445edo - Revision history

FloraC: /* Regular temperament properties */ quintile isn't defined beyond the 5-limit

2026-09-04T06:16:02Z

Regular temperament properties: quintile isn't defined beyond the 5-limit

← Older revision		Revision as of 06:16, 4 September 2026
Line 77:		Line 77:
	\| 18.88		\| 18.88
	\| 81/80		\| 81/80
	\| [[Quintile]] ~~(5-limit)~~		\| [[Quintile]]
	\|}		\|}
	<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]		<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]

FloraC: /* Regular temperament properties */ update

2026-09-04T06:13:12Z

Regular temperament properties: update

← Older revision		Revision as of 06:13, 4 September 2026
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	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[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
	\|-		\|-
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| -28 25 -5 }}, {{monzo\| -29 -11 20 }}		\| {{Monzo\| -28 25 -5 }}, {{monzo\| -29 -11 20 }}
	\| {{~~mapping~~\| 445 705 1033 }}		\| {{Mapping\| 445 705 1033 }}
	\| +0.2748		\| +0.2748
	\| 0.2149		\| 0.2149
Line 32:		Line 32:
	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 7381125/7340032, 43046721/42875000		\| 2401/2400, 7381125/7340032, 43046721/42875000
	\| {{~~mapping~~\| 445 705 1033 1249 }}		\| {{Mapping\| 445 705 1033 1249 }}
	\| +0.2716		\| +0.2716
	\| 0.1862		\| 0.1862
Line 39:		Line 39:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 2401/2400, 3025/3024, 8019/8000, 234375/234256		\| 2401/2400, 3025/3024, 8019/8000, 234375/234256
	\| {{~~mapping~~\| 445 705 1033 1249 1539 }}		\| {{Mapping\| 445 705 1033 1249 1539 }}
	\| +0.2870		\| +0.2870
	\| 0.1694		\| 0.1694
Line 49:		Line 49:
	\|+ style="font-size: 105%;" \| 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*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 74:		Line 74:
	\|-		\|-
	\| 5		\| 5
	\| ~~185\445<br>(~~7\445)		\| 7\445
	\| ~~498.88<br>(~~18.88)		\| 18.88
	\| ~~4/3<br>(~~81/80)		\| 81/80
	\| [[~~Pental (temperament)\|Pental~~]] (5-limit)		\| [[Quintile]] (5-limit)
	\|}		\|}
	<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~~		<nowiki/>* In [[normal forms #Minimal-generator form\|minimal-generator form]]

Fredg999: Update links

2026-07-08T04:06:59Z

Update links

← Older revision		Revision as of 04:06, 8 July 2026
Line 3:		Line 3:

	== Theory ==		== Theory ==
	445edo is [[enfactoring\|enfactored]] in the [[3-limit]] with the same tuning as [[89edo]], but the approximation to some of the higher harmonics are improved. It is [[consistent]] to the [[7-odd-limit]] with [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]] all tuned flat, and it allows an extension to the [[11-limit]]. The equal temperament [[tempering out\|tempers out]] [[2401/2400]], 7381125/7340032, 33756345/33554432, 43046721/42875000, and 48828125/48771072 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, 35937/35840, [[41503/41472]], 137781/137500, 151263/151250, and 234375/234256 in the 11-limit. It notably [[support]]s [[neptune]].		445edo is [[enfactoring\|enfactored]] in the [[3-limit]] with the same tuning as [[89edo]], but the approximation to some of the higher harmonics are improved. It is [[consistent]] to the [[7-odd-limit]] with [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]] all tuned flat, and it allows an extension to the [[11-limit]]. The equal temperament [[tempering out\|tempers out]] [[2401/2400]], 7381125/7340032, 33756345/33554432, 43046721/42875000, and 48828125/48771072 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, 35937/35840, [[41503/41472]], 137781/137500, 151263/151250, and 234375/234256 in the 11-limit. It notably [[support]]s [[Neptune (temperament)\|neptune]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 71:		Line 71:
	\| 582.47		\| 582.47
	\| 7/5		\| 7/5
	\| [[Neptune]] (7-limit)		\| [[Neptune (temperament)\|Neptune]] (7-limit)
	\|-		\|-
	\| 5		\| 5

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"

2026-03-13T13:33:06Z

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
Line 79:		Line 79:
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-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

2025-02-21T06:26:47Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:26, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|445~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:42, 15 January 2025

2025-01-15T17:42:39Z

← Older revision		Revision as of 17:42, 15 January 2025
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 445 factors into ~~5 × 89~~, 445edo has [[5edo]] and 89edo as its subsets.		Since 445 factors into {{factorisation\|445}}, 445edo has [[5edo]] and 89edo as its subsets.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 79:		Line 79:
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-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

2024-11-16T13:02:32Z

Partial undo

← Older revision		Revision as of 13:02, 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]] (%)
	\|-		\|-
	\| 2.3.5		\| 2.3.5
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	\| 0.1694		\| 0.1694
	\| 6.28		\| 6.28
	~~{{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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	\| 4/3<br>(81/80)		\| 4/3<br>(81/80)
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-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 02:47, 16 November 2024

2024-11-16T02:47:23Z

← Older revision		Revision as of 02:47, 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]] (%)~~
	\|-		\|-
	\| 2.3.5		\| 2.3.5
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	\| 0.1694		\| 0.1694
	\| 6.28		\| 6.28
	\|}		{{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
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	\| 4/3<br>(81/80)		\| 4/3<br>(81/80)
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-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}}

Fredg999: Skip disambiguation

2024-09-09T01:59:52Z

Skip disambiguation

← Older revision		Revision as of 01:59, 9 September 2024
Line 75:		Line 75:
	\| 498.88<br>(18.88)		\| 498.88<br>(18.88)
	\| 4/3<br>(81/80)		\| 4/3<br>(81/80)
	\| [[Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-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

FloraC: Review +1

2024-01-21T10:25:58Z

Review +1

← Older revision		Revision as of 10:25, 21 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	445edo is [[consistent]] to the [[7-odd-limit]] with [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]] all tuned flat, and it allows an extension to the [[11-limit]]. The equal temperament [[tempering out\|tempers out]] [[2401/2400]], 7381125/7340032, 33756345/33554432, 43046721/42875000, and 48828125/48771072 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, 35937/35840, [[41503/41472]], 137781/137500, 151263/151250, and 234375/234256 in the 11-limit. It notably [[support]]s [[neptune]].		445edo is [[enfactoring\|enfactored]] in the [[3-limit]] with the same tuning as [[89edo]], but the approximation to some of the higher harmonics are improved. It is [[consistent]] to the [[7-odd-limit]] with [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]] all tuned flat, and it allows an extension to the [[11-limit]]. The equal temperament [[tempering out\|tempers out]] [[2401/2400]], 7381125/7340032, 33756345/33554432, 43046721/42875000, and 48828125/48771072 in the 7-limit; [[3025/3024]], [[8019/8000]], 24057/24010, 35937/35840, [[41503/41472]], 137781/137500, 151263/151250, and 234375/234256 in the 11-limit. It notably [[support]]s [[neptune]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	445 factors into 5 × 89, ~~with~~ [[5edo]] and [[89edo]] as its ~~subset edos~~.		Since 445 factors into 5 × 89, 445edo has [[5edo]] and 89edo as its subsets.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 21:		Line 21:
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	! [[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-
	~~\| 2.3~~
	~~\| {{monzo\| -141 89 }}~~
	~~\| {{mapping\| 445 705 }}~~
	~~\| 0.2623~~
	~~\| 0.2623~~
	~~\| 9.73~~
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| -28 25 -5 }}, {{monzo\| -29 -11 20 }}		\| {{monzo\| -28 25 -5 }}, {{monzo\| -29 -11 20 }}
	\| {{mapping\| 445 705 1033 }}		\| {{mapping\| 445 705 1033 }}
	\| 0.2748		\| +0.2748
	\| 0.2149		\| 0.2149
	\| 7.97		\| 7.97
Line 39:		Line 32:
	\| 2401/2400, 7381125/7340032, 43046721/42875000		\| 2401/2400, 7381125/7340032, 43046721/42875000
	\| {{mapping\| 445 705 1033 1249 }}		\| {{mapping\| 445 705 1033 1249 }}
	\| 0.2716		\| +0.2716
	\| 0.1862		\| 0.1862
	\| 6.90		\| 6.90
Line 46:		Line 39:
	\| 2401/2400, 3025/3024, 8019/8000, 234375/234256		\| 2401/2400, 3025/3024, 8019/8000, 234375/234256
	\| {{mapping\| 445 705 1033 1249 1539 }}		\| {{mapping\| 445 705 1033 1249 1539 }}
	\| 0.2870		\| +0.2870
	\| 0.1694		\| 0.1694
	\| 6.28		\| 6.28