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo\| -29 -11 20 }} (gammic comma) and {{monzo\| 47 -15 -10 }} (quintosec comma), but the approximations to [[harmonic]]s [[7/1\|7]] and [[13/1\|13]] are much improved. It tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[~~canousma~~]]), and 48828125/48771072 (neptunisma) in the [[7-limit]]; [[5632/5625]], [[9801/9800]], [[14641/14580]], and 117649/117612 in the [[11-limit]]; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.		410edo is [[enfactored]] in the [[5-limit]], with the same tuning as [[205edo]] characterized by [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo\| -29 -11 20 }} (gammic comma) and {{monzo\| 47 -15 -10 }} (quintosec comma), but the approximations to [[harmonic]]s [[7/1\|7]] and [[13/1\|13]] are much improved. It tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[cathartic comma]]), and 48828125/48771072 (neptunisma) in the [[7-limit]]; [[5632/5625]], [[9801/9800]], [[14641/14580]], and 117649/117612 in the [[11-limit]]; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.

	410edo provides the [[optimal patent val]] for the 11- and 13-limit [[semiluna]], [[hemiluna]], and [[floral]] temperaments, the rank-3 [[~~semicanou~~]] temperament, and the rank-4 temperament tempering out 14641/14580.		410edo provides the [[optimal patent val]] for the 11- and 13-limit [[semiluna]], [[hemiluna]], and [[floral]] temperaments, the rank-3 [[semicathart]] temperament, and the rank-4 temperament tempering out 14641/14580.

	410edo works much better as a no-11 no-13 [[subgroup]] temperament, with a sharp tendency to harmonics up to 29. For example, it tempers out [[1216/1215]], [[1225/1224]], [[1445/1444]], and [[2500/2499]] in the 2.3.5.7.17.19 subgroup.		410edo works much better as a no-11 no-13 [[subgroup]] temperament, with a sharp tendency to harmonics up to 29. For example, it tempers out [[1216/1215]], [[1225/1224]], [[1445/1444]], and [[2500/2499]] in the 2.3.5.7.17.19 subgroup.
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	* [https://www.youtube.com/watch?v=-bm5UdmveZU ''All Time Best''] – decoid[40], cover of [[Phlub]]		* [https://www.youtube.com/watch?v=-bm5UdmveZU ''All Time Best''] – decoid[40], cover of [[Phlub]]

			[[Category:Hemiluna]]
			[[Category:Semiluna]]
	[[Category:Cathartic]]		[[Category:Cathartic]]
	[[Category:~~Hemiluna~~]]		[[Category:Semicathart]]
			[[Category:Semicathartismic]]
	[[Category:Listen]]		[[Category:Listen]]
	~~[[Category:Semicanou]]~~
	~~[[Category:Semicathartismic]]~~
	~~[[Category:Semiluna]]~~

FloraC: Text replacement - "Category:Semicanousmic" to "Category:Semicathartismic"

2026-08-10T12:57:38Z

Text replacement - "Category:Semicanousmic" to "Category:Semicathartismic"

← Older revision		Revision as of 12:57, 10 August 2026
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	[[Category:Listen]]		[[Category:Listen]]
	[[Category:Semicanou]]		[[Category:Semicanou]]
	[[Category:~~Semicanousmic~~]]		[[Category:Semicathartismic]]
	[[Category:Semiluna]]		[[Category:Semiluna]]

FloraC: Text replacement - "Category:Canou" to "Category:Cathartic"

2026-08-10T12:57:12Z

Text replacement - "Category:Canou" to "Category:Cathartic"

← Older revision		Revision as of 12:57, 10 August 2026
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	* [https://www.youtube.com/watch?v=-bm5UdmveZU ''All Time Best''] – decoid[40], cover of [[Phlub]]		* [https://www.youtube.com/watch?v=-bm5UdmveZU ''All Time Best''] – decoid[40], cover of [[Phlub]]

	[[Category:~~Canou~~]]		[[Category:Cathartic]]
	[[Category:Hemiluna]]		[[Category:Hemiluna]]
	[[Category:Listen]]		[[Category:Listen]]

Fredg999: Update link

2026-07-08T04:06:15Z

Update link

← Older revision		Revision as of 04:06, 8 July 2026
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	\| 582.44		\| 582.44
	\| 7/5		\| 7/5
	\| [[Neptune]]		\| [[Neptune (temperament)\|Neptune]]
	\|-		\|-
	\| 2		\| 2

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:38:13Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:38, 13 March 2026
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	\| [[Hemicountercomp]]		\| [[Hemicountercomp]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[normal ~~lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

ArrowHead294 at 19:27, 20 February 2025

2025-02-20T19:27:42Z

← Older revision		Revision as of 19:27, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|410~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Regular temperament properties */ cleanup

2025-02-06T10:10:54Z

Regular temperament properties: cleanup

← Older revision		Revision as of 10:10, 6 February 2025
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	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[Comma list]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal<br />8ve stretch (¢)		! rowspan="2" \| Optimal<br>8ve stretch (¢)
	! colspan="2" \| Tuning error		! colspan="2" \| Tuning error
	\|-		\|-
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	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 1600000/1594323, 48828125/48771072		\| 2401/2400, 1600000/1594323, 48828125/48771072
	\| {{~~mapping~~\| 410 650 952 1151 }}		\| {{Mapping\| 410 650 952 1151 }}
	\| −0.0753		\| −0.0753
	\| 0.1332		\| 0.1332
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	\| 2.3.5.7.17		\| 2.3.5.7.17
	\| 1225/1224, 2401/2400, 24576/24565, 295936/295245		\| 1225/1224, 2401/2400, 24576/24565, 295936/295245
	\| {{~~mapping~~\| 410 650 952 1151 1676 }}		\| {{Mapping\| 410 650 952 1151 1676 }}
	\| −0.0803		\| −0.0803
	\| 0.1196		\| 0.1196
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	\| 2.3.5.7.17.19		\| 2.3.5.7.17.19
	\| 1216/1215, 1225/1224, 1445/1444, 2401/2400, 24576/24565		\| 1216/1215, 1225/1224, 1445/1444, 2401/2400, 24576/24565
	\| {{~~mapping~~\| 410 650 952 1151 1676 1742 }}		\| {{Mapping\| 410 650 952 1151 1676 1742 }}
	\| −0.1071		\| −0.1071
	\| 0.1245		\| 0.1245
	\| 4.25		\| 4.25
	~~{{comma basis end}~~}		\|}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
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	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\|-		\|-
	\| 10		\| 10
	\| 85\410<br />(3\410)		\| 85\410<br>(3\410)
	\| 248.78<br />(8.78)		\| 248.78<br>(8.78)
	\| 15/13<br />(176/175)		\| 15/13<br>(176/175)
	\| [[Decoid]]		\| [[Decoid]]
	\|-		\|-
	\| 41		\| 41
	\| 61\410<br />(1\410)		\| 61\410<br>(1\410)
	\| 178.54<br />(2.93)		\| 178.54<br/>(2.93)
	\| 567/512<br />(352/351)		\| 567/512<br>(352/351)
	\| [[Hemicountercomp]]		\| [[Hemicountercomp]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal~~ lists\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==

FloraC: /* Theory */ cleanup

2025-01-17T16:13:29Z

Theory: cleanup

← Older revision		Revision as of 16:13, 17 January 2025
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	== Theory ==		== Theory ==
	410edo is [[enfactored]] in the [[5-limit]], with the same tuning as [[205edo]] characterized by [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo\| -29 -11 20 }} (gammic comma) and {{monzo\| 47 -15 -10 }} (quintosec comma), but the approximations to [[harmonic]]s [[7/1\|7]] and [[13/1\|13]] are much improved. It [[tempers out]] 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), and 48828125/48771072 (neptunisma) in the [[7-limit]]; [[5632/5625]], [[9801/9800]], [[14641/14580]], and 117649/117612 in the [[11-limit]]; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.		410edo is [[enfactored]] in the [[5-limit]], with the same tuning as [[205edo]] characterized by [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo\| -29 -11 20 }} (gammic comma) and {{monzo\| 47 -15 -10 }} (quintosec comma), but the approximations to [[harmonic]]s [[7/1\|7]] and [[13/1\|13]] are much improved. It tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), and 48828125/48771072 (neptunisma) in the [[7-limit]]; [[5632/5625]], [[9801/9800]], [[14641/14580]], and 117649/117612 in the [[11-limit]]; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.

	410edo provides the [[optimal patent val]] for the 11- and 13-limit [[semiluna]], [[hemiluna]], and [[floral]] temperaments, the rank-3 [[semicanou]] temperament, and the rank-4 temperament tempering out 14641/14580.		410edo provides the [[optimal patent val]] for the 11- and 13-limit [[semiluna]], [[hemiluna]], and [[floral]] temperaments, the rank-3 [[semicanou]] temperament, and the rank-4 temperament tempering out 14641/14580.
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|410~~\|columns=11~~}}		{{Harmonics in equal\|410}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 410 factors into ~~{{factorization\|410}}~~, 410edo has subset edos {{EDOs\| 2, 5, 10, 41, 82, and 205 }}. Meanwhile, as every sixth step of [[2460edo]], a step of 410edo is exactly 6 [[mina]]s.		Since 410 factors into 2 × 5 × 41, 410edo has subset edos {{EDOs\| 2, 5, 10, 41, 82, and 205 }}. Meanwhile, as every sixth step of [[2460edo]], a step of 410edo is exactly 6 [[mina]]s.

	== Regular temperament properties ==		== Regular temperament properties ==

ArrowHead294 at 14:57, 16 January 2025

2025-01-16T14:57:44Z

← Older revision		Revision as of 14:57, 16 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	410edo is [[~~enfactoring\|~~enfactored]] in the [[5-limit]], with the same tuning as [[205edo]] characterized by [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo\| -29 -11 20 }} (gammic comma) and {{monzo\| 47 -15 -10 }} (quintosec comma), but the approximations to [[harmonic]]s [[7/1\|7]] and [[13/1\|13]] are much improved. ~~The equal temperament~~ tempers out 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), and 48828125/48771072 (neptunisma) in the [[7-limit]]; [[5632/5625]], [[9801/9800]], [[14641/14580]], and 117649/117612 in the [[11-limit]]; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.		410edo is [[enfactored]] in the [[5-limit]], with the same tuning as [[205edo]] characterized by [[tempering out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 38 -2 -15 }} (luna/hemithirds comma), as well as {{monzo\| -29 -11 20 }} (gammic comma) and {{monzo\| 47 -15 -10 }} (quintosec comma), but the approximations to [[harmonic]]s [[7/1\|7]] and [[13/1\|13]] are much improved. It [[tempers out]] 2401/2400 ([[breedsma]]), 4802000/4782969 ([[canousma]]), and 48828125/48771072 (neptunisma) in the [[7-limit]]; [[5632/5625]], [[9801/9800]], [[14641/14580]], and 117649/117612 in the [[11-limit]]; [[676/675]], [[1001/1000]], [[1716/1715]], [[2080/2079]], [[4096/4095]], and [[4225/4224]] in the 13-limit.

	410edo provides the [[optimal patent val]] for the 11- and 13-limit [[semiluna]], [[hemiluna]], and [[floral]] temperaments, the rank-3 [[semicanou]] temperament, and the rank-4 temperament tempering out 14641/14580.		410edo provides the [[optimal patent val]] for the 11- and 13-limit [[semiluna]], [[hemiluna]], and [[floral]] temperaments, the rank-3 [[semicanou]] temperament, and the rank-4 temperament tempering out 14641/14580.
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	\| 2401/2400, 1600000/1594323, 48828125/48771072		\| 2401/2400, 1600000/1594323, 48828125/48771072
	\| {{mapping\| 410 650 952 1151 }}		\| {{mapping\| 410 650 952 1151 }}
	\| ~~−0~~.0753		\| −0.0753
	\| 0.1332		\| 0.1332
	\| 4.55		\| 4.55
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	\| 1225/1224, 2401/2400, 24576/24565, 295936/295245		\| 1225/1224, 2401/2400, 24576/24565, 295936/295245
	\| {{mapping\| 410 650 952 1151 1676 }}		\| {{mapping\| 410 650 952 1151 1676 }}
	\| ~~−0~~.0803		\| −0.0803
	\| 0.1196		\| 0.1196
	\| 4.09		\| 4.09
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	\| 1216/1215, 1225/1224, 1445/1444, 2401/2400, 24576/24565		\| 1216/1215, 1225/1224, 1445/1444, 2401/2400, 24576/24565
	\| {{mapping\| 410 650 952 1151 1676 1742 }}		\| {{mapping\| 410 650 952 1151 1676 1742 }}
	\| ~~−0~~.1071		\| −0.1071
	\| 0.1245		\| 0.1245
	\| 4.25		\| 4.25
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	\| [[Hemicountercomp]]		\| [[Hemicountercomp]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if ~~it is~~ distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	== Scales ==		== Scales ==
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	== Music ==		== Music ==
	; [[Mercury Amalgam]] (2023)		; [[Mercury Amalgam]] (2023)
	* [https://www.youtube.com/watch?v=-bm5UdmveZU ''All Time Best''] ~~–~~ decoid[40], cover of [[Phlub]]		* [https://www.youtube.com/watch?v=-bm5UdmveZU ''All Time Best''] – decoid[40], cover of [[Phlub]]

	[[Category:Canou]]		[[Category:Canou]]

ArrowHead294: No longer needed

2024-12-23T15:32:55Z

No longer needed

← Older revision		Revision as of 15:32, 23 December 2024
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	\| 567/512<br />(352/351)		\| 567/512<br />(352/351)
	\| [[Hemicountercomp]]		\| [[Hemicountercomp]]
	~~{{rank-2 end}~~}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct