# 3578edo

 ← 3577edo 3578edo 3579edo →
Prime factorization 2 × 1789
Step size 0.335383¢
Fifth 2093\3578 (701.956¢)
Semitones (A1:m2) 339:269 (113.7¢ : 90.22¢)
Consistency limit 21
Distinct consistency limit 21

3578 equal divisions of the octave (abbreviated 3578edo or 3578ed2), also called 3578-tone equal temperament (3578tet) or 3578 equal temperament (3578et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 3578 equal parts of about 0.335 ¢ each. Each step represents a frequency ratio of 21/3578, or the 3578th root of 2.

3578edo is consistent in the 21-odd-limit. It inherits the 2.5.11.13.29.31 subgroup mapping from 1789edo and tempers out the jacobin comma. Although it significantly improves the 2.3.17.19 subgroup, it does have a pretty rough 7th harmonic, with the roughly the same relative error as in 1789edo and is best considered as a 2.3.5.11.13.17.29.29.31 subgroup tuning.

### Prime harmonics

Approximation of prime harmonics in 3578edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.001 +0.047 +0.095 +0.052 -0.058 +0.019 -0.028 -0.102 +0.048 -0.038
Relative (%) +0.0 +0.4 +14.1 +28.4 +15.4 -17.3 +5.8 -8.5 -30.5 +14.4 -11.4
Steps
(reduced)
3578
(0)
5671
(2093)
8308
(1152)
10045
(2889)
12378
(1644)
13240
(2506)
14625
(313)
15199
(887)
16185
(1873)
17382
(3070)
17726
(3414)