1323edo - 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"

2026-03-13T13:33:12Z

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 13:33, 13 March 2026
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	\| [[Trinealimmal]]		\| [[Trinealimmal]]
	\|}		\|}
	<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

Tristanbay: /* Subsets and supersets */Added mention of 7edo and 27edo as zeta edos

2025-08-26T01:48:38Z

Subsets and supersets: Added mention of 7edo and 27edo as zeta edos

← Older revision		Revision as of 01:48, 26 August 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 1323 factors into {{factorization\|1323}}, 1323edo has subset edos {{EDOs\| 3, 7, 9, 21, 27, 49, 63, 147, 189, 441 }}, of which 441edo ~~is a member~~ of the [[zeta edo]]s.		Since 1323 factors into {{factorization\|1323}}, 1323edo has subset edos {{EDOs\| 3, 7, 9, 21, 27, 49, 63, 147, 189, 441 }}, of which 7, 27, and 441edo are members of the [[zeta edo]]s.

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

Francium: changed EDO intro to ED intro

2025-02-20T17:09:50Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:09, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1323~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 15:59, 15 January 2025

2025-01-15T15:59:44Z

← Older revision		Revision as of 15:59, 15 January 2025
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	\| [[Trinealimmal]]		\| [[Trinealimmal]]
	\|}		\|}
	<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

2024-11-16T13:23:06Z

Partial undo

← Older revision		Revision as of 13:23, 16 November 2024
Line 17:		Line 17:
	Note: 7-limit temperaments supported by 441et are not included.		Note: 7-limit temperaments supported by 441et 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
	\|-		\|-
	\| 27		\| 27
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	\| 1375/1176<br />(?)		\| 1375/1176<br />(?)
	\| [[Trinealimmal]]		\| [[Trinealimmal]]
	~~{{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

ArrowHead294 at 01:23, 16 November 2024

2024-11-16T01:23:56Z

← Older revision		Revision as of 01:23, 16 November 2024
Line 17:		Line 17:
	Note: 7-limit temperaments supported by 441et are not included.		Note: 7-limit temperaments supported by 441et are not included.

	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ style="font-size: 105%;" \| Table of~~ rank-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br />per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 27		\| 27
Line 31:		Line 24:
	\| 1375/1176<br />(?)		\| 1375/1176<br />(?)
	\| [[Trinealimmal]]		\| [[Trinealimmal]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 00:41, 16 November 2024

2024-11-16T00:41:09Z

← Older revision		Revision as of 00:41, 16 November 2024
Line 18:		Line 18:

	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+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*
Line 27:		Line 27:
	\|-		\|-
	\| 27		\| 27
	\| 299\1323<br>(5\1323)		\| 299\1323<br />(5\1323)
	\| 271.201<br>(4.535)		\| 271.201<br />(4.535)
	\| 1375/1176<br>(?)		\| 1375/1176<br />(?)
	\| [[Trinealimmal]]		\| [[Trinealimmal]]
	\|}		\|}
	~~<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: Rework on theory (this can't tune the "441 & 1308" temperament; there must be a mistake)

2023-10-31T09:37:07Z

Rework on theory (this can't tune the "441 & 1308" temperament; there must be a mistake)

← Older revision		Revision as of 09:37, 31 October 2023
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	== Theory ==		== Theory ==
	1323edo is the smallest edo [[consistency\|distinctly consistent]] in the [[29-odd-limit]].		1323edo is the smallest edo [[consistency\|distinctly consistent]] in the [[29-odd-limit]]. It is [[enfactoring\|enfactored]] in the 7-limit, sharing the same excellent 7-limit approximation with [[441edo]], but it makes for a great higher-limit system by splitting each step of 441edo into three.

	It provides the [[optimal patent val]] for the 11-limit [[trinealimmal]] temperament, which has a period of 1\27 octave~~. In addition, it tunes well 441 & 1308 temperament, which is a member of the augmented-cloudy equivalence continuum~~.		It provides the [[optimal patent val]] for the 11-limit [[trinealimmal]] temperament, which has a period of 1\27 octave.

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	1323~~'s divisors are~~ {{EDOs\| 3, 7, 9, 21, 27, 49, 63, 147, 189, 441 }}, of which 441edo is a member of the [[zeta edo]]s~~. 1323edo shares the 7-limit mapping with 441edo. As such, it can be interpreted as an improvement for 441edo into the 29-limit by splitting each step of 441edo into three~~.		Since 1323 factors into {{factorization\|1323}}, 1323edo has subset edos {{EDOs\| 3, 7, 9, 21, 27, 49, 63, 147, 189, 441 }}, of which 441edo is a member of the [[zeta edo]]s.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 18:		Line 18:

	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
			\|+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
	~~<!--~~
	\|-
	~~\| 3~~
	~~\| 177\1323~~
	~~\| 160.544~~
	~~\| 154478651796875/140737488355328~~
	~~\| [[Augmented-cloudy equivalence continuum#441 & 1308\|441 & 1308]]~~
	~~-->~~
	\|-		\|-
	\| 27		\| 27

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

2023-10-17T08:13:14Z

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

← Older revision		Revision as of 08:13, 17 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1323edo is the smallest ~~uniquely~~ consistent ~~EDO~~ in the 29-odd-limit.		1323edo is the smallest edo [[consistency\|distinctly consistent]] in the [[29-odd-limit]].

	It provides the optimal patent val for the 11-limit [[trinealimmal]] temperament, which has a period of 1\27 octave. In ~~additoin~~, it tunes well 441 & 1308 temperament, which is a member of the augmented-cloudy equivalence continuum.		It provides the [[optimal patent val]] for the 11-limit [[trinealimmal]] temperament, which has a period of 1\27 octave. In addition, it tunes well 441 & 1308 temperament, which is a member of the augmented-cloudy equivalence continuum.

	1323's divisors are {{EDOs\|1, 3, 7, 9, 21, 27, 49, 63, 147, 189, 441}}, of which 441EDO is a member of the zeta edos. 1323edo shares the 7-limit mapping with 441edo. As such, it can be interpreted as an improvement for 441edo into the 29-limit by splitting each step of 441edo into three.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|1323}}		{{Harmonics in equal\|1323}}

	[[~~Category:Equal divisions of the octave\|####~~]]		=== Subsets and supersets ===
			1323's divisors are {{EDOs\| 3, 7, 9, 21, 27, 49, 63, 147, 189, 441 }}, of which 441edo is a member of the [[zeta edo]]s. 1323edo shares the 7-limit mapping with 441edo. As such, it can be interpreted as an improvement for 441edo into the 29-limit by splitting each step of 441edo into three.

	== Regular temperament properties ==		== Regular temperament properties ==
			=== Rank-2 temperaments ===
			Note: 7-limit temperaments supported by 441et are not included.

	~~=== Rank-2 temperaments ===~~
	{\| 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
			<!--
	\|-		\|-
	\|3		\| 3
	\|177\1323		\| 177\1323
	\|160.544		\| 160.544
	\|154478651796875/140737488355328		\| 154478651796875/140737488355328
	\|[[Augmented-cloudy equivalence continuum#441 & 1308\|441 & 1308]]		\| [[Augmented-cloudy equivalence continuum#441 & 1308\|441 & 1308]]
			-->
	\|-		\|-
	\|27		\| 27
	\|299\1323<br>(5\1323)		\| 299\1323<br>(5\1323)
	\|271.201<br>(4.535)		\| 271.201<br>(4.535)
	\|1375/1176<br>(?)		\| 1375/1176<br>(?)
	\|[[Trinealimmal]]		\| [[Trinealimmal]]
	\|}<!-- ~~4-digit number -->~~		\|}
			<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 06:52, 9 July 2023

2023-07-09T06:52:41Z

← Older revision		Revision as of 06:52, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1323}}		{{EDO intro\|1323}}