# 355edo

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Prime factorization
5 × 71
Step size
3.38028¢
Fifth
208\355 (703.099¢)
Semitones (A1:m2)
36:25 (121.7¢ : 84.51¢)
Dual sharp fifth
208\355 (703.099¢)
Dual flat fifth
207\355 (699.718¢)
Dual major 2nd
60\355 (202.817¢) (→12\71)
Consistency limit
3
Distinct consistency limit
3

← 354edo | 355edo | 356edo → |

**355 equal divisions of the octave** (abbreviated **355edo** or **355ed2**), also called **355-tone equal temperament** (**355tet**) or **355 equal temperament** (**355et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 355 equal parts of about 3.38 ¢ each. Each step represents a frequency ratio of 2^{1/355}, or the 355th root of 2.

## Theory

355edo is only consistent to the 3-odd-limit since the errors of harmonics 3 and 5 are quite large. It is suitable for the 2.9.5.11.17.19.23.37.41 subgroup. The 2.3.7.13 subgroup is also worth noting.

### Odd harmonics

Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | +1.14 | -0.96 | +1.31 | -1.09 | -0.33 | +1.16 | +0.18 | -0.17 | -0.05 | -0.92 | +0.46 |

relative (%) | +34 | -28 | +39 | -32 | -10 | +34 | +5 | -5 | -1 | -27 | +14 | |

Steps (reduced) |
563 (208) |
824 (114) |
997 (287) |
1125 (60) |
1228 (163) |
1314 (249) |
1387 (322) |
1451 (31) |
1508 (88) |
1559 (139) |
1606 (186) |

### Subsets and supersets

Since 355 factors into 5 × 71, 355edo has 5edo and 71edo as its subsets. 710edo, 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 | [-225 71⟩ | [⟨355 1125]] | 0.1724 | 0.1724 | 5.10 |

2.9.5 | [-57 7 15⟩, [-37 19 -10⟩ | [⟨355 1125 824]] | 0.2530 | 0.1812 | 5.36 |