# 443edo

 ← 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 it is distinct

Francium