443edo: Difference between revisions

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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.
===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 & 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
Line 29: Line 35:
=== 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]]

Latest revision as of 12:51, 21 February 2025

← 442edo 443edo 444edo →
Prime factorization 443 (prime)
Step size 2.7088 ¢ 
Fifth 259\443 (701.58 ¢)
Semitones (A1:m2) 41:34 (111.1 ¢ : 92.1 ¢)
Consistency limit 3
Distinct consistency limit 3

443 equal divisions of the octave (abbreviated 443edo or 443ed2), also called 443-tone equal temperament (443tet) or 443 equal temperament (443et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 443 equal parts of about 2.71 ¢ each. Each step represents a frequency ratio of 21/443, or the 443rd root of 2.

Theory

443edo is inconsistent to the 5-odd-limit and the error of harmonic 5 is quite large. To start with, the patent val ⟨443 702 1029 1244 1533] as well as the 443cde val ⟨443 702 1028 1243 1532] are worth considering.

Using the patent val, the equal temperament 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 supports hemischis, the 130 & 313 temperament.

Prime harmonics

Approximation of prime harmonics in 443edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.37 +1.05 +0.93 +1.28 -0.80 +0.69 +0.46 +0.17 -0.23 +0.79
Relative (%) +0.0 -13.8 +38.6 +34.2 +47.2 -29.5 +25.4 +16.8 +6.2 -8.6 +29.1
Steps
(reduced) 		443
(0) 		702
(259) 		1029
(143) 		1244
(358) 		1533
(204) 		1639
(310) 		1811
(39) 		1882
(110) 		2004
(232) 		2152
(380) 		2195
(423)

Subsets and supersets

443edo is the 86th prime edo. 886edo, which doubles it, gives a good correction until the 11-limit.

Regular temperament properties

Subgroup Comma list Mapping Optimal
8ve stretch (¢) 		Tuning error
Absolute (¢) Relative (%)
2.3 [-702 443⟩ [⟨443 702]] +0.1183 0.1183 4.37

Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve 		Generator* Cents* Associated
ratio* 		Temperaments
1 92\443 249.21 15/13 Hemischis (443)

* Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct

Scales

Music

Francium
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