527edt
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Prime factorization
17 × 31
Step size
3.60902¢
Octave
332\527edt (1198.2¢)
Consistency limit
2
Distinct consistency limit
2
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| ← 526edt | 527edt | 528edt → |
527 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 527edt or 527ed3), is a nonoctave tuning system that divides the interval of 3/1 into 527 equal parts of about 3.61 ¢ each. Each step represents a frequency ratio of 31/527, or the 527th root of 3.
527edt is essentially identical to every other step of 665edo. It is additionally notable for every odd harmonic until 45 being tuned flatly, meaning that it possesses consistency to the no-twos 43-throdd limit, a record unbeaten by any previous edt.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.80 | +0.00 | -0.15 | -1.61 | -0.94 | -1.43 | -0.29 | -1.57 | -0.30 |
| Relative (%) | -50.0 | +0.0 | -4.1 | -44.5 | -26.1 | -39.6 | -8.1 | -43.6 | -8.4 | |
| Steps (reduced) |
332 (332) |
527 (0) |
772 (245) |
933 (406) |
1150 (96) |
1230 (176) |
1359 (305) |
1412 (358) |
1504 (450) | |
| Harmonic | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | 47 | 49 | 51 | 53 | 55 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.30 | +0.00 | -1.01 | -0.98 | -0.94 | -1.76 | -0.52 | -1.43 | -1.39 | -0.84 | -0.15 | +0.36 | +0.39 | -0.29 | +1.68 | -1.09 |
| Relative (%) | -8.2 | +0.0 | -27.9 | -27.0 | -26.1 | -48.7 | -14.3 | -39.6 | -38.6 | -23.3 | -4.1 | +9.9 | +10.9 | -8.1 | +46.7 | -30.2 | |
| Steps (reduced) |
1544 (490) |
1581 (0) |
1615 (34) |
1647 (66) |
1677 (96) |
1705 (124) |
1732 (151) |
1757 (176) |
1781 (200) |
1804 (223) |
1826 (245) |
1847 (266) |
1867 (286) |
1886 (305) |
1905 (324) |
1922 (341) | |