566edo - 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"

2026-03-13T13:32:19Z

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
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	\| [[Orga]]		\| [[Orga]]
	\|}		\|}
	<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

BudjarnLambeth at 01:14, 20 October 2025

2025-10-20T01:14:26Z

← Older revision		Revision as of 01:14, 20 October 2025
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	== Theory ==		== Theory ==
	566edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[~~skeetsma~~]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].		566edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[scheme comma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].

	The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.		The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.

Francium: changed EDO intro to ED intro

2025-02-21T06:30:13Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:30, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|566~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:24:37Z

Theory: cleanup

← Older revision		Revision as of 16:24, 17 January 2025
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	== Theory ==		== Theory ==
	566edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]]. It [[tempers out]] the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].		566edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]]. As an equal temperament, it [[tempering out\|tempers out]] the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].

	The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.		The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 566 factors into ~~{{factorization\|566}}~~, 566edo contains [[2edo]] and [[283edo]] as subsets.		Since 566 factors into 2 × 283, 566edo contains [[2edo]] and [[283edo]] as subsets.

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

ArrowHead294 at 18:06, 15 January 2025

2025-01-15T18:06:34Z

← Older revision		Revision as of 18:06, 15 January 2025
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	== Theory ==		== Theory ==
	566edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]]. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].		566edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]]. It [[tempers out]] the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].

	The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.		The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.
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	\| [[Orga]]		\| [[Orga]]
	\|}		\|}
	<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

2024-11-16T12:51:14Z

Partial undo

← Older revision		Revision as of 12:51, 16 November 2024
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	== 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
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	\| 0.1047		\| 0.1047
	\| 4.94		\| 4.94
	~~{{comma basis end}~~}		\|}
	* 566et (566g val) has a lower absolute error in the 23-limit than any previous equal temperaments, past [[525edo\|525]] and followed by [[581edo\|581]].		* 566et (566g val) has a lower absolute error in the 23-limit than any previous equal temperaments, past [[525edo\|525]] and followed by [[581edo\|581]].

	=== 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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	\| 8/7		\| 8/7
	\| [[Orga]]		\| [[Orga]]
	~~{{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 03:46, 16 November 2024

2024-11-16T03:46:50Z

← Older revision		Revision as of 03:46, 16 November 2024
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	== 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
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	\| 0.1047		\| 0.1047
	\| 4.94		\| 4.94
	\|}		{{comma basis end}}
	* 566et (566g val) has a lower absolute error in the 23-limit than any previous equal temperaments, past [[525edo\|525]] and followed by [[581edo\|581]].		* 566et (566g val) has a lower absolute error in the 23-limit than any previous equal temperaments, past [[525edo\|525]] and followed by [[581edo\|581]].

	=== 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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	\| 8/7		\| 8/7
	\| [[Orga]]		\| [[Orga]]
	\|}		{{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: Adopt template: Factorization

2023-11-02T13:41:47Z

Adopt template: Factorization

← Older revision		Revision as of 13:41, 2 November 2023
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	== Theory ==		== Theory ==
	566edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]]. The equal temperament tempers out the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].		566edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]]. The equal temperament [[tempering out\|tempers out]] the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].

	The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.		The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 566 factors into ~~2 × 283~~, 566edo ~~has~~ [[2edo]] and [[283edo]] as ~~its~~ subsets.		Since 566 factors into {{factorization\|566}}, 566edo contains [[2edo]] and [[283edo]] as subsets.

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

FloraC: Cleanup; clarify the title row of the rank-2 temp table

2023-10-29T08:56:32Z

Cleanup; clarify the title row of the rank-2 temp table

← Older revision		Revision as of 08:56, 29 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	566edo is ~~distinctly~~ [[consistent]] in the [[15-odd-limit]]. It tempers out the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].		566edo is [[consistency\|distinctly consistent]] in the [[15-odd-limit]]. The equal temperament tempers out the [[schisma]] in the 5-limit; 4375/4374 ([[ragisma]]), 65625/65536 ([[horwell comma]]), and 14348907/14336000 ([[skeetsma]]) in the 7-limit; [[3025/3024]] in the 11-limit; [[1716/1715]] and [[2080/2079]] in the 13-limit. It notably supports [[pontiac]] and [[orga]].

	The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.		The 566g val is interesting in the higher limits, and in the 23-limit in particular it has a great rating in terms of absolute error. It tempers out [[1156/1155]], 1275/1274, 2431/2430, [[2500/2499]] and [[2601/2600]] in the 17-limit; [[1445/1444]], [[1521/1520]] and [[1729/1728]] in the 19-limit; 1105/1104 and 2025/2024 in the 23-limit.
Line 11:		Line 11:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	566edo has ~~subset edos~~ [[2edo]] and [[283edo]].		Since 566 factors into 2 × 283, 566edo has [[2edo]] and [[283edo]] as its subsets.

	== Regular temperament properties ==		== Regular temperament properties ==
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	\| 2.3		\| 2.3
	\| {{monzo\| -897 566 }}		\| {{monzo\| -897 566 }}
	\| [{{~~val~~\| 566 897 }}]		\| {{mapping\| 566 897 }}
	\| +0.0594		\| +0.0594
	\| 0.0594		\| 0.0594
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	\| 2.3.5		\| 2.3.5
	\| 32805/32768, {{monzo\| -3 -86 60 }}		\| 32805/32768, {{monzo\| -3 -86 60 }}
	\| [{{~~val~~\| 566 897 1314 }}]		\| {{mapping\| 566 897 1314 }}
	\| +0.1039		\| +0.1039
	\| 0.0795		\| 0.0795
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	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 32805/32768, {{monzo\| 10 5 8 -13 }}		\| 4375/4374, 32805/32768, {{monzo\| 10 5 8 -13 }}
	\| [{{~~val~~\| 566 897 1314 1589 }}]		\| {{mapping\| 566 897 1314 1589 }}
	\| +0.0709		\| +0.0709
	\| 0.0894		\| 0.0894
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 3025/3024, 4375/4374, 32805/32768, 825000/823543		\| 3025/3024, 4375/4374, 32805/32768, 825000/823543
	\| [{{~~val~~\| 566 897 1314 1589 1958 }}]		\| {{mapping\| 566 897 1314 1589 1958 }}
	\| +0.0614		\| +0.0614
	\| 0.0822		\| 0.0822
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 1716/1715, 2080/2079, 3025/3024, 15379/15360, 31250/31213		\| 1716/1715, 2080/2079, 3025/3024, 15379/15360, 31250/31213
	\| [{{~~val~~\| 566 897 1314 1589 1958 2094 }}]		\| {{mapping\| 566 897 1314 1589 1958 2094 }}
	\| +0.0941		\| +0.0941
	\| 0.1047		\| 0.1047
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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*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Orga]]		\| [[Orga]]
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

BudjarnLambeth at 06:39, 9 July 2023

2023-07-09T06:39:23Z

← Older revision		Revision as of 06:39, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|566}}		{{EDO intro\|566}}