← 185edo 186edo 187edo →
Prime factorization 2 × 3 × 31
Step size 6.45161 ¢ 
Fifth 109\186 (703.226 ¢)
Semitones (A1:m2) 19:13 (122.6 ¢ : 83.87 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

186edo is closely related to 31edo, but the patent vals differ on the mapping for 3. The equal temperament tempers out 67108864/66430125 (misty comma) and 390625000/387420489 (quartonic comma) in the 5-limit, as well as 6115295232/6103515625 (vishnuzma); 3136/3125, 5120/5103 and 117649/116640 in the 7-limit. Using the patent val, it tempers out 385/384, 1331/1323, 2200/2187, and 3773/3750 in the 11-limit; 325/324, 352/351, 847/845, and 1573/1568 in the 13-limit.

Prime harmonics

Approximation of prime harmonics in 186edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 +1.27 +0.78 -1.08 -2.93 -1.82 -1.73 -0.74 -2.47 +2.68 -3.10
Relative (%) +0.0 +19.7 +12.1 -16.8 -45.4 -28.2 -26.8 -11.5 -38.3 +41.6 -48.1
Steps
(reduced)
186
(0)
295
(109)
432
(60)
522
(150)
643
(85)
688
(130)
760
(16)
790
(46)
841
(97)
904
(160)
921
(177)

Subsets and supersets

Since 186 factors into 2 × 3 × 31, 186edo has subset edos 2, 3, 6, 31, 62, and 93.