217edt
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Prime factorization
7 × 31
Step size
8.76477¢
Octave
137\217edt (1200.77¢)
Consistency limit
5
Distinct consistency limit
5
 |
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| ← 216edt | 217edt | 218edt → |
217 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 217edt or 217ed3), is a nonoctave tuning system that divides the interval of 3/1 into 217 equal parts of about 8.76 ¢ each. Each step represents a frequency ratio of 31/217, or the 217th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.77 | +0.00 | +1.55 | +0.88 | +0.77 | -3.15 | +2.32 | +0.00 | +1.66 | +3.18 | +1.55 |
| Relative (%) | +8.8 | +0.0 | +17.6 | +10.1 | +8.8 | -36.0 | +26.5 | +0.0 | +18.9 | +36.3 | +17.6 | |
| Steps (reduced) |
137 (137) |
217 (0) |
274 (57) |
318 (101) |
354 (137) |
384 (167) |
411 (194) |
434 (0) |
455 (21) |
474 (40) |
491 (57) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.21 | -2.38 | +0.88 | +3.09 | +3.32 | +0.77 | +3.58 | +2.43 | -3.15 | +3.96 | -2.88 |
| Relative (%) | +36.6 | -27.2 | +10.1 | +35.3 | +37.8 | +8.8 | +40.9 | +27.7 | -36.0 | +45.1 | -32.9 | |
| Steps (reduced) |
507 (73) |
521 (87) |
535 (101) |
548 (114) |
560 (126) |
571 (137) |
582 (148) |
592 (158) |
601 (167) |
611 (177) |
619 (185) | |