640edo: Difference between revisions
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{{Infobox ET}} | |||
[[Category: | {{ED intro}} | ||
[[Category: | |||
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 {{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:Hemipental]] | |||
Latest revision as of 15:43, 20 February 2025
| ← 639edo | 640edo | 641edo → |
640 equal divisions of the octave (abbreviated 640edo or 640ed2), also called 640-tone equal temperament (640tet) or 640 equal temperament (640et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 640 equal parts of about 1.88 ¢ each. Each step represents a frequency ratio of 21/640, or the 640th root of 2.
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.