# 358edo

 ← 357edo 358edo 359edo →
Prime factorization 2 × 179
Step size 3.35196¢
Fifth 209\358 (700.559¢)
Semitones (A1:m2) 31:29 (103.9¢ : 97.21¢)
Dual sharp fifth 210\358 (703.911¢) (→105\179)
Dual flat fifth 209\358 (700.559¢)
Dual major 2nd 61\358 (204.469¢)
Consistency limit 7
Distinct consistency limit 7

358 equal divisions of the octave (abbreviated 358edo or 358ed2), also called 358-tone equal temperament (358tet) or 358 equal temperament (358et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 358 equal parts of about 3.35 ¢ each. Each step represents a frequency ratio of 21/358, or the 358th root of 2.

## Theory

358edo is consistent to the 7-odd-limit, but the harmonic 3 is about halfway its steps. It is suitable for use with the 2.9.5.7.13 subgroup or even better the 2.9.15.7.13 subgroup.

In the 2.9.5.7.13 subgroup, the equal temperament tempers out 4096/4095, 13720/13689, 59150/59049, 60025/59904, 142884/142805, and 390625/388962.

The patent val supports hypnos in the 11-limit and lee in the 2.3.7 subgroup.

### Odd harmonics

Approximation of odd harmonics in 358edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.40 -0.84 -0.11 +0.56 -1.60 +0.81 +1.12 -1.04 +0.81 -1.51 -1.46
Relative (%) -41.7 -25.0 -3.3 +16.7 -47.7 +24.3 +33.3 -31.2 +24.2 -45.0 -43.5
Steps
(reduced)
567
(209)
831
(115)
1005
(289)
1135
(61)
1238
(164)
1325
(251)
1399
(325)
1463
(31)
1521
(89)
1572
(140)
1619
(187)

### Subset and supersets

358 factors into 2 × 179, with 2edo and 179edo as its subset edos. 716edo, which doubles it, gives a good correction to the harmonic 3.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.9 [1135 -358 [358 1135]] -0.0882 0.0882 2.63
2.9.5 [3 -9 11, [-98 17 19 [358 1135 831]] +0.0616 0.2238 6.68
2.9.5.7 390625/388962, 2100875/2097152, 4802000/4782969 [358 1135 831 1005]] +0.0561 0.1941 5.79