# 346edo

← 345edo | 346edo | 347edo → |

**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 2^{1/346}, 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

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.