218edt
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Prime factorization
2 × 109
Step size
8.72456¢
Octave
138\218edt (1203.99¢) (→69\109edt)
Consistency limit
2
Distinct consistency limit
2
 |
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| ← 217edt | 218edt | 219edt → |
218 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 218edt or 218ed3), is a nonoctave tuning system that divides the interval of 3/1 into 218 equal parts of about 8.72 ¢ each. Each step represents a frequency ratio of 31/218, or the 218th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +3.99 | +0.00 | -0.74 | -3.18 | +3.99 | -1.14 | +3.25 | +0.00 | +0.81 | +1.57 | -0.74 |
| Relative (%) | +45.7 | +0.0 | -8.5 | -36.4 | +45.7 | -13.1 | +37.2 | +0.0 | +9.3 | +18.0 | -8.5 | |
| Steps (reduced) |
138 (138) |
218 (0) |
275 (57) |
319 (101) |
356 (138) |
386 (168) |
413 (195) |
436 (0) |
457 (21) |
476 (40) |
493 (57) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.28 | +2.85 | -3.18 | -1.49 | -1.75 | +3.99 | -2.37 | -3.92 | -1.14 | -3.16 | -1.60 |
| Relative (%) | +3.2 | +32.6 | -36.4 | -17.1 | -20.1 | +45.7 | -27.1 | -45.0 | -13.1 | -36.2 | -18.3 | |
| Steps (reduced) |
509 (73) |
524 (88) |
537 (101) |
550 (114) |
562 (126) |
574 (138) |
584 (148) |
594 (158) |
604 (168) |
613 (177) |
622 (186) | |