# 439edo

 ← 438edo 439edo 440edo →
Prime factorization 439 (prime)
Step size 2.73349¢
Fifth 257\439 (702.506¢)
Semitones (A1:m2) 43:32 (117.5¢ : 87.47¢)
Consistency limit 3
Distinct consistency limit 3

439 equal divisions of the octave (abbreviated 439edo or 439ed2), also called 439-tone equal temperament (439tet) or 439 equal temperament (439et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 439 equal parts of about 2.73 ¢ each. Each step represents a frequency ratio of 21/439, or the 439th root of 2.

## Theory

439edo is inconsistent in the 5-odd-limit. In the 7-limit, the patent val 439 696 1019 1232], and the 439cd val 439 696 1020 1233] are about as viable.

The patent val tempers out 10976/10935, 15625/15552 and 703125/702464 in the 7-limit; 3025/3024, 4375/4356, 14700/14641, 59290/59049, 131072/130977, and 184877/184320 in the 11-limit.

The 439cd val tempers out 3136/3125, 2097152/2083725, and 4096000/4084101 in the 7-limit; 3136/3125, 15488/15435, 16384/16335, 19712/19683, 24057/24010, 43923/43750, 43923/43904, and 46656/46585 in the 11-limit.

### Prime harmonics

Approximation of prime harmonics in 439edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.55 -0.89 -1.17 +0.85 -1.35 -1.08 +0.44 +0.43 +0.95 +0.29
Relative (%) +0.0 +20.1 -32.6 -42.9 +31.0 -49.3 -39.6 +16.0 +15.6 +34.6 +10.8
Steps
(reduced)
439
(0)
696
(257)
1019
(141)
1232
(354)
1519
(202)
1624
(307)
1794
(38)
1865
(109)
1986
(230)
2133
(377)
2175
(419)

### Subsets and supersets

439edo is the 85th prime edo.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [696 -439 [439 696]] -0.1737 0.1737 6.36
2.3.5 15625/15552, [115 -74 1 [439 696 1019]] (439) +0.0122 0.2988 10.9
2.3.5.7 10976/10935, 15625/15552, [-25 6 -3 8 [439 696 1019 1232]] (439) +0.1135 0.3127 11.4
2.3.5 [24 -21 4, [36 11 -23 [439 696 1020]] (439c) -0.3801 0.3244 11.9
2.3.5.7 3136/3125, 2097152/2083725, 43046721/42875000 [439 696 1020 1233]] (439cd) -0.4241 0.2911 10.7

Francium