# 666edo

← 665edo | 666edo | 667edo → |

^{2}× 37**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

Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | +0.748 | -0.728 | +0.543 | -0.306 | +0.033 | -0.888 | +0.020 | -0.451 | -0.216 | -0.511 | +0.554 |

relative (%) | +41 | -40 | +30 | -17 | +2 | -49 | +1 | -25 | -12 | -28 | +31 | |

Steps (reduced) |
1056 (390) |
1546 (214) |
1870 (538) |
2111 (113) |
2304 (306) |
2464 (466) |
2602 (604) |
2722 (58) |
2829 (165) |
2925 (261) |
3013 (349) |

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