228edt
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Prime factorization
22 × 3 × 19
Step size
8.34191¢
Octave
144\228edt (1201.23¢) (→12\19edt)
Consistency limit
11
Distinct consistency limit
11
 |
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| ← 227edt | 228edt | 229edt → |
228 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 228edt or 228ed3), is a nonoctave tuning system that divides the interval of 3/1 into 228 equal parts of about 8.34 ¢ each. Each step represents a frequency ratio of 31/228, or the 228th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.23 | +0.00 | +2.47 | -0.12 | +1.23 | +1.30 | +3.70 | +0.00 | +1.12 | +2.95 | +2.47 |
| Relative (%) | +14.8 | +0.0 | +29.6 | -1.4 | +14.8 | +15.6 | +44.4 | +0.0 | +13.4 | +35.4 | +29.6 | |
| Steps (reduced) |
144 (144) |
228 (0) |
288 (60) |
334 (106) |
372 (144) |
404 (176) |
432 (204) |
456 (0) |
478 (22) |
498 (42) |
516 (60) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.63 | +2.54 | -0.12 | -3.40 | +0.09 | +1.23 | -0.61 | +2.35 | +1.30 | -4.15 | +2.31 |
| Relative (%) | -31.6 | +30.4 | -1.4 | -40.8 | +1.0 | +14.8 | -7.3 | +28.2 | +15.6 | -49.8 | +27.7 | |
| Steps (reduced) |
532 (76) |
548 (92) |
562 (106) |
575 (119) |
588 (132) |
600 (144) |
611 (155) |
622 (166) |
632 (176) |
641 (185) |
651 (195) | |