166edt
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Prime factorization
2 × 83
Step size
11.4576¢
Octave
105\166edt (1203.04¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 165edt | 166edt | 167edt → |
166 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 166edt or 166ed3), is a nonoctave tuning system that divides the interval of 3/1 into 166 equal parts of about 11.5 ¢ each. Each step represents a frequency ratio of 31/166, or the 166th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.04 | +0.00 | -5.37 | -2.13 | +3.04 | -0.30 | -2.33 | +0.00 | +0.92 | -3.68 | -5.37 |
| Relative (%) | +26.6 | +0.0 | -46.9 | -18.6 | +26.6 | -2.6 | -20.3 | +0.0 | +8.0 | -32.1 | -46.9 | |
| Steps (reduced) |
105 (105) |
166 (0) |
209 (43) |
243 (77) |
271 (105) |
294 (128) |
314 (148) |
332 (0) |
348 (16) |
362 (30) |
375 (43) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.01 | +2.74 | -2.13 | +0.72 | -1.12 | +3.04 | +1.10 | +3.96 | -0.30 | -0.64 | +2.61 |
| Relative (%) | +43.7 | +23.9 | -18.6 | +6.3 | -9.8 | +26.6 | +9.6 | +34.6 | -2.6 | -5.6 | +22.8 | |
| Steps (reduced) |
388 (56) |
399 (67) |
409 (77) |
419 (87) |
428 (96) |
437 (105) |
445 (113) |
453 (121) |
460 (128) |
467 (135) |
474 (142) | |