643edo - 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"

2026-03-13T13:32:54Z

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
Line 95:		Line 95:
	\| [[Helmholtz (temperament)\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|}		\|}
	<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: Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

2025-04-17T02:30:25Z

Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

← Older revision		Revision as of 02:30, 17 April 2025
Line 93:		Line 93:
	\| 498.29		\| 498.29
	\| 4/3		\| 4/3
	\| [[Helmholtz temperament\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|}		\|}
	<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

Nick Vuci: Edited Helmholtz redirect

2025-04-16T15:43:42Z

Edited Helmholtz redirect

← Older revision		Revision as of 15:43, 16 April 2025
Line 93:		Line 93:
	\| 498.29		\| 498.29
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz temperament\|Helmholtz]]
	\|}		\|}
	<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

Francium at 12:47, 6 April 2025

2025-04-06T12:47:54Z

← Older revision		Revision as of 12:47, 6 April 2025
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	\|}		\|}
	<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

			== Music ==
			; [[Francium]]
			* "Bobson Dugnutt" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/1ROUQlzxJR7pDpM8GLujol Spotify] \| [https://francium223.bandcamp.com/track/bobson-dugnutt Bandcamp] \| [https://www.youtube.com/watch?v=Bg2w1__AW4k YouTube] − in Botolphic, 643edo tuning

	[[Category:Sesquiquartififths]]		[[Category:Sesquiquartififths]]
	[[Category:Vili]]		[[Category:Vili]]

ArrowHead294 at 15:43, 20 February 2025

2025-02-20T15:43:59Z

← Older revision		Revision as of 15:43, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|643~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:31:55Z

Theory: cleanup

← Older revision		Revision as of 16:31, 17 January 2025
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	== Theory ==		== Theory ==
	643edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], with a generally flat tendency, but the [[5/1\|5th harmonic]] is only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo\|146]] and before [[4004edo\|4004]]. It [[tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s the [[sesquiquartififths]] temperament. In the 11-limit it tempers out [[3025/3024]] and 151263/151250; in the 13-limit [[1001/1000]], [[1716/1715]] and [[4225/4224]]; in the 17-limit [[1089/1088]], [[1701/1700]], [[2431/2430]] and [[2601/2600]]; and in the 19-limit 1331/1330, [[1521/1520]], [[1729/1728]], 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank-3 13-limit [[vili]] temperament.		643edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], with a generally flat tendency, but the [[5/1\|5th harmonic]] is only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo\|146]] and before [[4004edo\|4004]]. As an equal temperament, it [[tempering out\|tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s the [[sesquiquartififths]] temperament. In the 11-limit it tempers out [[3025/3024]] and 151263/151250; in the 13-limit [[1001/1000]], [[1716/1715]] and [[4225/4224]]; in the 17-limit [[1089/1088]], [[1701/1700]], [[2431/2430]] and [[2601/2600]]; and in the 19-limit 1331/1330, [[1521/1520]], [[1729/1728]], 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank-3 13-limit [[vili]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|643~~\|columns=11~~}}		{{Harmonics in equal\|643}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

ArrowHead294 at 18:44, 15 January 2025

2025-01-15T18:44:11Z

← Older revision		Revision as of 18:44, 15 January 2025
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	== Theory ==		== Theory ==
	643edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], with a generally flat tendency, but the [[5/1\|5th harmonic]] is only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo\|146]] and before [[4004edo\|4004]]. It [[~~tempering out\|~~tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s the [[sesquiquartififths]] temperament. In the 11-limit it tempers out [[3025/3024]] and 151263/151250; in the 13-limit [[1001/1000]], [[1716/1715]] and [[4225/4224]]; in the 17-limit [[1089/1088]], [[1701/1700]], [[2431/2430]] and [[2601/2600]]; and in the 19-limit 1331/1330, [[1521/1520]], [[1729/1728]], 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank-3 13-limit [[vili]] temperament.		643edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], with a generally flat tendency, but the [[5/1\|5th harmonic]] is only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo\|146]] and before [[4004edo\|4004]]. It [[tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s the [[sesquiquartififths]] temperament. In the 11-limit it tempers out [[3025/3024]] and 151263/151250; in the 13-limit [[1001/1000]], [[1716/1715]] and [[4225/4224]]; in the 17-limit [[1089/1088]], [[1701/1700]], [[2431/2430]] and [[2601/2600]]; and in the 19-limit 1331/1330, [[1521/1520]], [[1729/1728]], 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank-3 13-limit [[vili]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| [[Helmholtz]]		\| [[Helmholtz]]
	\|}		\|}
	<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:Sesquiquartififths]]		[[Category:Sesquiquartififths]]
	[[Category:Vili]]		[[Category:Vili]]

ArrowHead294: Partial undo

2024-11-16T12:37:36Z

Partial undo

← Older revision		Revision as of 12:37, 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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	\| 0.0801		\| 0.0801
	\| 4.29		\| 4.29
	~~{{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		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz]]
	~~{{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:Sesquiquartififths]]		[[Category:Sesquiquartififths]]
	[[Category:Vili]]		[[Category:Vili]]

ArrowHead294 at 04:16, 16 November 2024

2024-11-16T04:16:28Z

← Older revision		Revision as of 04:16, 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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	\| 0.0801		\| 0.0801
	\| 4.29		\| 4.29
	\|}		{{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		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz]]
	\|}		{{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:Sesquiquartififths]]		[[Category:Sesquiquartififths]]
	[[Category:Vili]]		[[Category:Vili]]

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

2023-10-25T06:27:14Z

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

← Older revision		Revision as of 06:27, 25 October 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	643edo is ~~uniquely~~ [[consistent]] to the 21-odd-limit, with a generally flat tendency, but the 5th harmonic is only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo\|146]] and before [[4004edo\|4004]]. It tempers out [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s the [[sesquiquartififths]] temperament. In the 11-limit it tempers out [[3025/3024]] and 151263/151250; in the 13-limit [[1001/1000]], [[1716/1715]] and [[4225/4224]]; in the 17-limit [[1089/1088]], [[1701/1700]], 2431/2430 and [[2601/2600]]; and in the 19-limit 1331/1330, [[1521/1520]], [[1729/1728]], 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank-3 13-limit [[vili]] temperament.		643edo is [[consistency\|distinctly consistent]] to the [[21-odd-limit]], with a generally flat tendency, but the [[5/1\|5th harmonic]] is only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo\|146]] and before [[4004edo\|4004]]. It [[tempering out\|tempers out]] [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s the [[sesquiquartififths]] temperament. In the 11-limit it tempers out [[3025/3024]] and 151263/151250; in the 13-limit [[1001/1000]], [[1716/1715]] and [[4225/4224]]; in the 17-limit [[1089/1088]], [[1701/1700]], [[2431/2430]] and [[2601/2600]]; and in the 19-limit 1331/1330, [[1521/1520]], [[1729/1728]], 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank-3 13-limit [[vili]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|643\|columns=11}}		{{Harmonics in equal\|643\|columns=11}}

	=== ~~Miscellaneous properties~~ ===		=== Subsets and supersets ===
	643edo is the 117th [[prime edo]].		643edo is the 117th [[prime edo]].

Line 24:		Line 24:
	\| 2.3		\| 2.3
	\| {{monzo\| -1019 643 }}		\| {{monzo\| -1019 643 }}
	\| [{{~~val~~\| 643 1019 }}]		\| {{mapping\| 643 1019 }}
	\| +0.0771		\| +0.0771
	\| 0.0771		\| 0.0771
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	\| 2.3.5		\| 2.3.5
	\| 32805/32768, {{monzo\| 1 99 -68 }}		\| 32805/32768, {{monzo\| 1 99 -68 }}
	\| [{{~~val~~\| 643 1019 1493 }}]		\| {{mapping\| 643 1019 1493 }}
	\| +0.0513		\| +0.0513
	\| 0.7270		\| 0.7270
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	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 32805/32768, {{monzo\| 9 21 -17 -1 }}		\| 2401/2400, 32805/32768, {{monzo\| 9 21 -17 -1 }}
	\| [{{~~val~~\| 643 1019 1493 1805 }}]		\| {{mapping\| 643 1019 1493 1805 }}
	\| +0.0600		\| +0.0600
	\| 0.0647		\| 0.0647
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 2401/2400, 3025/3024, 32805/32768, 391314/390625		\| 2401/2400, 3025/3024, 32805/32768, 391314/390625
	\| [{{~~val~~\| 643 1019 1493 1805 2224 }}]		\| {{mapping\| 643 1019 1493 1805 2224 }}
	\| +0.0927		\| +0.0927
	\| 0.0874		\| 0.0874
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 1001/1000, 1716/1715, 3025/3024, 4225/4224, 32805/32768		\| 1001/1000, 1716/1715, 3025/3024, 4225/4224, 32805/32768
	\| [{{~~val~~\| 643 1019 1493 1805 2224 2379 }}]		\| {{mapping\| 643 1019 1493 1805 2224 2379 }}
	\| +0.1094		\| +0.1094
	\| 0.0881		\| 0.0881
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	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 1001/1000, 1089/1088, 1701/1700, 1716/1715, 2601/2600, 4225/4224		\| 1001/1000, 1089/1088, 1701/1700, 1716/1715, 2601/2600, 4225/4224
	\| [{{~~val~~\| 643 1019 1493 1805 2224 2379 2628 }}]		\|{{mapping\| 643 1019 1493 1805 2224 2379 2628 }}
	\| +0.1094		\| +0.1094
	\| 0.0816		\| 0.0816
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	\| 2.3.5.7.11.13.17.19		\| 2.3.5.7.11.13.17.19
	\| 1001/1000, 1089/1088, 1521/1520, 1701/1700, 1716/1715, 1729/1728, 2601/2600		\| 1001/1000, 1089/1088, 1521/1520, 1701/1700, 1716/1715, 1729/1728, 2601/2600
	\| [{{~~val~~\| 643 1019 1493 1805 2224 2379 2628 2731 }}]		\| {{mapping\| 643 1019 1493 1805 2224 2379 2628 2731 }}
	\| +0.1186		\| +0.1186
	\| 0.0801		\| 0.0801
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	{\| 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*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\| [[Helmholtz]]		\| [[Helmholtz]]
	\|}		\|}
			<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:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:Sesquiquartififths]]		[[Category:Sesquiquartififths]]
	[[Category:Vili]]		[[Category:Vili]]
	~~[[Category:Prime EDO]]~~