666edo: Difference between revisions
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666 is divisible by {{EDOs|9, 18, 37, 74, 111, 222, and 333}}. | 666 is divisible by {{EDOs|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. | 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. | ||
==== Factor 9 | ==== Factor 9 Grid (general) - 495 & 666 ==== | ||
Subgroup: | Subgroup: 2.3.5.7.11.13.17.19.23 | ||
Comma list: 442/441, 715/714, 2300/2299, 3060/3059, 3179/3174, 9025/9009, 57375/57344 | |||
POTE Generator: 63.0631c (~27/26) | |||
Vals: 171f, 495, 666 | |||
== Rank two temperaments by generator == | |||
{| class="wikitable center-all left-5" | |||
!Periods | |||
per octave | |||
!Generator | |||
!Cents | |||
!Associated | |||
ratio | |||
!Temperaments | |||
|- | |||
|9 | |||
|35\666 | |||
|63.063 | |||
|~27/26 | |||
|Factor 9 Grid | |||
|} | |||
== References == | == References == | ||
* [http://x31eq.com/cgi-bin/rt.cgi?key=666_1289_1874_2426_2948_3443_3914_4363_4792_5203_5597_5976_6340_6691&ets=666&limit=15%2F14_16%2F14_17%2F14_18%2F14_19%2F14_20%2F14_21%2F14_22%2F14_23%2F14_24%2F14_25%2F14_26%2F14_27%2F14_28%2F14 Approximation of the Factor 9 grid in 666edo] | * [http://x31eq.com/cgi-bin/rt.cgi?key=666_1289_1874_2426_2948_3443_3914_4363_4792_5203_5597_5976_6340_6691&ets=666&limit=15%2F14_16%2F14_17%2F14_18%2F14_19%2F14_20%2F14_21%2F14_22%2F14_23%2F14_24%2F14_25%2F14_26%2F14_27%2F14_28%2F14 Approximation of the Factor 9 grid in 666edo] | ||
* [https://www.youtube.com/watch?v=ghUs-84NAAU&t=203s Testing 432 Hz Frequencies and Temperaments - Adam Neely] | * [https://www.youtube.com/watch?v=ghUs-84NAAU&t=203s Testing 432 Hz Frequencies and Temperaments - Adam Neely] | ||
Revision as of 19:50, 31 March 2022
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.
Factor 9 Grid (general) - 495 & 666
Subgroup: 2.3.5.7.11.13.17.19.23
Comma list: 442/441, 715/714, 2300/2299, 3060/3059, 3179/3174, 9025/9009, 57375/57344
POTE Generator: 63.0631c (~27/26)
Vals: 171f, 495, 666
Rank two temperaments by generator
| Periods
per octave |
Generator | Cents | Associated
ratio |
Temperaments |
|---|---|---|---|---|
| 9 | 35\666 | 63.063 | ~27/26 | Factor 9 Grid |