383edo - 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"

2026-03-13T13:31:53Z

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
Line 93:		Line 93:
	\| [[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)|"

2025-04-17T02:30:01Z

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

← Older revision		Revision as of 02:30, 17 April 2025
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	\| 498.17		\| 498.17
	\| 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

2025-04-16T15:41:20Z

Edited Helmholtz redirect

← Older revision		Revision as of 15:41, 16 April 2025
Line 91:		Line 91:
	\| 498.17		\| 498.17
	\| 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: changed EDO intro to ED intro

2025-02-19T18:16:14Z

changed EDO intro to ED intro

← Older revision		Revision as of 18:16, 19 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|383~~}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: +music

2025-02-04T12:23:38Z

+music

← Older revision		Revision as of 12:23, 4 February 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]]
			* "Mark A Player" from ''I Want To'' (2025) – [https://open.spotify.com/track/1M3LmqPfXRjpxuuTRgEufN Spotify] \| [https://francium223.bandcamp.com/track/mark-a-player Bandcamp] \| [https://www.youtube.com/watch?v=ePR_S5cNZvI YouTube] – in Marconic, 383edo tuning

	[[Category:Countertertiaschis]]		[[Category:Countertertiaschis]]

FloraC: /* Theory */ cleanup

2025-01-17T15:59:31Z

Theory: cleanup

← Older revision		Revision as of 15:59, 17 January 2025
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	== Theory ==		== Theory ==
	383edo is [[consistency\|distinctly consistent]] through the [[15-odd-limit]] with a flat tendency. It [[tempers out]] 32805/32768 ([[schisma]]) in the 5-limit; [[2401/2400]] in the 7-limit; [[3025/3024]], [[4000/3993]] and [[6250/6237]] in the 11-limit; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher ~~limit~~.		383edo is [[consistency\|distinctly consistent]] through the [[15-odd-limit]] with a flat tendency. As an equal temperament, it [[tempering out\|tempers out]] 32805/32768 ([[schisma]]) in the [[5-limit]]; [[2401/2400]] in the [[7-limit]]; [[3025/3024]], [[4000/3993]] and [[6250/6237]] in the [[11-limit]]; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher limits.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|383~~\|columns=11~~}}		{{Harmonics in equal\|383}}

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

ArrowHead294 at 18:01, 15 January 2025

2025-01-15T18:01:10Z

← Older revision		Revision as of 18:01, 15 January 2025
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	== Theory ==		== Theory ==
	383edo is [[consistency\|distinctly consistent]] through the [[15-odd-limit]] with a flat tendency. ~~The equal temperament~~ [[~~tempering out\|~~tempers out]] 32805/32768 ([[schisma]]) in the 5-limit; [[2401/2400]] in the 7-limit; [[3025/3024]], [[4000/3993]] and [[6250/6237]] in the 11-limit; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher limit.		383edo is [[consistency\|distinctly consistent]] through the [[15-odd-limit]] with a flat tendency. It [[tempers out]] 32805/32768 ([[schisma]]) in the 5-limit; [[2401/2400]] in the 7-limit; [[3025/3024]], [[4000/3993]] and [[6250/6237]] in the 11-limit; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher limit.

	=== 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:Countertertiaschis]]		[[Category:Countertertiaschis]]

ArrowHead294: Partial undo

2024-11-16T13:05:45Z

Partial undo

← Older revision		Revision as of 13:05, 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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	\| 0.1525		\| 0.1525
	\| 4.87		\| 4.87
	~~{{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:Countertertiaschis]]		[[Category:Countertertiaschis]]

ArrowHead294 at 02:38, 16 November 2024

2024-11-16T02:38:08Z

← Older revision		Revision as of 02:38, 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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	\| 0.1525		\| 0.1525
	\| 4.87		\| 4.87
	\|}		{{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:Countertertiaschis]]		[[Category:Countertertiaschis]]

FloraC: Adopt template: EDO intro; cleanup; clarify the title row of the rank-2 temp table; -redundant categories

2023-11-09T14:03:45Z

Adopt template: EDO intro; cleanup; clarify the title row of the rank-2 temp table; -redundant categories

← Older revision		Revision as of 14:03, 9 November 2023
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	{{Infobox ET}}		{{Infobox ET}}
	~~The '''383 equal divisions of the octave''' ('''383edo'''), or the '''383(-tone) equal temperament''' ('''383tet''', '''383et''') when viewed from a [[regular temperament]] perspective, is the [[~~EDO\|~~equal division of the octave]] into~~ 383 ~~parts of about 3.13 [[cent]]s each.~~		{{EDO intro\|383}}

	== Theory ==		== Theory ==
	383edo is ~~distinctly~~ [[consistent]] through the [[15-odd-limit]] with a flat tendency. It tempers out 32805/32768 ([[schisma]]) in the 5-limit; [[2401/2400]] in the 7-limit; [[~~6250~~/~~6237~~]], [[4000/3993]] and [[~~3025~~/~~3024~~]] in the 11-limit; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher limit.		383edo is [[consistency\|distinctly consistent]] through the [[15-odd-limit]] with a flat tendency. The equal temperament [[tempering out\|tempers out]] 32805/32768 ([[schisma]]) in the 5-limit; [[2401/2400]] in the 7-limit; [[3025/3024]], [[4000/3993]] and [[6250/6237]] in the 11-limit; and [[625/624]], [[1575/1573]] and [[2080/2079]] in the 13-limit. It provides the [[optimal patent val]] for the [[countertertiaschis]] temperament, and a good tuning for [[sesquiquartififths]] in the higher limit.

	~~383edo is the 76th [[prime edo]]~~.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|383\|columns=11}}		{{Harmonics in equal\|383\|columns=11}}

			=== Subsets and supersets ===
			383edo is the 76th [[prime edo]].

	== Regular temperament properties ==		== Regular temperament properties ==
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	\| 2.3		\| 2.3
	\| {{monzo\| -607 383 }}		\| {{monzo\| -607 383 }}
	\| [{{~~val~~\| 383 607 }}]		\| {{mapping\| 383 607 }}
	\| +0.0402		\| +0.0402
	\| 0.0402		\| 0.0402
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	\| 2.3.5		\| 2.3.5
	\| 32805/32768, {{monzo\| -8 -55 41}}		\| 32805/32768, {{monzo\| -8 -55 41}}
	\| [{{~~val~~\| 383 607 889 }}]		\| {{mapping\| 383 607 889 }}
	\| +0.1610		\| +0.1610
	\| 0.1741		\| 0.1741
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	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 32805/32768, 68359375/68024448		\| 2401/2400, 32805/32768, 68359375/68024448
	\| [{{~~val~~\| 383 607 889 1075 }}]		\| {{mapping\| 383 607 889 1075 }}
	\| +0.1813		\| +0.1813
	\| 0.1548		\| 0.1548
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 2401/2400, 3025/3024, 4000/3993, 32805/32768		\| 2401/2400, 3025/3024, 4000/3993, 32805/32768
	\| [{{~~val~~\| 383 607 889 1075 1325 }}]		\| {{mapping\| 383 607 889 1075 1325 }}
	\| +0.1382		\| +0.1382
	\| 0.1631		\| 0.1631
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976		\| 625/624, 1575/1573, 2080/2079, 2401/2400, 10985/10976
	\| [{{~~val~~\| 383 607 889 1075 1325 1417 }}]		\| {{mapping\| 383 607 889 1075 1325 1417 }}
	\| +0.1531		\| +0.1531
	\| 0.1525		\| 0.1525
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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:Prime EDO]]~~
	[[Category:Countertertiaschis]]		[[Category:Countertertiaschis]]