2814edo - 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"

2026-03-13T13:32:57Z

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 13:32, 13 March 2026
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	\| [[Double bastille]]		\| [[Double bastille]]
	\|}		\|}
	<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:Jacobin]]		[[Category:Jacobin]]

ArrowHead294 at 23:08, 20 February 2025

2025-02-20T23:08:04Z

← Older revision		Revision as of 23:08, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|2814~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:01, 15 January 2025

2025-01-15T16:01:30Z

← Older revision		Revision as of 16:01, 15 January 2025
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	\| [[Double bastille]]		\| [[Double bastille]]
	\|}		\|}
	<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

	[[Category:Jacobin]]		[[Category:Jacobin]]

ArrowHead294: Partial undo

2024-11-16T13:22:38Z

Partial undo

← Older revision		Revision as of 13:22, 16 November 2024
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	Note: 7-limit temperaments represented by [[1407edo]] are not included.		Note: 7-limit temperaments represented by [[1407edo]] are not included.
	{~~{Rank~~-2 ~~begin}}~~		{\| class="wikitable center-all left-5"
			\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
			\|-
			! Periods<br />per 8ve
			! Generator*
			! Cents*
			! Associated<br />ratio*
			! Temperaments
	\|-		\|-
	\| 1		\| 1
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	\| 53094899/45875200		\| 53094899/45875200
	\| [[Double bastille]]		\| [[Double bastille]]
	~~{{Rank-2 end}~~}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	[[Category:Jacobin]]		[[Category:Jacobin]]

ArrowHead294 at 01:24, 16 November 2024

2024-11-16T01:24:36Z

← Older revision		Revision as of 01:24, 16 November 2024
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	Note: 7-limit temperaments represented by [[1407edo]] are not included.		Note: 7-limit temperaments represented by [[1407edo]] are not included.
	{~~\| class="wikitable center~~-~~all left-5"~~		{{Rank-2 begin}}
	\|-
	~~! Periods<br />per 8ve~~
	! Generator*
	! Cents*
	~~! Associated<br />Ratio~~
	~~! Temperament~~
	\|-		\|-
	\| 1		\| 1
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	\| 53094899/45875200		\| 53094899/45875200
	\| [[Double bastille]]		\| [[Double bastille]]
	\|}		{{Rank-2 end}}
	{{orf}}		{{orf}}

	[[Category:Jacobin]]		[[Category:Jacobin]]

ArrowHead294 at 00:42, 16 November 2024

2024-11-16T00:42:53Z

← Older revision		Revision as of 00:42, 16 November 2024
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	Note: 7-limit temperaments represented by [[1407edo]] are not included.		Note: 7-limit temperaments represented by [[1407edo]] are not included.
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	! Periods<br>per 8ve		\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br />Ratio
	! Temperament		! Temperament
	\|-		\|-
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	\| [[Double bastille]]		\| [[Double bastille]]
	\|}		\|}
	~~<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct~~		{{orf}}

	[[Category:Jacobin]]		[[Category:Jacobin]]

FloraC: +subsets and supersets

2023-10-30T10:15:09Z

+subsets and supersets

← Older revision		Revision as of 10:15, 30 October 2023
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	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|2814}}		{{Harmonics in equal\|2814}}

			=== Subsets and supersets ===
			Since 2814 factors into {{factorization\|2814}}, 2814edo has subset edos {{EDOs\| 2, 3, 6, 7, 14, 21, 42, 67, 134, 201, 402, 469, 938 and 1407 }}.

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

FloraC: /* Regular temperament properties */ -formatting error

2023-10-15T11:59:13Z

Regular temperament properties: -formatting error

← Older revision		Revision as of 11:59, 15 October 2023
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	Note: 7-limit temperaments represented by [[1407edo]] are not included.		Note: 7-limit temperaments represented by [[1407edo]] are not included.
	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-5"
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*

FloraC: Cleanup; clarify the title row of the rank-2 temp table

2023-10-15T11:49:04Z

Cleanup; clarify the title row of the rank-2 temp table

← Older revision		Revision as of 11:49, 15 October 2023
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	== Theory ==		== Theory ==
	2814edo has all the ~~harmonics~~ from 3 to 17 approximated below 1/3 relative error and it is as a corollary [[consistent]] in the [[17-odd-limit]].		2814edo has all the [[harmonic]]s from 3 to 17 approximated below 1/3 relative error and it is as a corollary [[consistent]] in the [[17-odd-limit]].

	In the 7-limit, it is ~~contorted~~, with the same ~~commas~~ tempered out as [[1407edo]].		In the 7-limit, it is [[Enfactoring\|enfactored]], with the same [[comma]]s [[Tempering out\|tempered out]] as [[1407edo]]. In the 11-limit, it supports rank-3 [[odin]] temperament. In the 13-limit it tempers out [[6656/6655]] and supports the 2.5.7.11.13 [[subgroup]] [[double bastille]] temperament.

	In the 11-limit, it supports rank-3 [[odin]] temperament.

	In the 13-limit it tempers out [[6656/6655]] and supports the 2.5.7.11.13 subgroup [[~~Double Bastille~~]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
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	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio
	! Temperament		! Temperament
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	\| 252.878		\| 252.878
	\| 53094899/45875200		\| 53094899/45875200
	\| [[Double ~~Bastille~~]]		\| [[Double bastille]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

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

BudjarnLambeth at 07:03, 9 July 2023

2023-07-09T07:03:30Z

← Older revision		Revision as of 07:03, 9 July 2023
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	~~{{novelty}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|2814}}		{{EDO intro\|2814}}