355edo

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← 354edo355edo356edo →
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 355-tone equal temperament (355tet), 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 of 355edo 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 (%) +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