419edo - 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
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	\| [[Helmholtz (temperament)\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|}		\|}
	<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 ==

Francium: /* Music */ +links

2026-02-26T11:48:30Z

Music: +links

← Older revision		Revision as of 11:48, 26 February 2026
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	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=cXvlQxvwUIM ''Cultural Appropriation?''] (2023) – in Sextilifourths, 419edo tuning		* [https://www.youtube.com/watch?v=cXvlQxvwUIM ''Cultural Appropriation?''] (2023) – in Sextilifourths, 419edo tuning
	* "Mixed Sea Food Iraq Government Office Surface" from ''Unsuspecting Tyrant Double-Decker Beef Fort'' (2026) – [https://francium223.bandcamp.com/track/mixed-sea-food-iraq-government-office-surface Bandcamp] \| [https://www.youtube.com/watch?v=n9R_vZEVFuM YouTube]		* "Mixed Sea Food Iraq Government Office Surface" from ''Unsuspecting Tyrant Double-Decker Beef Fort'' (2026) – [https://open.spotify.com/track/4OMxyKUsrmNzIw9FnzOl8y Spotify] \| [https://francium223.bandcamp.com/track/mixed-sea-food-iraq-government-office-surface Bandcamp] \| [https://www.youtube.com/watch?v=n9R_vZEVFuM YouTube]

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

Francium: /* Music */ +music

2026-02-24T12:56:03Z

Music: +music

← Older revision		Revision as of 12:56, 24 February 2026
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	== Music ==		== Music ==
	; [[Francium]]		; [[Francium]]
	* [https://www.youtube.com/watch?v=cXvlQxvwUIM ''Cultural Appropriation?''] (2023)		* [https://www.youtube.com/watch?v=cXvlQxvwUIM ''Cultural Appropriation?''] (2023) – in Sextilifourths, 419edo tuning
			* "Mixed Sea Food Iraq Government Office Surface" from ''Unsuspecting Tyrant Double-Decker Beef Fort'' (2026) – [https://francium223.bandcamp.com/track/mixed-sea-food-iraq-government-office-surface Bandcamp] \| [https://www.youtube.com/watch?v=n9R_vZEVFuM YouTube]

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

Lériendil: Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

2025-04-17T02:29:03Z

Text replacement - "[[Helmholtz temperament|" to "[[Helmholtz (temperament)|"

← Older revision		Revision as of 02:29, 17 April 2025
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	\| 498.33		\| 498.33
	\| 162/125		\| 162/125
	\| [[Helmholtz temperament\|Helmholtz]]		\| [[Helmholtz (temperament)\|Helmholtz]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

Sintel: fix helmholtz link

2025-04-16T15:33:55Z

fix helmholtz link

← Older revision		Revision as of 15:33, 16 April 2025
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	\| 498.33		\| 498.33
	\| 162/125		\| 162/125
	\| [[Helmholtz]]		\| [[Helmholtz temperament\|Helmholtz]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

Lériendil at 20:50, 1 April 2025

2025-04-01T20:50:45Z

← Older revision		Revision as of 20:50, 1 April 2025
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	\| 83.05		\| 83.05
	\| 21/20		\| 21/20
	\| [[~~Sextilififths~~]] (419f)		\| [[Sextilifourths]] (419f)
	\|-		\|-
	\| 1		\| 1
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	== Scales ==		== Scales ==
	* [[~~Sextilififths13~~]]		* [[Sextilifourths13]]

	== Music ==		== Music ==

Lériendil: renamed sextilififths to sextilifourths

2025-04-01T20:49:26Z

renamed sextilififths to sextilifourths

← Older revision		Revision as of 20:49, 1 April 2025
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	[[Category:Listen]]		[[Category:Listen]]
	[[Category:~~Sextilififths~~]]		[[Category:Sextilifourths]]

Lériendil at 20:47, 1 April 2025

2025-04-01T20:47:53Z

← Older revision		Revision as of 20:47, 1 April 2025
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	== Theory ==		== Theory ==
	419edo is a decent 7-limit system, and is [[consistent]] to the [[9-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 32805/32768 ([[schisma]]) in the 5-limit; 235298/234375 (triwellisma), 420175/419904 (wizma) in the 7-limit. It [[support]]s and provides the [[optimal patent val]] for [[~~sextilififths~~]], the {{nowrap\|130 & 289}} temperament, in the 7-limit.		419edo is a decent 7-limit system, and is [[consistent]] to the [[9-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 32805/32768 ([[schisma]]) in the 5-limit; 235298/234375 (triwellisma), 420175/419904 (wizma) in the 7-limit. It [[support]]s and provides the [[optimal patent val]] for [[sextilifourths]], the {{nowrap\|130 & 289}} temperament, in the 7-limit.

	Extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far off the mark. Using the 419e [[val]], it tempers out [[3025/3024]], [[5632/5625]], and [[8019/8000]]. Using the [[patent val]], it tempers out [[441/440]], [[4000/3993]], and 14700/14641 in the 11-limit. The patent val supports 11-limit ~~sextilififths~~, though [[289edo]] is better suited for that purpose.		Extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far off the mark. Using the 419e [[val]], it tempers out [[3025/3024]], [[5632/5625]], and [[8019/8000]]. Using the [[patent val]], it tempers out [[441/440]], [[4000/3993]], and 14700/14641 in the 11-limit. The patent val supports 11-limit sextilifourths, though [[289edo]] is better suited for that purpose.

	The same can be said of the mapping for 13, with the 419e val tempering out [[676/675]], [[1716/1715]], [[4225/4224]], and 4459/4455, and the 419f val tempering out [[729/728]], [[2200/2197]], 2205/2197, 3584/3575, and 4459/4455.		The same can be said of the mapping for 13, with the 419e val tempering out [[676/675]], [[1716/1715]], [[4225/4224]], and 4459/4455, and the 419f val tempering out [[729/728]], [[2200/2197]], 2205/2197, 3584/3575, and 4459/4455.

Francium: changed EDO intro to ED intro

2025-02-21T06:17:48Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:17, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|419~~}}		{{ED intro}}

	== Theory ==		== Theory ==

ArrowHead294 at 17:58, 15 January 2025

2025-01-15T17:58:36Z

← Older revision		Revision as of 17:58, 15 January 2025
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	== Theory ==		== Theory ==
	419edo is a decent 7-limit system, and is [[consistent]] to the [[9-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 32805/32768 ([[schisma]]) in the 5-limit; 235298/234375 (triwellisma), 420175/419904 (wizma) in the 7-limit. It [[support]]s and provides the [[optimal patent val]] for [[sextilififths]], the 130 & 289 temperament, in the 7-limit.		419edo is a decent 7-limit system, and is [[consistent]] to the [[9-odd-limit]]. The equal temperament [[tempering out\|tempers out]] 32805/32768 ([[schisma]]) in the 5-limit; 235298/234375 (triwellisma), 420175/419904 (wizma) in the 7-limit. It [[support]]s and provides the [[optimal patent val]] for [[sextilififths]], the {{nowrap\|130 & 289}} temperament, in the 7-limit.

	Extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far off the mark. Using the 419e [[val]], it tempers out [[3025/3024]], [[5632/5625]], and [[8019/8000]]. Using the [[patent val]], it tempers out [[441/440]], [[4000/3993]], and 14700/14641 in the 11-limit. The patent val supports 11-limit sextilififths, though [[289edo]] is better suited for that purpose.		Extending it to the 11-limit requires choosing which mapping one wants to use, as both are nearly equally far off the mark. Using the 419e [[val]], it tempers out [[3025/3024]], [[5632/5625]], and [[8019/8000]]. Using the [[patent val]], it tempers out [[441/440]], [[4000/3993]], and 14700/14641 in the 11-limit. The patent val supports 11-limit sextilififths, though [[289edo]] is better suited for that purpose.
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	\| 441/440, 4000/3993, 32805/32768, 420175/419904		\| 441/440, 4000/3993, 32805/32768, 420175/419904
	\| {{mapping\| 419 664 973 1176 1450 }} (419)		\| {{mapping\| 419 664 973 1176 1450 }} (419)
	\| ~~−0~~.0168		\| −0.0168
	\| 0.2460		\| 0.2460
	\| 8.59		\| 8.59
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	\| [[Helmholtz]]		\| [[Helmholtz]]
	\|}		\|}
	<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 ==