171edt
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Prime factorization
32 × 19
Step size
11.1225¢
Octave
108\171edt (1201.23¢) (→12\19edt)
Consistency limit
8
Distinct consistency limit
8
 |
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| ← 170edt | 171edt | 172edt → |
171 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 171edt or 171ed3), is a nonoctave tuning system that divides the interval of 3/1 into 171 equal parts of about 11.1 ¢ each. Each step represents a frequency ratio of 31/171, or the 171st root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.23 | +0.00 | +2.47 | +5.44 | +1.23 | +1.30 | +3.70 | +0.00 | -4.44 | -2.61 | +2.47 |
| Relative (%) | +11.1 | +0.0 | +22.2 | +49.0 | +11.1 | +11.7 | +33.3 | +0.0 | -39.9 | -23.5 | +22.2 | |
| Steps (reduced) |
108 (108) |
171 (0) |
216 (45) |
251 (80) |
279 (108) |
303 (132) |
324 (153) |
342 (0) |
358 (16) |
373 (31) |
387 (45) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | +2.54 | +5.44 | +4.94 | +0.09 | +1.23 | -3.39 | -3.21 | +1.30 | -1.37 | -0.47 |
| Relative (%) | -23.7 | +22.8 | +49.0 | +44.4 | +0.8 | +11.1 | -30.5 | -28.8 | +11.7 | -12.4 | -4.3 | |
| Steps (reduced) |
399 (57) |
411 (69) |
422 (80) |
432 (90) |
441 (99) |
450 (108) |
458 (116) |
466 (124) |
474 (132) |
481 (139) |
488 (146) | |