301edo - 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"

2026-03-13T13:31:41Z

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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	\| [[Meridic]]		\| [[Meridic]]
	\|}		\|}
	<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:Meridic]]		[[Category:Meridic]]

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

2025-04-17T02:29:53Z

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

← Older revision		Revision as of 02:29, 17 April 2025
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	\| 498.34		\| 498.34
	\| 4/3		\| 4/3
	\| [[Helmholtz temperament\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|-		\|-
	\| 7		\| 7

Nick Vuci: Edited Helmholtz redirect

2025-04-16T15:40:17Z

Edited Helmholtz redirect

← Older revision		Revision as of 15:40, 16 April 2025
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	\| 498.34		\| 498.34
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz temperament\|Helmholtz]]
	\|-		\|-
	\| 7		\| 7

ArrowHead294 at 14:33, 20 February 2025

2025-02-20T14:33:43Z

← Older revision		Revision as of 14:33, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|301~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 19:40, 15 January 2025

2025-01-15T19:40:52Z

← Older revision		Revision as of 19:40, 15 January 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 301 factors into ~~7 × 43~~, 301edo has [[7edo]] and [[43edo]] as its subsets. This is related to the proposal of the deaf French mathematician and acoustician {{w\|Joseph Sauveur}} to divide the octave in 43 parts called ''merides'', and those into seven more parts called ''heptamerides''. Back in the days of slide rules and log tables, this made sense since by multiplying the log base ten of the interval in question by 1000, one came close to how many heptamerides it constituted.		Since 301 factors into {{factorisation\|301}}, 301edo has [[7edo]] and [[43edo]] as its subsets. This is related to the proposal of the deaf French mathematician and acoustician {{w\|Joseph Sauveur}} to divide the octave in 43 parts called ''merides'', and those into seven more parts called ''heptamerides''. Back in the days of slide rules and log tables, this made sense since by multiplying the log base ten of the interval in question by 1000, one came close to how many heptamerides it constituted.

	301edo also tempers out {{monzo\| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic\|meridic temperament]].		301edo also tempers out {{monzo\| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic\|meridic temperament]].
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	\| [[Meridic]]		\| [[Meridic]]
	\|}		\|}
	<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:Meridic]]		[[Category:Meridic]]

BudjarnLambeth: EDOs this large do not need automatic interval tables because they slow the loading of the page for some users

2024-12-24T13:36:13Z

EDOs this large do not need automatic interval tables because they slow the loading of the page for some users

← Older revision		Revision as of 13:36, 24 December 2024
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	301edo also tempers out {{monzo\| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic\|meridic temperament]].		301edo also tempers out {{monzo\| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic\|meridic temperament]].

	~~== Intervals ==~~
	~~{{Interval table}}~~

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

FloraC: Put things where appropriate

2024-12-23T11:55:31Z

Put things where appropriate

← Older revision		Revision as of 11:55, 23 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|301}}		{{EDO intro\|301}}
	~~{{Interval table}}~~

	== Theory ==		== Theory ==
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	301edo also tempers out {{monzo\| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic\|meridic temperament]].		301edo also tempers out {{monzo\| 168 -43 -43 }} and 5250987/5242880, so it supports the [[Mitonismic temperaments #Meridic\|meridic temperament]].

			== Intervals ==
			{{Interval table}}

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

MisterShafXen at 11:42, 23 December 2024

2024-12-23T11:42:56Z

← Older revision		Revision as of 11:42, 23 December 2024
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	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|301}}		{{EDO intro\|301}}
			{{Interval table}}

	== Theory ==		== Theory ==

ArrowHead294: Partial undo

2024-11-16T12:29:16Z

Partial undo

← Older revision		Revision as of 12:29, 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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	\| 0.1973		\| 0.1973
	\| 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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	\|-		\|-
	\| 7		\| 7
	\| 125\301<br>(4\301)		\| 125\301<br />(4\301)
	\| 498.34<br>(15.95)		\| 498.34<br />(15.95)
	\| 4/3<br>(245/243)		\| 4/3<br />(245/243)
	\| [[Septant]]		\| [[Septant]]
	\|-		\|-
	\| 43		\| 43
	\| 125\301<br>(1\301)		\| 125\301<br />(1\301)
	\| 498.34<br>(3.99)		\| 498.34<br />(3.99)
	\| 4/3<br>(540/539)		\| 4/3<br />(540/539)
	\| [[Meridic]]		\| [[Meridic]]
	~~{{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:Meridic]]		[[Category:Meridic]]

ArrowHead294 at 04:35, 16 November 2024

2024-11-16T04:35:38Z

← Older revision		Revision as of 04:35, 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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	\| 0.1973		\| 0.1973
	\| 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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	\| 4/3<br>(540/539)		\| 4/3<br>(540/539)
	\| [[Meridic]]		\| [[Meridic]]
	\|}		{{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:Meridic]]		[[Category:Meridic]]