419edo: Difference between revisions
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m 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" Tags: Mobile edit Mobile web edit |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
== 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 [[ | 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 | 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. | ||
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| 83.05 | | 83.05 | ||
| 21/20 | | 21/20 | ||
| [[ | | [[Sextilifourths]] (419f) | ||
|- | |- | ||
| 1 | | 1 | ||
| Line 82: | Line 82: | ||
| 498.33 | | 498.33 | ||
| 162/125 | | 162/125 | ||
| [[Helmholtz]] | | [[Helmholtz (temperament)|Helmholtz]] | ||
|} | |} | ||
<nowiki />* [[Normal | <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 == | ||
* [[ | * [[Sextilifourths13]] | ||
== 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://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: | [[Category:Sextilifourths]] | ||