194edo

← 193edo

194edo

195edo →

Prime factorization	2 × 97
Step size	6.18557¢
Fifth	113\194 (698.969¢)
Semitones (A1:m2)	15:17 (92.78¢ : 105.2¢)
Dual sharp fifth	114\194 (705.155¢) (→57\97)
Dual flat fifth	113\194 (698.969¢)
Dual major 2nd	33\194 (204.124¢)
Consistency limit	5
Distinct consistency limit	5

194 equal divisions of the octave (abbreviated 194edo or 194ed2), also called 194-tone equal temperament (194tet) or 194 equal temperament (194et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 194 equal parts of about 6.19 ¢ each. Each step represents a frequency ratio of 2^1/194, or the 194th root of 2.

194edo is consistent to the 5-odd-limit, but 194b and 194bc vals are also possible as having a large relative error for the 5-limit. Using the patent val, the equal temperament tempers out 43046721/41943040 (lalagu comma) and 1224440064/1220703125 (parakleisma) in the 5-limit. it tempers out 1728/1715, 78125/76832, and 177147/175000 in the 7-limit; 2187/2156, 2420/2401, 2835/2816, and 4000/3993 in the 11-limit; 351/350, 640/637, 1573/1568, 1625/1617, and 1701/1690 in the 13-limit. Using the 194b val, it tempers out 245/243, 65536/64827, and 78125/76832 in the 7-limit; 385/384, 896/891, 2420/2401, and 9375/9317 in the 11-limit; 275/273, 572/567, 640/637, and 1573/1568 in the 13-limit. Using the 194bc val, it tempers out 2048/2025 (diaschisma) and [0 -41 28⟩ (28edt no-twos comma) in the 5-limit; 2401/2400, 65536/64827, and 1071875/1062882 in the 7-limit; 176/175, 896/891, 3773/3750, and 6655/6561 in the 11-limit; 325/324, 572/567, 847/845, 1573/1568, and 6656/6561 in the 13-limit. Using the 194d val, it tempers out 225/224, 118098/117649, and 15752961/15625000 in the 7-limit; 385/384, 540/539, 4000/3993, and 3720087/3660250 in the 11-limit; 847/845, 1188/1183, 1875/1859, 4225/4224, and 6561/6500 in the 13-limit.

Odd harmonics

Approximation of odd harmonics in 194edo

Harmonic		3	5	7	9	11	13	15	17	19	21	23
Error	Absolute (¢)	-2.99	-2.81	+2.31	+0.21	-0.80	+0.71	+0.39	+0.20	-0.61	-0.68	+2.65
	Relative (%)	-48.3	-45.4	+37.3	+3.5	-13.0	+11.5	+6.3	+3.2	-9.8	-11.0	+42.9
Steps (reduced)		307 (113)	450 (62)	545 (157)	615 (33)	671 (89)	718 (136)	758 (176)	793 (17)	824 (48)	852 (76)	878 (102)

Subsets and supersets

Since 194 factors into 2 × 97, 194edo contains 2edo and 97edo as subsets.