814edo - 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"

2026-03-13T13:31:55Z

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 13:31, 13 March 2026
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	\| [[Sesquiquartififths]]		\| [[Sesquiquartififths]]
	\|}		\|}
	<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:Sesquiquartififths]]		[[Category:Sesquiquartififths]]

ArrowHead294 at 16:19, 20 February 2025

2025-02-20T16:19:41Z

← Older revision		Revision as of 16:19, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|814~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:50, 15 January 2025

2025-01-15T18:50:57Z

← Older revision		Revision as of 18:50, 15 January 2025
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	== Theory ==		== Theory ==
	814edo is [[consistency\|distinctly consistent]] to the [[17-odd-limit]] and is a strong 17-limit system. The equal temperament is [[enfactoring\|enfactored]] in the 5-limit, tempering out the [[schisma]] as does 407et. In the 7-limit it tempers out [[2401/2400]] so that it [[support]]s and gives a good tuning for [[sesquiquartififths]]. In the 11-limit it tempers out [[9801/9800]], in the 13-limit [[4225/4224]] and [[6656/6655]], and in the 17-limit [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]] and [[5832/5831]]. The 171 & 643 temperament gives an extension of sesquiquartififths to the 17-limit for which 814edo provides the [[optimal patent val]].		814edo is [[consistency\|distinctly consistent]] to the [[17-odd-limit]] and is a strong 17-limit system. The equal temperament is [[enfactoring\|enfactored]] in the 5-limit, tempering out the [[schisma]] as does 407et. In the 7-limit it tempers out [[2401/2400]] so that it [[support]]s and gives a good tuning for [[sesquiquartififths]]. In the 11-limit it tempers out [[9801/9800]], in the 13-limit [[4225/4224]] and [[6656/6655]], and in the 17-limit [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]] and [[5832/5831]]. The {{nowrap\|171 & 643}} temperament gives an extension of sesquiquartififths to the 17-limit for which 814edo provides the [[optimal patent val]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| [[Sesquiquartififths]]		\| [[Sesquiquartififths]]
	\|}		\|}
	<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]]

ArrowHead294: Partial undo

2024-11-16T12:30:58Z

Partial undo

← Older revision		Revision as of 12:30, 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]] (%)
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
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	\| 0.0595		\| 0.0595
	\| 4.04		\| 4.04
	~~{{comma basis end}~~}		\|}
	* 814et is notable in the 17- and 23-limit with lower absolute errors than any previous equal temperaments, beating [[764edo\|764]] in the 17-limit and [[742edo\|742i]] in the 23-limit, and is only bettered by [[935edo\|935]] in either subgroup.		* 814et is notable in the 17- and 23-limit with lower absolute errors than any previous equal temperaments, beating [[764edo\|764]] in the 17-limit and [[742edo\|742i]] in the 23-limit, and is only bettered by [[935edo\|935]] in either subgroup.

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	Note: 5-limit temperaments supported by 407edo are not included.		Note: 5-limit temperaments supported by 407edo are not included.

	{{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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	\| 448/405		\| 448/405
	\| [[Sesquiquartififths]]		\| [[Sesquiquartififths]]
	~~{{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]]

ArrowHead294 at 04:32, 16 November 2024

2024-11-16T04:32:28Z

← Older revision		Revision as of 04:32, 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]] (%)~~
	\|-		\|-
	\| 2.3.5.7		\| 2.3.5.7
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	\| 0.0595		\| 0.0595
	\| 4.04		\| 4.04
	\|}		{{comma basis end}}
	* 814et is notable in the 17- and 23-limit with lower absolute errors than any previous equal temperaments, beating [[764edo\|764]] in the 17-limit and [[742edo\|742i]] in the 23-limit, and is only bettered by [[935edo\|935]] in either subgroup.		* 814et is notable in the 17- and 23-limit with lower absolute errors than any previous equal temperaments, beating [[764edo\|764]] in the 17-limit and [[742edo\|742i]] in the 23-limit, and is only bettered by [[935edo\|935]] in either subgroup.

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	Note: 5-limit temperaments supported by 407edo are not included.		Note: 5-limit temperaments supported by 407edo are not included.

	{~~\| 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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	\| 448/405		\| 448/405
	\| [[Sesquiquartififths]]		\| [[Sesquiquartififths]]
	\|}		{{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]]

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T11:43:47Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 11:43, 2 November 2023
Line 3:		Line 3:

	== Theory ==		== Theory ==
	814edo is ~~distinctly~~ [[consistent]] to the [[17-odd-limit]] and is a strong 17-limit system. The equal temperament is [[enfactoring\|enfactored]] in the 5-limit, tempering out the [[schisma]] as does 407et. In the 7-limit it tempers out [[2401/2400]] so that it [[support]]s and gives a good tuning for [[sesquiquartififths]]. In the 11-limit it tempers out [[9801/9800]], in the 13-limit [[4225/4224]] and [[6656/6655]], and in the 17-limit [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]] and [[5832/5831]]. The 171 & 643 temperament gives an extension of sesquiquartififths to the 17-limit for which 814edo provides the [[optimal patent val]].		814edo is [[consistency\|distinctly consistent]] to the [[17-odd-limit]] and is a strong 17-limit system. The equal temperament is [[enfactoring\|enfactored]] in the 5-limit, tempering out the [[schisma]] as does 407et. In the 7-limit it tempers out [[2401/2400]] so that it [[support]]s and gives a good tuning for [[sesquiquartififths]]. In the 11-limit it tempers out [[9801/9800]], in the 13-limit [[4225/4224]] and [[6656/6655]], and in the 17-limit [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]] and [[5832/5831]]. The 171 & 643 temperament gives an extension of sesquiquartififths to the 17-limit for which 814edo provides the [[optimal patent val]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 814 factors into ~~2 × 11 × 37~~, 814edo has subset edos {{EDOs\| 2, 11, 22, 37, 74, and 407 }}.		Since 814 factors into {{factorization\|814}}, 814edo has subset edos {{EDOs\| 2, 11, 22, 37, 74, and 407 }}.

	== Regular temperament properties ==		== Regular temperament properties ==
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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*		! Generator*
	! Cents*		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-

FloraC: Clarify the title row of the rank-2 temp table

2023-10-20T11:46:37Z

Clarify the title row of the rank-2 temp table

← Older revision		Revision as of 11:46, 20 October 2023
Line 72:		Line 72:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per Octave		! Periods<br>per Octave
	! Generator~~<br>(Reduced)~~		! Generator*
	! Cents~~<br>(Reduced)~~		! Cents*
	! Associated<br>Ratio		! Associated<br>Ratio
	! Temperaments		! Temperaments
Line 83:		Line 83:
	\| [[Sesquiquartififths]]		\| [[Sesquiquartififths]]
	\|}		\|}
			<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:Sesquiquartififths]]		[[Category:Sesquiquartififths]]

FloraC: +19- and 23-limit data

2023-09-08T13:11:39Z

+19- and 23-limit data

← Older revision		Revision as of 13:11, 8 September 2023
Line 6:		Line 6:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|814~~\|columns=11~~}}		{{Harmonics in equal\|814}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
Line 24:		Line 24:
	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 32805/32768, {{monzo\| 25 20 -22 -2 }}		\| 2401/2400, 32805/32768, {{monzo\| 25 20 -22 -2 }}
	\| [{{~~val~~\| 814 1290 1890 2285 }}]		\| {{mapping\| 814 1290 1890 2285 }}
	\| +0.0695		\| +0.0695
	\| 0.0577		\| 0.0577
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 2401/2400, 9801/9800, 32805/32768, 20155392/20131375		\| 2401/2400, 9801/9800, 32805/32768, 20155392/20131375
	\| [{{~~val~~\| 814 1290 1890 2285 2816 }}]		\| {{mapping\| 814 1290 1890 2285 2816 }}
	\| +0.0536		\| +0.0536
	\| 0.0605		\| 0.0605
Line 38:		Line 38:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 2401/2400, 4225/4224, 6656/6655, 9801/9800, 32805/32768		\| 2401/2400, 4225/4224, 6656/6655, 9801/9800, 32805/32768
	\| [{{~~val~~\| 814 1290 1890 2285 2816 3012 }}]		\| {{mapping\| 814 1290 1890 2285 2816 3012 }}
	\| +0.0552		\| +0.0552
	\| 0.0554		\| 0.0554
Line 45:		Line 45:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 1701/1700, 2058/2057, 2401/2400, 2601/2600, 4225/4224, 6656/6655		\| 1701/1700, 2058/2057, 2401/2400, 2601/2600, 4225/4224, 6656/6655
	\| [{{~~val~~\| 814 1290 1890 2285 2816 3012 3327 }}]		\| {{mapping\| 814 1290 1890 2285 2816 3012 3327 }}
	\| +0.0573		\| +0.0573
	\| 0.0528		\| 0.0528
	\| 3.50		\| 3.50
			\|-
			\| 2.3.5.7.11.13.17.19
			\| 1445/1444, 1521/1520, 1701/1700, 2058/2057, 2376/2375, 2401/2400, 2601/2600
			\| {{mapping\| 814 1290 1890 2285 2816 3012 3327 3458 }}
			\| +0.0421
			\| 0.0629
			\| 4.27
			\|-
			\| 2.3.5.7.11.13.17.19.23
			\| 1445/1444, 1521/1520, 1701/1700, 1863/1862, 2058/2057, 2376/2375, 2401/2400, 2601/2600
			\| {{mapping\| 814 1290 1890 2285 2816 3012 3327 3682 }}
			\| +0.0439
			\| 0.0595
			\| 4.04
	\|}		\|}
	* 814et is notable in the 17- and 23-limit with lower absolute errors than any previous equal temperaments, beating [[764edo\|764]] in the 17-limit and [[742edo\|742i]] in the 23-limit, and is only bettered by [[935edo\|935]] in either subgroup.		* 814et is notable in the 17- and 23-limit with lower absolute errors than any previous equal temperaments, beating [[764edo\|764]] in the 17-limit and [[742edo\|742i]] in the 23-limit, and is only bettered by [[935edo\|935]] in either subgroup.

BudjarnLambeth at 06:46, 9 July 2023

2023-07-09T06:46:14Z

← Older revision		Revision as of 06:46, 9 July 2023
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	~~{{novelty}}{{stub}}~~{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|814}}		{{EDO intro\|814}}

BudjarnLambeth at 05:29, 9 July 2023

2023-07-09T05:29:27Z

← Older revision		Revision as of 05:29, 9 July 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{novelty}}{{stub}}{{Infobox ET}}
	{{EDO intro\|814}}		{{EDO intro\|814}}