170edo

← 169edo

170edo

171edo →

Prime factorization	2 × 5 × 17
Step size	7.05882 ¢
Fifth	99\170 (698.824 ¢)
Semitones (A1:m2)	13:15 (91.76 ¢ : 105.9 ¢)
Dual sharp fifth	100\170 (705.882 ¢) (→ 10\17)
Dual flat fifth	99\170 (698.824 ¢)
Dual major 2nd	29\170 (204.706 ¢)
Consistency limit	3
Distinct consistency limit	3

170edo is inconsistent to the 5-odd-limit and higher limits, with four mappings possible for the 7-limit: ⟨170 269 395 477] (patent val), ⟨170 270 395 477] (170b), ⟨170 270 395 478] (170bd), and ⟨170 269 394 477] (170c).

Using the patent val, it tempers out the valentine comma, 1990656/1953125 and 3486784401/3355443200 in the 5-limit; 126/125, 1029/1024, and 215233605/210827008 in the 7-limit, supporting the 7-limit valentine temperament; 540/539, 1944/1925, 2835/2816, and 43923/43904 in the 11-limit; 847/845, 1188/1183, 1287/1280, and 1575/1573 in the 13-limit.

Using the 170c val, it tempers out the python comma, 43046721/41943040 and the sycamore comma, 48828125/47775744 in the 5-limit; 1029/1024, 4375/4374, and 78125/76832 in the 7-limit; 385/384, 441/440, and 8019/8000 in the 11-limit, supporting the 11-limit unidec temperament; 975/968, 1188/1183, 1625/1617, and 3159/3136 in the 13-limit.

The 170b val is enfactored in the 5-limit, with the same tuning as 34edo, tempering out the diaschisma, 2048/2025 and the kleisma, 15625/15552. It tempers out 33614/32805, 50421/50000, and 84035/82944 in the 7-limit; 385/384, 1232/1215, 1331/1323, and 6250/6237 in the 11-limit; 196/195, 364/363, 572/567, and 3146/3125 in the 13-limit.

Using the 170bd val, it tempers out 16875/16807, 51200/50421, and 420175/419904 in the 7-limit; 176/175, 896/891, and 6875/6804 in the 11-limit; 169/168, 640/637, 1001/1000, 2704/2673, and 4235/4212 in the 13-limit. Using the alternative 170bdef val, it tempers out 540/539, 1375/1372, 4375/4356, and 8192/8085 in the 11-limit; 325/324, 364/363, 512/507, 625/624, and 1625/1617 in the 13-limit.