666edo: Difference between revisions
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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 == | ||
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|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 == | ||
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* [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 --> | ||
Revision as of 20:30, 12 September 2022
| ← 665edo | 666edo | 667edo → |
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 (%) | +41.5 | -40.4 | +30.2 | -17.0 | +1.9 | -49.3 | +1.1 | -25.0 | -12.0 | -28.3 | +30.8 | |
| 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