227edo - 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"

2026-03-13T13:31:37Z

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 13:31, 13 March 2026
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	\| [[Undecental]]		\| [[Undecental]]
	\|}		\|}
	<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 ==

ArrowHead294 at 14:20, 20 February 2025

2025-02-20T14:20:08Z

← Older revision		Revision as of 14:20, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|227~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: /* Theory */ cleanup

2025-01-17T15:33:55Z

Theory: cleanup

← Older revision		Revision as of 15:33, 17 January 2025
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	== Theory ==		== Theory ==
	~~227edo~~ [[tempers out]] 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| 61 -37 -1 }} in the 5-limit; [[5120/5103]], [[65625/65536]], and 117649/116640 in the 7-limit, so that it [[support]]s [[countercata]]. In the 11-limit, it tempers out [[385/384]], [[2200/2187]], [[3388/3375]], and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case.		227et [[tempering out\|tempers out]] 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| 61 -37 -1 }} in the [[5-limit]]; [[5120/5103]], [[65625/65536]], and 117649/116640 in the [[7-limit]], so that it [[support]]s [[countercata]]. In the [[11-limit]], it tempers out [[385/384]], [[2200/2187]], [[3388/3375]], and [[12005/11979]], so that it provides the [[optimal patent val]] for 11-limit countercata. In the [[13-limit]], it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case.

	227edo is accurate for the [[13/1\|13th harmonic]], as the denominator of a convergent to log<sub>2</sub>13, after [[10edo\|10]] and before [[5231edo\|5231]].		227edo is accurate for the [[13/1\|13th harmonic]], as the denominator of a convergent to log<sub>2</sub>13, after [[10edo\|10]] and before [[5231edo\|5231]].

ArrowHead294 at 19:05, 15 January 2025

2025-01-15T19:05:27Z

← Older revision		Revision as of 19:05, 15 January 2025
Line 99:		Line 99:
	\| [[Undecental]]		\| [[Undecental]]
	\|}		\|}
	<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 18:59, 15 January 2025

2025-01-15T18:59:35Z

← Older revision		Revision as of 18:59, 15 January 2025
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	== Theory ==		== Theory ==
	~~The equal temperament~~ [[~~tempering out\|~~tempers out]] 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| 61 -37 -1 }} in the 5-limit; [[5120/5103]], [[65625/65536]], and 117649/116640 in the 7-limit, so that it [[support]]s [[countercata]]. In the 11-limit, it tempers out [[385/384]], [[2200/2187]], [[3388/3375]], and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case.		227edo [[tempers out]] 15625/15552 ([[15625/15552\|kleisma]]) and {{monzo\| 61 -37 -1 }} in the 5-limit; [[5120/5103]], [[65625/65536]], and 117649/116640 in the 7-limit, so that it [[support]]s [[countercata]]. In the 11-limit, it tempers out [[385/384]], [[2200/2187]], [[3388/3375]], and 12005/11979, so that it provides the [[optimal patent val]] for 11-limit countercata. In the 13-limit, it tempers out [[325/324]], [[352/351]], [[625/624]], [[676/675]], and [[847/845]], and again supplies a good tuning for 13-limit countercata, although [[140edo]] tunes it better in this case.

	227edo is accurate for the [[13/1\|13th harmonic]], as the denominator of a convergent to log<sub>2</sub>13, after [[10edo\|10]] and before [[5231edo\|5231]].		227edo is accurate for the [[13/1\|13th harmonic]], as the denominator of a convergent to log<sub>2</sub>13, after [[10edo\|10]] and before [[5231edo\|5231]].
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	\| {{monzo\| 360 -227 }}		\| {{monzo\| 360 -227 }}
	\| {{mapping\| 227 360 }}		\| {{mapping\| 227 360 }}
	\| ~~−0~~.3561		\| −0.3561
	\| 0.3560		\| 0.3560
	\| 6.73		\| 6.73
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	\| 15625/15552, {{monzo\| 61 -37 -1 }}		\| 15625/15552, {{monzo\| 61 -37 -1 }}
	\| {{mapping\| 227 360 527 }}		\| {{mapping\| 227 360 527 }}
	\| ~~−0~~.1785		\| −0.1785
	\| 0.3842		\| 0.3842
	\| 7.27		\| 7.27
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	\| 5120/5103, 15625/15552, 117649/116640		\| 5120/5103, 15625/15552, 117649/116640
	\| {{mapping\| 227 360 527 637 }}		\| {{mapping\| 227 360 527 637 }}
	\| ~~−0~~.0071		\| −0.0071
	\| 0.4461		\| 0.4461
	\| 8.44		\| 8.44
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	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "little hope" from ''hope in dark times'' (2024) ~~–~~ [https://open.spotify.com/track/1J6VKSGTkTRFs75WlEb6GP Spotify] \| [https://francium223.bandcamp.com/track/little-hope Bandcamp] \| [https://www.youtube.com/watch?v=juMfOpUu25I YouTube]		* "little hope" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1J6VKSGTkTRFs75WlEb6GP Spotify] \| [https://francium223.bandcamp.com/track/little-hope Bandcamp] \| [https://www.youtube.com/watch?v=juMfOpUu25I YouTube]
	* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) ~~–~~ [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] \| [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]		* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] \| [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]
	* "Did You Put Resistors In My Brain?" from ''Questions'' (2024) ~~–~~ [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] \| [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] \| [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube]		* "Did You Put Resistors In My Brain?" from ''Questions'' (2024) – [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] \| [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] \| [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube]
	* "Too Bad Homeboy" from ''Abbreviations Gone Wrong'' (2024) ~~–~~ [https://open.spotify.com/track/6VPup7pwSC10c0VzsBU4PG Spotify] \| [https://francium223.bandcamp.com/track/too-bad-homeboy Bandcamp] \| [https://www.youtube.com/watch?v=Y246sdIRbwQ YouTube]		* "Too Bad Homeboy" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6VPup7pwSC10c0VzsBU4PG Spotify] \| [https://francium223.bandcamp.com/track/too-bad-homeboy Bandcamp] \| [https://www.youtube.com/watch?v=Y246sdIRbwQ YouTube]

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

ArrowHead294: Partial undo

2024-11-16T12:26:51Z

Partial undo

← Older revision		Revision as of 12:26, 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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	\| 0.3821		\| 0.3821
	\| 7.23		\| 7.23
	~~{{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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	\| 4/3		\| 4/3
	\| [[Undecental]]		\| [[Undecental]]
	~~{{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 04:41, 16 November 2024

2024-11-16T04:41:46Z

← Older revision		Revision as of 04:41, 16 November 2024
Line 17:		Line 17:

	== 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
	\| {{monzo\| 360 -227 }}		\| {{monzo\| 360 -227 }}
	\| {{mapping\| 227 360 }}		\| {{mapping\| 227 360 }}
	\| -0.3561		\| −0.3561
	\| 0.3560		\| 0.3560
	\| 6.73		\| 6.73
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	\| 15625/15552, {{monzo\| 61 -37 -1 }}		\| 15625/15552, {{monzo\| 61 -37 -1 }}
	\| {{mapping\| 227 360 527 }}		\| {{mapping\| 227 360 527 }}
	\| -0.1785		\| −0.1785
	\| 0.3842		\| 0.3842
	\| 7.27		\| 7.27
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	\| 5120/5103, 15625/15552, 117649/116640		\| 5120/5103, 15625/15552, 117649/116640
	\| {{mapping\| 227 360 527 637 }}		\| {{mapping\| 227 360 527 637 }}
	\| -0.0071		\| −0.0071
	\| 0.4461		\| 0.4461
	\| 8.44		\| 8.44
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	\| 0.3821		\| 0.3821
	\| 7.23		\| 7.23
	\|}		{{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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	\| 4/3		\| 4/3
	\| [[Undecental]]		\| [[Undecental]]
	\|}		{{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]]
	* "little hope" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1J6VKSGTkTRFs75WlEb6GP Spotify] \| [https://francium223.bandcamp.com/track/little-hope Bandcamp] \| [https://www.youtube.com/watch?v=juMfOpUu25I YouTube]		* "little hope" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1J6VKSGTkTRFs75WlEb6GP Spotify] \| [https://francium223.bandcamp.com/track/little-hope Bandcamp] \| [https://www.youtube.com/watch?v=juMfOpUu25I YouTube]
	* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] \| [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]		* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] \| [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]
	* "Did You Put Resistors In My Brain?" from ''Questions'' (2024) – [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] \| [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] \| [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube]		* "Did You Put Resistors In My Brain?" from ''Questions'' (2024) – [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] \| [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] \| [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube]
	* "Too Bad Homeboy" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6VPup7pwSC10c0VzsBU4PG Spotify] \| [https://francium223.bandcamp.com/track/too-bad-homeboy Bandcamp] \| [https://www.youtube.com/watch?v=Y246sdIRbwQ YouTube]		* "Too Bad Homeboy" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6VPup7pwSC10c0VzsBU4PG Spotify] \| [https://francium223.bandcamp.com/track/too-bad-homeboy Bandcamp] \| [https://www.youtube.com/watch?v=Y246sdIRbwQ YouTube]

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

Francium: /* Music */ +music

2024-10-03T12:14:19Z

Music: +music

← Older revision		Revision as of 12:14, 3 October 2024
Line 104:		Line 104:
	* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] \| [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]		* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] \| [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]
	* "Did You Put Resistors In My Brain?" from ''Questions'' (2024) – [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] \| [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] \| [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube]		* "Did You Put Resistors In My Brain?" from ''Questions'' (2024) – [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] \| [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] \| [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube]
			* "Too Bad Homeboy" from ''Abbreviations Gone Wrong'' (2024) – [https://open.spotify.com/track/6VPup7pwSC10c0VzsBU4PG Spotify] \| [https://francium223.bandcamp.com/track/too-bad-homeboy Bandcamp] \| [https://www.youtube.com/watch?v=Y246sdIRbwQ YouTube]

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

Francium: /* Music */ +music

2024-07-31T12:07:10Z

Music: +music

← Older revision		Revision as of 12:07, 31 July 2024
Line 103:		Line 103:
	* "little hope" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1J6VKSGTkTRFs75WlEb6GP Spotify] \| [https://francium223.bandcamp.com/track/little-hope Bandcamp] \| [https://www.youtube.com/watch?v=juMfOpUu25I YouTube]		* "little hope" from ''hope in dark times'' (2024) – [https://open.spotify.com/track/1J6VKSGTkTRFs75WlEb6GP Spotify] \| [https://francium223.bandcamp.com/track/little-hope Bandcamp] \| [https://www.youtube.com/watch?v=juMfOpUu25I YouTube]
	* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] \| [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]		* "Cuckoo Cucumber" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/4WSc7cTf1ctWIiOXjTSAmc Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-cucumber Bandcamp] \| [https://www.youtube.com/watch?v=po7hrgzSeb8 YouTube]
			* "Did You Put Resistors In My Brain?" from ''Questions'' (2024) – [https://open.spotify.com/track/3QS6mj3GAMSmfJuQSsOE7Y Spotify] \| [https://francium223.bandcamp.com/track/did-you-put-resistors-in-my-brain Bandcamp] \| [https://www.youtube.com/watch?v=-FzOGzpxPv4 YouTube]

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

Francium: +intervals

2024-04-07T18:37:27Z

+intervals

← Older revision		Revision as of 18:37, 7 April 2024
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	227edo is the 49th [[prime edo]].		227edo is the 49th [[prime edo]].

			== Intervals ==
			{{Main\|Table of 227edo intervals}}

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