167edt
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Prime factorization
167 (prime)
Step size
11.389¢
Octave
105\167edt (1195.84¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 166edt | 167edt | 168edt → |
167 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 167edt or 167ed3), is a nonoctave tuning system that divides the interval of 3/1 into 167 equal parts of about 11.4 ¢ each. Each step represents a frequency ratio of 31/167, or the 167th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.16 | +0.00 | +3.07 | +3.98 | -4.16 | +2.30 | -1.09 | +0.00 | -0.18 | +5.65 | +3.07 |
| Relative (%) | -36.5 | +0.0 | +26.9 | +34.9 | -36.5 | +20.2 | -9.6 | +0.0 | -1.6 | +49.6 | +26.9 | |
| Steps (reduced) |
105 (105) |
167 (0) |
211 (44) |
245 (78) |
272 (105) |
296 (129) |
316 (149) |
334 (0) |
350 (16) |
365 (31) |
378 (44) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.16 | -1.86 | +3.98 | -5.25 | +3.68 | -4.16 | +4.74 | -4.34 | +2.30 | +1.49 | +4.26 |
| Relative (%) | +10.2 | -16.3 | +34.9 | -46.1 | +32.3 | -36.5 | +41.6 | -38.1 | +20.2 | +13.1 | +37.4 | |
| Steps (reduced) |
390 (56) |
401 (67) |
412 (78) |
421 (87) |
431 (97) |
439 (105) |
448 (114) |
455 (121) |
463 (129) |
470 (136) |
477 (143) | |