433edo - 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"

2026-03-13T13:32:31Z

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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	\| [[Orson]]		\| [[Orson]]
	\|}		\|}
	<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

	== Music ==		== Music ==

Lériendil: typo

2025-09-15T17:45:34Z

typo

← Older revision		Revision as of 17:45, 15 September 2025
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	== Theory ==		== Theory ==
	~~443edo~~ is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. To start with, the [[patent val]] {{val\| 433 686 1005 '''1216''' }} as well as the 433d [[val]] {{val\| 433 686 1005 '''1215''' }} are worth considering.		433edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. To start with, the [[patent val]] {{val\| 433 686 1005 '''1216''' }} as well as the 433d [[val]] {{val\| 433 686 1005 '''1215''' }} are worth considering.

	Using the patent val, it [[tempering out\|tempers out]] [[19683/19600]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 161280/161051, and 180224/180075 in the 11-limit.		Using the patent val, it [[tempering out\|tempers out]] [[19683/19600]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 161280/161051, and 180224/180075 in the 11-limit.

Francium: changed EDO intro to ED intro

2025-02-21T06:01:08Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:01, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|433~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:16:30Z

Theory: cleanup

← Older revision		Revision as of 16:16, 17 January 2025
Line 5:		Line 5:
	443edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. To start with, the [[patent val]] {{val\| 433 686 1005 '''1216''' }} as well as the 433d [[val]] {{val\| 433 686 1005 '''1215''' }} are worth considering.		443edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. To start with, the [[patent val]] {{val\| 433 686 1005 '''1216''' }} as well as the 433d [[val]] {{val\| 433 686 1005 '''1215''' }} are worth considering.

	Using the patent val, it [[tempers out]] [[19683/19600]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 161280/161051, and 180224/180075 in the 11-limit.		Using the patent val, it [[tempering out\|tempers out]] [[19683/19600]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 161280/161051, and 180224/180075 in the 11-limit.

	=== Odd harmonics ===		=== Odd harmonics ===

ArrowHead294 at 18:49, 15 January 2025

2025-01-15T18:49:04Z

← Older revision		Revision as of 18:49, 15 January 2025
Line 5:		Line 5:
	443edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. To start with, the [[patent val]] {{val\| 433 686 1005 '''1216''' }} as well as the 433d [[val]] {{val\| 433 686 1005 '''1215''' }} are worth considering.		443edo is only [[consistent]] to the [[5-odd-limit]] since [[harmonic]] [[7/1\|7]] is about halfway between its steps. To start with, the [[patent val]] {{val\| 433 686 1005 '''1216''' }} as well as the 433d [[val]] {{val\| 433 686 1005 '''1215''' }} are worth considering.

	Using the patent val, ~~the equal temperament~~ [[~~tempering out\|~~tempers out]] [[19683/19600]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 161280/161051, and 180224/180075 in the 11-limit.		Using the patent val, it [[tempers out]] [[19683/19600]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 161280/161051, and 180224/180075 in the 11-limit.

	=== Odd harmonics ===		=== Odd harmonics ===
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	\| {{monzo\| -686 433 }}		\| {{monzo\| -686 433 }}
	\| {{mapping\| 433 686 }}		\| {{mapping\| 433 686 }}
	\| 0.2525		\| +0.2525
	\| 0.2525		\| 0.2525
	\| 9.11		\| 9.11
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	\| 2109375/2097152, {{monzo\| -29 52 -23 }}		\| 2109375/2097152, {{monzo\| -29 52 -23 }}
	\| {{mapping\| 433 686 1005 }}		\| {{mapping\| 433 686 1005 }}
	\| 0.3254		\| +0.3254
	\| 0.2306		\| 0.2306
	\| 8.32		\| 8.32
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	\| 19683/19600, 4096000/4084101, 2109375/2097152		\| 19683/19600, 4096000/4084101, 2109375/2097152
	\| {{mapping\| 433 686 1005 1216 }}		\| {{mapping\| 433 686 1005 1216 }}
	\| 0.1414		\| +0.1414
	\| 0.3759		\| 0.3759
	\| 13.56		\| 13.56
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	\| 3025/3024, 6250/6237, 30375/30184, 180224/180075		\| 3025/3024, 6250/6237, 30375/30184, 180224/180075
	\| {{mapping\| 433 686 1005 1216 1498 }}		\| {{mapping\| 433 686 1005 1216 1498 }}
	\| 0.1026		\| +0.1026
	\| 0.3451		\| 0.3451
	\| 12.45		\| 12.45
Line 56:		Line 56:
	\| 2080/2079, 625/624, 3025/3024, 18954/18865, 41472/41405		\| 2080/2079, 625/624, 3025/3024, 18954/18865, 41472/41405
	\| {{mapping\| 433 686 1005 1216 1498 1602 }}		\| {{mapping\| 433 686 1005 1216 1498 1602 }}
	\| 0.1217		\| +0.1217
	\| 0.3179		\| 0.3179
	\| 11.47		\| 11.47
Line 63:		Line 63:
	\| 2080/2079, 375/374, 715/714, 936/935, 1377/1372, 76032/75803		\| 2080/2079, 375/374, 715/714, 936/935, 1377/1372, 76032/75803
	\| {{mapping\| 433 686 1005 1216 1498 1602 1770 }}		\| {{mapping\| 433 686 1005 1216 1498 1602 1770 }}
	\| 0.0919		\| +0.0919
	\| 0.3033		\| 0.3033
	\| 10.94		\| 10.94
Line 84:		Line 84:
	\| [[Orson]]		\| [[Orson]]
	\|}		\|}
	<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

	== Music ==		== Music ==

ArrowHead294: Partial undo

2024-11-16T13:16:05Z

Partial undo

← Older revision		Revision as of 13:16, 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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	\| 0.3033		\| 0.3033
	\| 10.94		\| 10.94
	~~{{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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	\| 75/64		\| 75/64
	\| [[Orson]]		\| [[Orson]]
	~~{{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

	== Music ==		== Music ==

ArrowHead294 at 01:45, 16 November 2024

2024-11-16T01:45:45Z

← Older revision		Revision as of 01:45, 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 66:		Line 57:
	\| 0.3033		\| 0.3033
	\| 10.94		\| 10.94
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ 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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	\| 75/64		\| 75/64
	\| [[Orson]]		\| [[Orson]]
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 01:06, 16 November 2024

2024-11-16T01:06:36Z

← Older revision		Revision as of 01:06, 16 November 2024
Line 15:		Line 15:
	== 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
	\|-		\|-
Line 69:		Line 70:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+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
	\|-		\|-
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	\| [[Orson]]		\| [[Orson]]
	\|}		\|}
	~~<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}}

	== Music ==		== Music ==

FloraC: /* Theory */ put to the right subsection; -6701edo (addressed in the relevant edo page)

2024-06-21T04:56:28Z

Theory: put to the right subsection; -6701edo (addressed in the relevant edo page)

← Older revision		Revision as of 04:56, 21 June 2024
Line 6:		Line 6:

	Using the patent val, the equal temperament [[tempering out\|tempers out]] [[19683/19600]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 161280/161051, and 180224/180075 in the 11-limit.		Using the patent val, the equal temperament [[tempering out\|tempers out]] [[19683/19600]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 161280/161051, and 180224/180075 in the 11-limit.

	It might be interesting due to being the smallest subset edo of the nanotemperament [[2901533edo]] (an extremely high precision/complexity [[microtemperament]]) (the only other edo subset being the much larger prime edo [[6701edo]]).

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	433edo is the 84th [[prime edo]].		433edo is the 84th [[prime edo]]. It might be interesting due to being the smallest subset edo of the nanotemperament [[2901533edo]], an extremely high-precision/complexity [[microtemperament]].

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

Godtone: /* Theory */ less confusing highlighting

2024-06-20T17:39:49Z

Theory: less confusing highlighting

← Older revision		Revision as of 17:39, 20 June 2024
Line 7:		Line 7:
	Using the patent val, the equal temperament [[tempering out\|tempers out]] [[19683/19600]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 161280/161051, and 180224/180075 in the 11-limit.		Using the patent val, the equal temperament [[tempering out\|tempers out]] [[19683/19600]] and 4096000/4084101 in the 7-limit; [[3025/3024]], [[4000/3993]], [[6250/6237]], 161280/161051, and 180224/180075 in the 11-limit.

	It might be interesting due to being the smallest subset edo of the ~~[[microtemperament\|~~nanotemperament]] [[2901533edo]] (an extremely high precision/complexity microtemperament) (the only other edo subset being the much larger prime edo [[6701edo]]).		It might be interesting due to being the smallest subset edo of the nanotemperament [[2901533edo]] (an extremely high precision/complexity [[microtemperament]]) (the only other edo subset being the much larger prime edo [[6701edo]]).

	=== Odd harmonics ===		=== Odd harmonics ===