429edo - 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"

2026-03-13T13:32:36Z

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
Line 93:		Line 93:
	\| [[Mutt]]		\| [[Mutt]]
	\|}		\|}
	<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

2025-02-21T06:25:45Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:25, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|429~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:15, 15 January 2025

2025-01-15T18:15:33Z

← Older revision		Revision as of 18:15, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	429et is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] [[65625/65536]], [[250047/250000]], and 823543/820125 in the 7-limit; [[3025/3024]], 12005/11979, [[19712/19683]], 42875/42768, and 102487/102400 in the 11-limit. It [[support]]s [[vavoom]], [[turkey]], [[counterhanson]] and [[aluminium]].		429et is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] [[65625/65536]], [[250047/250000]], and 823543/820125 in the 7-limit; [[3025/3024]], 12005/11979, [[19712/19683]], 42875/42768, and 102487/102400 in the 11-limit. It [[support]]s [[vavoom]], [[turkey]], [[counterhanson]], and [[aluminium]].

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

	=== Subsets and supersets ===		=== Subsets and supersets ===
	429 factors into ~~3 × 11 × 13~~, with subset edos {{EDOs\|3, 11, 13, 33, 39, and 143}}.		429 factors into {{factorisation\|429}}, with subset edos {{EDOs\|3, 11, 13, 33, 39, and 143}}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 26:		Line 26:
	\| {{monzo\| 680 -429 }}		\| {{monzo\| 680 -429 }}
	\| {{mapping\| 429 680 }}		\| {{mapping\| 429 680 }}
	\| ~~−0~~.0451		\| −0.0451
	\| 0.0451		\| 0.0451
	\| 1.61		\| 1.61
Line 93:		Line 93:
	\| [[Mutt]]		\| [[Mutt]]
	\|}		\|}
	<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

2024-11-16T13:06:56Z

Partial undo

← Older revision		Revision as of 13:06, 16 November 2024
Line 12:		Line 12:

	== 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 48:		Line 57:
	\| 0.1708		\| 0.1708
	\| 6.11		\| 6.11
	~~{{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
Line 76:		Line 92:
	\| 5/4<br />(126/125)		\| 5/4<br />(126/125)
	\| [[Mutt]]		\| [[Mutt]]
	~~{{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 02:31, 16 November 2024

2024-11-16T02:31:56Z

← Older revision		Revision as of 02:31, 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
	\| {{monzo\| 680 -429 }}		\| {{monzo\| 680 -429 }}
	\| {{mapping\| 429 680 }}		\| {{mapping\| 429 680 }}
	\| -0.0451		\| −0.0451
	\| 0.0451		\| 0.0451
	\| 1.61		\| 1.61
Line 56:		Line 48:
	\| 0.1708		\| 0.1708
	\| 6.11		\| 6.11
	\|}		{{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 86:		Line 72:
	\|-		\|-
	\| 3		\| 3
	\| 138\429<br>(5\429)		\| 138\429<br />(5\429)
	\| 386.01<br>(13.99)		\| 386.01<br />(13.99)
	\| 5/4<br>(126/125)		\| 5/4<br />(126/125)
	\| [[Mutt]]		\| [[Mutt]]
	\|}		{{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

2024-01-21T10:08:40Z

Review

← Older revision		Revision as of 10:08, 21 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	429et is consistent to the [[11-odd-limit]]. It tempers out ~~48828125/48771072,~~ [[65625/65536]], [[250047/250000]], ~~359661568/358722675~~ and ~~5250987~~/~~5242880~~ in the 7-limit; [[~~117440512~~/~~117406179~~]]~~, 806736/805255, 234375/234256, 26214400/26198073~~, 12005/11979~~, 1953125/1951488, 496125/495616~~, [[~~1953125~~/~~1948617]], [[200704/200475~~]], 42875/42768, 4302592/4296875, 352947/352000, 1879453125/1879048192, 184549376/184528125, [[19712/19683]], 1684375/1679616, 422576/421875, 184877/184320, 47265625/47258883, [[3025/3024]], 9453125/9437184, 160083/160000, 16808715/16777216, [[532400/531441]], 456533/455625, 102487/102400~~, [[1771561/1769472]] and 781258401/781250000~~ in the 11-limit. It [[support]]s [[vavoom]], [[turkey]], [[counterhanson]] and [[aluminium]].		429et is [[consistent]] to the [[11-odd-limit]]. The equal temperament [[tempering out\|tempers out]] [[65625/65536]], [[250047/250000]], and 823543/820125 in the 7-limit; [[3025/3024]], 12005/11979, [[19712/19683]], 42875/42768, and 102487/102400 in the 11-limit. It [[support]]s [[vavoom]], [[turkey]], [[counterhanson]] and [[aluminium]].

	=== Prime harmonics ===		=== Prime harmonics ===
Line 13:		Line 13:
	== 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\|680 -429}}		\| {{monzo\| 680 -429 }}
	\|{{mapping\|429 680}}		\| {{mapping\| 429 680 }}
	\| -0.0451		\| -0.0451
	\| 0.0451		\| 0.0451
	\| 1.61		\| 1.61
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|24 -21 4}}, {{monzo\|-20 -24 25}}		\| {{monzo\| 24 -21 4 }}, {{monzo\| -20 -24 25 }}
	\|{{mapping\|429 680 996}}		\| {{mapping\| 429 680 996 }}
	\| +0.0130		\| +0.0130
	\| 0.0900		\| 0.0900
	\| 3.22		\| 3.22
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|250047/250000, 823543/820125~~, 65625/65536~~		\| 65625/65536, 250047/250000, 823543/820125
	\|{{mapping\|429 680 996 1204}}		\| {{mapping\| 429 680 996 1204 }}
	\| +0.0982		\| +0.0982
	\| 0.1670		\| 0.1670
	\| 5.97		\| 5.97
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|3025/3024, ~~42875~~/~~42768~~, ~~160083~~/~~160000~~, ~~456533~~/~~455625~~		\| 3025/3024, 12005/11979, 19712/19683, 102487/102400
	\|{{mapping\|429 680 996 1204 1484}}		\| {{mapping\| 429 680 996 1204 1484 }}
	\| +0.0941		\| +0.0941
	\| 0.1496		\| 0.1496
	\| 5.35		\| 5.35
	\|-		\|-
	\|2.3.5.7.11.13		\| 2.3.5.7.11.13
	\|1001/1000~~, 676/675~~, 3025/3024, ~~47432~~/~~47385~~, ~~12005~~/~~11979~~		\| 676/675, 1001/1000, 3025/3024, 12005/11979, 19712/19683
	\|{{mapping\|429 680 996 1204 1484 1587}}		\| {{mapping\| 429 680 996 1204 1484 1587 }}
	\| +0.1400		\| +0.1400
	\| 0.1708		\| 0.1708
Line 67:		Line 67:
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|40\429		\| 40\429
	\|111.89		\| 111.89
	\|16/15		\| 16/15
	\|[[Vavoom]]		\| [[Vavoom]]
	\|-		\|-
	\|1		\| 1
	\|113\429		\| 113\429
	\|316.08		\| 316.08
	\|6/5		\| 6/5
	\|[[Counterhanson]]		\| [[Counterhanson]]
	\|-		\|-
	\|1		\| 1
	\|170\429		\| 170\429
	\|475.52		\| 475.52
	\|320/243		\| 320/243
	\|[[Vulture]]		\| [[Vulture]]
	\|-		\|-
	\|3		\| 3
	\|138\429<br>(5\429)		\| 138\429<br>(5\429)
	\|386.01<br>(13.99)		\| 386.01<br>(13.99)
	\|5/4<br>(~~393216~~/~~390625~~)		\| 5/4<br>(126/125)
	\|[[Mutt]]		\| [[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		<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|429}} == Theory == 429et is consistent to the 11-odd-limit. It tempers out 48828125/48771072, 65625/65536, 250047/250000, 359661568/358..."

2024-01-18T08:50:06Z

Created page with "{{Infobox ET}} {{EDO intro|429}} == Theory == 429et is consistent to the 11-odd-limit. It tempers out 48828125/48771072, 65625/65536, 250047/250000, 359661568/358..."

New page

{{Infobox ET}}
{{EDO intro|429}}

== Theory ==
429et is consistent to the [[11-odd-limit]]. It tempers out 48828125/48771072, [[65625/65536]], [[250047/250000]], 359661568/358722675 and 5250987/5242880 in the 7-limit; [[117440512/117406179]], 806736/805255, 234375/234256, 26214400/26198073, 12005/11979, 1953125/1951488, 496125/495616, [[1953125/1948617]], [[200704/200475]], 42875/42768, 4302592/4296875, 352947/352000, 1879453125/1879048192, 184549376/184528125, [[19712/19683]], 1684375/1679616, 422576/421875, 184877/184320, 47265625/47258883, [[3025/3024]], 9453125/9437184, 160083/160000, 16808715/16777216, [[532400/531441]], 456533/455625, 102487/102400, [[1771561/1769472]] and 781258401/781250000 in the 11-limit. It [[support]]s [[vavoom]], [[turkey]], [[counterhanson]] and [[aluminium]].

=== Prime harmonics ===
{{Harmonics in equal|429}}

=== Subsets and supersets ===
429 factors into 3 × 11 × 13, with subset edos {{EDOs|3, 11, 13, 33, 39, and 143}}.

== 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|680 -429}}
|{{mapping|429 680}}
| -0.0451
| 0.0451
| 1.61
|-
|2.3.5
|{{monzo|24 -21 4}}, {{monzo|-20 -24 25}}
|{{mapping|429 680 996}}
| +0.0130
| 0.0900
| 3.22
|-
|2.3.5.7
|250047/250000, 823543/820125, 65625/65536
|{{mapping|429 680 996 1204}}
| +0.0982
| 0.1670
| 5.97
|-
|2.3.5.7.11
|3025/3024, 42875/42768, 160083/160000, 456533/455625
|{{mapping|429 680 996 1204 1484}}
| +0.0941
| 0.1496
| 5.35
|-
|2.3.5.7.11.13
|1001/1000, 676/675, 3025/3024, 47432/47385, 12005/11979
|{{mapping|429 680 996 1204 1484 1587}}
| +0.1400
| 0.1708
| 6.11
|}

=== 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
|40\429
|111.89
|16/15
|[[Vavoom]]
|-
|1
|113\429
|316.08
|6/5
|[[Counterhanson]]
|-
|1
|170\429
|475.52
|320/243
|[[Vulture]]
|-
|3
|138\429 (5\429)
|386.01 (13.99)
|5/4 (393216/390625)
|[[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