256ed6
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| ← 255ed6 | 256ed6 | 257ed6 → |
256 equal divisions of the 6th harmonic (abbreviated 256ed6) is a nonoctave tuning system that divides the interval of 6/1 into 256 equal parts of about 12.1 ¢ each. Each step represents a frequency ratio of 61/256, or the 256th root of 6.
Theory
256ed6 is closely related to 99edo, but with the 6th harmonic instead of the octave tuned just. The octave is compressed by about 0.416 cents. Like 99edo, 256ed6 is consistent to the 10-integer-limit. It is well optimized for the 7-limit, tuning prime harmonics 3 and 5 sharp, and 2 and 7 flat.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.42 | +0.42 | -0.83 | +0.60 | +0.00 | -0.30 | -1.25 | +0.83 | +0.18 | +4.82 | -0.42 |
| Relative (%) | -3.4 | +3.4 | -6.9 | +4.9 | +0.0 | -2.4 | -10.3 | +6.9 | +1.5 | +39.8 | -3.4 | |
| Steps (reduced) |
99 (99) |
157 (157) |
198 (198) |
230 (230) |
256 (0) |
278 (22) |
297 (41) |
314 (58) |
329 (73) |
343 (87) |
355 (99) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -5.70 | -0.71 | +1.01 | -1.66 | +2.43 | +0.42 | +3.75 | -0.23 | +0.12 | +4.40 | +0.15 | -0.83 |
| Relative (%) | -47.1 | -5.9 | +8.4 | -13.7 | +20.1 | +3.4 | +30.9 | -1.9 | +1.0 | +36.3 | +1.2 | -6.9 | |
| Steps (reduced) |
366 (110) |
377 (121) |
387 (131) |
396 (140) |
405 (149) |
413 (157) |
421 (165) |
428 (172) |
435 (179) |
442 (186) |
448 (192) |
454 (198) | |
Subsets and supersets
Since 256 factors into primes as 28, 256ed6 contains subset ed6's 2, 4, 8, 16, 32, 64, and 128.