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443edo: Difference between revisions

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Created page with "{{Infobox ET}} {{EDO intro|443}} == Theory == 443et tempers out 67108864/66976875, 6144/6125 and 32805/32768 in the 7-limit; 806736/805255, 35156250/35153041, 759375/7..."
 
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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|443}}
{{ED intro}}
 
== 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.
===Odd 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 & 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" |[[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
| 0.1183
| 4.37
| 4.37
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=== 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
|-
! Generator<br>(reduced)
! Periods<br />per 8ve
! Cents<br>(reduced)
! Generator*
! Associated<br>ratio
! Cents*
! 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 />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
== Scales ==
* [[Hemischis19]]


== Music ==
== 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]]
Retrieved from "https://en.xen.wiki/w/443edo"