426edo - 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"

2026-03-13T13:31:44Z

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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	\| [[Mutt]] (7-limit)		\| [[Mutt]] (7-limit)
	\|}		\|}
	<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

2025-02-21T06:22:29Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:22, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|426~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:43, 15 January 2025

2025-01-15T17:43:37Z

← Older revision		Revision as of 17:43, 15 January 2025
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 426 factors into ~~2 × 3 × 71~~, 426edo has subset edos {{EDOs\| 2, 3, 6, 71, 142, and 213 }}.		Since 426 factors into {{factorisation\|426}}, 426edo has subset edos {{EDOs\| 2, 3, 6, 71, 142, and 213 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 73:		Line 73:
	\| [[Mutt]] (7-limit)		\| [[Mutt]] (7-limit)
	\|}		\|}
	<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

2024-11-16T13:20:29Z

Partial undo

← Older revision		Revision as of 13:20, 16 November 2024
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	== Regular temperament properties ==		== Regular temperament properties ==
	{~~{comma basis begin}}~~		{\| class="wikitable center-4 center-5 center-6"
			\|-
			! rowspan="2" \| [[Subgroup]]
			! rowspan="2" \| [[Comma list]]
			! rowspan="2" \| [[Mapping]]
			! rowspan="2" \| Optimal<br />8ve stretch (¢)
			! colspan="2" \| Tuning error
			\|-
			! [[TE error\|Absolute]] (¢)
			! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\| 2.3		\| 2.3
Line 34:		Line 43:
	\| 0.1600		\| 0.1600
	\| 5.68		\| 5.68
	~~{{comma basis end}~~}		\|}

	=== 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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	\| 5/4<br />(126/125)		\| 5/4<br />(126/125)
	\| [[Mutt]] (7-limit)		\| [[Mutt]] (7-limit)
	~~{{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 01:33, 16 November 2024

2024-11-16T01:33:52Z

← Older revision		Revision as of 01:33, 16 November 2024
Line 12:		Line 12:

	== Regular temperament properties ==		== Regular temperament properties ==
	{~~\| class="wikitable center-4 center-5 center-6"~~		{{comma basis begin}}
	~~! rowspan="2" \| [[Subgroup]]~~
	~~! rowspan="2" \| [[Comma list\|Comma List]]~~
	~~! rowspan="2" \| [[Mapping]]~~
	~~! rowspan="2" \| Optimal<br>8ve Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
Line 42:		Line 34:
	\| 0.1600		\| 0.1600
	\| 5.68		\| 5.68
	\|}		{{comma basis end}}

	=== 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
Line 66:		Line 52:
	\|-		\|-
	\| 3		\| 3
	\| 137\426<br>(5\426)		\| 137\426<br />(5\426)
	\| 385.92<br>(14.08)		\| 385.92<br />(14.08)
	\| 5/4<br>(126/125)		\| 5/4<br />(126/125)
	\| [[Mutt]] (7-limit)		\| [[Mutt]] (7-limit)
	\|}		{{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}}

FloraC: Review

2024-01-21T10:01:55Z

Review

← Older revision		Revision as of 10:01, 21 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~426et~~ is consistent to the [[9-odd-limit]]. Using the patent val, it tempers out ~~283115520/282475249, 48828125/48771072,~~ [[65625/65536]], [[250047/250000]] ~~and 5250987/5242880~~ in the 7-limit; [[~~117440512~~/~~117406179~~]]~~, 806736/805255, 25165824/25109315, 2097152/2096325~~, [[4000/3993]]~~, 2734375/2725888, 166698/166375, 151263/151250, 104857600/104825259, 2359296/2358125~~, [[~~540~~/~~539~~]], ~~1265625~~/~~1261568, 107495424/107421875~~, 137781/137500, ~~5767168/5764801, 825000/823543, 24057/24010, 17537553/17500000, [[9801/9800]]~~ and ~~3294225~~/~~3294172~~ in the 11-limit. It [[support]]s [[untriton]].		426edo is [[consistent]] to the [[9-odd-limit]]. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[65625/65536]], 118098/117649, [[250047/250000]] in the 7-limit; [[540/539]], [[4000/3993]], [[9801/9800]], 24057/24010, 137781/137500, and 151263/151250 in the 11-limit. It [[support]]s the 5-limit version of [[untriton]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	426 factors into 2 × 3 × 71, ~~with~~ subset edos {{EDOs\|2, 3, 6, 71, 142, and 213}}.		Since 426 factors into 2 × 3 × 71, 426edo has subset edos {{EDOs\| 2, 3, 6, 71, 142, and 213 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|-225 142}}		\| {{monzo\| -225 142 }}
	\|{{mapping\|426 675}}		\| {{mapping\| 426 675 }}
	\| 0.1724		\| +0.1724
	\| 0.1724		\| 0.1724
	\| 6.12		\| 6.12
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|-7 22 -12}}, {{monzo\|-44 -3 21}}		\| {{monzo\| -7 22 -12 }}, {{monzo\| -44 -3 21 }}
	\|{{mapping\|426 675 989}}		\| {{mapping\| 426 675 989 }}
	\| 0.1721		\| +0.1721
	\| 0.1408		\| 0.1408
	\| 5.00		\| 5.00
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|~~250047~~/~~250000~~, 118098/117649, ~~65625~~/~~65536~~		\| 65625/65536, 118098/117649, 250047/250000
	\|{{mapping\|426 675 989 1196}}		\| {{mapping\| 426 675 989 1196 }}
	\| 0.1123		\| +0.1123
	\| 0.1600		\| 0.1600
	\| 5.68		\| 5.68
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	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|199\426		\| 199\426
	\|560.56		\| 560.56
	\|864/625		\| 864/625
	\|[[Whoosh]]		\| [[Whoosh]]
	\|-		\|-
	\|1		\| 1
	\|209\426		\| 209\426
	\|588.73		\| 588.73
	\|7/5		\| 45/32
	\|[[Untriton]]		\| [[Untriton]] (5-limit)
	\|-		\|-
	\|3		\| 3
	\|137\426<br>(5\426)		\| 137\426<br>(5\426)
	\|385.92<br>(14.08)		\| 385.92<br>(14.08)
	\|5/4<br>(~~8393216~~/~~390625~~)		\| 5/4<br>(126/125)
	\|[[Mutt]]		\| [[Mutt]] (7-limit)
	\|}		\|}

	<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

Francium: Created page with "{{Infobox ET}} {{EDO intro|426}} == Theory == 426et is consistent to the 9-odd-limit. Using the patent val, it tempers out 283115520/282475249, 48828125/48771072, 65625..."

2024-01-17T21:04:47Z

Created page with "{{Infobox ET}} {{EDO intro|426}} == Theory == 426et is consistent to the 9-odd-limit. Using the patent val, it tempers out 283115520/282475249, 48828125/48771072, 65625..."

New page

{{Infobox ET}}
{{EDO intro|426}}

== Theory ==
426et is consistent to the [[9-odd-limit]]. Using the patent val, it tempers out 283115520/282475249, 48828125/48771072, [[65625/65536]], [[250047/250000]] and 5250987/5242880 in the 7-limit; [[117440512/117406179]], 806736/805255, 25165824/25109315, 2097152/2096325, [[4000/3993]], 2734375/2725888, 166698/166375, 151263/151250, 104857600/104825259, 2359296/2358125, [[540/539]], 1265625/1261568, 107495424/107421875, 137781/137500, 5767168/5764801, 825000/823543, 24057/24010, 17537553/17500000, [[9801/9800]] and 3294225/3294172 in the 11-limit. It [[support]]s [[untriton]].

=== Prime harmonics ===
{{Harmonics in equal|426}}

=== Subsets and supersets ===
426 factors into 2 × 3 × 71, with subset edos {{EDOs|2, 3, 6, 71, 142, and 213}}.

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! rowspan="2" |[[Subgroup]]
! rowspan="2" |[[Comma list|Comma List]]
! rowspan="2" |[[Mapping]]
! rowspan="2" |Optimal 8ve Stretch (¢)
! colspan="2" |Tuning Error
|-
![[TE error|Absolute]] (¢)
![[TE simple badness|Relative]] (%)
|-
|2.3
|{{monzo|-225 142}}
|{{mapping|426 675}}
| 0.1724
| 0.1724
| 6.12
|-
|2.3.5
|{{monzo|-7 22 -12}}, {{monzo|-44 -3 21}}
|{{mapping|426 675 989}}
| 0.1721
| 0.1408
| 5.00
|-
|2.3.5.7
|250047/250000, 118098/117649, 65625/65536
|{{mapping|426 675 989 1196}}
| 0.1123
| 0.1600
| 5.68
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods per 8ve
! Generator*
! Cents*
! Associated Ratio*
! Temperaments
|-
|1
|199\426
|560.56
|864/625
|[[Whoosh]]
|-
|1
|209\426
|588.73
|7/5
|[[Untriton]]
|-
|3
|137\426 (5\426)
|385.92 (14.08)
|5/4 (8393216/390625)
|[[Mutt]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct