331edo - 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"

2026-03-13T13:32:10Z

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
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	\| [[Würschmidt]] (331, 5-limit)		\| [[Würschmidt]] (331, 5-limit)
	\|}		\|}
	<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

	== Scales ==		== Scales ==

Francium: /* Music */ +music

2026-02-26T12:07:11Z

Music: +music

← Older revision		Revision as of 12:07, 26 February 2026
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	== Music ==		== Music ==
	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* "Silent Silence" from ''Edson EP'' (2023) – [https://open.spotify.com/track/6q3xr4E4QIL9BMaZyf6LXd Spotify] \| [https://francium223.bandcamp.com/track/silent-silence Bandcamp] \| [https://www.youtube.com/watch?v=g3FF6oqnilk YouTube] – ~~edson~~ in 331edo tuning		* "Silent Silence" from ''Edson EP'' (2023) – [https://open.spotify.com/track/6q3xr4E4QIL9BMaZyf6LXd Spotify] \| [https://francium223.bandcamp.com/track/silent-silence Bandcamp] \| [https://www.youtube.com/watch?v=g3FF6oqnilk YouTube] – in Edson, 331edo tuning
			* "Moth Mustard" from ''Unsuspecting Tyrant Double-Decker Beef Fort'' (2026) – [https://open.spotify.com/track/6M1I3YWmWvHM5bnMUz4bYg Spotify] \| [https://francium223.bandcamp.com/track/moth-mustard Bandcamp] \| [https://www.youtube.com/watch?v=arg4hjvpeuY YouTube]

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

Francium: changed EDO intro to ED intro

2025-02-21T06:14:10Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:14, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|331~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 19:24, 15 January 2025

2025-01-15T19:24:04Z

← Older revision		Revision as of 19:24, 15 January 2025
Line 28:		Line 28:
	\| {{monzo\| -1049 331 }}		\| {{monzo\| -1049 331 }}
	\| {{mapping\| 331 1049 }}		\| {{mapping\| 331 1049 }}
	\| 0.1402		\| +0.1402
	\| 0.1402		\| 0.1402
	\| 3.87		\| 3.87
Line 84:		Line 84:
	\| [[Würschmidt]] (331, 5-limit)		\| [[Würschmidt]] (331, 5-limit)
	\|}		\|}
	<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

	== Scales ==		== Scales ==
Line 93:		Line 93:
	== Music ==		== Music ==
	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* "Silent Silence" from ''Edson EP'' (2023) ~~–~~ [https://open.spotify.com/track/6q3xr4E4QIL9BMaZyf6LXd Spotify] \| [https://francium223.bandcamp.com/track/silent-silence Bandcamp] \| [https://www.youtube.com/watch?v=g3FF6oqnilk YouTube] ~~–~~ edson in 331edo tuning		* "Silent Silence" from ''Edson EP'' (2023) – [https://open.spotify.com/track/6q3xr4E4QIL9BMaZyf6LXd Spotify] \| [https://francium223.bandcamp.com/track/silent-silence Bandcamp] \| [https://www.youtube.com/watch?v=g3FF6oqnilk YouTube] – edson in 331edo tuning

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

ArrowHead294: Partial undo

2024-11-16T12:51:24Z

Partial undo

← Older revision		Revision as of 12:51, 16 November 2024
Line 14:		Line 14:

	== 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]] (%)
	\|-		\|-
	\| 2.9		\| 2.9
Line 57:		Line 66:
	\| 0.1537		\| 0.1537
	\| 4.24		\| 4.24
	~~{{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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	\| 5/4		\| 5/4
	\| [[Würschmidt]] (331, 5-limit)		\| [[Würschmidt]] (331, 5-limit)
	~~{{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

	== Scales ==		== Scales ==

ArrowHead294 at 03:46, 16 November 2024

2024-11-16T03:46:04Z

← Older revision		Revision as of 03:46, 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]] (%)~~
	\|-		\|-
	\| 2.9		\| 2.9
Line 65:		Line 57:
	\| 0.1537		\| 0.1537
	\| 4.24		\| 4.24
	\|}		{{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
Line 81:		Line 67:
	\| 5/4		\| 5/4
	\| [[Würschmidt]] (331, 5-limit)		\| [[Würschmidt]] (331, 5-limit)
	\|}		{{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}}

	== Scales ==		== Scales ==
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	== Music ==		== Music ==
	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* "Silent Silence" from ''Edson EP'' (2023) – [https://open.spotify.com/track/6q3xr4E4QIL9BMaZyf6LXd Spotify] \| [https://francium223.bandcamp.com/track/silent-silence Bandcamp] \| [https://www.youtube.com/watch?v=g3FF6oqnilk YouTube] – edson in 331edo tuning		* "Silent Silence" from ''Edson EP'' (2023) – [https://open.spotify.com/track/6q3xr4E4QIL9BMaZyf6LXd Spotify] \| [https://francium223.bandcamp.com/track/silent-silence Bandcamp] \| [https://www.youtube.com/watch?v=g3FF6oqnilk YouTube] – edson in 331edo tuning

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

Francium: +categories

2024-02-13T18:00:37Z

+categories

← Older revision		Revision as of 18:00, 13 February 2024
Line 92:		Line 92:
	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* "Silent Silence" from ''Edson EP'' (2023) – [https://open.spotify.com/track/6q3xr4E4QIL9BMaZyf6LXd Spotify] \| [https://francium223.bandcamp.com/track/silent-silence Bandcamp] \| [https://www.youtube.com/watch?v=g3FF6oqnilk YouTube] – edson in 331edo tuning		* "Silent Silence" from ''Edson EP'' (2023) – [https://open.spotify.com/track/6q3xr4E4QIL9BMaZyf6LXd Spotify] \| [https://francium223.bandcamp.com/track/silent-silence Bandcamp] \| [https://www.youtube.com/watch?v=g3FF6oqnilk YouTube] – edson in 331edo tuning

			[[Category:Listen]]

FloraC: /* Regular temperament properties */ review (2/2): adopt subgroup temperament measures

2023-12-15T09:58:51Z

Regular temperament properties: review (2/2): adopt subgroup temperament measures

← Older revision		Revision as of 09:58, 15 December 2023
Line 32:		Line 32:
	\|-		\|-
	\| 2.9.15		\| 2.9.15
	\| {{monzo\| -7 17 -12 }}, {{monzo\| -~~74 -5 23~~ }}		\| {{monzo\| -7 17 -12 }}, {{monzo\| -81 12 11 }}
	\| {{mapping\| 331 1049 1293 }}		\| {{mapping\| 331 1049 1293 }}
	\| 0.~~1494~~		\| +0.1238
	\| 0.~~1152~~		\| 0.1168
	\| 3.18		\| 3.22
	\|-		\|-
	\| 2.9.15.7		\| 2.9.15.7
	\| 65625/65536, 420175/419904, 80387359983/80000000000		\| 65625/65536, 420175/419904, 80387359983/80000000000
	\| {{mapping\| 331 1049 1293 929 }}		\| {{mapping\| 331 1049 1293 929 }}
	\| 0.~~1878~~		\| +0.1685
	\| 0.~~1199~~		\| 0.1275
	\| 3.31		\| 3.52
	\|-		\|-
	\| 2.9.15.7.11		\| 2.9.15.7.11
	\| 9801/9800, 41503/41472, 137781/137500, 759375/758912		\| 9801/9800, 41503/41472, 137781/137500, 759375/758912
	\| {{mapping\| 331 1049 1293 929 1145 }}		\| {{mapping\| 331 1049 1293 929 1145 }}
	\| 0.~~1653~~		\| +0.1499
	\| 0.~~1163~~		\| 0.1200
	\| 3.21		\| 3.31
	\|-		\|-
	\| 2.9.15.7.11.13		\| 2.9.15.7.11.13
	\| 729/728, 1575/1573, 10648/10647, 41503/41472, 43904/43875~~, 53361/53248, 20336647/2028000~~		\| 729/728, 1575/1573, 10648/10647, 41503/41472, 43904/43875
	\| {{mapping\| 331 1049 1293 929 1145 1225 }}		\| {{mapping\| 331 1049 1293 929 1145 1225 }}
	\| 0.~~1125~~		\| +0.0997
	\| 0.~~1587~~		\| 0.1568
	\| 4.38		\| 4.33
	\|-		\|-
	\| 2.9.15.7.11.13.17		\| 2.9.15.7.11.13.17
	\| 729/728, 833/832, 1089/1088, 2025/2023, 10648/10647~~, 14161/14157, 14175/14144, 43904/43875~~, 18816/18785~~, 92823/95744~~		\| 729/728, 833/832, 1089/1088, 2025/2023, 10648/10647, 18816/18785
	\| {{mapping\| 331 1049 1293 929 1145 1225 1353 }}		\| {{mapping\| 331 1049 1293 929 1145 1225 1353 }}
	\| 0.~~0901~~		\| +0.0791
	\| 0.~~1568~~		\| 0.1537
	\| 4.33		\| 4.24
	\|}		\|}

Line 75:		Line 75:
	! Associated<br>Ratio*		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-
	~~\| 1~~
	~~\| 89\331~~
	~~\| 322.66~~
	~~\| 6/5~~
	~~\| [[Magicaltet]]~~
	\|-		\|-
	\| 1		\| 1
Line 86:		Line 80:
	\| 387.92		\| 387.92
	\| 5/4		\| 5/4
	\| [[Würschmidt]]		\| [[Würschmidt]] (331, 5-limit)
	\|-
	~~\| 1~~
	~~\| 137\331~~
	~~\| 496.68~~
	~~\| 5457/4096~~
	~~\| [[Edson]]~~
	\|}		\|}
			<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct

	== Scales ==		== Scales ==

FloraC: Review (1/2)

2023-12-15T09:14:58Z

Review (1/2)

← Older revision		Revision as of 09:14, 15 December 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|331}}		{{EDO intro\|331}}

	== Theory ==		== Theory ==
	~~331et tempers out~~ [[~~78125000~~/~~78121827~~]], [[5120/5103]] ~~and~~ 1959552/1953125 in the 7-limit; ~~806736~~/~~805255, 1835008/1830125, 1019215872/1019046875~~, 12005/11979, [[16384/16335]]~~, 2359296/2358125~~, 42875/42768, ~~180224~~/~~180075, 1684375/1679616, 968000/964467, [[3025/3024]]~~, 78408/78125, ~~1362944/1361367, 4108797/4096000~~ and ~~43923~~/~~43750~~ in the 11-limit.		331edo is only [[consistent]] to the [[5-odd-limit]] and the errors of both [[harmonic]]s [[3/1\|3]] and [[5/1\|5]] are quite large, commending itself as a temperament of the 2.9.15.7.11.13.17.19 [[subgroup]].
	===Odd harmonics===
			Using the [[patent val]] nonetheless, the equal temperament [[tempering out\|tempers out]] [[5120/5103]], 1959552/1953125 and [[78125000/78121827]] in the 7-limit; [[3025/3024]], 12005/11979, [[16384/16335]], 42875/42768, 43923/43750, 78408/78125, and 180224/180075 in the 11-limit.

			=== Odd harmonics ===
	{{Harmonics in equal\|331}}		{{Harmonics in equal\|331}}
	===Subsets and supersets===
			=== Subsets and supersets ===
	331edo is the 67th [[prime edo]]. 662edo, which doubles it, gives a good correction to the harmonics 3 and 5.		331edo is the 67th [[prime edo]]. 662edo, which doubles it, gives a good correction to the harmonics 3 and 5.
	==Regular temperament properties==
			== Regular temperament properties ==
	{\| class="wikitable center-4 center-5 center-6"		{\| class="wikitable center-4 center-5 center-6"
	! rowspan="2" \|[[Subgroup]]		! rowspan="2" \| [[Subgroup]]
	! rowspan="2" \|[[Comma list\|Comma List]]		! rowspan="2" \| [[Comma list\|Comma List]]
	! rowspan="2" \|[[Mapping]]		! rowspan="2" \| [[Mapping]]
	! rowspan="2" \|Optimal<br>8ve Stretch (¢)		! rowspan="2" \| Optimal<br>8ve Stretch (¢)
	! colspan="2" \|Tuning Error		! colspan="2" \| Tuning Error
	\|-		\|-
	![[TE error\|Absolute]] (¢)		! [[TE error\|Absolute]] (¢)
	![[TE simple badness\|Relative]] (%)		! [[TE simple badness\|Relative]] (%)
	\|-		\|-
	\|2.9		\| 2.9
	\|{{monzo\|-1049 331}}		\| {{monzo\| -1049 331 }}
	\|{{~~val~~\|331 1049}}		\| {{mapping\| 331 1049 }}
	\| 0.1402		\| 0.1402
	\| 0.1402		\| 0.1402
	\| 3.87		\| 3.87
	\|-		\|-
	\|2.9.15		\| 2.9.15
	\|{{monzo\|-7 17 -12}}, {{monzo\|-74 -5 23}}		\| {{monzo\| -7 17 -12 }}, {{monzo\| -74 -5 23 }}
	\|{{~~val~~\|331 1049 1293}}		\| {{mapping\| 331 1049 1293 }}
	\| 0.1494		\| 0.1494
	\| 0.1152		\| 0.1152
	\| 3.18		\| 3.18
	\|-		\|-
	\|2.9.15.7		\| 2.9.15.7
	\|65625/65536, 420175/419904, 80387359983/80000000000		\| 65625/65536, 420175/419904, 80387359983/80000000000
	\|{{~~val~~\|331 1049 1293 929}}		\| {{mapping\| 331 1049 1293 929 }}
	\| 0.1878		\| 0.1878
	\| 0.1199		\| 0.1199
	\| 3.31		\| 3.31
	\|-		\|-
	\|2.9.15.7.11		\| 2.9.15.7.11
	\|9801/9800, 41503/41472, 137781/137500, 759375/758912		\| 9801/9800, 41503/41472, 137781/137500, 759375/758912
	\|{{~~val~~\|331 1049 1293 929 1145}}		\| {{mapping\| 331 1049 1293 929 1145 }}
	\| 0.1653		\| 0.1653
	\| 0.1163		\| 0.1163
	\| 3.21		\| 3.21
	\|-		\|-
	\|2.9.15.7.11.13		\| 2.9.15.7.11.13
	\|729/728, 1575/1573, 10648/10647, 41503/41472, 43904/43875, 53361/53248, 20336647/2028000		\| 729/728, 1575/1573, 10648/10647, 41503/41472, 43904/43875, 53361/53248, 20336647/2028000
	\|{{~~val~~\|331 1049 1293 929 1145 1225}}		\| {{mapping\| 331 1049 1293 929 1145 1225 }}
	\| 0.1125		\| 0.1125
	\| 0.1587		\| 0.1587
	\| 4.38		\| 4.38
	\|-		\|-
	\|2.9.15.7.11.13.17		\| 2.9.15.7.11.13.17
	\|729/728, 833/832, 1089/1088, 2025/2023, 10648/10647, 14161/14157, 14175/14144, 43904/43875, 18816/18785, 92823/95744		\| 729/728, 833/832, 1089/1088, 2025/2023, 10648/10647, 14161/14157, 14175/14144, 43904/43875, 18816/18785, 92823/95744
	\|{{~~val~~\|331 1049 1293 929 1145 1225 1353}}		\| {{mapping\| 331 1049 1293 929 1145 1225 1353 }}
	\| 0.0901		\| 0.0901
	\| 0.1568		\| 0.1568
Line 65:		Line 71:
	\|+Table of rank-2 temperaments by generator		\|+Table of rank-2 temperaments by generator
	! Periods<br>per 8ve		! Periods<br>per 8ve
	! Generator~~<br>(reduced)~~		! Generator*
	! Cents~~<br>(reduced)~~		! Cents*
	! Associated<br>~~ratio~~		! Associated<br>Ratio*
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|89\331		\| 89\331
	\|322.66		\| 322.66
	\|6/5		\| 6/5
	\|[[Magicaltet]]		\| [[Magicaltet]]
	\|-		\|-
	\|1		\| 1
	\|107\331		\| 107\331
	\|387.92		\| 387.92
	\|5/4		\| 5/4
	\|[[Würschmidt]]		\| [[Würschmidt]]
	\|-		\|-
	\|1		\| 1
	\|137\331		\| 137\331
	\|496.68		\| 496.68
	\|5457/4096		\| 5457/4096
	\|[[Edson]]		\| [[Edson]]
	\|}		\|}

	==Scales==		== Scales ==
	*[[Magicaltet7]]		* [[Magicaltet7]]
	*[[Magicaltet11]]		* [[Magicaltet11]]
	*[[Magicaltet15]]		* [[Magicaltet15]]

	==Music==		== Music ==
	*[https://www.youtube.com/watch?v=g3FF6oqnilk ~~Silent Silence] by [[User:Francium\|Francium]~~]		; [[User:Francium\|Francium]]
			* "Silent Silence" from ''Edson EP'' (2023) – [https://open.spotify.com/track/6q3xr4E4QIL9BMaZyf6LXd Spotify] \| [https://francium223.bandcamp.com/track/silent-silence Bandcamp] \| [https://www.youtube.com/watch?v=g3FF6oqnilk YouTube] – edson in 331edo tuning

Francium: /* Rank-2 temperaments */

2023-05-14T14:52:28Z

Rank-2 temperaments

← Older revision		Revision as of 14:52, 14 May 2023
Line 74:		Line 74:
	\|322.66		\|322.66
	\|6/5		\|6/5
	\|Magicaltet		\|[[Magicaltet]]
			\|-
			\|1
			\|107\331
			\|387.92
			\|5/4
			\|[[Würschmidt]]
	\|-		\|-
	\|1		\|1
Line 80:		Line 86:
	\|496.68		\|496.68
	\|5457/4096		\|5457/4096
	\|Edson		\|[[Edson]]
	\|}		\|}