467edo: Difference between revisions

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== 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]].

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 ===

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|}

<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]

[[Category:Ursulismic]]

[[Category:Counterkleismic]]

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 == Theory ==
-edo 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.
+edo 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]].
-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 ===
@@ 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
 == 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]
+[[Category:Ursulismic]]
+[[Category:Counterkleismic]]