666edo
Prime factorization | 2 × 3^{2} × 37 |
Step size | 1.8018¢ |
Fifth | 390\666 (702.702¢) (→195\333) |
Major 2nd | 114\666 (205.405¢) |
Semitones (A1:m2) | 66:48 (118.92¢:86.49¢) |
The 666 equal divisions of the octave (666edo), or the 666-tone equal temperament (666tet), 666 equal temperament (666et) when viewed from a regular temperament perspective, divides the octave into 666 equal parts of about 1.8 cents each.
Theory
Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | |
---|---|---|---|---|---|---|---|---|---|---|---|
Error | absolute (¢) | +0.748 | -0.728 | +0.543 | -0.306 | +0.033 | -0.888 | +0.020 | -0.451 | -0.216 | -0.511 |
relative (%) | +41 | -40 | +30 | -17 | +2 | -49 | +1 | -25 | -12 | -28 | |
Steps (reduced) |
1056 (390) |
1546 (214) |
1870 (538) |
2111 (113) |
2304 (306) |
2464 (466) |
2602 (604) |
2722 (58) |
2829 (165) |
2925 (261) |
666edo is appropriate for use with the 2.11.19.41.43 subgroup. If significant errors are allowed, 666edo can be used with 2.7.11.17.19.23. 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. 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 9edo.
Using the 666c val, it tempres out 2401/2400, 4375/4374, and 9801/9800 in the 11-limit.
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 | ~28/27 | Factor 9 Grid |