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 2^1/294, 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.