467edo - 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"

2026-03-13T13:32:59Z

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 71:		Line 71:
	\| [[Counterhanson]]		\| [[Counterhanson]]
	\|}		\|}
	<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: changed EDO intro to ED intro

2025-02-21T06:14:34Z

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~~\|467~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 18:47, 15 January 2025

2025-01-15T18:47:25Z

← Older revision		Revision as of 18:47, 15 January 2025
Line 30:		Line 30:
	\| {{monzo\| -740 467 }}		\| {{monzo\| -740 467 }}
	\| {{mapping\| 467 740 }}		\| {{mapping\| 467 740 }}
	\| 0.1439		\| +0.1439
	\| 0.1439		\| 0.1439
	\| 5.38		\| 5.38
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	\| {{monzo\| -36 11 8 }}, {{monzo\| -16 35 -17 }}		\| {{monzo\| -36 11 8 }}, {{monzo\| -16 35 -17 }}
	\| {{mapping\| 467 740 1084 }}		\| {{mapping\| 467 740 1084 }}
	\| 0.2215		\| +0.2215
	\| 0.1608		\| 0.1608
	\| 6.02		\| 6.02
Line 44:		Line 44:
	\| 4375/4374, 2100875/2097152, {{monzo\| -16 4 9 -4 }}		\| 4375/4374, 2100875/2097152, {{monzo\| -16 4 9 -4 }}
	\| {{mapping\| 467 740 1084 1311 }}		\| {{mapping\| 467 740 1084 1311 }}
	\| 0.1741		\| +0.1741
	\| 0.1617		\| 0.1617
	\| 6.05		\| 6.05
Line 71:		Line 71:
	\| [[Counterhanson]]		\| [[Counterhanson]]
	\|}		\|}
	<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 Mackerel" from ''Cursed Cuckoo Creations'' (2024) ~~–~~ [https://open.spotify.com/track/6d9Ip2EuZkqQdx0OUJkw86 Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-mackerel Bandcamp] \| [https://www.youtube.com/watch?v=MjgQWmcKQB4 YouTube]		* "Cuckoo Mackerel" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/6d9Ip2EuZkqQdx0OUJkw86 Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-mackerel Bandcamp] \| [https://www.youtube.com/watch?v=MjgQWmcKQB4 YouTube]
	* "livemywarmlive" from ''albumwithoutspaces'' (2024) ~~–~~ [https://open.spotify.com/track/4jwETd5M7kbxkcR1TOflMk Spotify] \| [https://francium223.bandcamp.com/track/livemywarmlive Bandcamp] \| [https://www.youtube.com/watch?v=G2CH958nhOk YouTube] ~~–~~ counterkleismic[19] in 467edo tuning		* "livemywarmlive" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/4jwETd5M7kbxkcR1TOflMk Spotify] \| [https://francium223.bandcamp.com/track/livemywarmlive Bandcamp] \| [https://www.youtube.com/watch?v=G2CH958nhOk YouTube] – counterkleismic[19] in 467edo tuning

	[[Category:Counterkleismic]]		[[Category:Counterkleismic]]
	[[Category:Listen]]		[[Category:Listen]]
	[[Category:Ursulismic]]		[[Category:Ursulismic]]

ArrowHead294: Partial undo

2024-11-16T12:51:37Z

Partial undo

← Older revision		Revision as of 12:51, 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
Line 38:		Line 47:
	\| 0.1617		\| 0.1617
	\| 6.05		\| 6.05
	~~{{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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	\| 6/5		\| 6/5
	\| [[Counterhanson]]		\| [[Counterhanson]]
	~~{{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 03:45, 16 November 2024

2024-11-16T03:45:22Z

← Older revision		Revision as of 03:45, 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:
	\| 0.1617		\| 0.1617
	\| 6.05		\| 6.05
	\|}		{{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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	\| 6/5		\| 6/5
	\| [[Counterhanson]]		\| [[Counterhanson]]
	\|}		{{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 Mackerel" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/6d9Ip2EuZkqQdx0OUJkw86 Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-mackerel Bandcamp] \| [https://www.youtube.com/watch?v=MjgQWmcKQB4 YouTube]		* "Cuckoo Mackerel" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/6d9Ip2EuZkqQdx0OUJkw86 Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-mackerel Bandcamp] \| [https://www.youtube.com/watch?v=MjgQWmcKQB4 YouTube]
	* "livemywarmlive" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/4jwETd5M7kbxkcR1TOflMk Spotify] \| [https://francium223.bandcamp.com/track/livemywarmlive Bandcamp] \| [https://www.youtube.com/watch?v=G2CH958nhOk YouTube] – counterkleismic[19] in 467edo tuning		* "livemywarmlive" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/4jwETd5M7kbxkcR1TOflMk Spotify] \| [https://francium223.bandcamp.com/track/livemywarmlive Bandcamp] \| [https://www.youtube.com/watch?v=G2CH958nhOk YouTube] – counterkleismic[19] in 467edo tuning

			[[Category:Counterkleismic]]
			[[Category:Listen]]
	[[Category:Ursulismic]]		[[Category:Ursulismic]]
	~~[[Category:Counterkleismic]]~~

Francium: /* Music */ +music

2024-06-10T12:06:06Z

Music: +music

← Older revision		Revision as of 12:06, 10 June 2024
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	; [[Francium]]		; [[Francium]]
	* "Cuckoo Mackerel" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/6d9Ip2EuZkqQdx0OUJkw86 Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-mackerel Bandcamp] \| [https://www.youtube.com/watch?v=MjgQWmcKQB4 YouTube]		* "Cuckoo Mackerel" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/6d9Ip2EuZkqQdx0OUJkw86 Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-mackerel Bandcamp] \| [https://www.youtube.com/watch?v=MjgQWmcKQB4 YouTube]
			* "livemywarmlive" from ''albumwithoutspaces'' (2024) – [https://open.spotify.com/track/4jwETd5M7kbxkcR1TOflMk Spotify] \| [https://francium223.bandcamp.com/track/livemywarmlive Bandcamp] \| [https://www.youtube.com/watch?v=G2CH958nhOk YouTube] – counterkleismic[19] in 467edo tuning

	[[Category:Ursulismic]]		[[Category:Ursulismic]]
	[[Category:Counterkleismic]]		[[Category:Counterkleismic]]

FloraC: Note it's the OPV for ursulismic and counterkleismic

2024-03-28T09:26:00Z

Note it's the OPV for ursulismic and counterkleismic

← Older revision		Revision as of 09:26, 28 March 2024
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	== Theory ==		== Theory ==
	467edo is [[consistent]] to the [[9-odd-limit]] with [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] all tuned flat. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[4375/4374]], [[2100875/2097152]], 5250987/5242880, and {{monzo\| -16 4 9 -4 }} in the 7-limit.		467edo is [[consistent]] to the [[9-odd-limit]] with [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] all tuned flat. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[4375/4374]], [[2100875/2097152]], 5250987/5242880, and {{monzo\| -16 4 9 -4 }} in the 7-limit. It [[support]]s [[mitonic]] and [[counterkleismic]], supplying the [[optimal patent val]] for the latter.

	In the 11-limit, the 467e [[val]] scores much better than the [[patent val]]. The 467e val tempers out 1375/1372, 24057/24010, 35937/35840, and 41503/41472, and in the 13-limit, [[625/624]], [[729/728]], [[1716/1715]], and [[2200/2197]]. The patent val tempers out [[540/539]], [[6250/6237]], 12005/11979, and 14700/14641, and in the 13-limit, 625/624, 729/728, and [[2080/2079]].		In the 11-limit, the 467e [[val]] scores much better than the [[patent val]]. The 467e val tempers out 1375/1372, 24057/24010, 35937/35840, and 41503/41472, and in the 13-limit, [[625/624]], [[729/728]], [[1716/1715]], and [[2200/2197]]. The patent val tempers out [[540/539]], [[6250/6237]], 12005/11979, and 14700/14641, and in the 13-limit, 625/624, 729/728, and [[2080/2079]].

	It [[~~support]]s [[mitonic]] and [[counterkleismic~~]].		In the 17-limit, it supplies the optimal patent val for the rank-6 temperament tempering out [[375/374]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 70:		Line 70:
	\|}		\|}
	<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 ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Cuckoo Mackerel" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/6d9Ip2EuZkqQdx0OUJkw86 Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-mackerel Bandcamp] \| [https://www.youtube.com/watch?v=MjgQWmcKQB4 YouTube]		* "Cuckoo Mackerel" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/6d9Ip2EuZkqQdx0OUJkw86 Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-mackerel Bandcamp] \| [https://www.youtube.com/watch?v=MjgQWmcKQB4 YouTube]

			[[Category:Ursulismic]]
			[[Category:Counterkleismic]]

Francium: +music

2024-03-25T13:33:17Z

+music

← Older revision		Revision as of 13:33, 25 March 2024
Line 70:		Line 70:
	\|}		\|}
	<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 Mackerel" from ''Cursed Cuckoo Creations'' (2024) – [https://open.spotify.com/track/6d9Ip2EuZkqQdx0OUJkw86 Spotify] \| [https://francium223.bandcamp.com/track/cuckoo-mackerel Bandcamp] \| [https://www.youtube.com/watch?v=MjgQWmcKQB4 YouTube]

FloraC: Review

2024-02-17T12:51:46Z

Review

← Older revision		Revision as of 12:51, 17 February 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	~~467et~~ is consistent to ~~thr~~ [[9-odd-limit]]. Using the patent val, it tempers out [[4375/4374]], [[~~1640558367~~/~~1638400000~~]], 5250987/5242880 and ~~[[2100875/2097152]]~~ in the 7-limit~~; 25165824/25109315~~, ~~1019215872~~/~~1019046875~~, ~~2097152~~/~~2096325~~, ~~26214400~~/~~26198073~~, ~~104162436~~/~~103984375~~, ~~166698/166375~~, ~~12005~~/~~11979~~, ~~151263~~/~~151250~~, ~~117649~~/~~117612~~, ~~514714375~~/~~514434888, 226492416/226474325, 104857600/104825259, 472392/471625,~~ [[540/539]], [[6250/6237]], ~~[[1953125~~/~~1948617]]~~, ~~825000~~/~~823543~~, ~~85937500~~/~~85766121~~, ~~47265625~~/~~47258883~~ and ~~9453125~~/~~9437184 in the 11-limit~~. It [[support]]s [[~~counterkleismic~~]] and [[~~minos~~]].		467edo is [[consistent]] to the [[9-odd-limit]] with [[harmonic]]s [[3/1\|3]], [[5/1\|5]], and [[7/1\|7]] all tuned flat. Using the [[patent val]], the equal temperament [[tempering out\|tempers out]] [[4375/4374]], [[2100875/2097152]], 5250987/5242880, and {{monzo\| -16 4 9 -4 }} in the 7-limit.

			In the 11-limit, the 467e [[val]] scores much better than the [[patent val]]. The 467e val tempers out 1375/1372, 24057/24010, 35937/35840, and 41503/41472, and in the 13-limit, [[625/624]], [[729/728]], [[1716/1715]], and [[2200/2197]]. The patent val tempers out [[540/539]], [[6250/6237]], 12005/11979, and 14700/14641, and in the 13-limit, 625/624, 729/728, and [[2080/2079]].

			It [[support]]s [[mitonic]] and [[counterkleismic]].

	=== Odd harmonics ===		=== Odd harmonics ===
Line 13:		Line 17:
	== 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\|-740 467}}		\| {{monzo\| -740 467 }}
	\|{{~~val~~\|467 740}}		\| {{mapping\| 467 740 }}
	\| 0.1439		\| 0.1439
	\| 0.1439		\| 0.1439
	\| 5.38		\| 5.38
	\|-		\|-
	\|2.3.5		\| 2.3.5
	\|{{monzo\|-36 11 8}}, {{monzo\|-16 35 -17}}		\| {{monzo\| -36 11 8 }}, {{monzo\| -16 35 -17 }}
	\|{{~~val~~\|467 740 1084}}		\| {{mapping\| 467 740 1084 }}
	\| 0.2215		\| 0.2215
	\| 0.1608		\| 0.1608
	\| 6.02		\| 6.02
	\|-		\|-
	\|2.3.5.7		\| 2.3.5.7
	\|4375/4374, 2100875/2097152, ~~5250987/5242880~~		\| 4375/4374, 2100875/2097152, {{monzo\| -16 4 9 -4 }}
	\|{{~~val~~\|467 740 1084 1311}}		\| {{mapping\| 467 740 1084 1311 }}
	\| 0.1741		\| 0.1741
	\| 0.1617		\| 0.1617
Line 53:		Line 57:
	! Temperaments		! Temperaments
	\|-		\|-
	\|1		\| 1
	\|71\467		\| 71\467
	\|182.441		\| 182.441
	\|10/9		\| 10/9
	\|~~[[Minortone]] /~~ [[Mitonic]]		\| [[Mitonic]]
	\|-		\|-
	\|1		\| 1
	\|123\467		\| 123\467
	\|316.060		\| 316.060
	\|6/5		\| 6/5
	\|[[Counterhanson]]		\| [[Counterhanson]]
	\|}		\|}

	<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

Francium: Created page with "{{Infobox ET}} {{EDO intro|467}} == Theory == 467et is consistent to thr 9-odd-limit. Using the patent val, it tempers out 4375/4374, 1640558367/1638400000, 52509..."

2024-02-15T15:35:41Z

Created page with "{{Infobox ET}} {{EDO intro|467}} == Theory == 467et is consistent to thr 9-odd-limit. Using the patent val, it tempers out 4375/4374, 1640558367/1638400000, 52509..."

New page

{{Infobox ET}}
{{EDO intro|467}}

== Theory ==
467et is consistent to thr [[9-odd-limit]]. Using the patent val, it tempers out [[4375/4374]], [[1640558367/1638400000]], 5250987/5242880 and [[2100875/2097152]] in the 7-limit; 25165824/25109315, 1019215872/1019046875, 2097152/2096325, 26214400/26198073, 104162436/103984375, 166698/166375, 12005/11979, 151263/151250, 117649/117612, 514714375/514434888, 226492416/226474325, 104857600/104825259, 472392/471625, [[540/539]], [[6250/6237]], [[1953125/1948617]], 825000/823543, 85937500/85766121, 47265625/47258883 and 9453125/9437184 in the 11-limit. It [[support]]s [[counterkleismic]] and [[minos]].

=== Odd harmonics ===
{{Harmonics in equal|467}}

=== Subsets and supersets ===
467edo is the 91st [[prime edo]].

== Regular temperament properties ==
{| class="wikitable center-4 center-5 center-6"
! 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
|{{monzo|-740 467}}
|{{val|467 740}}
| 0.1439
| 0.1439
| 5.38
|-
|2.3.5
|{{monzo|-36 11 8}}, {{monzo|-16 35 -17}}
|{{val|467 740 1084}}
| 0.2215
| 0.1608
| 6.02
|-
|2.3.5.7
|4375/4374, 2100875/2097152, 5250987/5242880
|{{val|467 740 1084 1311}}
| 0.1741
| 0.1617
| 6.05
|}

=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
|1
|71\467
|182.441
|10/9
|[[Minortone]] / [[Mitonic]]
|-
|1
|123\467
|316.060
|6/5
|[[Counterhanson]]
|}

<nowiki>*</nowiki> [[Normal lists|octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if it is distinct