175edt
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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 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -4.49 | +0.00 | +1.90 | -4.03 | -4.49 | +0.35 | -2.59 | +0.00 | +2.36 | +0.38 | +1.90 |
| Relative (%) | -41.3 | +0.0 | +17.5 | -37.0 | -41.3 | +3.2 | -23.8 | +0.0 | +21.7 | +3.5 | +17.5 | |
| Steps (reduced) |
110 (110) |
175 (0) |
221 (46) |
256 (81) |
285 (110) |
310 (135) |
331 (156) |
350 (0) |
367 (17) |
382 (32) |
396 (46) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +4.61 | -4.13 | -4.03 | +3.79 | -3.35 | -4.49 | -0.27 | -2.13 | +0.35 | -4.11 | -4.99 |
| Relative (%) | +42.4 | -38.0 | -37.0 | +34.9 | -30.8 | -41.3 | -2.5 | -19.6 | +3.2 | -37.8 | -45.9 | |
| Steps (reduced) |
409 (59) |
420 (70) |
431 (81) |
442 (92) |
451 (101) |
460 (110) |
469 (119) |
477 (127) |
485 (135) |
492 (142) |
499 (149) | |