320edo - 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"

2026-03-13T13:33:02Z

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 163:		Line 163:
	\| [[Octogintic]]		\| [[Octogintic]]
	\|}		\|}
	<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

	[[Category:Varuna]]		[[Category:Varuna]]
	[[Category:Werckismic]]		[[Category:Werckismic]]

Francium: changed EDO intro to ED intro

2025-02-19T17:52:45Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:52, 19 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|320~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Regular temperament properties */ cleanup and update

2025-02-19T14:40:37Z

Regular temperament properties: cleanup and update

← Older revision		Revision as of 14:40, 19 February 2025
Line 19:		Line 19:
	! 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
	\|-		\|-
Line 26:		Line 26:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| -507 320 }}		\| {{Monzo\| -507 320 }}
	\| {{~~mapping~~\| 320 507 }}		\| {{Mapping\| 320 507 }}
	\| +0.2224		\| +0.2224
	\| 0.2224		\| 0.2224
Line 33:		Line 33:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 23 6 -14 }}, {{monzo\| -28 25 -5 }}		\| {{Monzo\| 23 6 -14 }}, {{monzo\| -28 25 -5 }}
	\| {{~~mapping~~\| 320 507 743 }}		\| {{Mapping\| 320 507 743 }}
	\| +0.1574		\| +0.1574
	\| 0.2036		\| 0.2036
Line 41:		Line 41:
	\| 2.3.5.7		\| 2.3.5.7
	\| 65625/65536, 235298/234375, 321489/320000		\| 65625/65536, 235298/234375, 321489/320000
	\| {{~~mapping~~\| 320 507 743 898 }}		\| {{Mapping\| 320 507 743 898 }}
	\| +0.2361		\| +0.2361
	\| 0.2229		\| 0.2229
Line 48:		Line 48:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 441/440, 8019/8000, 41503/41472, 65625/65536		\| 441/440, 8019/8000, 41503/41472, 65625/65536
	\| {{~~mapping~~\| 320 507 743 898 1107 }}		\| {{Mapping\| 320 507 743 898 1107 }}
	\| +0.1928		\| +0.1928
	\| 0.2173		\| 0.2173
Line 55:		Line 55:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 441/440, 729/728, 1001/1000, 4225/4224, 6656/6655		\| 441/440, 729/728, 1001/1000, 4225/4224, 6656/6655
	\| {{~~mapping~~\| 320 507 743 898 1107 1184 }}		\| {{Mapping\| 320 507 743 898 1107 1184 }}
	\| +0.1845		\| +0.1845
	\| 0.1993		\| 0.1993
Line 62:		Line 62:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 441/440, 729/728, 833/832, 1001/1000, 1089/1088, 4225/4224		\| 441/440, 729/728, 833/832, 1001/1000, 1089/1088, 4225/4224
	\| {{~~mapping~~\| 320 507 743 898 1107 1184 1308 }}		\| {{Mapping\| 320 507 743 898 1107 1184 1308 }}
	\| +0.1565		\| +0.1565
	\| 0.1968		\| 0.1968
Line 69:		Line 69:
	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 441/440, 513/512, 729/728, 833/832, 969/968, 1001/1000, 1521/1520		\| 441/440, 513/512, 729/728, 833/832, 969/968, 1001/1000, 1521/1520
	\| {{~~mapping~~\| 320 507 743 898 1107 1184 1308 1359 }}		\| {{Mapping\| 320 507 743 898 1107 1184 1308 1359 }}
	\| +0.1741		\| +0.1741
	\| 0.1899		\| 0.1899
Line 79:		Line 79:
	\|+ 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 88:		Line 88:
	\| 7\320		\| 7\320
	\| 26.25		\| 26.25
	\| {{~~monzo~~\| -2 13 -8 }}		\| {{Monzo\| -2 13 -8 }}
	\| [[Sfourth]] (5-limit)		\| [[Sfourth]] (5-limit)
	\|-		\|-
Line 116:		Line 116:
	\|-		\|-
	\| 5		\| 5
	\| 133\320<br />(5\320)		\| 133\320<br>(5\320)
	\| 498.75<br />(18.75)		\| 498.75<br>(18.75)
	\| 4/3<br />(81/80)		\| 4/3<br>(81/80)
	\| [[~~Pental (temperament)\|Pental~~]]		\| [[Quintile]]
	\|-		\|-
	\| 8		\| 8
	\| 133\320<br />(9\320)		\| 133\320<br>(9\320)
	\| 566.25<br />(33.75)		\| 566.25<br>(33.75)
	\| 104/75<br />(55/54)		\| 104/75<br>(55/54)
	\| [[Octowerck]]		\| [[Octowerck]]
	\|-		\|-
	\| 10		\| 10
	\| 19\320<br />(13\320)		\| 19\320<br>(13\320)
	\| 71.25<br />(48.75)		\| 71.25<br>(48.75)
	\| 25/24<br />(36/35)		\| 25/24<br>(36/35)
	\| [[Decavish]]		\| [[Decavish]]
	\|-		\|-
	\| 10		\| 10
	\| 133\320<br />(5\320)		\| 133\320<br>(5\320)
	\| 498.75<br />(18.75)		\| 498.75<br>(18.75)
	\| 4/3<br />(81/80)		\| 4/3<br>(81/80)
	\| [[~~Decal~~]]		\| [[Decile]]
	\|-		\|-
	\| 20		\| 20
	\| 151\320<br />(7\320)		\| 151\320<br>(7\320)
	\| 566.25<br />(26.25)		\| 566.25<br>(26.25)
	\| 165/119<br />(?)		\| 165/119<br>(?)
	\| [[Soviet ferris wheel]]		\| [[Soviet ferris wheel]]
	\|-		\|-
	\| 32		\| 32
	\| 133\320<br />(3\320)		\| 133\320<br>(3\320)
	\| 498.75<br />(11.25)		\| 498.75<br>(11.25)
	\| 4/3<br />(?)		\| 4/3<br>(?)
	\| [[Bezique]]		\| [[Bezique]]
	\|-		\|-
	\| 80		\| 80
	\| 99\320<br />(3\320)		\| 99\320<br>(3\320)
	\| 371.25<br />(11.25)		\| 371.25<br>(11.25)
	\| 2275/1836<br />(?)		\| 2275/1836<br>(?)
	\| [[Mercury]]		\| [[Mercury]]
	\|-		\|-
	\| 80		\| 80
	\| 133\320<br />(1\320)		\| 133\320<br>(1\320)
	\| 498.75<br />(3.75)		\| 498.75<br>(3.75)
	\| 4/3<br />(245/243)		\| 4/3<br>(245/243)
	\| [[Octogintic]]		\| [[Octogintic]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	[[Category:Varuna]]		[[Category:Varuna]]
	[[Category:Werckismic]]		[[Category:Werckismic]]

FloraC: /* Theory */ cleanup

2025-01-17T15:53:51Z

Theory: cleanup

← Older revision		Revision as of 15:53, 17 January 2025
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	320edo is [[consistent]] in the [[19-odd-limit]] and a fairly good tuning for the [[19-limit]]. It has a flat tendency for most [[prime harmonic]]s from 3 to 19, with the sole exception of [[17/1\|17]].		320edo is [[consistent]] in the [[19-odd-limit]] and a fairly good tuning for the [[19-limit]]. It has a flat tendency for most [[prime harmonic]]s from 3 to 19, with the sole exception of [[17/1\|17]].

	It [[tempers out]] 65625/65536 ([[horwell comma]]) and 420175/419904 ([[wizma]]) in the 7-limit and [[441/440]], [[8019/8000]] and [[9801/9800]] in the 11-limit, and so [[support]]s the [[varuna]] temperament, the rank-3 temperament tempering out 441/440, 8019/8000 and 9801/9800, for which it provides the [[optimal patent val]]. It also provides the optimal patent val for the rank-4 werckismic temperament tempering out 441/440. It tempers out [[729/728]], [[1001/1000]], [[1575/1573]], [[4225/4224]] and [[6656/6655]] in the 13-limit, leading to further temperaments for which it provides the optimal patent val, such as tempering out 441/440 with 729/728, 1001/1000 or both, or with 8019/8000, leading to an extension of varuna.		As an equal temperament, it [[tempering out\|tempers out]] 65625/65536 ([[horwell comma]]) and 420175/419904 ([[wizma]]) in the 7-limit and [[441/440]], [[8019/8000]] and [[9801/9800]] in the 11-limit, and so [[support]]s the [[varuna]] temperament, the rank-3 temperament tempering out 441/440, 8019/8000 and 9801/9800, for which it provides the [[optimal patent val]]. It also provides the optimal patent val for the rank-4 werckismic temperament tempering out 441/440. It tempers out [[729/728]], [[1001/1000]], [[1575/1573]], [[4225/4224]] and [[6656/6655]] in the 13-limit, leading to further temperaments for which it provides the optimal patent val, such as tempering out 441/440 with 729/728, 1001/1000 or both, or with 8019/8000, leading to an extension of varuna.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 320 factors into ~~{{factorisation\|320}}~~, 320edo has subset edos {{EDOs\| 2, 4, 5, 10, 16, 20, 32, 40, 64, 80, and 160 }}.		Since 320 factors into 2<sup>6</sup> × 5, 320edo has subset edos {{EDOs\| 2, 4, 5, 10, 16, 20, 32, 40, 64, 80, and 160 }}.

	== Regular temperament properties ==		== Regular temperament properties ==

ArrowHead294 at 14:18, 16 January 2025

2025-01-16T14:18:58Z

← Older revision		Revision as of 14:18, 16 January 2025
Line 5:		Line 5:
	320edo is [[consistent]] in the [[19-odd-limit]] and a fairly good tuning for the [[19-limit]]. It has a flat tendency for most [[prime harmonic]]s from 3 to 19, with the sole exception of [[17/1\|17]].		320edo is [[consistent]] in the [[19-odd-limit]] and a fairly good tuning for the [[19-limit]]. It has a flat tendency for most [[prime harmonic]]s from 3 to 19, with the sole exception of [[17/1\|17]].

	~~The equal temperament~~ [[~~tempering out\|~~tempers out]] 65625/65536 ([[horwell comma]]) and 420175/419904 ([[wizma]]) in the 7-limit and [[441/440]], [[8019/8000]] and [[9801/9800]] in the 11-limit, and so [[support]]s the [[varuna]] temperament, the rank-3 temperament tempering out 441/440, 8019/8000 and 9801/9800, for which it provides the [[optimal patent val]]. It also provides the optimal patent val for the rank-4 werckismic temperament tempering out 441/440. It tempers out [[729/728]], [[1001/1000]], [[1575/1573]], [[4225/4224]] and [[6656/6655]] in the 13-limit, leading to further temperaments for which it provides the optimal patent val, such as tempering out 441/440 with 729/728, 1001/1000 or both, or with 8019/8000, leading to an extension of varuna.		It [[tempers out]] 65625/65536 ([[horwell comma]]) and 420175/419904 ([[wizma]]) in the 7-limit and [[441/440]], [[8019/8000]] and [[9801/9800]] in the 11-limit, and so [[support]]s the [[varuna]] temperament, the rank-3 temperament tempering out 441/440, 8019/8000 and 9801/9800, for which it provides the [[optimal patent val]]. It also provides the optimal patent val for the rank-4 werckismic temperament tempering out 441/440. It tempers out [[729/728]], [[1001/1000]], [[1575/1573]], [[4225/4224]] and [[6656/6655]] in the 13-limit, leading to further temperaments for which it provides the optimal patent val, such as tempering out 441/440 with 729/728, 1001/1000 or both, or with 8019/8000, leading to an extension of varuna.

	=== Prime harmonics ===		=== Prime harmonics ===
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 320 factors into ~~2<sup>6</sup> × 5~~, 320edo has subset edos {{EDOs\| 2, 4, 5, 10, 16, 20, 32, 40, 64, 80, and 160 }}.		Since 320 factors into {{factorisation\|320}}, 320edo has subset edos {{EDOs\| 2, 4, 5, 10, 16, 20, 32, 40, 64, 80, and 160 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 163:		Line 163:
	\| [[Octogintic]]		\| [[Octogintic]]
	\|}		\|}
	<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

	[[Category:Varuna]]		[[Category:Varuna]]
	[[Category:Werckismic]]		[[Category:Werckismic]]

BudjarnLambeth: Scales this big do not need automatic interval tables because they slow the page load time for some users (~110 notes is the cutoff)

2024-12-24T13:42:14Z

Scales this big do not need automatic interval tables because they slow the page load time for some users (~110 notes is the cutoff)

← Older revision		Revision as of 13:42, 24 December 2024
Line 12:		Line 12:
	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 320 factors into 2<sup>6</sup> × 5, 320edo has subset edos {{EDOs\| 2, 4, 5, 10, 16, 20, 32, 40, 64, 80, and 160 }}.		Since 320 factors into 2<sup>6</sup> × 5, 320edo has subset edos {{EDOs\| 2, 4, 5, 10, 16, 20, 32, 40, 64, 80, and 160 }}.

	~~== Intervals ==~~
	~~{{Interval table}}~~

	== Regular temperament properties ==		== Regular temperament properties ==

FloraC: Put things where appropriate

2024-12-22T14:25:00Z

Put things where appropriate

← Older revision		Revision as of 14:25, 22 December 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|320}}		{{EDO intro\|320}}
	~~{{Interval table}}~~

	== Theory ==		== Theory ==
Line 13:		Line 12:
	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 320 factors into 2<sup>6</sup> × 5, 320edo has subset edos {{EDOs\| 2, 4, 5, 10, 16, 20, 32, 40, 64, 80, and 160 }}.		Since 320 factors into 2<sup>6</sup> × 5, 320edo has subset edos {{EDOs\| 2, 4, 5, 10, 16, 20, 32, 40, 64, 80, and 160 }}.

			== Intervals ==
			{{Interval table}}

	== Regular temperament properties ==		== Regular temperament properties ==

MisterShafXen at 14:21, 22 December 2024

2024-12-22T14:21:53Z

← Older revision		Revision as of 14:21, 22 December 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|320}}		{{EDO intro\|320}}
			{{Interval table}}

	== Theory ==		== Theory ==

ArrowHead294: Partial undo

2024-11-16T12:15:17Z

Partial undo

← Older revision		Revision as of 12:15, 16 November 2024
Line 14:		Line 14:

	== 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 64:		Line 73:
	\| 0.1899		\| 0.1899
	\| 5.06		\| 5.06
	~~{{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 146:		Line 162:
	\| 4/3<br />(245/243)		\| 4/3<br />(245/243)
	\| [[Octogintic]]		\| [[Octogintic]]
	~~{{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

	[[Category:Varuna]]		[[Category:Varuna]]
	[[Category:Werckismic]]		[[Category:Werckismic]]

ArrowHead294 at 05:12, 16 November 2024

2024-11-16T05:12:21Z

← Older revision		Revision as of 05:12, 16 November 2024
Line 14:		Line 14:

	== 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 72:		Line 64:
	\| 0.1899		\| 0.1899
	\| 5.06		\| 5.06
	\|}		{{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 114:		Line 100:
	\|-		\|-
	\| 5		\| 5
	\| 133\320<br>(5\320)		\| 133\320<br />(5\320)
	\| 498.75<br>(18.75)		\| 498.75<br />(18.75)
	\| 4/3<br>(81/80)		\| 4/3<br />(81/80)
	\| [[Pental (temperament)\|Pental]]		\| [[Pental (temperament)\|Pental]]
	\|-		\|-
	\| 8		\| 8
	\| 133\320<br>(9\320)		\| 133\320<br />(9\320)
	\| 566.25<br>(33.75)		\| 566.25<br />(33.75)
	\| 104/75<br>(55/54)		\| 104/75<br />(55/54)
	\| [[Octowerck]]		\| [[Octowerck]]
	\|-		\|-
	\| 10		\| 10
	\| 19\320<br>(13\320)		\| 19\320<br />(13\320)
	\| 71.25<br>(48.75)		\| 71.25<br />(48.75)
	\| 25/24<br>(36/35)		\| 25/24<br />(36/35)
	\| [[Decavish]]		\| [[Decavish]]
	\|-		\|-
	\| 10		\| 10
	\| 133\320<br>(5\320)		\| 133\320<br />(5\320)
	\| 498.75<br>(18.75)		\| 498.75<br />(18.75)
	\| 4/3<br>(81/80)		\| 4/3<br />(81/80)
	\| [[Decal]]		\| [[Decal]]
	\|-		\|-
	\| 20		\| 20
	\| 151\320<br>(7\320)		\| 151\320<br />(7\320)
	\| 566.25<br>(26.25)		\| 566.25<br />(26.25)
	\| 165/119<br>(?)		\| 165/119<br />(?)
	\| [[Soviet ferris wheel]]		\| [[Soviet ferris wheel]]
	\|-		\|-
	\| 32		\| 32
	\| 133\320<br>(3\320)		\| 133\320<br />(3\320)
	\| 498.75<br>(11.25)		\| 498.75<br />(11.25)
	\| 4/3<br>(?)		\| 4/3<br />(?)
	\| [[Bezique]]		\| [[Bezique]]
	\|-		\|-
	\| 80		\| 80
	\| 99\320<br>(3\320)		\| 99\320<br />(3\320)
	\| 371.25<br>(11.25)		\| 371.25<br />(11.25)
	\| 2275/1836<br>(?)		\| 2275/1836<br />(?)
	\| [[Mercury]]		\| [[Mercury]]
	\|-		\|-
	\| 80		\| 80
	\| 133\320<br>(1\320)		\| 133\320<br />(1\320)
	\| 498.75<br>(3.75)		\| 498.75<br />(3.75)
	\| 4/3<br>(245/243)		\| 4/3<br />(245/243)
	\| [[Octogintic]]		\| [[Octogintic]]
	\|}		{{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}}

	[[Category:Varuna]]		[[Category:Varuna]]
	[[Category:Werckismic]]		[[Category:Werckismic]]