293edt
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Prime factorization
293 (prime)
Step size
6.49131¢
Octave
185\293edt (1200.89¢)
Consistency limit
4
Distinct consistency limit
4
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293 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 293edt or 293ed3), is a nonoctave tuning system that divides the interval of 3/1 into 293 equal parts of about 6.49 ¢ each. Each step represents a frequency ratio of 31/293, or the 293rd root of 3.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.89 | +0.00 | +1.79 | -1.54 | +0.89 | +0.17 | +2.68 | +0.00 | -0.65 | +3.12 | +1.79 |
| Relative (%) | +13.8 | +0.0 | +27.5 | -23.7 | +13.8 | +2.6 | +41.3 | +0.0 | -10.0 | +48.1 | +27.5 | |
| Steps (reduced) |
185 (185) |
293 (0) |
370 (77) |
429 (136) |
478 (185) |
519 (226) |
555 (262) |
586 (0) |
614 (28) |
640 (54) |
663 (77) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.47 | +1.06 | -1.54 | -2.92 | +2.48 | +0.89 | -1.83 | +0.25 | +0.17 | -2.48 | -1.54 |
| Relative (%) | -7.2 | +16.3 | -23.7 | -45.0 | +38.2 | +13.8 | -28.2 | +3.8 | +2.6 | -38.1 | -23.7 | |
| Steps (reduced) |
684 (98) |
704 (118) |
722 (136) |
739 (153) |
756 (170) |
771 (185) |
785 (199) |
799 (213) |
812 (226) |
824 (238) |
836 (250) | |