346edo

← 345edo

346edo

347edo →

Prime factorization	2 × 173
Step size	3.46821¢
Fifth	202\346 (700.578¢) (→101\173)
Semitones (A1:m2)	30:28 (104¢ : 97.11¢)
Dual sharp fifth	203\346 (704.046¢)
Dual flat fifth	202\346 (700.578¢) (→101\173)
Dual major 2nd	59\346 (204.624¢)
Consistency limit	7
Distinct consistency limit	7

346 equal divisions of the octave (abbreviated 346edo or 346ed2), also called 346-tone equal temperament (346tet) or 346 equal temperament (346et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 346 equal parts of about 3.47 ¢ each. Each step represents a frequency ratio of 2^1/346, or the 346th root of 2.

346edo is consistent to the 7-odd-limit, but the errors of harmonics 3, 5, and 7 are all quite large, commending itself as a 2.9.15.21.11 subgroup temperament. Using the patent val nonetheless, the equal temperament tempers out 243/242, 441/440, 540/539, 2401/2400, 4000/3993, 9801/9800 and 19683/19600. It is an excellent tuning for the 11-limit version of harry, the 72 & 274 temperament, as well as the rank-3 temperament jove, which tempers out 243/242 and 441/440.

Odd harmonics

Approximation of odd harmonics in 346edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	absolute (¢)	-1.38	-1.34	-1.20	+0.71	+0.13	-1.22	+0.75	-0.91	+0.75	+0.90	-0.53
	relative (%)	-40	-39	-34	+21	+4	-35	+22	-26	+22	+26	-15
Steps (reduced)		548 (202)	803 (111)	971 (279)	1097 (59)	1197 (159)	1280 (242)	1352 (314)	1414 (30)	1470 (86)	1520 (136)	1565 (181)

Subsets and supersets

Since 346 factors into 2 × 173, 346edo contains 2edo and 173edo as subsets.