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 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.23 | +0.00 | +2.47 | -1.63 | +1.23 | -1.73 | +3.70 | +0.00 | -0.40 | -1.60 | +2.47 |
| Relative (%) | +13.6 | +0.0 | +27.1 | -17.9 | +13.6 | -19.0 | +40.7 | +0.0 | -4.4 | -17.6 | +27.1 | |
| Steps (reduced) |
132 (132) |
209 (0) |
264 (55) |
306 (97) |
341 (132) |
370 (161) |
396 (187) |
418 (0) |
438 (20) |
456 (38) |
473 (55) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.40 | -0.49 | -1.63 | -4.16 | +0.09 | +1.23 | -1.37 | +0.84 | -1.73 | -0.36 | -4.52 |
| Relative (%) | +4.4 | -5.4 | -17.9 | -45.7 | +0.9 | +13.6 | -15.0 | +9.2 | -19.0 | -4.0 | -49.6 | |
| Steps (reduced) |
488 (70) |
502 (84) |
515 (97) |
527 (109) |
539 (121) |
550 (132) |
560 (142) |
570 (152) |
579 (161) |
588 (170) |
596 (178) | |