# 294edo

 ← 293edo 294edo 295edo →
Prime factorization 2 × 3 × 72
Step size 4.08163¢
Fifth 172\294 (702.041¢) (→86\147)
Semitones (A1:m2) 28:22 (114.3¢ : 89.8¢)
Consistency limit 5
Distinct consistency limit 5

294 equal divisions of the octave (abbreviated 294edo or 294ed2), also called 294-tone equal temperament (294tet) or 294 equal temperament (294et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 294 equal parts of about 4.08 ¢ each. Each step represents a frequency ratio of 21/294, or the 294th root of 2.

294edo has a very accurate fifth inherited from 147edo, only 0.086 cents sharp, but it has a 5/4 which is 1.441 cents sharp and a 7/4 which is 1.479 cents flat, so that 7/5 is 2.920 cents flat, rendering it inconsistent in the 7-odd-limit.

In the 5-limit the equal temperament tempers out 393216/390625, the würschmidt comma, and [54 -37 2, the monzisma. The patent val tempers out 10976/10935, the hemimage comma, and 50421/50000, the trimyna comma, and supplies the optimal patent val for trimyna temperament, as well as its 11-limit extension, and also supplies the optimal patent val for the rank-4 temperament tempering out 3773/3750. The 294d val tempers out 16875/16807 and 19683/19600 instead, supporting mirkat, whereas 294c tempers out 126/125 and 1029/1024, supporting valentine.

### Prime harmonics

Approximation of prime harmonics in 294edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +0.09 +1.44 -1.48 -0.30 +0.29 +1.17 +0.45 +0.30 -1.01 +1.90
Relative (%) +0.0 +2.1 +35.3 -36.2 -7.3 +7.1 +28.6 +10.9 +7.3 -24.6 +46.6
Steps
(reduced)
294
(0)
466
(172)
683
(95)
825
(237)
1017
(135)
1088
(206)
1202
(26)
1249
(73)
1330
(154)
1428
(252)
1457
(281)

### Subsets and supersets

Since 294 factors into 2 × 3 × 49, 294edo has 2, 3, 6, 7, 14, 21, 42, 49, 98, and 147 as its subsets.