# 355edo

 ← 354edo 355edo 356edo →
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

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 21/355, 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

Approximation of odd harmonics in 355edo
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 (%) +33.8 -28.4 +38.9 -32.3 -9.8 +34.4 +5.4 -4.9 -1.4 -27.3 +13.6
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