224edt
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224 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 224edt or 224ed3), is a nonoctave tuning system that divides the interval of 3/1 into 224 equal parts of about 8.49 ¢ each. Each step represents a frequency ratio of 31/224, or the 224th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.79 | +0.00 | +2.92 | -1.31 | -2.79 | +2.05 | +0.13 | +0.00 | -4.10 | +0.72 | +2.92 |
| Relative (%) | -32.8 | +0.0 | +34.3 | -15.4 | -32.8 | +24.1 | +1.5 | +0.0 | -48.2 | +8.5 | +34.3 | |
| Steps (reduced) |
141 (141) |
224 (0) |
283 (59) |
328 (104) |
365 (141) |
397 (173) |
424 (200) |
448 (0) |
469 (21) |
489 (41) |
507 (59) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.20 | -0.74 | -1.31 | -2.66 | +2.77 | -2.79 | -2.99 | +1.61 | +2.05 | -2.07 | -2.61 |
| Relative (%) | +2.3 | -8.7 | -15.4 | -31.3 | +32.6 | -32.8 | -35.2 | +18.9 | +24.1 | -24.4 | -30.7 | |
| Steps (reduced) |
523 (75) |
538 (90) |
552 (104) |
565 (117) |
578 (130) |
589 (141) |
600 (152) |
611 (163) |
621 (173) |
630 (182) |
639 (191) | |