# 346edo

 ← 345edo 346edo 347edo →
Prime factorization 2 × 173
Step size 3.46821¢
Fifth 202\346 (700.578¢) (→101\173)
Semitones (A1:m2) 30:28 (104¢ : 97.11¢)
Dual sharp fifth 203\346 (704.046¢)
Dual flat fifth 202\346 (700.578¢) (→101\173)
Dual major 2nd 59\346 (204.624¢)
Consistency limit 7
Distinct consistency limit 7

346 equal divisions of the octave (abbreviated 346edo or 346ed2), also called 346-tone equal temperament (346tet) or 346 equal temperament (346et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 346 equal parts of about 3.47 ¢ each. Each step represents a frequency ratio of 21/346, or the 346th root of 2.

346edo is consistent to the 7-odd-limit, but the errors of harmonics 3, 5, and 7 are all quite large, commending itself as a 2.9.15.21.11 subgroup temperament. Using the patent val nonetheless, the equal temperament tempers out 243/242, 441/440, 540/539, 2401/2400, 4000/3993, 9801/9800 and 19683/19600. It is an excellent tuning for the 11-limit version of harry, the 72 & 274 temperament, as well as the rank-3 temperament jove, which tempers out 243/242 and 441/440.

### Odd harmonics

Approximation of odd harmonics in 346edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.38 -1.34 -1.20 +0.71 +0.13 -1.22 +0.75 -0.91 +0.75 +0.90 -0.53
Relative (%) -39.7 -38.7 -34.5 +20.6 +3.7 -35.2 +21.6 -26.2 +21.7 +25.8 -15.2
Steps
(reduced)
548
(202)
803
(111)
971
(279)
1097
(59)
1197
(159)
1280
(242)
1352
(314)
1414
(30)
1470
(86)
1520
(136)
1565
(181)

### Subsets and supersets

Since 346 factors into 2 × 173, 346edo contains 2edo and 173edo as subsets.