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 (¢) | +5.20 | +0.00 | +0.71 | +1.97 | -8.45 | +3.64 | -8.83 | +5.75 | -4.88 | +8.11 | +5.64 |
| Relative (%) | +27.6 | +0.0 | +3.8 | +10.4 | -44.8 | +19.4 | -46.9 | +30.5 | -25.9 | +43.0 | +29.9 | |
| Steps (reduced) |
64 (64) |
101 (0) |
148 (47) |
179 (78) |
220 (18) |
236 (34) |
260 (58) |
271 (69) |
288 (86) |
310 (7) |
316 (13) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.63 | -7.61 | +4.09 | +0.75 | -0.10 | +2.54 | +1.32 | +8.38 | +2.15 | -8.28 | +5.62 |
| Relative (%) | +3.3 | -40.4 | +21.7 | +4.0 | -0.5 | +13.5 | +7.0 | +44.5 | +11.4 | -44.0 | +29.8 | |
| Steps (reduced) |
332 (29) |
341 (38) |
346 (43) |
354 (51) |
365 (62) |
375 (72) |
378 (75) |
387 (84) |
392 (89) |
394 (91) |
402 (99) | |