571edo - Revision history

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
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	\| [[Maviloid]]		\| [[Maviloid]]
	\|}		\|}
	<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: /* Regular temperament properties */ emmthird

2025-09-04T15:14:30Z

Regular temperament properties: emmthird

← Older revision		Revision as of 15:14, 4 September 2025
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	! 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
	\|-		\|-
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	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| -905 571 }}		\| {{Monzo\| -905 571 }}
	\| {{~~mapping~~\| 571 905 }}		\| {{Mapping\| 571 905 }}
	\| +0.0090		\| +0.0090
	\| 0.0090		\| 0.0090
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	\|-		\|-
	\| 2.3.5		\| 2.3.5
	\| {{~~monzo~~\| 8 14 -13 }}, {{monzo\| -69 45 -1 }}		\| {{Monzo\| 8 14 -13 }}, {{monzo\| -69 45 -1 }}
	\| {{~~mapping~~\| 571 905 1326 }}		\| {{Mapping\| 571 905 1326 }}
	\| −0.0480		\| −0.0480
	\| 0.0810		\| 0.0810
Line 39:		Line 39:
	\| 2.3.5.7		\| 2.3.5.7
	\| 2401/2400, 14348907/14336000, 29360128/29296875		\| 2401/2400, 14348907/14336000, 29360128/29296875
	\| {{~~mapping~~\| 571 905 1326 1603 }}		\| {{Mapping\| 571 905 1326 1603 }}
	\| −0.0361		\| −0.0361
	\| 0.0731		\| 0.0731
Line 46:		Line 46:
	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 2401/2400, 3025/3024, 5632/5625, 14348907/14336000		\| 2401/2400, 3025/3024, 5632/5625, 14348907/14336000
	\| {{~~mapping~~\| 571 905 1326 1603 1975 }}		\| {{Mapping\| 571 905 1326 1603 1975 }}
	\| +0.0119		\| +0.0119
	\| 0.1161		\| 0.1161
Line 53:		Line 53:
	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653		\| 1001/1000, 1716/1715, 3025/3024, 4096/4095, 107811/107653
	\| {{~~mapping~~\| 571 905 1326 1603 1975 2113 }}		\| {{Mapping\| 571 905 1326 1603 1975 2113 }}
	\| +0.0053		\| +0.0053
	\| 0.1070		\| 0.1070
Line 60:		Line 60:
	\| 2.3.5.7.11.13.17		\| 2.3.5.7.11.13.17
	\| 1001/1000, 1089/1088, 1716/1715, 2601/2600, 3025/3024, 4096/4095		\| 1001/1000, 1089/1088, 1716/1715, 2601/2600, 3025/3024, 4096/4095
	\| {{~~mapping~~\| 571 905 1326 1603 1975 2113 2334 }}		\| {{Mapping\| 571 905 1326 1603 1975 2113 2334 }}
	\| +0.0002		\| +0.0002
	\| 0.0999		\| 0.0999
Line 70:		Line 70:
	\|+ 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
	\|-		\|-
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	\| 123\571		\| 123\571
	\| 258.49		\| 258.49
	\| {{~~monzo~~\| -32 13 5 }}		\| {{Monzo\| -32 13 5 }}
	\| [[Lafa]]		\| [[Lafa]]
	\|-		\|-
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	\| 6/5		\| 6/5
	\| [[Parakleismic]] (5-limit)		\| [[Parakleismic]] (5-limit)
			\|-
			\| 1
			\| 187\571
			\| 392.99
			\| 2744/2187
			\| [[Emmthird]] (7-limit)
	\|-		\|-
	\| 1		\| 1
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	\| [[Maviloid]]		\| [[Maviloid]]
	\|}		\|}
	<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 ==

Francium: /* Music */ +music

2025-04-05T12:50:20Z

Music: +music

← Older revision		Revision as of 12:50, 5 April 2025
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	* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] \| [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]		* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] \| [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]
	* "LEARN TO CAR" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/2icA5S4LIFCdKA7aZPkLgr Spotify] \| [https://francium223.bandcamp.com/track/learn-to-car Bandcamp] \| [https://www.youtube.com/watch?v=ceVF2FMNKbE YouTube]		* "LEARN TO CAR" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/2icA5S4LIFCdKA7aZPkLgr Spotify] \| [https://francium223.bandcamp.com/track/learn-to-car Bandcamp] \| [https://www.youtube.com/watch?v=ceVF2FMNKbE YouTube]
			* "George Crispell" from ''Don't Give Your Kids These Names!'' (2025) − [https://open.spotify.com/track/3mZBLdkeEvHYMDgmHNJu4H Spotify] \| [https://francium223.bandcamp.com/track/george-crispell Bandcamp] \| [https://www.youtube.com/watch?v=I7SdSaP1UJs YouTube] − in Gentic, 571edo tuning

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

ArrowHead294 at 19:08, 20 February 2025

2025-02-20T19:08:37Z

← Older revision		Revision as of 19:08, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|571~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T16:21:47Z

Theory: cleanup

← Older revision		Revision as of 16:21, 17 January 2025
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	== Theory ==		== Theory ==
	~~571edo~~ [[tempers out]] the [[parakleisma]], {{monzo\| 8 14 -13 }}, and the [[counterschisma]], {{monzo\| -69 45 -1 }}, in the [[5-limit]], as well as the lafa comma, {{monzo\| 77 -31 -12 }}; [[2401/2400]], 14348907/14336000, and 29360128/29296875 in the [[7-limit]]; [[3025/3024]], [[5632/5625]], [[41503/41472]], and 17537553/17500000 in the [[11-limit]]; [[1001/1000]], [[1716/1715]], [[4096/4095]], 17303/17280, and 107811/107653 in the [[13-limit]], supporting the 13-limit [[quasiorwell]] temperament; [[1089/1088]], [[1701/1700]], [[2431/2430]], [[2601/2600]], [[5832/5831]] and 7744/7735 in the [[17-limit]]. The 7th harmonic is only 0.0007135 cents sharp in 571edo, as the denominator of a convergent to log<sub>2</sub>7, after [[109edo\|109]] and before [[2393edo\|2393]].		571et [[tempering out\|tempers out]] the [[parakleisma]], {{monzo\| 8 14 -13 }}, and the [[counterschisma]], {{monzo\| -69 45 -1 }}, in the [[5-limit]], as well as the lafa comma, {{monzo\| 77 -31 -12 }}; [[2401/2400]], 14348907/14336000, and 29360128/29296875 in the [[7-limit]]; [[3025/3024]], [[5632/5625]], [[41503/41472]], and 17537553/17500000 in the [[11-limit]]; [[1001/1000]], [[1716/1715]], [[4096/4095]], 17303/17280, and 107811/107653 in the [[13-limit]], supporting the 13-limit [[quasiorwell]] temperament; [[1089/1088]], [[1701/1700]], [[2431/2430]], [[2601/2600]], [[5832/5831]] and 7744/7735 in the [[17-limit]]. The 7th harmonic is only 0.0007135 cents sharp in 571edo, as the denominator of a convergent to log<sub>2</sub>7, after [[109edo\|109]] and before [[2393edo\|2393]].

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|571~~\|columns=11~~}}		{{Harmonics in equal\|571}}

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

ArrowHead294 at 14:48, 16 January 2025

2025-01-16T14:48:18Z

← Older revision		Revision as of 14:48, 16 January 2025
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	== Theory ==		== Theory ==
	~~The equal temperament~~ [[~~tempering out\|~~tempers out]] the [[parakleisma]], {{monzo\| 8 14 -13 }}, and the [[counterschisma]], {{monzo\| -69 45 -1 }}, in the [[5-limit]], as well as the lafa comma, {{monzo\| 77 -31 -12 }}; [[2401/2400]], 14348907/14336000, and 29360128/29296875 in the [[7-limit]]; [[3025/3024]], [[5632/5625]], [[41503/41472]], and 17537553/17500000 in the [[11-limit]]; [[1001/1000]], [[1716/1715]], [[4096/4095]], 17303/17280, and 107811/107653 in the [[13-limit]], supporting the 13-limit [[quasiorwell]] temperament; [[1089/1088]], [[1701/1700]], [[2431/2430]], [[2601/2600]], [[5832/5831]] and 7744/7735 in the [[17-limit]]. The 7th harmonic is only 0.0007135 cents sharp in 571edo, as the denominator of a convergent to log<sub>2</sub>7, after [[109edo\|109]] and before [[2393edo\|2393]].		571edo [[tempers out]] the [[parakleisma]], {{monzo\| 8 14 -13 }}, and the [[counterschisma]], {{monzo\| -69 45 -1 }}, in the [[5-limit]], as well as the lafa comma, {{monzo\| 77 -31 -12 }}; [[2401/2400]], 14348907/14336000, and 29360128/29296875 in the [[7-limit]]; [[3025/3024]], [[5632/5625]], [[41503/41472]], and 17537553/17500000 in the [[11-limit]]; [[1001/1000]], [[1716/1715]], [[4096/4095]], 17303/17280, and 107811/107653 in the [[13-limit]], supporting the 13-limit [[quasiorwell]] temperament; [[1089/1088]], [[1701/1700]], [[2431/2430]], [[2601/2600]], [[5832/5831]] and 7744/7735 in the [[17-limit]]. The 7th harmonic is only 0.0007135 cents sharp in 571edo, as the denominator of a convergent to log<sub>2</sub>7, after [[109edo\|109]] and before [[2393edo\|2393]].

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| {{monzo\| 8 14 -13 }}, {{monzo\| -69 45 -1 }}		\| {{monzo\| 8 14 -13 }}, {{monzo\| -69 45 -1 }}
	\| {{mapping\| 571 905 1326 }}		\| {{mapping\| 571 905 1326 }}
	\| ~~−0~~.0480		\| −0.0480
	\| 0.0810		\| 0.0810
	\| 3.85		\| 3.85
Line 40:		Line 40:
	\| 2401/2400, 14348907/14336000, 29360128/29296875		\| 2401/2400, 14348907/14336000, 29360128/29296875
	\| {{mapping\| 571 905 1326 1603 }}		\| {{mapping\| 571 905 1326 1603 }}
	\| ~~−0~~.0361		\| −0.0361
	\| 0.0731		\| 0.0731
	\| 3.48		\| 3.48
Line 106:		Line 106:
	\| [[Maviloid]]		\| [[Maviloid]]
	\|}		\|}
	<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]]
	* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) ~~–~~ [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] \| [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]		* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] \| [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]
	* "LEARN TO CAR" from ''CAPSLOCK'' (2024) ~~–~~ [https://open.spotify.com/track/2icA5S4LIFCdKA7aZPkLgr Spotify] \| [https://francium223.bandcamp.com/track/learn-to-car Bandcamp] \| [https://www.youtube.com/watch?v=ceVF2FMNKbE YouTube]		* "LEARN TO CAR" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/2icA5S4LIFCdKA7aZPkLgr Spotify] \| [https://francium223.bandcamp.com/track/learn-to-car Bandcamp] \| [https://www.youtube.com/watch?v=ceVF2FMNKbE YouTube]

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

ArrowHead294: Partial undo

2024-11-16T12:31:59Z

Partial undo

← Older revision		Revision as of 12:31, 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
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	\| 0.0999		\| 0.0999
	\| 4.75		\| 4.75
	~~{{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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	\| 875/648		\| 875/648
	\| [[Maviloid]]		\| [[Maviloid]]
	~~{{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 04:30, 16 November 2024

2024-11-16T04:30:53Z

← Older revision		Revision as of 04:30, 16 November 2024
Line 12:		Line 12:

	== 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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	\| {{monzo\| 8 14 -13 }}, {{monzo\| -69 45 -1 }}		\| {{monzo\| 8 14 -13 }}, {{monzo\| -69 45 -1 }}
	\| {{mapping\| 571 905 1326 }}		\| {{mapping\| 571 905 1326 }}
	\| -0.0480		\| −0.0480
	\| 0.0810		\| 0.0810
	\| 3.85		\| 3.85
Line 39:		Line 31:
	\| 2401/2400, 14348907/14336000, 29360128/29296875		\| 2401/2400, 14348907/14336000, 29360128/29296875
	\| {{mapping\| 571 905 1326 1603 }}		\| {{mapping\| 571 905 1326 1603 }}
	\| -0.0361		\| −0.0361
	\| 0.0731		\| 0.0731
	\| 3.48		\| 3.48
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	\| 0.0999		\| 0.0999
	\| 4.75		\| 4.75
	\|}		{{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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	\| 875/648		\| 875/648
	\| [[Maviloid]]		\| [[Maviloid]]
	\|}		{{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]]
	* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] \| [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]		* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] \| [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]
	* "LEARN TO CAR" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/2icA5S4LIFCdKA7aZPkLgr Spotify] \| [https://francium223.bandcamp.com/track/learn-to-car Bandcamp] \| [https://www.youtube.com/watch?v=ceVF2FMNKbE YouTube]		* "LEARN TO CAR" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/2icA5S4LIFCdKA7aZPkLgr Spotify] \| [https://francium223.bandcamp.com/track/learn-to-car Bandcamp] \| [https://www.youtube.com/watch?v=ceVF2FMNKbE YouTube]

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

Francium: /* Music */ +music

2024-08-27T12:09:08Z

Music: +music

← Older revision		Revision as of 12:09, 27 August 2024
Line 109:		Line 109:
	; [[Francium]]		; [[Francium]]
	* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] \| [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]		* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] \| [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]
			* "LEARN TO CAR" from ''CAPSLOCK'' (2024) – [https://open.spotify.com/track/2icA5S4LIFCdKA7aZPkLgr Spotify] \| [https://francium223.bandcamp.com/track/learn-to-car Bandcamp] \| [https://www.youtube.com/watch?v=ceVF2FMNKbE YouTube]

	[[Category:Quasiorwell]]		[[Category:Quasiorwell]]

Francium: +music

2024-04-01T09:20:00Z

+music

← Older revision		Revision as of 09:20, 1 April 2024
Line 105:		Line 105:
	\|}		\|}
	<nowiki>*</nowiki> [[Normal lists\|octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if it is distinct		<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 ==
			; [[Francium]]
			* "Cuckoo Raccoon" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/3oXpSrGT3590Zw4JDQJ1wO Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-raccoon Bandcamp] \| [https://www.youtube.com/watch?v=mBdbJkdirkw YouTube]

	[[Category:Quasiorwell]]		[[Category:Quasiorwell]]