631edo - 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"

2026-03-13T13:32:06Z

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
Line 85:		Line 85:
	\| [[Helmholtz (temperament)\|Helmholtz]] / [[Pontiac]]		\| [[Helmholtz (temperament)\|Helmholtz]] / [[Pontiac]]
	\|}		\|}
	<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 ==

Francium: /* Music */ +music

2025-07-04T11:50:46Z

Music: +music

← Older revision		Revision as of 11:50, 4 July 2025
Line 90:		Line 90:
	; [[Francium]]		; [[Francium]]
	* "DUMPSTER FIRE" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/7noSmEcwOfZpnFsiQ6vYNv Spotify] \| [https://francium223.bandcamp.com/track/dumpster-fire Bandcamp] \| [https://www.youtube.com/watch?v=PWP2o71Kqes YouTube]		* "DUMPSTER FIRE" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/7noSmEcwOfZpnFsiQ6vYNv Spotify] \| [https://francium223.bandcamp.com/track/dumpster-fire Bandcamp] \| [https://www.youtube.com/watch?v=PWP2o71Kqes YouTube]
	* "Remember To Forget It." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/7h0mRNT7iS8L722566rzlJ Spotify] \| [https://francium223.bandcamp.com/track/remember-to-forget-it Bandcamp] \| [https://www.youtube.com/watch?v=Jwuqj4BJHwY YouTube] – ~~in Gabic, 631edo tuning~~		* "Remember To Forget It." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/7h0mRNT7iS8L722566rzlJ Spotify] \| [https://francium223.bandcamp.com/track/remember-to-forget-it Bandcamp] \| [https://www.youtube.com/watch?v=Jwuqj4BJHwY YouTube]
			* "Don't Have a Problem With You" from ''Don't'' (2025) – [https://open.spotify.com/track/2dBYarUaS8dxuHx91zGVEt Spotify] \| [https://francium223.bandcamp.com/track/dont-have-a-problem-with-you Bandcamp] \| [https://www.youtube.com/watch?v=bxuOZQwOO30 YouTube]

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

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

2025-04-17T02:29:00Z

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

← Older revision		Revision as of 02:29, 17 April 2025
Line 83:		Line 83:
	\| 498.257		\| 498.257
	\| 4/3		\| 4/3
	\| [[Helmholtz temperament\|Helmholtz]] / [[Pontiac]]		\| [[Helmholtz (temperament)\|Helmholtz]] / [[Pontiac]]
	\|}		\|}
	<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

Sintel: fix helmholtz link

2025-04-16T15:32:55Z

fix helmholtz link

← Older revision		Revision as of 15:32, 16 April 2025
Line 83:		Line 83:
	\| 498.257		\| 498.257
	\| 4/3		\| 4/3
	\| [[Helmholtz]] / [[Pontiac]]		\| [[Helmholtz temperament\|Helmholtz]] / [[Pontiac]]
	\|}		\|}
	<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: +interval chapter

2025-02-26T16:12:42Z

+interval chapter

← Older revision		Revision as of 16:12, 26 February 2025
Line 10:		Line 10:
	=== Subsets and supersets ===		=== Subsets and supersets ===
	631edo is the 115th [[prime edo]].		631edo is the 115th [[prime edo]].

			== Intervals ==
			{{Main\|Table of 631edo intervals}}

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

Francium: changed EDO intro to ED intro

2025-02-21T06:09:21Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:09, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro}}		{{ED intro}}

	== Theory ==		== Theory ==

Francium: /* Music */ +music

2025-02-18T12:17:10Z

Music: +music

← Older revision		Revision as of 12:17, 18 February 2025
Line 87:		Line 87:
	; [[Francium]]		; [[Francium]]
	* "DUMPSTER FIRE" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/7noSmEcwOfZpnFsiQ6vYNv Spotify] \| [https://francium223.bandcamp.com/track/dumpster-fire Bandcamp] \| [https://www.youtube.com/watch?v=PWP2o71Kqes YouTube]		* "DUMPSTER FIRE" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/7noSmEcwOfZpnFsiQ6vYNv Spotify] \| [https://francium223.bandcamp.com/track/dumpster-fire Bandcamp] \| [https://www.youtube.com/watch?v=PWP2o71Kqes YouTube]
			* "Remember To Forget It." from ''Random Sentences'' (2025) – [https://open.spotify.com/track/7h0mRNT7iS8L722566rzlJ Spotify] \| [https://francium223.bandcamp.com/track/remember-to-forget-it Bandcamp] \| [https://www.youtube.com/watch?v=Jwuqj4BJHwY YouTube] – in Gabic, 631edo tuning

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

FloraC: /* Theory */ cleanup

2025-01-17T16:30:51Z

Theory: cleanup

← Older revision		Revision as of 16:30, 17 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	631edo is [[consistent]] to the [[9-odd-limit]], with all of the odd harmonics having a flat tendency. Using the [[patent val]], it [[tempers out]] [[~~4375~~/~~4374~~]], [[~~41503~~/~~41472~~]], [[~~32805~~/~~32768~~]] and [[~~12005~~/~~11979~~]] in the [[11-limit]]; [[1575/1573]]~~, 4375/4374~~, [[~~4459~~/~~4455~~]], [[~~4225~~/~~4224~~]], and 83349/83200 in the [[13-limit]].		631edo is [[consistent]] to the [[9-odd-limit]], with all of the odd harmonics having a flat tendency. Using the [[patent val]], it [[tempering out\|tempers out]] [[32805/32768]] in the 5-limit; [[4375/4374]] in the 7-limit; [[12005/11979]] and [[41503/41472]] in the [[11-limit]]; [[1575/1573]], [[4225/4224]], [[4459/4455]], and 83349/83200 in the [[13-limit]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 9:		Line 9:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	631edo is the 115th [[prime ~~EDO~~]].		631edo is the 115th [[prime edo]].

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

ArrowHead294 at 19:25, 15 January 2025

2025-01-15T19:25:21Z

← Older revision		Revision as of 19:25, 15 January 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	631edo is [[consistent]] to the [[9-odd-limit]], with all of the odd harmonics having a flat tendency. Using the [[patent val]], ~~the equal temperament~~ [[~~tempering out\|~~tempers out]] [[4375/4374]], [[41503/41472]], [[32805/32768]] and [[12005/11979]] in the [[11-limit]]; [[1575/1573]], 4375/4374, [[4459/4455]], [[4225/4224]] and 83349/83200 in the [[13-limit]].		631edo is [[consistent]] to the [[9-odd-limit]], with all of the odd harmonics having a flat tendency. Using the [[patent val]], it [[tempers out]] [[4375/4374]], [[41503/41472]], [[32805/32768]] and [[12005/11979]] in the [[11-limit]]; [[1575/1573]], 4375/4374, [[4459/4455]], [[4225/4224]], and 83349/83200 in the [[13-limit]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 26:		Line 26:
	\| {{monzo\|-1000 631}}		\| {{monzo\|-1000 631}}
	\| {{mapping\|631 1000}}		\| {{mapping\|631 1000}}
	\| 0.0668		\| +0.0668
	\| 0.0668		\| 0.0668
	\| 3.51		\| 3.51
Line 33:		Line 33:
	\| 32805/32768, {{monzo\|-50 -71 70}}		\| 32805/32768, {{monzo\|-50 -71 70}}
	\| {{mapping\|631 1000 1465}}		\| {{mapping\|631 1000 1465}}
	\| 0.0818		\| +0.0818
	\| 0.0585		\| 0.0585
	\| 3.08		\| 3.08
Line 40:		Line 40:
	\| 4375/4374, 32805/32768, 678223072849/675000000000		\| 4375/4374, 32805/32768, 678223072849/675000000000
	\| {{mapping\|631 1000 1465 1771}}		\| {{mapping\|631 1000 1465 1771}}
	\| 0.1361		\| +0.1361
	\| 0.1067		\| 0.1067
	\| 5.61		\| 5.61
Line 47:		Line 47:
	\| 4375/4374, 41503/41472, 32805/32768, 12005/11979		\| 4375/4374, 41503/41472, 32805/32768, 12005/11979
	\| {{mapping\|631 1000 1465 1771 2183}}		\| {{mapping\|631 1000 1465 1771 2183}}
	\| 0.0980		\| +0.0980
	\| 0.1221		\| 0.1221
	\| 6.42		\| 6.42
Line 54:		Line 54:
	\| 1575/1573, 4375/4374, 4459/4455, 4225/4224, 83349/83200		\| 1575/1573, 4375/4374, 4459/4455, 4225/4224, 83349/83200
	\| {{mapping\|631 1000 1465 1771 2183 2335}}		\| {{mapping\|631 1000 1465 1771 2183 2335}}
	\| 0.0797		\| +0.0797
	\| 0.1187		\| 0.1187
	\| 6.24		\| 6.24
Line 61:		Line 61:
	\| 1225/1224, 1701/1700, 833/832, 1575/1573, 4459/4455, 4225/4224		\| 1225/1224, 1701/1700, 833/832, 1575/1573, 4459/4455, 4225/4224
	\| {{mapping\|631 1000 1465 1771 2183 2335 2579}}		\| {{mapping\|631 1000 1465 1771 2183 2335 2579}}
	\| 0.0809		\| +0.0809
	\| 0.1099		\| 0.1099
	\| 5.78		\| 5.78
Line 82:		Line 82:
	\| [[Helmholtz]] / [[Pontiac]]		\| [[Helmholtz]] / [[Pontiac]]
	\|}		\|}
	<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]]
	* "DUMPSTER FIRE" from ''CAPSLOCK'' (2024) ~~–~~ [https://open.spotify.com/track/7noSmEcwOfZpnFsiQ6vYNv Spotify] \| [https://francium223.bandcamp.com/track/dumpster-fire Bandcamp] \| [https://www.youtube.com/watch?v=PWP2o71Kqes YouTube]		* "DUMPSTER FIRE" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/7noSmEcwOfZpnFsiQ6vYNv Spotify] \| [https://francium223.bandcamp.com/track/dumpster-fire Bandcamp] \| [https://www.youtube.com/watch?v=PWP2o71Kqes YouTube]

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

ArrowHead294: Partial undo

2024-11-16T13:08:06Z

Partial undo

← Older revision		Revision as of 13:08, 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		\| 2.3
Line 55:		Line 64:
	\| 0.1099		\| 0.1099
	\| 5.78		\| 5.78
	~~{{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
Line 65:		Line 81:
	\| 4/3		\| 4/3
	\| [[Helmholtz]] / [[Pontiac]]		\| [[Helmholtz]] / [[Pontiac]]
	~~{{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 ==