444edo

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← 443edo444edo445edo →
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