212edt
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212 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 212edt or 212ed3), is a nonoctave tuning system that divides the interval of 3/1 into 212 equal parts of about 8.97 ¢ each. Each step represents a frequency ratio of 31/212, or the 212th root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +2.18 | +0.00 | +4.36 | +3.82 | +2.18 | +4.45 | -2.43 | +0.00 | -2.97 | +2.48 | +4.36 |
| Relative (%) | +24.3 | +0.0 | +48.6 | +42.6 | +24.3 | +49.6 | -27.1 | +0.0 | -33.1 | +27.6 | +48.6 | |
| Steps (reduced) |
134 (134) |
212 (0) |
268 (56) |
311 (99) |
346 (134) |
376 (164) |
401 (189) |
424 (0) |
444 (20) |
463 (39) |
480 (56) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.36 | -2.34 | +3.82 | -0.26 | +2.45 | +2.18 | -1.71 | -0.79 | +4.45 | -4.31 | -0.53 |
| Relative (%) | +4.0 | -26.1 | +42.6 | -2.8 | +27.3 | +24.3 | -19.0 | -8.9 | +49.6 | -48.1 | -5.9 | |
| Steps (reduced) |
495 (71) |
509 (85) |
523 (99) |
535 (111) |
547 (123) |
558 (134) |
568 (144) |
578 (154) |
588 (164) |
596 (172) |
605 (181) | |