172edt
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Prime factorization
22 × 43
Step size
11.0579¢
Octave
109\172edt (1205.31¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 171edt | 172edt | 173edt → |
172 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 172edt or 172ed3), is a nonoctave tuning system that divides the interval of 3/1 into 172 equal parts of about 11.1 ¢ each. Each step represents a frequency ratio of 31/172, or the 172nd root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.31 | +0.00 | -0.44 | +0.27 | +5.31 | +3.83 | +4.87 | +0.00 | -5.48 | -4.61 | -0.44 |
| Relative (%) | +48.0 | +0.0 | -4.0 | +2.5 | +48.0 | +34.6 | +44.0 | +0.0 | -49.5 | -41.7 | -4.0 | |
| Steps (reduced) |
109 (109) |
172 (0) |
217 (45) |
252 (80) |
281 (109) |
305 (133) |
326 (154) |
344 (0) |
360 (16) |
375 (31) |
389 (45) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.74 | -1.92 | +0.27 | -0.88 | +4.74 | +5.31 | +0.17 | -0.17 | +3.83 | +0.69 | +1.14 |
| Relative (%) | +42.9 | -17.4 | +2.5 | -8.0 | +42.9 | +48.0 | +1.5 | -1.5 | +34.6 | +6.3 | +10.3 | |
| Steps (reduced) |
402 (58) |
413 (69) |
424 (80) |
434 (90) |
444 (100) |
453 (109) |
461 (117) |
469 (125) |
477 (133) |
484 (140) |
491 (147) | |