168edt
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Prime factorization
23 × 3 × 7
Step size
11.3212¢
Octave
106\168edt (1200.04¢) (→53\84edt)
Consistency limit
5
Distinct consistency limit
5
 |
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| ← 167edt | 168edt | 169edt → |
168 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 168edt or 168ed3), is a nonoctave tuning system that divides the interval of 3/1 into 168 equal parts of about 11.3 ¢ each. Each step represents a frequency ratio of 31/168, or the 168th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.04 | +0.00 | +0.09 | -1.31 | +0.04 | +4.88 | +0.13 | +0.00 | -1.27 | +3.55 | +0.09 |
| Relative (%) | +0.4 | +0.0 | +0.8 | -11.6 | +0.4 | +43.1 | +1.1 | +0.0 | -11.2 | +31.3 | +0.8 | |
| Steps (reduced) |
106 (106) |
168 (0) |
212 (44) |
246 (78) |
274 (106) |
298 (130) |
318 (150) |
336 (0) |
352 (16) |
367 (31) |
380 (44) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | +4.92 | -1.31 | +0.17 | -2.89 | +0.04 | -2.99 | -1.22 | +4.88 | +3.59 | -5.44 |
| Relative (%) | -23.3 | +43.5 | -11.6 | +1.5 | -25.6 | +0.4 | -26.4 | -10.8 | +43.1 | +31.7 | -48.0 | |
| Steps (reduced) |
392 (56) |
404 (68) |
414 (78) |
424 (88) |
433 (97) |
442 (106) |
450 (114) |
458 (122) |
466 (130) |
473 (137) |
479 (143) | |