219edt
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Prime factorization
3 × 73
Step size
8.68473¢
Octave
138\219edt (1198.49¢) (→46\73edt)
Consistency limit
4
Distinct consistency limit
4
 |
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| ← 218edt | 219edt | 220edt → |
219 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 219edt or 219ed3), is a nonoctave tuning system that divides the interval of 3/1 into 219 equal parts of about 8.68 ¢ each. Each step represents a frequency ratio of 31/219, or the 219th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -1.51 | +0.00 | -3.02 | +1.48 | -1.51 | +0.85 | +4.16 | +0.00 | -0.02 | -0.02 | -3.02 |
| Relative (%) | -17.4 | +0.0 | -34.7 | +17.1 | -17.4 | +9.8 | +47.9 | +0.0 | -0.3 | -0.2 | -34.7 | |
| Steps (reduced) |
138 (138) |
219 (0) |
276 (57) |
321 (102) |
357 (138) |
388 (169) |
415 (196) |
438 (0) |
459 (21) |
478 (40) |
495 (57) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | -0.66 | +1.48 | +2.65 | +1.91 | -1.51 | +0.42 | -1.53 | +0.85 | -1.53 | -0.32 |
| Relative (%) | -30.3 | -7.6 | +17.1 | +30.6 | +22.0 | -17.4 | +4.8 | -17.6 | +9.8 | -17.6 | -3.7 | |
| Steps (reduced) |
511 (73) |
526 (88) |
540 (102) |
553 (115) |
565 (127) |
576 (138) |
587 (149) |
597 (159) |
607 (169) |
616 (178) |
625 (187) | |