209edt
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209 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 209edt or 209ed3), is a nonoctave tuning system that divides the interval of 3/1 into 209 equal parts of about 9.1 ¢ each. Each step represents a frequency ratio of 31/209, or the 209th root of 3.
Harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.23 | +0.00 | -1.63 | -1.73 | -1.60 | +0.40 | +0.09 | -1.37 | -4.52 |
| Relative (%) | +13.6 | +0.0 | -17.9 | -19.0 | -17.6 | +4.4 | +0.9 | -15.0 | -49.6 | |
| Steps (reduced) |
132 (132) |
209 (0) |
306 (97) |
370 (161) |
456 (38) |
488 (70) |
539 (121) |
560 (142) |
596 (178) | |
| Harmonic | 25 | 27 | 29 | 31 | 33 | 35 | 37 | 39 | 41 | 43 | 45 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -3.27 | +0.00 | +3.69 | -2.56 | -1.60 | -3.36 | +0.54 | +0.40 | -4.28 | +4.27 | -1.63 |
| Relative (%) | -35.9 | +0.0 | +40.6 | -28.2 | -17.6 | -36.9 | +5.9 | +4.4 | -47.0 | +46.9 | -17.9 | |
| Steps (reduced) |
612 (194) |
627 (0) |
641 (14) |
653 (26) |
665 (38) |
676 (49) |
687 (60) |
697 (70) |
706 (79) |
716 (89) |
724 (97) | |