170edt
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170 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 170edt or 170ed3), is a nonoctave tuning system that divides the interval of 3/1 into 170 equal parts of about 11.2 ¢ each. Each step represents a frequency ratio of 31/170, or the 170th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.89 | +0.00 | +5.41 | -0.51 | -2.89 | -1.25 | +2.53 | +0.00 | -3.40 | -0.58 | +5.41 |
| Relative (%) | -25.8 | +0.0 | +48.4 | -4.5 | -25.8 | -11.1 | +22.6 | +0.0 | -30.4 | -5.2 | +48.4 | |
| Steps (reduced) |
107 (107) |
170 (0) |
215 (45) |
249 (79) |
277 (107) |
301 (131) |
322 (152) |
340 (0) |
356 (16) |
371 (31) |
385 (45) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.10 | -4.13 | -0.51 | -0.36 | -4.62 | -2.89 | +4.20 | +4.90 | -1.25 | -3.47 | -2.11 |
| Relative (%) | +9.8 | -36.9 | -4.5 | -3.2 | -41.3 | -25.8 | +37.6 | +43.8 | -11.1 | -31.0 | -18.8 | |
| Steps (reduced) |
397 (57) |
408 (68) |
419 (79) |
429 (89) |
438 (98) |
447 (107) |
456 (116) |
464 (124) |
471 (131) |
478 (138) |
485 (145) | |