213edt
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Prime factorization
3 × 71
Step size
8.92937¢
Octave
134\213edt (1196.54¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 212edt | 213edt | 214edt → |
213 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 213edt or 213ed3), is a nonoctave tuning system that divides the interval of 3/1 into 213 equal parts of about 8.93 ¢ each. Each step represents a frequency ratio of 31/213, or the 213th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.46 | +0.00 | +2.00 | -0.35 | -3.46 | -2.45 | -1.47 | +0.00 | -3.82 | +0.84 | +2.00 |
| Relative (%) | -38.8 | +0.0 | +22.4 | -3.9 | -38.8 | -27.5 | -16.4 | +0.0 | -42.7 | +9.4 | +22.4 | |
| Steps (reduced) |
134 (134) |
213 (0) |
269 (56) |
312 (99) |
347 (134) |
377 (164) |
403 (190) |
426 (0) |
446 (20) |
465 (39) |
482 (56) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | +3.01 | -0.35 | +4.00 | -2.73 | -3.46 | +1.16 | +1.65 | -2.45 | -2.63 | +0.78 |
| Relative (%) | -29.5 | +33.7 | -3.9 | +44.8 | -30.6 | -38.8 | +12.9 | +18.5 | -27.5 | -29.4 | +8.7 | |
| Steps (reduced) |
497 (71) |
512 (86) |
525 (99) |
538 (112) |
549 (123) |
560 (134) |
571 (145) |
581 (155) |
590 (164) |
599 (173) |
608 (182) | |