443edo - 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"

2026-03-13T13:32:34Z

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 49:		Line 49:
	\| [[Hemischis]] (443)		\| [[Hemischis]] (443)
	\|}		\|}
	<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

	== Scales ==		== Scales ==

ArrowHead294 at 12:51, 21 February 2025

2025-02-21T12:51:21Z

← Older revision		Revision as of 12:51, 21 February 2025
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	\| {{monzo\|-702 443}}		\| {{monzo\|-702 443}}
	\| {{mapping\| 443 702 }}		\| {{mapping\| 443 702 }}
	\| 0.1183		\| +0.1183
	\| 0.1183		\| 0.1183
	\| 4.37		\| 4.37

Francium: changed EDO intro to ED intro

2025-02-21T05:58:26Z

changed EDO intro to ED intro

← Older revision		Revision as of 05:58, 21 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|443~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 16:20, 15 January 2025

2025-01-15T16:20:19Z

← Older revision		Revision as of 16:20, 15 January 2025
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	443edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[5/1\|5]] is quite large. To start with, the [[patent val]] {{val\| 443 702 '''1029''' '''1244''' '''1533''' }} as well as the 443cde [[val]] {{val\| 443 702 '''1028''' '''1243''' '''1532''' }} are worth considering.		443edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[5/1\|5]] is quite large. To start with, the [[patent val]] {{val\| 443 702 '''1029''' '''1244''' '''1533''' }} as well as the 443cde [[val]] {{val\| 443 702 '''1028''' '''1243''' '''1532''' }} are worth considering.

	Using the patent val, the equal temperament [[tempering out\|tempers out]] [[6144/6125]], [[32805/32768]], and 67108864/66976875 in the 7-limit; [[540/539]], [[5632/5625]], [[8019/8000]], and [[131072/130977]] in the 11-limit. It [[support]]s [[hemischis]], the 130 & 313 temperament.		Using the patent val, the equal temperament [[tempering out\|tempers out]] [[6144/6125]], [[32805/32768]], and 67108864/66976875 in the 7-limit; [[540/539]], [[5632/5625]], [[8019/8000]], and [[131072/130977]] in the 11-limit. It [[support]]s [[hemischis]], the {{nowrap\|130 & 313}} temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
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	\| [[Hemischis]] (443)		\| [[Hemischis]] (443)
	\|}		\|}
	<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

	== Scales ==		== Scales ==

ArrowHead294: Partial undo

2024-11-16T13:15:43Z

Partial undo

← Older revision		Revision as of 13:15, 16 November 2024
Line 14:		Line 14:

	== 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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	\| 0.1183		\| 0.1183
	\| 4.37		\| 4.37
	~~{{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 32:		Line 48:
	\| 15/13		\| 15/13
	\| [[Hemischis]] (443)		\| [[Hemischis]] (443)
	~~{{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

	== Scales ==		== Scales ==

ArrowHead294 at 01:46, 16 November 2024

2024-11-16T01:46:50Z

← Older revision		Revision as of 01:46, 16 November 2024
Line 14:		Line 14:

	== 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 31:		Line 22:
	\| 0.1183		\| 0.1183
	\| 4.37		\| 4.37
	\|}		{{comma basis end}}

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{~~\| class="wikitable center-all left-5"~~		{{rank-2 begin}}
	~~\|+ 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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	\| 15/13		\| 15/13
	\| [[Hemischis]] (443)		\| [[Hemischis]] (443)
	\|}		{{rank-2 end}}
	{{orf}}		{{orf}}

ArrowHead294 at 01:07, 16 November 2024

2024-11-16T01:07:42Z

← Older revision		Revision as of 01:07, 16 November 2024
Line 15:		Line 15:
	== 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
	\|-		\|-
Line 34:		Line 35:
	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+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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	\| [[Hemischis]] (443)		\| [[Hemischis]] (443)
	\|}		\|}
	~~<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}}

	== Scales ==		== Scales ==
Line 54:		Line 56:
	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* "Confusion" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/72Pc4tty5rlLazQXW3tcCe Spotify] \| [https://francium223.bandcamp.com/track/confusion Bandcamp] \| [https://youtu.be/et0Qd4YAEP4?si=yRYbMo8sVz1qRvEE YouTube] – [[hemischis]] in 443edo tuning		* "Confusion" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/72Pc4tty5rlLazQXW3tcCe Spotify] \| [https://francium223.bandcamp.com/track/confusion Bandcamp] \| [https://youtu.be/et0Qd4YAEP4?si=yRYbMo8sVz1qRvEE YouTube] – [[hemischis]] in 443edo tuning

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

Francium: +categories

2024-02-13T18:11:12Z

+categories

← Older revision		Revision as of 18:11, 13 February 2024
Line 53:		Line 53:

	== Music ==		== Music ==
	; [[~~User:Francium\|~~Francium]]		; [[Francium]]
	* "Confusion" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/72Pc4tty5rlLazQXW3tcCe Spotify] \| [https://francium223.bandcamp.com/track/confusion Bandcamp] \| [https://youtu.be/et0Qd4YAEP4?si=yRYbMo8sVz1qRvEE YouTube] – [[hemischis]] in 443edo tuning		* "Confusion" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/72Pc4tty5rlLazQXW3tcCe Spotify] \| [https://francium223.bandcamp.com/track/confusion Bandcamp] \| [https://youtu.be/et0Qd4YAEP4?si=yRYbMo8sVz1qRvEE YouTube] – [[hemischis]] in 443edo tuning

			[[Category:Listen]]

Francium: +scales

2023-12-04T07:56:06Z

+scales

← Older revision		Revision as of 07:56, 4 December 2023
Line 48:		Line 48:
	\|}		\|}
	<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

			== Scales ==
			* [[Hemischis19]]

	== Music ==		== Music ==
	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* "Confusion" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/72Pc4tty5rlLazQXW3tcCe Spotify] \| [https://francium223.bandcamp.com/track/confusion Bandcamp] \| [https://youtu.be/et0Qd4YAEP4?si=yRYbMo8sVz1qRvEE YouTube] – [[hemischis]] in 443edo tuning		* "Confusion" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/72Pc4tty5rlLazQXW3tcCe Spotify] \| [https://francium223.bandcamp.com/track/confusion Bandcamp] \| [https://youtu.be/et0Qd4YAEP4?si=yRYbMo8sVz1qRvEE YouTube] – [[hemischis]] in 443edo tuning

FloraC: Rework; cleanup; clarify the title row of the rank-2 temp table

2023-11-03T07:55:16Z

Rework; cleanup; clarify the title row of the rank-2 temp table

← Older revision		Revision as of 07:55, 3 November 2023
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{EDO intro\|443}}		{{EDO intro\|443}}

	== Theory ==		== Theory ==
	~~443et~~ tempers out ~~67108864/66976875,~~ [[6144/6125]] ~~and~~ [[32805/32768]] in the 7-limit; ~~806736/805255, 35156250/35153041, 759375/758912, [[131072/130977]],~~ [[540/539]]~~, 184549376/184528125~~, [[5632/5625]], [[8019/8000]], ~~160083/160000, 391314/390625, 202397184/201768035, 3294225/3294172~~ and ~~20614528~~/~~20588575~~ in the 11-limit.		443edo is in[[consistent]] to the [[5-odd-limit]] and the error of [[harmonic]] [[5/1\|5]] is quite large. To start with, the [[patent val]] {{val\| 443 702 '''1029''' '''1244''' '''1533''' }} as well as the 443cde [[val]] {{val\| 443 702 '''1028''' '''1243''' '''1532''' }} are worth considering.
	===Prime harmonics===
			Using the patent val, the equal temperament [[tempering out\|tempers out]] [[6144/6125]], [[32805/32768]], and 67108864/66976875 in the 7-limit; [[540/539]], [[5632/5625]], [[8019/8000]], and [[131072/130977]] in the 11-limit. It [[support]]s [[hemischis]], the 130 & 313 temperament.

			=== Prime harmonics ===
	{{Harmonics in equal\|443}}		{{Harmonics in equal\|443}}

	===Subsets and supersets===		=== Subsets and supersets ===
	443edo is the 86th [[prime edo]]. 886edo, which doubles it, gives a good correction until the 11-limit.		443edo is the 86th [[prime edo]]. 886edo, which doubles it, gives a good correction until the 11-limit.
	==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\|-702 443}}		\| {{monzo\|-702 443}}
	\|{{~~val~~\|443 702}}		\| {{mapping\| 443 702 }}
	\| 0.1183		\| 0.1183
	\| 0.1183		\| 0.1183
Line 31:		Line 36:
	\|+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
	\|92\443		\| 92\443
	\|249.21		\| 249.21
	\|81/70		\| 15/13
	\|[[Hemischis]] (~~7-limit~~)		\| [[Hemischis]] (443)
	\|}		\|}
			<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 ==
	; [[User:Francium\|Francium]]		; [[User:Francium\|Francium]]
	* "Confusion" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/72Pc4tty5rlLazQXW3tcCe Spotify] \| [https://francium223.bandcamp.com/track/confusion Bandcamp] \| [https://youtu.be/et0Qd4YAEP4?si=yRYbMo8sVz1qRvEE YouTube] – [[hemischis]] in 443edo tuning		* "Confusion" from ''HemischisMatic EP'' (2023) – [https://open.spotify.com/track/72Pc4tty5rlLazQXW3tcCe Spotify] \| [https://francium223.bandcamp.com/track/confusion Bandcamp] \| [https://youtu.be/et0Qd4YAEP4?si=yRYbMo8sVz1qRvEE YouTube] – [[hemischis]] in 443edo tuning