258edt
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| ← 257edt | 258edt | 259edt → |
258 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 258edt or 258ed3), is a nonoctave tuning system that divides the interval of 3/1 into 258 equal parts of about 7.37 ¢ each. Each step represents a frequency ratio of 31/258, or the 258th root of 3.
Theory
271edt acts as a stretched version of 163edo using the 163d val, but with 3/1 instead of 2/1 just. The octave is stretched by about 1.62 cents, which brings harmonics 5 and 7 much closer to just, though harmonics 11, 13, and 17 become worse.
Considered as a no-twos system, 271edt does very well in the 3.5.7-subgroup. Notably, it tempers out 13841287201/13839609375, the izar comma.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +1.62 | +0.00 | +0.27 | +0.14 | -0.93 | -2.63 | -2.63 | -3.52 | -2.54 | +1.61 | -3.27 |
| Relative (%) | +22.0 | +0.0 | +3.7 | +1.9 | -12.6 | -35.7 | -35.7 | -47.7 | -34.5 | +21.8 | -44.3 | |
| Steps (reduced) |
163 (163) |
258 (0) |
378 (120) |
457 (199) |
563 (47) |
602 (86) |
665 (149) |
691 (175) |
736 (220) |
791 (17) |
806 (32) | |