186edt
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Prime factorization
2 × 3 × 31
Step size
10.2256¢
Octave
117\186edt (1196.39¢) (→39\62edt)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 185edt | 186edt | 187edt → |
186 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 186edt or 186ed3), is a nonoctave tuning system that divides the interval of 3/1 into 186 equal parts of about 10.2 ¢ each. Each step represents a frequency ratio of 31/186, or the 186th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.61 | +0.00 | +3.01 | -4.96 | -3.61 | -4.62 | -0.60 | +0.00 | +1.66 | +0.26 | +3.01 |
| Relative (%) | -35.3 | +0.0 | +29.4 | -48.5 | -35.3 | -45.1 | -5.9 | +0.0 | +16.2 | +2.6 | +29.4 | |
| Steps (reduced) |
117 (117) |
186 (0) |
235 (49) |
272 (86) |
303 (117) |
329 (143) |
352 (166) |
372 (0) |
390 (18) |
406 (34) |
421 (49) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | +2.00 | -4.96 | -4.21 | +3.32 | -3.61 | +5.04 | -1.95 | -4.62 | -3.35 | +1.50 |
| Relative (%) | -25.7 | +19.6 | -48.5 | -41.2 | +32.4 | -35.3 | +49.3 | -19.1 | -45.1 | -32.7 | +14.7 | |
| Steps (reduced) |
434 (62) |
447 (75) |
458 (86) |
469 (97) |
480 (108) |
489 (117) |
499 (127) |
507 (135) |
515 (143) |
523 (151) |
531 (159) | |