666edo: Difference between revisions
m Categories |
No edit summary |
||
| Line 13: | Line 13: | ||
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]]. | 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 | Using the 666c val, it tempres out [[2401/2400]], [[4375/4374]], and [[9801/9800]] in the 11 limit. | ||
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. A more general 23 | 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 == | == Rank two temperaments by generator == | ||
| Line 35: | Line 35: | ||
|Factor 9 Grid | |Factor 9 Grid | ||
|} | |} | ||
== Scales == | |||
* Factor9Grid[14]: 39 38 36 35 66 62 59 55 52 49 46 44 42 41 | |||
== Music == | == Music == | ||
| Line 43: | Line 47: | ||
* [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 | * [https://www.youtube.com/watch?v=ghUs-84NAAU&t=203s Testing 432 Hz Frequencies and Temperaments Adam Neely] | ||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||