1012edo - 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"

2026-03-13T13:32:01Z

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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	\| [[Ruthenium]]		\| [[Ruthenium]]
	\|}		\|}
	<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

ArrowHead294 at 16:45, 18 February 2025

2025-02-18T16:45:51Z

← Older revision		Revision as of 16:45, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|1012~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:18, 15 January 2025

2025-01-15T16:18:00Z

← Older revision		Revision as of 16:18, 15 January 2025
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	\| [[Ruthenium]]		\| [[Ruthenium]]
	\|}		\|}
	<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

2024-11-16T13:08:42Z

Partial undo

← Older revision		Revision as of 13:08, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{{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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	\| 4/3<br />(18375/18304)		\| 4/3<br />(18375/18304)
	\| [[Ruthenium]]		\| [[Ruthenium]]
	~~{{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 02:25, 16 November 2024

2024-11-16T02:25:36Z

← Older revision		Revision as of 02:25, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+Table of~~ rank-2 ~~temperaments by generator~~
	\|-
	~~! Periods<br>per 8ve~~
	! Generator*
	! Cents*
	! Associated<br>Ratio*
	~~! Temperaments~~
	\|-		\|-
	\| 1		\| 1
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	\|-		\|-
	\| 44		\| 44
	\| 420\1012<br>(6\1012)		\| 420\1012<br />(6\1012)
	\| 498.023<br>(7.115)		\| 498.023<br />(7.115)
	\| 4/3<br>(18375/18304)		\| 4/3<br />(18375/18304)
	\| [[Ruthenium]]		\| [[Ruthenium]]
	\|}		{{rank-2 end}}
	~~<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}}

Eliora: /* Regular temperament properties */ oops remove that as that is already supported by 506et

2024-01-05T22:17:58Z

Regular temperament properties: oops remove that as that is already supported by 506et

← Older revision		Revision as of 22:17, 5 January 2024
Line 40:		Line 40:
	\| 7/5		\| 7/5
	\| [[Quarvish]]		\| [[Quarvish]]
	\|-
	~~\|22~~
	~~\|420\1012<br>(6\1012)~~
	~~\|498.023<br>(7.115)~~
	~~\|4/3~~
	~~({{monzo\|16 -13 2}})~~
	~~\|[[Major arcana]]~~
	\|-		\|-
	\| 44		\| 44

Eliora: /* Regular temperament properties */ +major arcana

2024-01-05T22:13:18Z

Regular temperament properties: +major arcana

← Older revision		Revision as of 22:13, 5 January 2024
Line 40:		Line 40:
	\| 7/5		\| 7/5
	\| [[Quarvish]]		\| [[Quarvish]]
			\|-
			\|22
			\|420\1012<br>(6\1012)
			\|498.023<br>(7.115)
			\|4/3
			({{monzo\|16 -13 2}})
			\|[[Major arcana]]
	\|-		\|-
	\| 44		\| 44

FloraC: Adopt template: Factorization; misc. cleanup

2023-10-31T10:59:38Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 10:59, 31 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	1012edo is a strong 13-limit system, ~~distinctly~~ [[consistent]] through the 15-odd-limit. It is a [[~~The Riemann zeta function and tuning #Zeta EDO lists\|~~zeta peak edo]], though not zeta integral nor zeta gap. A basis for the 13-limit ~~commas is~~ [[2401/2400]], [[4096/4095]], [[6656/6655]], [[9801/9800]] and {{monzo\| 2 6 -1 2 0 4 }}.		1012edo is a strong 13-limit system, [[consistency\|distinctly consistent]] through the [[15-odd-limit]]. It is a [[zeta peak edo]], though not [[zeta integral edo\|zeta integral]] nor [[zeta gap edo\|zeta gap]]. A basis for the 13-limit [[comma]]s consists of [[2401/2400]], [[4096/4095]], [[6656/6655]], [[9801/9800]] and {{monzo\| 2 6 -1 2 0 4 }}.

	In the 5-limit, 1012edo is enfactored, with the same ~~mapping~~ as [[506edo]], ~~providing a tuning for~~ [[vishnu]], [[monzismic]], and [[lafa]]. In the 7-limit, it tempers out the [[breedsma]], 2401/2400, and tunes [[osiris]] temperament. Furthermore, noting its exceptional strength in the 2.3.7 subgroup, it is a [[septiruthenia]]n system, tempering 64/63 comma to 1/44th of the octave, that is 23 steps. It provides the [[optimal patent val]] for [[quarvish]] temperament in the 7-limit and also in the 11-limit.		In the 5-limit, 1012edo is [[enfactoring\|enfactored]], with the same tuning as [[506edo]], [[support]]ing [[vishnu]], [[monzismic]], and [[lafa]]. In the 7-limit, it [[tempering out\|tempers out]] the [[breedsma]], 2401/2400, and tunes the [[osiris]] temperament. Furthermore, noting its exceptional strength in the 2.3.7 [[subgroup]], it is a [[septiruthenia]]n system, tempering 64/63 comma to 1/44th of the octave, that is 23 steps. It provides the [[optimal patent val]] for [[quarvish]] temperament in the 7-limit and also in the 11-limit.

	=== Other techniques ===		=== Other techniques ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	1012 has subset edos {{EDOs\| 2, 4, 11, 22, 23, 44, 46, 92, 253, 506 }}.		Since 1012 factors into {{factorization\|1012}}, 1012edo has subset edos {{EDOs\| 2, 4, 11, 22, 23, 44, 46, 92, 253, 506 }}. [[2024edo]], which divides the edostep in two, provides a good correction for the 17th harmonic.

	[[2024edo]], which divides the edostep in two, provides a good correction for the 17th harmonic.

	== Regular temperament properties ==		== Regular temperament properties ==
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| 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
	\|-		\|-

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

2023-10-19T15:38:24Z

Clarify the title row of the rank-2 temp table

← Older revision		Revision as of 15:38, 19 October 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1012}}		{{EDO intro\|1012}}

	== Theory ==		== Theory ==
	1012edo is a strong 13-limit system, distinctly [[consistent]] through the 15-odd-limit. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]], though not zeta integral nor zeta gap. A basis for the 13-limit commas is [[2401/2400]], [[4096/4095]], [[6656/6655]], [[9801/9800]] and {{monzo\| 2 6 -1 2 0 4 }}.		1012edo is a strong 13-limit system, distinctly [[consistent]] through the 15-odd-limit. It is a [[The Riemann zeta function and tuning #Zeta EDO lists\|zeta peak edo]], though not zeta integral nor zeta gap. A basis for the 13-limit commas is [[2401/2400]], [[4096/4095]], [[6656/6655]], [[9801/9800]] and {{monzo\| 2 6 -1 2 0 4 }}.
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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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	\| [[Ruthenium]]		\| [[Ruthenium]]
	\|}		\|}
			<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 06:49, 9 July 2023

2023-07-09T06:49:24Z

← Older revision		Revision as of 06:49, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|1012}}		{{EDO intro\|1012}}
	== Theory ==		== Theory ==