# 444edo

 ← 443edo 444edo 445edo →
Prime factorization 22 × 3 × 37
Step size 2.7027¢
Fifth 260\444 (702.703¢) (→65\111)
Semitones (A1:m2) 44:32 (118.9¢ : 86.49¢)
Consistency limit 5
Distinct consistency limit 5

444 equal divisions of the octave (abbreviated 444edo or 444ed2), also called 444-tone equal temperament (444tet) or 444 equal temperament (444et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 444 equal parts of about 2.7 ¢ each. Each step represents a frequency ratio of 21/444, or the 444th root of 2.

## Theory

444edo is only consistent to the 5-odd-limit since harmonic 7 is about halfway between its steps. 444 = 4 × 111, and its harmonic 3 derives from 111edo. Using the patent val, the equal temperament tempers out 250047/250000, 29360128/29296875, 67108864/66976875 and in the 7-limit; 3025/3024, 5632/5625, 42592/42525, 102487/102400, 131072/130977, 160083/160000, 172032/171875, 322102/321489, 391314/390625 and 1771561/1769472 in the 11-limit. It supports the magnesium temperament.

### Odd harmonics

Approximation of odd harmonics in 444edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +0.75 +0.17 -1.26 -1.21 +0.03 +0.01 +0.92 +0.45 -0.22 -0.51 -1.25
Relative (%) +27.7 +6.4 -46.6 -44.7 +1.2 +0.5 +34.1 +16.6 -8.0 -18.9 -46.2
Steps
(reduced)
704
(260)
1031
(143)
1246
(358)
1407
(75)
1536
(204)
1643
(311)
1735
(403)
1815
(39)
1886
(110)
1950
(174)
2008
(232)

### Subsets and supersets

Since 444 factors into 22 × 3 × 37, 444edo has subset edos 2, 3, 4, 6, 12, 37, 74, 111, 148, and 222. 1332edo, which triples it, gives a good correction to the harmonic 7.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3.5 [41 -20 -4, [-29 -11 20 [444 704 1031]] -0.1821 0.2071 7.66

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 13\444 35.14 1990656/1953125 Gammic (5-limit)
4 184\444
(38\444)
497.30
(102.70)
4/3
(35/33)
Undim (444d)

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