666edo
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666 EDO divides the octave into steps of 1.801 cents each.
Theory
| Prime number | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.000 | +0.748 | -0.728 | +0.543 | +0.033 | -0.888 | -0.451 | -0.216 | +0.554 | -0.748 | -0.891 | -0.894 | -0.234 | +0.194 |
| relative (%) | +0 | +41 | -40 | +30 | +2 | -49 | -25 | -12 | +31 | -42 | -49 | -50 | -13 | +11 | |
| Steps (reduced) | 666 (0) | 1056 (390) | 1546 (214) | 1870 (538) | 2304 (306) | 2464 (466) | 2722 (58) | 2829 (165) | 3013 (349) | 3235 (571) | 3299 (635) | 3469 (139) | 3568 (238) | 3614 (284) | |
666edo is appropriate for use with the 2.11.19.41.43 subgroup, a choice with very large prime harmonics. If significant errors are allowed, 666edo can be used with 2.7.11.17.19.23. The alternations between approxmation make 666edo a good choice for "no-number" subgroups which skip particular harmonics.
Using the 666c val, it tempres out 2401/2400, 4375/4374, and 9801/9800 in the 11-limit.
666edo provides good approximations for: 15/11, 16/11, 16/15, 13/12, 13/10, 22/15, 23/14.