255edo - 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"

2026-03-13T13:33:07Z

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 110:		Line 110:
	\| [[Chlorine]] (5-limit)		\| [[Chlorine]] (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

	[[Category:Mirkat]]		[[Category:Mirkat]]

Francium: changed EDO intro to ED intro

2025-02-19T17:53:23Z

changed EDO intro to ED intro

← Older revision		Revision as of 17:53, 19 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|255~~}}		{{ED intro}}

	== Theory ==		== Theory ==

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

2025-02-19T14:37:51Z

Regular temperament properties: cleanup and update

← Older revision		Revision as of 14:37, 19 February 2025
Line 17:		Line 17:
	! 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 24:		Line 24:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| -404 255 }}		\| {{Monzo\| -404 255 }}
	\| {{~~mapping~~\| 255 404 }}		\| {{Mapping\| 255 404 }}
	\| +0.246		\| +0.246
	\| 0.246		\| 0.246
Line 31:		Line 31:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 8 14 -13 }}, {{monzo\| -36 11 8 }}		\| {{Monzo\| 8 14 -13 }}, {{monzo\| -36 11 8 }}
	\| {{~~mapping~~\| 255 404 592 }}		\| {{Mapping\| 255 404 592 }}
	\| +0.226		\| +0.226
	\| 0.203		\| 0.203
Line 39:		Line 39:
	\| 2.3.5.7		\| 2.3.5.7
	\| 16875/16807, 19683/19600, 65625/65536		\| 16875/16807, 19683/19600, 65625/65536
	\| {{~~mapping~~\| 255 404 592 716 }}		\| {{Mapping\| 255 404 592 716 }}
	\| +0.117		\| +0.117
	\| 0.257		\| 0.257
Line 46:		Line 46:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 540/539, 1375/1372, 8019/8000, 65625/65536		\| 540/539, 1375/1372, 8019/8000, 65625/65536
	\| {{~~mapping~~\| 255 404 592 716 882 }}		\| {{Mapping\| 255 404 592 716 882 }}
	\| +0.136		\| +0.136
	\| 0.233		\| 0.233
Line 56:		Line 56:
	\|+ 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 87:		Line 87:
	\|-		\|-
	\| 3		\| 3
	\| 82\255<br />(3\255)		\| 82\255<br>(3\255)
	\| 385.88<br />(14.12)		\| 385.88<br>(14.12)
	\| 5/4<br />(126/125)		\| 5/4<br>(126/125)
	\| [[Mutt]] (7-limit)		\| [[Mutt]] (7-limit)
	\|-		\|-
	\| 5		\| 5
	\| 53\255<br />(2\255)		\| 53\255<br>(2\255)
	\| 249.41<br />(9.41)		\| 249.41<br>(9.41)
	\| 81/70<br />(176/175)		\| 81/70<br>(176/175)
	\| [[~~Hemipental~~]] / ~~hemipent~~ (255) / ~~hemipentalis~~ (255f)		\| [[Hemiquintile]] / hemiquint (255) / hemiquintilis (255f)
	\|-		\|-
	\| 5		\| 5
	\| 106\255<br />(4\255)		\| 106\255<br>(4\255)
	\| 498.82<br />(18.82)		\| 498.82<br>(18.82)
	\| 4/3<br />(81/80)		\| 4/3<br>(81/80)
	\| [[~~Pental (temperament)\|Pental~~]] ~~(5-limit)~~		\| [[Quintile]]
	\|-		\|-
	\| 17		\| 17
	\| 53\255<br />(7\255)		\| 53\255<br>(7\255)
	\| 249.41<br />(32.94)		\| 249.41<br>(32.94)
	\| {{~~monzo~~\| -25 -9 17 }}<br />(1990656/1953125)		\| {{Monzo\| -25 -9 17 }}<br>(1990656/1953125)
	\| [[Chlorine]] (5-limit)		\| [[Chlorine]] (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 lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	[[Category:Mirkat]]		[[Category:Mirkat]]

ArrowHead294 at 18:49, 15 January 2025

2025-01-15T18:49:20Z

← Older revision		Revision as of 18:49, 15 January 2025
Line 110:		Line 110:
	\| [[Chlorine]] (5-limit)		\| [[Chlorine]] (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

	[[Category:Mirkat]]		[[Category:Mirkat]]

ArrowHead294: Partial undo

2024-11-16T12:45:19Z

Partial undo

← Older revision		Revision as of 12:45, 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 41:		Line 50:
	\| 0.233		\| 0.233
	\| 4.95		\| 4.95
	~~{{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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	\| {{monzo\| -25 -9 17 }}<br />(1990656/1953125)		\| {{monzo\| -25 -9 17 }}<br />(1990656/1953125)
	\| [[Chlorine]] (5-limit)		\| [[Chlorine]] (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

	[[Category:Mirkat]]		[[Category:Mirkat]]

ArrowHead294 at 04:01, 16 November 2024

2024-11-16T04:01:09Z

← Older revision		Revision as of 04:01, 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 8ve <br>Stretch (¢)~~
	~~! colspan="2" \| Tuning Error~~
	\|-
	~~! [[TE error\|Absolute]] (¢)~~
	~~! [[TE simple badness\|Relative]] (%)~~
	\|-		\|-
	\| 2.3		\| 2.3
Line 49:		Line 41:
	\| 0.233		\| 0.233
	\| 4.95		\| 4.95
	\|}		{{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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	\|-		\|-
	\| 3		\| 3
	\| 82\255<br>(3\255)		\| 82\255<br />(3\255)
	\| 385.88<br>(14.12)		\| 385.88<br />(14.12)
	\| 5/4<br>(126/125)		\| 5/4<br />(126/125)
	\| [[Mutt]] (7-limit)		\| [[Mutt]] (7-limit)
	\|-		\|-
	\| 5		\| 5
	\| 53\255<br>(2\255)		\| 53\255<br />(2\255)
	\| 249.41<br>(9.41)		\| 249.41<br />(9.41)
	\| 81/70<br>(176/175)		\| 81/70<br />(176/175)
	\| [[Hemipental]] / hemipent (255) / hemipentalis (255f)		\| [[Hemipental]] / hemipent (255) / hemipentalis (255f)
	\|-		\|-
	\| 5		\| 5
	\| 106\255<br>(4\255)		\| 106\255<br />(4\255)
	\| 498.82<br>(18.82)		\| 498.82<br />(18.82)
	\| 4/3<br>(81/80)		\| 4/3<br />(81/80)
	\| [[Pental (temperament)\|Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|-		\|-
	\| 17		\| 17
	\| 53\255<br>(7\255)		\| 53\255<br />(7\255)
	\| 249.41<br>(32.94)		\| 249.41<br />(32.94)
	\| {{monzo\| -25 -9 17 }}<br>(1990656/1953125)		\| {{monzo\| -25 -9 17 }}<br />(1990656/1953125)
	\| [[Chlorine]] (5-limit)		\| [[Chlorine]] (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}}

	[[Category:Mirkat]]		[[Category:Mirkat]]

Fredg999: Skip disambiguation

2024-09-09T01:57:17Z

Skip disambiguation

← Older revision		Revision as of 01:57, 9 September 2024
Line 100:		Line 100:
	\| 498.82<br>(18.82)		\| 498.82<br>(18.82)
	\| 4/3<br>(81/80)		\| 4/3<br>(81/80)
	\| [[Pental]] (5-limit)		\| [[Pental (temperament)\|Pental]] (5-limit)
	\|-		\|-
	\| 17		\| 17

FloraC: Cleanup; +subsets and supersets

2024-03-14T08:55:26Z

Cleanup; +subsets and supersets

← Older revision		Revision as of 08:55, 14 March 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~255et~~ tempers out the [[parakleisma]], {{monzo\| 8 14 -13 }}, and the [[septendecima]], {{monzo\| -52 -17 34 }}, in the 5-limit. In the 7-limit it tempers out [[cataharry]], 19683/19600, [[mirkwai]], 16875/16807 and [[horwell]], 65625/65536, so that it [[support]]s the [[mirkat]] temperament, and in fact provides the [[optimal patent val]]. It also gives the optimal patent val for mirkat in the 11-limit, tempering out [[540/539]], 1375/1372, [[3025/3024]] and [[8019/8000]]. In the 13-limit it tempers out [[847/845]], [[625/624]], [[1575/1573]] and [[1716/1715]].		The equal temperament [[tempering out\|tempers out]] the [[parakleisma]], {{monzo\| 8 14 -13 }}, and the [[septendecima]], {{monzo\| -52 -17 34 }}, in the 5-limit. In the 7-limit it tempers out [[cataharry]], 19683/19600, [[mirkwai]], 16875/16807 and [[horwell]], 65625/65536, so that it [[support]]s the [[mirkat]] temperament, and in fact provides the [[optimal patent val]]. It also gives the optimal patent val for mirkat in the 11-limit, tempering out [[540/539]], 1375/1372, [[3025/3024]] and [[8019/8000]]. In the 13-limit it tempers out [[847/845]], [[625/624]], [[1575/1573]] and [[1716/1715]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|255}}		{{Harmonics in equal\|255}}

			=== Subsets and supersets ===
			Since 255 factors into {{factorization\|255}}, 255edo has subset edos {{EDOs\| 3, 5, 15, 17, 51, and 85 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
Line 21:		Line 24:
	\| 2.3		\| 2.3
	\| {{monzo\| -404 255 }}		\| {{monzo\| -404 255 }}
	\| [{{~~val~~\| 255 404 }}]		\| {{mapping\| 255 404 }}
	\| +0.246		\| +0.246
	\| 0.246		\| 0.246
Line 28:		Line 31:
	\| 2.3.5		\| 2.3.5
	\| {{monzo\| 8 14 -13 }}, {{monzo\| -36 11 8 }}		\| {{monzo\| 8 14 -13 }}, {{monzo\| -36 11 8 }}
	\| [{{~~val~~\| 255 404 592 }}]		\| {{mapping\| 255 404 592 }}
	\| +0.226		\| +0.226
	\| 0.203		\| 0.203
Line 35:		Line 38:
	\| 2.3.5.7		\| 2.3.5.7
	\| 16875/16807, 19683/19600, 65625/65536		\| 16875/16807, 19683/19600, 65625/65536
	\| [{{~~val~~\| 255 404 592 716 }}]		\| {{mapping\| 255 404 592 716 }}
	\| +0.117		\| +0.117
	\| 0.257		\| 0.257
Line 42:		Line 45:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 540/539, 1375/1372, 8019/8000, 65625/65536		\| 540/539, 1375/1372, 8019/8000, 65625/65536
	\| [{{~~val~~\| 255 404 592 716 882 }}]		\| {{mapping\| 255 404 592 716 882 }}
	\| +0.136		\| +0.136
	\| 0.233		\| 0.233
Line 52:		Line 55:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Chlorine]] (5-limit)		\| [[Chlorine]] (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

	[[Category:Mirkat]]		[[Category:Mirkat]]

FloraC: /* Regular temperament properties */ -typo and cleanup

2023-05-08T08:25:52Z

Regular temperament properties: -typo and cleanup

← Older revision		Revision as of 08:25, 8 May 2023
Line 10:		Line 10:
	== 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]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \| [[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \| Optimal 8ve <br>~~stretch~~ (¢)		! rowspan="2" \| Optimal 8ve <br>Stretch (¢)
	! colspan="2" \| Tuning ~~error~~		! colspan="2" \| Tuning Error
	\|-		\|-
	! [[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
Line 34:		Line 34:
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
	\| ~~1687~~/16807, 19683/19600, 65625/65536		\| 16875/16807, 19683/19600, 65625/65536
	\| [{{val\| 255 404 592 716 }}]		\| [{{val\| 255 404 592 716 }}]
	\| +0.117		\| +0.117
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	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator<br>(~~reduced~~)		! Generator<br>(Reduced)
	! Cents<br>(~~reduced~~)		! Cents<br>(Reduced)
	! Associated<br>~~ratio~~		! Associated<br>Ratio
	! Temperaments		! Temperaments
	\|-		\|-
Line 106:		Line 106:
	\|}		\|}

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:Mirkat]]		[[Category:Mirkat]]

Eliora: /* Rank-2 temperaments */

2023-05-07T20:34:48Z

Rank-2 temperaments

← Older revision		Revision as of 20:34, 7 May 2023
Line 51:		Line 51:
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per ~~octave~~		! Periods<br>per 8ve
	! Generator<br>(reduced)		! Generator<br>(reduced)
	! Cents<br>(reduced)		! Cents<br>(reduced)