666edo

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← 665edo666edo667edo →
Prime factorization 2 × 32 × 37
Step size 1.8018¢
Fifth 390\666 (702.703¢) (→65\111)
Semitones (A1:m2) 66:48 (118.9¢ : 86.49¢)
Sharp fifth 390\666 (702.703¢) (→65\111)
Flat fifth 389\666 (700.901¢)
Major 2nd 113\666 (203.604¢)
Consistency limit 3
Distinct consistency limit 3

666 equal divisions of the octave (666edo), or 666-tone equal temperament (666tet), 666 equal temperament (666et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 666 equal parts of about 1.8 ¢ each.

Theory

Approximation of odd harmonics in 666edo
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

Scales

  • Factor9Grid[14]: 39 38 36 35 66 62 59 55 52 49 46 44 42 41

Music

References