666edo
Theory
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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. Harmonics from 2 to 17 for 666edo all land on even numbers, meaning its contorted order 2 and they ultimately derive from 333edo. As such, 666edo provides the optimal patent val for novemkleismic temperament just as 333edo does. 11/8 of 666edo ultimately derives from 37edo.
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. Its 11/8 ultimately derives from 37edo, and 7/6 from 18edo.
666 is divisible by 9, 18, 37, 74, 111, 222, and 333.
666edo also approximates the "Factor 9 grid", or the just intonation esoteric scale deconstructed and debunked by Adam Neely. The best rank two temperament for this scale is 495 & 666. A more general 23-limit version of this temperament can be described also, which results in a temperament with period 1/9 octave.
Rank two temperaments by generator
| Periods
per octave |
Generator | Cents | Associated
ratio |
Temperaments |
|---|---|---|---|---|
| 9 | 35\666 | 63.063 | ~27/26 | Factor 9 Grid |