196edo

← 195edo

196edo

197edo →

Prime factorization	22 × 72
Step size	6.12245 ¢
Fifth	115\196 (704.082 ¢)
Semitones (A1:m2)	21:13 (128.6 ¢ : 79.59 ¢)
Dual sharp fifth	115\196 (704.082 ¢)
Dual flat fifth	114\196 (697.959 ¢) (→ 57\98)
Dual major 2nd	33\196 (202.041 ¢)
Consistency limit	5
Distinct consistency limit	5

196edo is the equal division of the octave into 196 parts of 6.1224 cents each. It tempers out 9765625/9565938 (fifive comma) and 4294967296/4271484375 (escapade comma) in the 5-limit. Using the patent val, it tempers out 245/243, 65625/65536, and 235298/234375 in the 7-limit; 385/384, 896/891, 3388/3375, and 117649/117128 in the 11-limit; 352/351, 364/363, 625/624, 1001/1000, and 9295/9261 in the 13-limit; 289/288, 442/441, 715/714, and 1156/1155 in the 17-limit.

196edo can also treated as a 2.5.7.9.11.13.17 subgroup temperament (with the patent 9), providing a distinct flat tendency for harmonics 5, 7, 9, 11, 13, and 17. With the patent 9, it tempers out 321489/320000, 420175/419904, and 703125/702464 in the 2.5.7.9 subgroup; 441/440, 8019/8000, 41503/41472, and 9453125/9437184 in the 2.5.7.9.11 subgroup; 729/728, 1001/1000, 1575/1573, 6656/6655, and 10985/10976 in the 2.5.7.9.11.13 subgroup; 833/832, 936/935, 1089/1088, 1225/1224, 2025/2023, and 14365/14336 in the 2.5.7.9.11.13.17 subgroup.

Since it's part of the Fibonacci sequence beginning with 5 and 12, it closely approximates peppermint temperament.