443edo: Difference between revisions

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@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-{{EDO intro|443}}
+{{ED intro}}
 == Theory ==
-et 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.
+edo 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 {{nowrap|130 &amp; 313}} temperament.
+=== Prime harmonics ===
 {{Harmonics in equal|443}}
-===Subsets and supersets===
+=== Subsets and supersets ===
 edo 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"
-! 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
+! rowspan="2" | [[Subgroup]]
-|{{monzo|-702 443}}
+! rowspan="2" | [[Comma list]]
-|{{val|443 702}}
+! rowspan="2" | [[Mapping]]
-| 0.1183
+! rowspan="2" | Optimal<br />8ve stretch (¢)
+! colspan="2" | Tuning error
+|-
+! [[TE error|Absolute]] (¢)
+! [[TE simple badness|Relative]] (%)
+|-
+| 2.3
+| {{monzo|-702 443}}
+| {{mapping| 443 702 }}
+| +0.1183
 | 0.1183
 | 4.37
@@ Line 29: / Line 35: @@
 === Rank-2 temperaments ===
 {| 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
+|-
-! Generator<br>(reduced)
+! Periods<br />per 8ve
-! Cents<br>(reduced)
+! Generator*
-! Associated<br>ratio
+! Cents*
+! Associated<br />ratio*
 ! Temperaments
 |-
-|1
+| 1
-|92\443
+| 92\443
-|249.21
+| 249.21
-|81/70
+| 15/13
-|[[Hemischis]] (7-limit)
+| [[Hemischis]] (443)
 |}
+<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+== Scales ==
+* [[Hemischis19]]
 == Music ==
-*[https://www.youtube.com/watch?v=et0Qd4YAEP4 Confusion] by [[User:Francium|Francium]]
+; [[Francium]]
+* "Confusion" from ''HemischisMatic EP'' (2023) &ndash; [https://open.spotify.com/track/72Pc4tty5rlLazQXW3tcCe Spotify] | [https://francium223.bandcamp.com/track/confusion Bandcamp] | [https://youtu.be/et0Qd4YAEP4?si=yRYbMo8sVz1qRvEE YouTube] &ndash; [[hemischis]] in 443edo tuning
+[[Category:Listen]]