251edo - Revision history

Francium: /* Music */ +music

2026-05-03T11:38:27Z

Music: +music

← Older revision		Revision as of 11:38, 3 May 2026
Line 94:		Line 94:
	; [[Francium]]		; [[Francium]]
	* "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] \| [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] \| [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube]		* "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] \| [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] \| [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube]
			* "The Living Space" from ''Check Us Out'' (2026) – [https://open.spotify.com/track/66H2fQ5ogT1j33ludkD0ug Spotify] \| [https://francium223.bandcamp.com/track/the-living-space Bandcamp] \| [https://www.youtube.com/watch?v=Q4O5l0SnZMI YouTube]

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

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave" to "Octave-reduced form, reduced to the first half-octave"

2026-03-13T13:34:37Z

Text replacement - "Octave-reduced form, reduced to the first half-octave" to "Octave-reduced form, reduced to the first half-octave"

← Older revision		Revision as of 13:34, 13 March 2026
Line 89:		Line 89:
	\| [[Maquila]]		\| [[Maquila]]
	\|}		\|}
	<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms\|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 form]] in parentheses if distinct

	== Music ==		== Music ==

FloraC: Cleanup

2025-10-27T13:28:55Z

Cleanup

← Older revision		Revision as of 13:28, 27 October 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	251et [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 49 -6 -17 }} ([[maquila comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], and 40500000/40353607 in the 7-limit, [[support]]ing [[amity]], [[supermajor]], and [[acrokleismic]].		251et [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 49 -6 -17 }} ([[maquila comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], and 40500000/40353607 in the 7-limit, [[support]]ing [[amity]], [[supermajor (temperament)\|supermajor]], and [[acrokleismic]].

	Using the [[patent val]] {{val\| 251 398 583 705 '''868''' }}, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; [[352/351]], [[676/675]], [[847/845]], and [[1573/1568]] in the 13-limit.		Using the [[patent val]] {{val\| 251 398 583 705 '''868''' }}, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; [[352/351]], [[676/675]], [[847/845]], and [[1573/1568]] in the 13-limit.
Line 21:		Line 21:
	! rowspan="2" \| [[Comma list]]		! rowspan="2" \| [[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
	\|-		\|-
Line 28:		Line 28:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 398 -251 }}		\| {{Monzo\| 398 -251 }}
	\| {{~~mapping~~\| 251 398 }}		\| {{Mapping\| 251 398 }}
	\| −0.2630		\| −0.2630
	\| 0.2630		\| 0.2630
Line 35:		Line 35:
	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 9 -13 5 }}, {{monzo\| 49 -6 -17 }}		\| {{Monzo\| 9 -13 5 }}, {{monzo\| 49 -6 -17 }}
	\| {{~~mapping~~\| 251 398 583 }}		\| {{Mapping\| 251 398 583 }}
	\| −0.3099		\| −0.3099
	\| 0.2247		\| 0.2247
Line 43:		Line 43:
	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 5120/5103, 40500000/40353607		\| 4375/4374, 5120/5103, 40500000/40353607
	\| {{~~mapping~~\| 251 398 583 705 }}		\| {{Mapping\| 251 398 583 705 }}
	\| −0.3830		\| −0.3830
	\| 0.2322		\| 0.2322
Line 53:		Line 53:
	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
Line 75:		Line 75:
	\| 435.06		\| 435.06
	\| 9/7		\| 9/7
	\| [[Supermajor]]		\| [[Supermajor (temperament)\|Supermajor]]
	\|-		\|-
	\| 1		\| 1
Line 89:		Line 89:
	\| [[Maquila]]		\| [[Maquila]]
	\|}		\|}
	<nowiki />* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[Normal ~~lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms\|Octave-reduced form]], reduced to the first half-octave, and [[Normal forms\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

ArrowHead294 at 19:28, 20 February 2025

2025-02-20T19:28:11Z

← Older revision		Revision as of 19:28, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|251~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:43, 15 January 2025

2025-01-15T18:43:31Z

← Older revision		Revision as of 18:43, 15 January 2025
Line 89:		Line 89:
	\| [[Maquila]]		\| [[Maquila]]
	\|}		\|}
	<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 ==

ArrowHead294 at 18:17, 15 January 2025

2025-01-15T18:17:13Z

← Older revision		Revision as of 18:17, 15 January 2025
Line 30:		Line 30:
	\| {{monzo\| 398 -251 }}		\| {{monzo\| 398 -251 }}
	\| {{mapping\| 251 398 }}		\| {{mapping\| 251 398 }}
	\| ~~−0~~.2630		\| −0.2630
	\| 0.2630		\| 0.2630
	\| 5.50		\| 5.50
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	\| {{monzo\| 9 -13 5 }}, {{monzo\| 49 -6 -17 }}		\| {{monzo\| 9 -13 5 }}, {{monzo\| 49 -6 -17 }}
	\| {{mapping\| 251 398 583 }}		\| {{mapping\| 251 398 583 }}
	\| ~~−0~~.3099		\| −0.3099
	\| 0.2247		\| 0.2247
	\| 4.70		\| 4.70
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	\| 4375/4374, 5120/5103, 40500000/40353607		\| 4375/4374, 5120/5103, 40500000/40353607
	\| {{mapping\| 251 398 583 705 }}		\| {{mapping\| 251 398 583 705 }}
	\| ~~−0~~.3830		\| −0.3830
	\| 0.2322		\| 0.2322
	\| 4.86		\| 4.86
Line 93:		Line 93:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "hope in dark times" from ''hope in dark times'' (2024) ~~–~~ [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] \| [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] \| [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube]		* "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] \| [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] \| [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube]

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

ArrowHead294: Partial undo

2024-11-16T12:58:23Z

Partial undo

← Older revision		Revision as of 12:58, 16 November 2024
Line 16:		Line 16:

	== 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
	\| {{monzo\| 398 -251 }}		\| {{monzo\| 398 -251 }}
	\| {{mapping\| 251 398 }}		\| {{mapping\| 251 398 }}
	\| -0.2630		\| −0.2630
	\| 0.2630		\| 0.2630
	\| 5.50		\| 5.50
Line 28:		Line 37:
	\| {{monzo\| 9 -13 5 }}, {{monzo\| 49 -6 -17 }}		\| {{monzo\| 9 -13 5 }}, {{monzo\| 49 -6 -17 }}
	\| {{mapping\| 251 398 583 }}		\| {{mapping\| 251 398 583 }}
	\| -0.3099		\| −0.3099
	\| 0.2247		\| 0.2247
	\| 4.70		\| 4.70
Line 35:		Line 44:
	\| 4375/4374, 5120/5103, 40500000/40353607		\| 4375/4374, 5120/5103, 40500000/40353607
	\| {{mapping\| 251 398 583 705 }}		\| {{mapping\| 251 398 583 705 }}
	\| -0.3830		\| −0.3830
	\| 0.2322		\| 0.2322
	\| 4.86		\| 4.86
	~~{{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 72:		Line 88:
	\| 512/375		\| 512/375
	\| [[Maquila]]		\| [[Maquila]]
	~~{{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 03:04, 16 November 2024

2024-11-16T03:04:01Z

← Older revision		Revision as of 03:04, 16 November 2024
Line 16:		Line 16:

	== 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
Line 46:		Line 38:
	\| 0.2322		\| 0.2322
	\| 4.86		\| 4.86
	\|}		{{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 86:		Line 72:
	\| 512/375		\| 512/375
	\| [[Maquila]]		\| [[Maquila]]
	\|}		{{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]]
	* "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] \| [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] \| [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube]		* "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] \| [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] \| [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube]

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

FloraC: Review

2024-03-22T14:48:44Z

Review

← Older revision		Revision as of 14:48, 22 March 2024
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|251}}		{{EDO intro\|251}}

	== Theory ==		== Theory ==
	251et tempers out 1600000/1594323 (amity comma) and ~~562949953421312/556182861328125~~ (maquila comma) in the 5-limit; 4375/4374, 5120/5103, and 40500000/40353607 in the 7-limit.		251et [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 49 -6 -17 }} ([[maquila comma]]) in the 5-limit; [[4375/4374]], [[5120/5103]], and 40500000/40353607 in the 7-limit, [[support]]ing [[amity]], [[supermajor]], and [[acrokleismic]].

	Using the patent val, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; 352/351, 676/675, 847/845, and 1573/1568 in the 13-limit.		Using the [[patent val]] {{val\| 251 398 583 705 '''868''' }}, it tempers out 1331/1323, 1375/1372, 16896/16807, and 24057/24010 in the 11-limit; [[352/351]], [[676/675]], [[847/845]], and [[1573/1568]] in the 13-limit.

	Using the 251e val, it tempers out 540/539, 5632/5625, 6250/6237, and 12005/11979 in the 11-limit; 364/363, 676/675, 1716/1715, and 3584/3575 in the 13-limit.		Using the 251e val {{val\| 251 398 583 705 '''869''' }}, it tempers out [[540/539]], [[5632/5625]], [[6250/6237]], and 12005/11979 in the 11-limit; [[364/363]], [[676/675]], [[1716/1715]], and 3584/3575 in the 13-limit.

	=== Odd harmonics ===		=== Odd harmonics ===
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	251edo is the 54th [[prime ~~EDO~~]].		251edo is the 54th [[prime edo]].

	==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]] (%)
	\|-		\|-
	\|2.3		\| 2.3
	\|{{monzo\|398 -251}}		\| {{monzo\| 398 -251 }}
	\|{{~~val~~\|251 398}}		\| {{mapping\| 251 398 }}
	\| -0.2630		\| -0.2630
	\| 0.2630		\| 0.2630
	\| 5.50		\| 5.50
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|9 -13 5}}, {{monzo\|49 -6 -17}}		\| {{monzo\| 9 -13 5 }}, {{monzo\| 49 -6 -17 }}
	\|{{~~val~~\|251 398 583}}		\| {{mapping\| 251 398 583 }}
	\| -0.3099		\| -0.3099
	\| 0.2247		\| 0.2247
	\| 4.70		\| 4.70
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|4375/4374, 5120/5103, ~~6144~~/~~6125~~		\| 4375/4374, 5120/5103, 40500000/40353607
	\|{{~~val~~\|251 398 583 705}}		\| {{mapping\| 251 398 583 705 }}
	\| -0.3830		\| -0.3830
	\| 0.2322		\| 0.2322
Line 51:		Line 52:
	\|+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
	\|71\251		\| 66\251
	\|~~339.44~~		\| 315.54
	~~\|243/200~~		\| 6/5
	~~\|[[Amity]]~~		\| [[Acrokleismic]]
	\|-
	\|1
	~~\|75\251~~
	~~\|358~~.57
	\|~~315~~/~~256~~
	\|[[~~Restles~~]]
	\|-		\|-
	\|1		\| 1
	\|91\251		\| 71\251
	\|~~435~~.06		\| 339.44
	\|9/7		\| 243/200
	\|[[~~Supermajor~~]]		\| [[Amity]]
	\|-		\|-
	\|1		\| 1
	\|96\251		\| 91\251
	\|~~458~~.96		\| 435.06
	\|~~125~~/96		\| 9/7
	\|[[~~Majvam~~]]		\| [[Supermajor]]
	\|-		\|-
	\|1		\| 1
	\|~~112~~\251		\| 96\251
	\|~~535~~.46		\| 458.96
	\|~~512~~/~~375~~		\| 125/96
	\|[[~~Maquila~~]]		\| [[Majvam]]
	\|-		\|-
	\|1		\| 1
	\|~~117~~\251		\| 112\251
	\|~~559~~.26		\| 535.46
	\|~~864~~/~~625~~		\| 512/375
	\|[[~~Tritriple~~]]		\| [[Maquila]]
	\|}		\|}
			<nowiki>*</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 ==
Line 97:		Line 93:
	* "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] \| [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] \| [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube]		* "hope in dark times" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1zSiYXz46ugWAmqySaEN2A Spotify] \| [https://francium223.bandcamp.com/track/hope-in-dark-times Bandcamp] \| [https://www.youtube.com/watch?v=yHl3oku_NmY YouTube]

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	~~[[Category:Prime EDO]]~~
	[[Category:Listen]]		[[Category:Listen]]

Francium: +categories

2024-02-13T17:55:25Z

+categories

← Older revision		Revision as of 17:55, 13 February 2024
Line 99:		Line 99:
	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Prime EDO]]		[[Category:Prime EDO]]
			[[Category:Listen]]