640edo: Difference between revisions
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Adopt template: EDO intro; +prime error table; +subsets and supersets |
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{{Infobox ET}} | {{Infobox ET}} | ||
{{EDO intro|640}} | |||
640edo is [[enfactoring|enfactored]] in the 5-limit, [[tempering out]] the [[vishnuzma]], {{monzo| 23 6 -14 }}, with the same tuning as [[320edo]]. In the 7-limit it tempers out [[19683/19600]] and {{monzo| 16 2 -1 -6 }} and in the 11-limit it tempers out [[540/539]], [[8019/8000]] and {{monzo| 14 -1 -2 -4 1 }}. It provides the [[optimal patent val]] for the rank-3 [[albus]] temperament tempering out 540/539 and 8019/8000, and [[hemipental]], the 255 & 385 temperament. | |||
=== Odd harmonics === | |||
{{Harmonics in equal|640}} | |||
=== Subsets and supersets === | |||
Since 640 factors into 2<sup>7</sup> × 5, 640edo has subset edos {{EDOs| 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, and 320 }}. | |||
[[Category:Albus]] | [[Category:Albus]] | ||
[[Category: | [[Category:Hemipental]] | ||
Revision as of 06:32, 25 October 2023
| ← 639edo | 640edo | 641edo → |
640edo is enfactored in the 5-limit, tempering out the vishnuzma, [23 6 -14⟩, with the same tuning as 320edo. In the 7-limit it tempers out 19683/19600 and [16 2 -1 -6⟩ and in the 11-limit it tempers out 540/539, 8019/8000 and [14 -1 -2 -4 1⟩. It provides the optimal patent val for the rank-3 albus temperament tempering out 540/539 and 8019/8000, and hemipental, the 255 & 385 temperament.
Odd harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.705 | -0.064 | +0.549 | +0.465 | -0.068 | -0.528 | -0.769 | +0.045 | +0.612 | -0.156 | -0.149 |
| Relative (%) | -37.6 | -3.4 | +29.3 | +24.8 | -3.6 | -28.1 | -41.0 | +2.4 | +32.6 | -8.3 | -8.0 | |
| Steps (reduced) |
1014 (374) |
1486 (206) |
1797 (517) |
2029 (109) |
2214 (294) |
2368 (448) |
2500 (580) |
2616 (56) |
2719 (159) |
2811 (251) |
2895 (335) | |
Subsets and supersets
Since 640 factors into 27 × 5, 640edo has subset edos 2, 4, 5, 8, 10, 16, 20, 32, 40, 64, 80, 128, 160, and 320.