431edo - 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"

2026-03-13T13:33:16Z

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 13:33, 13 March 2026
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	\| [[Ostara]]		\| [[Ostara]]
	\|}		\|}
	<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)|"

2025-04-17T02:30:22Z

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

← Older revision		Revision as of 02:30, 17 April 2025
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	\| 498.55		\| 498.55
	\| 4/3		\| 4/3
	\| [[Helmholtz temperament\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|-		\|-
	\| 1		\| 1

Sintel: fix helmholtz link

2025-04-16T15:36:10Z

fix helmholtz link

← Older revision		Revision as of 15:36, 16 April 2025
Line 90:		Line 90:
	\| 498.55		\| 498.55
	\| 4/3		\| 4/3
	\| [[Helmholtz]]		\| [[Helmholtz temperament\|Helmholtz]]
	\|-		\|-
	\| 1		\| 1

Francium: +link to table of intervals

2025-02-23T12:27:09Z

+link to table of intervals

← Older revision		Revision as of 12:27, 23 February 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	431edo is the 83rd [[prime edo]].		431edo is the 83rd [[prime edo]].

			== Intervals ==
			{{Main\|Table of 431edo intervals}}

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

Francium: /* Music */ +music

2025-02-22T12:14:35Z

Music: +music

← Older revision		Revision as of 12:14, 22 February 2025
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	* "Take Advantage" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/1mIxaoZYVo7DHLhePsWqmu Spotify] \| [https://francium223.bandcamp.com/track/take-advantage Bandcamp] \| [https://www.youtube.com/watch?v=CiFES4z6bMM YouTube]		* "Take Advantage" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/1mIxaoZYVo7DHLhePsWqmu Spotify] \| [https://francium223.bandcamp.com/track/take-advantage Bandcamp] \| [https://www.youtube.com/watch?v=CiFES4z6bMM YouTube]
	* "Help Me Understand" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6AiaohFI5RNNTAVncif4Ob Spotify] \| [https://francium223.bandcamp.com/track/help-me-understand Bandcamp] \| [https://www.youtube.com/watch?v=wWgIV-MlrSw YouTube]		* "Help Me Understand" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6AiaohFI5RNNTAVncif4Ob Spotify] \| [https://francium223.bandcamp.com/track/help-me-understand Bandcamp] \| [https://www.youtube.com/watch?v=wWgIV-MlrSw YouTube]
			* "I Will Get You." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/1FkxDVzNv6SuSfB5vc8T5y Spotify] \| [https://francium223.bandcamp.com/track/i-will-get-you Bandcamp] \| [https://www.youtube.com/watch?v=_jioqFrcwz8 YouTube] – in Nordenmarkic, 431edo tuning

	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294 at 22:59, 20 February 2025

2025-02-20T22:59:01Z

← Older revision		Revision as of 22:59, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|431~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:08, 15 January 2025

2025-01-15T18:08:09Z

← Older revision		Revision as of 18:08, 15 January 2025
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	\| 32805/32768, {{monzo\| 7 63 -46 }}		\| 32805/32768, {{monzo\| 7 63 -46 }}
	\| {{mapping\| 431 683 1001 }}		\| {{mapping\| 431 683 1001 }}
	\| ~~−0~~.0230		\| −0.0230
	\| 0.2082		\| 0.2082
	\| 7.48		\| 7.48
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	\| 2401/2400, 32805/32768, {{monzo\| 3 16 -11 -1 }}		\| 2401/2400, 32805/32768, {{monzo\| 3 16 -11 -1 }}
	\| {{mapping\| 431 683 1001 1210 }}		\| {{mapping\| 431 683 1001 1210 }}
	\| ~~−0~~.0299		\| −0.0299
	\| 0.1803		\| 0.1803
	\| 6.48		\| 6.48
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	\| 2401/2400, 5632/5625, 8019/8000, 43923/43904		\| 2401/2400, 5632/5625, 8019/8000, 43923/43904
	\| {{mapping\| 431 683 1001 1210 1491 }}		\| {{mapping\| 431 683 1001 1210 1491 }}
	\| ~~−0~~.0215		\| −0.0215
	\| 0.1621		\| 0.1621
	\| 5.82		\| 5.82
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	\| 729/728, 1001/1000, 1716/1715, 4096/4095, 6656/6655		\| 729/728, 1001/1000, 1716/1715, 4096/4095, 6656/6655
	\| {{mapping\| 431 683 1001 1210 1491 1595 }}		\| {{mapping\| 431 683 1001 1210 1491 1595 }}
	\| ~~−0~~.0318		\| −0.0318
	\| 0.1498		\| 0.1498
	\| 5.38		\| 5.38
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	\| [[Ostara]]		\| [[Ostara]]
	\|}		\|}
	<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 ==
	; [[Francium]]		; [[Francium]]
	* "Take Advantage" from ''Take Advantage'' (2024) ~~–~~ [https://open.spotify.com/track/1mIxaoZYVo7DHLhePsWqmu Spotify] \| [https://francium223.bandcamp.com/track/take-advantage Bandcamp] \| [https://www.youtube.com/watch?v=CiFES4z6bMM YouTube]		* "Take Advantage" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/1mIxaoZYVo7DHLhePsWqmu Spotify] \| [https://francium223.bandcamp.com/track/take-advantage Bandcamp] \| [https://www.youtube.com/watch?v=CiFES4z6bMM YouTube]
	* "Help Me Understand" from ''Abbreviations Gone Wrong'' (2024) ~~–~~ [https://open.spotify.com/track/6AiaohFI5RNNTAVncif4Ob Spotify] \| [https://francium223.bandcamp.com/track/help-me-understand Bandcamp] \| [https://www.youtube.com/watch?v=wWgIV-MlrSw YouTube]		* "Help Me Understand" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6AiaohFI5RNNTAVncif4Ob Spotify] \| [https://francium223.bandcamp.com/track/help-me-understand Bandcamp] \| [https://www.youtube.com/watch?v=wWgIV-MlrSw YouTube]

	[[Category:Listen]]		[[Category:Listen]]

ArrowHead294: Partial undo

2024-11-16T12:56:29Z

Partial undo

← Older revision		Revision as of 12:56, 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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	\| 0.1498		\| 0.1498
	\| 5.38		\| 5.38
	~~{{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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	\| 19/14		\| 19/14
	\| [[Ostara]]		\| [[Ostara]]
	~~{{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 03:10, 16 November 2024

2024-11-16T03:10:46Z

← Older revision		Revision as of 03:10, 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
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	\| 32805/32768, {{monzo\| 7 63 -46 }}		\| 32805/32768, {{monzo\| 7 63 -46 }}
	\| {{mapping\| 431 683 1001 }}		\| {{mapping\| 431 683 1001 }}
	\| -0.0230		\| −0.0230
	\| 0.2082		\| 0.2082
	\| 7.48		\| 7.48
Line 41:		Line 33:
	\| 2401/2400, 32805/32768, {{monzo\| 3 16 -11 -1 }}		\| 2401/2400, 32805/32768, {{monzo\| 3 16 -11 -1 }}
	\| {{mapping\| 431 683 1001 1210 }}		\| {{mapping\| 431 683 1001 1210 }}
	\| -0.0299		\| −0.0299
	\| 0.1803		\| 0.1803
	\| 6.48		\| 6.48
Line 48:		Line 40:
	\| 2401/2400, 5632/5625, 8019/8000, 43923/43904		\| 2401/2400, 5632/5625, 8019/8000, 43923/43904
	\| {{mapping\| 431 683 1001 1210 1491 }}		\| {{mapping\| 431 683 1001 1210 1491 }}
	\| -0.0215		\| −0.0215
	\| 0.1621		\| 0.1621
	\| 5.82		\| 5.82
Line 55:		Line 47:
	\| 729/728, 1001/1000, 1716/1715, 4096/4095, 6656/6655		\| 729/728, 1001/1000, 1716/1715, 4096/4095, 6656/6655
	\| {{mapping\| 431 683 1001 1210 1491 1595 }}		\| {{mapping\| 431 683 1001 1210 1491 1595 }}
	\| -0.0318		\| −0.0318
	\| 0.1498		\| 0.1498
	\| 5.38		\| 5.38
	\|}		{{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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	\| 19/14		\| 19/14
	\| [[Ostara]]		\| [[Ostara]]
	\|}		{{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}}

	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Take Advantage" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/1mIxaoZYVo7DHLhePsWqmu Spotify] \| [https://francium223.bandcamp.com/track/take-advantage Bandcamp] \| [https://www.youtube.com/watch?v=CiFES4z6bMM YouTube]		* "Take Advantage" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/1mIxaoZYVo7DHLhePsWqmu Spotify] \| [https://francium223.bandcamp.com/track/take-advantage Bandcamp] \| [https://www.youtube.com/watch?v=CiFES4z6bMM YouTube]
	* "Help Me Understand" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6AiaohFI5RNNTAVncif4Ob Spotify] \| [https://francium223.bandcamp.com/track/help-me-understand Bandcamp] \| [https://www.youtube.com/watch?v=wWgIV-MlrSw YouTube]		* "Help Me Understand" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6AiaohFI5RNNTAVncif4Ob Spotify] \| [https://francium223.bandcamp.com/track/help-me-understand Bandcamp] \| [https://www.youtube.com/watch?v=wWgIV-MlrSw YouTube]

			[[Category:Listen]]

Francium: /* Music */ +music

2024-10-04T12:06:37Z

Music: +music

← Older revision		Revision as of 12:06, 4 October 2024
Line 98:		Line 98:
	; [[Francium]]		; [[Francium]]
	* "Take Advantage" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/1mIxaoZYVo7DHLhePsWqmu Spotify] \| [https://francium223.bandcamp.com/track/take-advantage Bandcamp] \| [https://www.youtube.com/watch?v=CiFES4z6bMM YouTube]		* "Take Advantage" from ''Take Advantage'' (2024) – [https://open.spotify.com/track/1mIxaoZYVo7DHLhePsWqmu Spotify] \| [https://francium223.bandcamp.com/track/take-advantage Bandcamp] \| [https://www.youtube.com/watch?v=CiFES4z6bMM YouTube]
			* "Help Me Understand" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6AiaohFI5RNNTAVncif4Ob Spotify] \| [https://francium223.bandcamp.com/track/help-me-understand Bandcamp] \| [https://www.youtube.com/watch?v=wWgIV-MlrSw YouTube]