# 378edo

 ← 377edo 378edo 379edo →
Prime factorization 2 × 33 × 7
Step size 3.1746¢
Fifth 221\378 (701.587¢)
Semitones (A1:m2) 35:29 (111.1¢ : 92.06¢)
Consistency limit 7
Distinct consistency limit 7

378 equal divisions of the octave (abbreviated 378edo or 378ed2), also called 378-tone equal temperament (378tet) or 378 equal temperament (378et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 378 equal parts of about 3.17 ¢ each. Each step represents a frequency ratio of 21/378, or the 378th root of 2.

The equal temperament tempers out 32805/32768 (schisma) in the 5-limit and 3136/3125 in the 7-limit, so that it supports bischismic, and in fact provides the optimal patent val. It tempers out 441/440 and 8019/8000 in the 11-limit and 729/728 and 1001/1000 in the 13-limit so that it supports 11- and 13-limit bischismatic, and it also gives the optimal patent val for 13-limit bischismic.

### Prime harmonics

Approximation of prime harmonics in 378edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.37 +0.99 -0.57 +1.06 +0.74 -0.19 +0.90 +0.30 -1.01 +1.00
Relative (%) +0.0 -11.6 +31.1 -18.0 +33.5 +23.4 -6.1 +28.3 +9.4 -31.7 +31.4
Steps
(reduced)
378
(0)
599
(221)
878
(122)
1061
(305)
1308
(174)
1399
(265)
1545
(33)
1606
(94)
1710
(198)
1836
(324)
1873
(361)

### Subsets and supersets

Since 378 factors into 2 × 33 × 7, 378edo has subset edos 2, 3, 6, 7, 9, 14, 18, 21, 27, 42, 54, 63, 126, and 189.