175edt
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Prime factorization
52 × 7
Step size
10.8683¢
Octave
110\175edt (1195.51¢) (→22\35edt)
Consistency limit
2
Distinct consistency limit
2
| ← 174edt | 175edt | 176edt → |
175 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 175edt or 175ed3), is a nonoctave tuning system that divides the interval of 3/1 into 175 equal parts of about 10.9 ¢ each. Each step represents a frequency ratio of 31/175, or the 175th root of 3.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.49 | +0.00 | -4.03 | +0.35 | +0.38 | +4.61 | -3.35 | -0.27 | -4.99 |
| Relative (%) | -41.3 | +0.0 | -37.0 | +3.2 | +3.5 | +42.4 | -30.8 | -2.5 | -45.9 | |
| Steps (reduced) |
110 (110) |
175 (0) |
256 (81) |
310 (135) |
382 (32) |
409 (59) |
451 (101) |
469 (119) |
499 (149) | |
| Harmonic | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.82 | +0.00 | -4.16 | -0.07 | +0.38 | -3.67 | -2.06 | +4.61 | +4.98 | -1.40 | -4.03 |
| Relative (%) | +25.9 | +0.0 | -38.3 | -0.6 | +3.5 | -33.8 | -19.0 | +42.4 | +45.8 | -12.9 | -37.0 | |
| Steps (reduced) |
513 (163) |
525 (0) |
536 (11) |
547 (22) |
557 (32) |
566 (41) |
575 (50) |
584 (59) |
592 (67) |
599 (74) |
606 (81) | |
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