783edo - 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"

2026-03-13T13:32:24Z

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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	\| [[87th-octave temperaments #Francium\|Francium]]		\| [[87th-octave temperaments #Francium\|Francium]]
	\|}		\|}
	<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

Francium: changed EDO intro to ED intro

2025-02-21T06:16:19Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:16, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|783~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:15, 15 January 2025

2025-01-15T16:15:54Z

← Older revision		Revision as of 16:15, 15 January 2025
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	\| [[87th-octave temperaments #Francium\|Francium]]		\| [[87th-octave temperaments #Francium\|Francium]]
	\|}		\|}
	<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

ArrowHead294: Partial undo

2024-11-16T13:24:44Z

Partial undo

← Older revision		Revision as of 13:24, 16 November 2024
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	\| [[87th-octave temperaments #Francium\|Francium]]		\| [[87th-octave temperaments #Francium\|Francium]]
	\|}		\|}
	~~{{orf}}~~		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

ArrowHead294 at 00:49, 16 November 2024

2024-11-16T00:49:38Z

← Older revision		Revision as of 00:49, 16 November 2024
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	=== 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
			\|-
			! Periods<br />per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>~~Ratio~~*		! Associated<br />ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\|-		\|-
	\| 9		\| 9
	\| 206\783<br>(32\783)		\| 206\783<br />(32\783)
	\| 315.709<br>(49.042)		\| 315.709<br />(49.042)
	\| 6/5<br>(36/35)		\| 6/5<br />(36/35)
	\| [[Ennealimmal]]		\| [[Ennealimmal]]
	\|-		\|-
	\| 29		\| 29
	\| 325\783<br>(1\723)		\| 325\783<br />(1\723)
	\| 498.084<br>(1.533)		\| 498.084<br />(1.533)
	\| 4/3<br>(32805/32768)		\| 4/3<br />(32805/32768)
	\| [[Copper]]		\| [[Copper]]
	\|-		\|-
	\| 87		\| 87
	\| 308\783<br>(2\783)		\| 308\783<br />(2\783)
	\| 472.031<br>(3.065)		\| 472.031<br />(3.065)
	\| {{monzo\| 35 1 -6 -3 -4 }}<br>(?)		\| {{monzo\| 35 1 -6 -3 -4 }}<br />(?)
	\| [[87th-octave temperaments #Francium\|Francium]]		\| [[87th-octave temperaments #Francium\|Francium]]
	\|}		\|}
	~~<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}}

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T12:04:15Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 12:04, 2 November 2023
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	== Theory ==		== Theory ==
	783edo provides solid approximations of the 5-limit, the 7-limit and to some extent the 11-limit, and is [[consistent]] up to the 11-limit, making it a flexible and versatile tuning. It tempers out the [[ennealimma]] and the [[counterschisma]] in the 5-limit; [[2401/2400]], and [[4375/4374]] in the 7-limit. It ~~supports~~ [[counterschismic]], [[dodifo]], [[ennealimmal]], [[raider]], [[vavoom]], and [[Very high accuracy temperaments#Francium\|francium]].		783edo provides solid approximations of the 5-limit, the 7-limit and to some extent the 11-limit, and is [[consistent]] up to the [[11-odd-limit]], making it a flexible and versatile tuning. The equal temperament [[tempering out\|tempers out]] the [[ennealimma]] and the [[counterschisma]] in the 5-limit; [[2401/2400]], and [[4375/4374]] in the 7-limit. It [[support]]s [[counterschismic]], [[dodifo]], [[ennealimmal]], [[raider]], [[vavoom]], and [[Very high accuracy temperaments #Francium\|francium]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 783 factors into ~~3<sup>3</sup> × 29~~, 783edo has subset edos {{EDOs\| 3, 9, 27, 29, 87, and 261 }}.		Since 783 factors into {{factorization\|783}}, 783edo has subset edos {{EDOs\| 3, 9, 27, 29, 87, and 261 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
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	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| 472.031<br>(3.065)		\| 472.031<br>(3.065)
	\| {{monzo\| 35 1 -6 -3 -4 }}<br>(?)		\| {{monzo\| 35 1 -6 -3 -4 }}<br>(?)
	\| [[87th-octave temperaments#Francium\|Francium]]		\| [[87th-octave temperaments #Francium\|Francium]]
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

FloraC: Clarify the title row of the rank-2 temp table

2023-10-20T11:47:42Z

Clarify the title row of the rank-2 temp table

← Older revision		Revision as of 11:47, 20 October 2023
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	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio
	! Temperaments		! Temperaments
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	\| [[87th-octave temperaments#Francium\|Francium]]		\| [[87th-octave temperaments#Francium\|Francium]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

BudjarnLambeth at 06:45, 9 July 2023

2023-07-09T06:45:55Z

← Older revision		Revision as of 06:45, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|783}}		{{EDO intro\|783}}

BudjarnLambeth at 05:29, 9 July 2023

2023-07-09T05:29:51Z

← Older revision		Revision as of 05:29, 9 July 2023
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	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|783}}		{{EDO intro\|783}}

Eliora: /* Regular temperament properties */

2023-06-30T14:46:32Z

Regular temperament properties

← Older revision		Revision as of 14:46, 30 June 2023
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	\| 472.031<br>(3.065)		\| 472.031<br>(3.065)
	\| {{monzo\| 35 1 -6 -3 -4 }}<br>(?)		\| {{monzo\| 35 1 -6 -3 -4 }}<br>(?)
	\| [[Francium]]		\| [[87th-octave temperaments#Francium\|Francium]]
	\|}		\|}