189edt
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Prime factorization
33 × 7
Step size
10.0633¢
Octave
119\189edt (1197.53¢) (→17\27edt)
Consistency limit
4
Distinct consistency limit
4
 |
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| ← 188edt | 189edt | 190edt → |
189 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 189edt or 189ed3), is a nonoctave tuning system that divides the interval of 3/1 into 189 equal parts of about 10.1 ¢ each. Each step represents a frequency ratio of 31/189, or the 189th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.47 | +0.00 | -4.95 | +1.21 | -2.47 | +2.36 | +2.64 | +0.00 | -1.27 | +4.81 | -4.95 |
| Relative (%) | -24.6 | +0.0 | -49.1 | +12.0 | -24.6 | +23.5 | +26.3 | +0.0 | -12.6 | +47.8 | -49.1 | |
| Steps (reduced) |
119 (119) |
189 (0) |
238 (49) |
277 (88) |
308 (119) |
335 (146) |
358 (169) |
378 (0) |
396 (18) |
413 (35) |
427 (49) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | -0.11 | +1.21 | +0.17 | -4.15 | -2.47 | +4.56 | -3.74 | +2.36 | +2.33 | -4.18 |
| Relative (%) | -26.2 | -1.1 | +12.0 | +1.7 | -41.2 | -24.6 | +45.3 | -37.1 | +23.5 | +23.2 | -41.5 | |
| Steps (reduced) |
441 (63) |
454 (76) |
466 (88) |
477 (99) |
487 (109) |
497 (119) |
507 (129) |
515 (137) |
524 (146) |
532 (154) |
539 (161) | |