640edo: Difference between revisions
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Adopt template: EDO intro; +prime error table; +subsets and supersets |
m Adopt template: Factorization |
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=== Subsets and supersets === | === Subsets and supersets === | ||
Since 640 factors into | Since 640 factors into {{factorization|640}}, 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:Hemipental]] | [[Category:Hemipental]] | ||
Revision as of 13:01, 2 November 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.