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 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.23 | +0.00 | -1.63 | -1.73 | -1.60 | +0.40 | +0.09 | -1.37 | -4.52 | +3.69 | -2.56 |
| Relative (%) | +13.6 | +0.0 | -17.9 | -19.0 | -17.6 | +4.4 | +0.9 | -15.0 | -49.6 | +40.6 | -28.2 | |
| Steps (reduced) |
132 (132) |
209 (0) |
306 (97) |
370 (161) |
456 (38) |
488 (70) |
539 (121) |
560 (142) |
596 (178) |
641 (14) |
653 (26) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.54 | -4.28 | +4.27 | -4.11 | -2.81 | +2.63 | -0.48 | +0.90 | +0.62 | -1.97 | -2.22 |
| Relative (%) | +5.9 | -47.0 | +46.9 | -45.2 | -30.8 | +28.9 | -5.3 | +9.9 | +6.8 | -21.7 | -24.4 | |
| Steps (reduced) |
687 (60) |
706 (79) |
716 (89) |
732 (105) |
755 (128) |
776 (149) |
782 (155) |
800 (173) |
811 (184) |
816 (189) |
831 (204) | |