258ed12
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| ← 257ed12 | 258ed12 | 259ed12 → |
258 equal divisions of the 12th harmonic (abbreviated 258ed12) is a nonoctave tuning system that divides the interval of 12/1 into 258 equal parts of about 16.7 ¢ each. Each step represents a frequency ratio of 121/258, or the 258th root of 12.
Theory
258ed12 is very nearly identical to 72edo, but with the 12th harmonic rather than the octave being just. The octave is about 0.546 cents stretched. Like 72edo, 258ed12 is consistent to the 18-integer-limit. While it tunes 2 and 11 sharp, the 3, 5, and 7 remain flat as in 72edo but a little less so. The 13 and 17 are improved compared to 72edo, although the 19 becomes slightly worse.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.55 | -1.09 | +1.09 | -1.71 | -0.55 | -0.63 | +1.64 | -2.18 | -1.17 | +0.57 | +0.00 |
| Relative (%) | +3.3 | -6.5 | +6.5 | -10.3 | -3.3 | -3.8 | +9.8 | -13.1 | -7.0 | +3.4 | +0.0 | |
| Steps (reduced) |
72 (72) |
114 (114) |
144 (144) |
167 (167) |
186 (186) |
202 (202) |
216 (216) |
228 (228) |
239 (239) |
249 (249) |
258 (0) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.18 | -0.08 | -2.81 | +2.18 | -2.73 | -1.64 | +4.81 | -0.62 | -1.72 | +1.11 | +7.53 | +0.55 |
| Relative (%) | -31.1 | -0.5 | -16.8 | +13.1 | -16.4 | -9.8 | +28.8 | -3.7 | -10.3 | +6.7 | +45.2 | +3.3 | |
| Steps (reduced) |
266 (8) |
274 (16) |
281 (23) |
288 (30) |
294 (36) |
300 (42) |
306 (48) |
311 (53) |
316 (58) |
321 (63) |
326 (68) |
330 (72) | |