445edo - 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"

2026-03-13T13:33:06Z

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
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	\| [[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
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	=== 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 ==
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	\| [[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 ==
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	! [[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
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	\| 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

FloraC: Review

2024-01-21T10:17:45Z

Review

← Older revision		Revision as of 10:17, 21 January 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~445et~~ is consistent to the [[7-odd-limit]]~~. Using the patent val~~, ~~it tempers out 1220703125~~/~~1219784832~~, ~~48828125~~/~~48771072~~, ~~95703125/95551488~~ and [[2401/2400]] ~~in the 7-limit; 78121827/77948684~~, ~~56723625~~/~~56689952~~, ~~10333575~~/~~10307264~~, ~~35156250~~/~~35153041~~, ~~234375~~/~~234256, 1366875~~/~~1362944, 104162436/103984375, 1953125/1951488, 151263/151250, 472392/471625, 137781/137500, 24057/24010~~, [[8019/8000]], ~~[[3025~~/~~3024]]~~, [[41503/41472]], ~~539055~~/~~537824~~, ~~35937~~/~~35840~~, ~~244515348~~/~~244140625, 805255/802816, 39135393/39062500~~ in the 11-limit. It [[support]]s [[~~misneb~~]].		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]].

	=== Odd harmonics ===		=== Odd 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\|-141 89}}		\| {{monzo\| -141 89 }}
	\|{{mapping\|445 705}}		\| {{mapping\| 445 705 }}
	\| 0.2623		\| 0.2623
	\| 0.2623		\| 0.2623
	\| 9.73		\| 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
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|2401/2400, ~~48828125~~/~~48771072~~, 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
	\|-		\|-
	\|2.3.5.7.11		\| 2.3.5.7.11
	\|3025/3024~~, 2401/2400~~, 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
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	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|13\445		\| 13\445
	\|35.06		\| 35.06
	\|1990656/1953125		\| 1990656/1953125
	\|[[Gammic]]		\| [[Gammic]] (5-limit)
	\|-		\|-
	\|1		\| 1
	\|42\445		\| 42\445
	\|113.26		\| 113.26
	\|16/15		\| 16/15
	\|[[Misneb]]		\| [[Misneb]]
	\|-		\|-
	\|1		\| 1
	\|216\445		\| 216\445
	\|582.47		\| 582.47
	\|7/5		\| 7/5
	\|[[Neptune]]		\| [[Neptune]] (7-limit)
	\|-		\|-
	\|5		\| 5
	\|185\445<br>(7\445)		\| 185\445<br>(7\445)
	\|498.88<br>(18.88)		\| 498.88<br>(18.88)
	\|4/3<br>(81/80)		\| 4/3<br>(81/80)
	\|[[Pental]]		\| [[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

Francium: Created page with "{{Infobox ET}} {{EDO intro|445}} == Theory == 445et is consistent to the 7-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 48828125/48771072, 95703..."

2024-01-18T09:30:33Z

Created page with "{{Infobox ET}} {{EDO intro|445}} == Theory == 445et is consistent to the 7-odd-limit. Using the patent val, it tempers out 1220703125/1219784832, 48828125/48771072, 95703..."

New page

{{Infobox ET}}
{{EDO intro|445}}

== Theory ==
445et is consistent to the [[7-odd-limit]]. Using the patent val, it tempers out 1220703125/1219784832, 48828125/48771072, 95703125/95551488 and [[2401/2400]] in the 7-limit; 78121827/77948684, 56723625/56689952, 10333575/10307264, 35156250/35153041, 234375/234256, 1366875/1362944, 104162436/103984375, 1953125/1951488, 151263/151250, 472392/471625, 137781/137500, 24057/24010, [[8019/8000]], [[3025/3024]], [[41503/41472]], 539055/537824, 35937/35840, 244515348/244140625, 805255/802816, 39135393/39062500 in the 11-limit. It [[support]]s [[misneb]].

=== Odd harmonics ===
{{Harmonics in equal|445}}

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

== 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|-141 89}}
|{{mapping|445 705}}
| 0.2623
| 0.2623
| 9.73
|-
|2.3.5
|{{monzo|-28 25 -5}}, {{monzo|-29 -11 20}}
|{{mapping|445 705 1033}}
| 0.2748
| 0.2149
| 7.97
|-
|2.3.5.7
|2401/2400, 48828125/48771072, 43046721/42875000
|{{mapping|445 705 1033 1249}}
| 0.2716
| 0.1862
| 6.90
|-
|2.3.5.7.11
|3025/3024, 2401/2400, 8019/8000, 234375/234256
|{{mapping|445 705 1033 1249 1539}}
| 0.2870
| 0.1694
| 6.28
|}

=== 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
|13\445
|35.06
|1990656/1953125
|[[Gammic]]
|-
|1
|42\445
|113.26
|16/15
|[[Misneb]]
|-
|1
|216\445
|582.47
|7/5
|[[Neptune]]
|-
|5
|185\445 (7\445)
|498.88 (18.88)
|4/3 (81/80)
|[[Pental]]
|}

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