3776edo - Revision history

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"

2026-03-13T13:31:41Z

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 13:31, 13 March 2026
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	\| [[Oganesson]]		\| [[Oganesson]]
	\|}		\|}
	<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

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

ArrowHead294 at 23:15, 20 February 2025

2025-02-20T23:15:18Z

← Older revision		Revision as of 23:15, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|3776~~}}		{{ED intro}}
	==Theory==		== Theory ==
	3776edo is a good 2.3.11.13.19 subgroup system. It does not tune the [[15-odd-limit]] consistently, though a reasonable represenation exists through the 19-limit patent val. There, it provides the [[optimal patent val]] for the [[oganesson]] temperament in the 7-, 11-, 13-, 17-, and the 19-limit. It tempers out the [[quartisma]] in the 11-limit, and is a tuning for the rank-3 [[van gogh]] temperament.		3776edo is a good 2.3.11.13.19 subgroup system. It does not tune the [[15-odd-limit]] consistently, though a reasonable represenation exists through the 19-limit patent val. There, it provides the [[optimal patent val]] for the [[oganesson]] temperament in the 7-, 11-, 13-, 17-, and the 19-limit. It tempers out the [[quartisma]] in the 11-limit, and is a tuning for the rank-3 [[van gogh]] temperament.

	In the 19-limit, and 2.3.5.17.19 subgroup, 3776edo tempers out the comma that associates [[171/170]] to 1 step of 118edo, hence enabling usage of this interval as microchroma. This is strengthened by 3776edo's strong and consistent approximations of [[19/17]] and [[10/9]], intervals that are one 171/170 apart.		In the 19-limit, and 2.3.5.17.19 subgroup, 3776edo tempers out the comma that associates [[171/170]] to 1 step of 118edo, hence enabling usage of this interval as microchroma. This is strengthened by 3776edo's strong and consistent approximations of [[19/17]] and [[10/9]], intervals that are one 171/170 apart.

	=== Odd harmonics ===		=== Odd harmonics ===
	{{harmonics in equal\|3776}}		{{harmonics in equal\|3776}}
Line 14:		Line 15:

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

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	!Periods<br>per 8ve		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	!Generator~~<br>(reduced)~~		\|-
	!Cents~~<br>(reduced)~~		! Periods<br />per 8ve
	!Associated<br>ratio		! Generator*
	!Temperaments		! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\|118		\| 118
	\|1781\3776<br>(21\3776)		\| 1781\3776<br>(21\3776)
	\|565.995<br>(6.67)		\| 565.995<br>(6.67)
	\|165/119<br>(?)		\| 165/119<br>(?)
	\|[[Oganesson]]		\| [[Oganesson]]
	\|}		\|}
			<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

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

Eliora at 00:34, 1 September 2024

2024-09-01T00:34:54Z

← Older revision		Revision as of 00:34, 1 September 2024
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	{{15-odd-limit\|3776\|19}}		{{15-odd-limit\|3776\|19}}

			=== Subsets and supersets ===
			Since 3776 factors as {{Factorization\|3776}}, 3776edo has subset edos {{EDOs\|2, 4, 8, 16, 32, 59, 64, 118, 236, 472, 944, 1888}}, of which [[16edo]], [[118edo]] and [[472edo]] are particularly notable.

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

Eliora at 16:09, 27 August 2024

2024-08-27T16:09:02Z

← Older revision		Revision as of 16:09, 27 August 2024
Line 2:		Line 2:
	{{EDO intro\|3776}}		{{EDO intro\|3776}}
	==Theory==		==Theory==
	3776edo is a good 2.3.11.13.19 subgroup system. It does not tune the [[15-odd-limit]] consistently, though a reasonable represenation exists through the 19-limit patent val. There, it provides the [[optimal patent val]] for the [[oganesson]] temperament in the 7-, 11-, 13-, 17-, and the 19-limit.		3776edo is a good 2.3.11.13.19 subgroup system. It does not tune the [[15-odd-limit]] consistently, though a reasonable represenation exists through the 19-limit patent val. There, it provides the [[optimal patent val]] for the [[oganesson]] temperament in the 7-, 11-, 13-, 17-, and the 19-limit. It tempers out the [[quartisma]] in the 11-limit, and is a tuning for the rank-3 [[van gogh]] temperament.

	It tempers out the [[~~quartisma~~]] ~~in the 11-limit~~, and ~~is a tuning for the rank-3~~ [[~~van gogh~~]] ~~temperament~~.		In the 19-limit, and 2.3.5.17.19 subgroup, 3776edo tempers out the comma that associates [[171/170]] to 1 step of 118edo, hence enabling usage of this interval as microchroma. This is strengthened by 3776edo's strong and consistent approximations of [[19/17]] and [[10/9]], intervals that are one 171/170 apart.
	=== Odd harmonics ===		=== Odd harmonics ===
	{{harmonics in equal\|3776}}		{{harmonics in equal\|3776}}

Eliora at 16:03, 27 August 2024

2024-08-27T16:03:06Z

← Older revision		Revision as of 16:03, 27 August 2024
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	{{harmonics in equal\|3776}}		{{harmonics in equal\|3776}}

	~~[[Category:Equal divisions of the octave~~\|~~####]]~~		{{15-odd-limit\|3776\|19}}

	== Regular temperament properties ==		== Regular temperament properties ==
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	\|165/119<br>(?)		\|165/119<br>(?)
	\|[[Oganesson]]		\|[[Oganesson]]
	\|}<!-- 4-digit number -->		\|}

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

Eliora: /* Theory */

2024-03-21T17:58:31Z

Theory

← Older revision		Revision as of 17:58, 21 March 2024
Line 4:		Line 4:
	3776edo is a good 2.3.11.13.19 subgroup system. It does not tune the [[15-odd-limit]] consistently, though a reasonable represenation exists through the 19-limit patent val. There, it provides the [[optimal patent val]] for the [[oganesson]] temperament in the 7-, 11-, 13-, 17-, and the 19-limit.		3776edo is a good 2.3.11.13.19 subgroup system. It does not tune the [[15-odd-limit]] consistently, though a reasonable represenation exists through the 19-limit patent val. There, it provides the [[optimal patent val]] for the [[oganesson]] temperament in the 7-, 11-, 13-, 17-, and the 19-limit.

	It tempers out the [[quartisma]] in the 11-limit, and is a tuning for the rank-3 ~~Van Gogh~~ temperament.		It tempers out the [[quartisma]] in the 11-limit, and is a tuning for the rank-3 [[van gogh]] temperament.
	=== Odd harmonics ===		=== Odd harmonics ===
	{{harmonics in equal\|3776}}		{{harmonics in equal\|3776}}

Eliora: /* Theory */ cleanup

2023-08-09T10:30:37Z

Theory: cleanup

← Older revision		Revision as of 10:30, 9 August 2023
Line 2:		Line 2:
	{{EDO intro\|3776}}		{{EDO intro\|3776}}
	==Theory==		==Theory==
	3776edo is a good 2.3.11.13.19. system. It does not tune the [[15-odd-limit]] consistently, though a reasonable represenation exists through the 19-limit patent val, ~~where~~ it ~~is a tuning~~ for the [[oganesson]] temperament in the 19-~~limit~~, ~~which sets 1/118th of the octave to an interval that represents 169/168~~, ~~170/169~~, and ~~171/170 tempered together~~.		3776edo is a good 2.3.11.13.19 subgroup system. It does not tune the [[15-odd-limit]] consistently, though a reasonable represenation exists through the 19-limit patent val. There, it provides the [[optimal patent val]] for the [[oganesson]] temperament in the 7-, 11-, 13-, 17-, and the 19-limit.

	It tempers out the [[quartisma]] in the 11-limit, and is a tuning for the rank-3 Van Gogh temperament.		It tempers out the [[quartisma]] in the 11-limit, and is a tuning for the rank-3 Van Gogh temperament.

BudjarnLambeth at 07:06, 9 July 2023

2023-07-09T07:06:09Z

← Older revision		Revision as of 07:06, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|3776}}		{{EDO intro\|3776}}
	==Theory==		==Theory==

BudjarnLambeth at 04:27, 9 July 2023

2023-07-09T04:27:42Z

← Older revision		Revision as of 04:27, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|3776}}		{{EDO intro\|3776}}
	==Theory==		==Theory==

Eliora: /* Theory */

2023-06-10T14:16:42Z

Theory

← Older revision		Revision as of 14:16, 10 June 2023
Line 2:		Line 2:
	{{EDO intro\|3776}}		{{EDO intro\|3776}}
	==Theory==		==Theory==
	3776edo is a tuning for the [[oganesson]] temperament in the 17-limit, which sets 1/118th of the octave to an interval that represents 169/168~170/169 tempered together.		3776edo is a good 2.3.11.13.19. system. It does not tune the [[15-odd-limit]] consistently, though a reasonable represenation exists through the 19-limit patent val, where it is a tuning for the [[oganesson]] temperament in the 19-limit, which sets 1/118th of the octave to an interval that represents 169/168, 170/169, and 171/170 tempered together.

	It tempers out the [[quartisma]] in the 11-limit, and is a tuning for the rank-3 Van Gogh temperament.		It tempers out the [[quartisma]] in the 11-limit, and is a tuning for the rank-3 Van Gogh temperament.

	~~While it does tune both 13th and 17th prime harmonic resonably, it is no longer consistent in the [[15-odd-limit]].~~
	=== Odd harmonics ===		=== Odd harmonics ===
	{{harmonics in equal\|3776}}		{{harmonics in equal\|3776}}