443edo

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← 442edo443edo444edo →
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 443-tone equal temperament (443tet), 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 of 443edo 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 -14 +39 +34 +47 -29 +25 +17 +6 -9 +29
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

Scales

Music

Francium