221edt
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Prime factorization
13 × 17
Step size
8.60613¢
Octave
139\221edt (1196.25¢)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 220edt | 221edt | 222edt → |
221 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 221edt or 221ed3), is a nonoctave tuning system that divides the interval of 3/1 into 221 equal parts of about 8.61 ¢ each. Each step represents a frequency ratio of 31/221, or the 221st root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.75 | +0.00 | +1.11 | +2.07 | -3.75 | -3.83 | -2.64 | +0.00 | -1.67 | -3.16 | +1.11 |
| Relative (%) | -43.5 | +0.0 | +12.9 | +24.1 | -43.5 | -44.5 | -30.6 | +0.0 | -19.5 | -36.7 | +12.9 | |
| Steps (reduced) |
139 (139) |
221 (0) |
279 (58) |
324 (103) |
360 (139) |
391 (170) |
418 (197) |
442 (0) |
463 (21) |
482 (40) |
500 (58) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.24 | +1.03 | +2.07 | +2.22 | +0.54 | -3.75 | -2.68 | +3.18 | -3.83 | +1.70 | +2.19 |
| Relative (%) | +2.7 | +12.0 | +24.1 | +25.8 | +6.3 | -43.5 | -31.2 | +37.0 | -44.5 | +19.7 | +25.5 | |
| Steps (reduced) |
516 (74) |
531 (89) |
545 (103) |
558 (116) |
570 (128) |
581 (139) |
592 (150) |
603 (161) |
612 (170) |
622 (180) |
631 (189) | |