71edo: Difference between revisions
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The '''71 equal temperament''' or '''71-EDO''' divides the octave into 71 equal parts of 16.901 cents each | The '''71 equal temperament''' or '''71-EDO''' divides the octave into 71 equal parts of 16.901 cents each. | ||
71edo is the 20th [[prime EDO]]. | 71edo is the 20th [[prime EDO]]. | ||
{| | == Theory == | ||
| | {{Harmonics in equal|71}} | ||
[[Category:Equal divisions of the octave|##]] | |||
It tempers out 20480/19683 and [[393216/390625]] in the [[5-limit]], 875/864, 4000/3969 and 1029/1024 in the [[7-limit]], 245/242 and [[100/99]] in the [[11-limit]], and 91/90 in the [[13-limit]]. In the 13-limit it supplies the optimal [[patent val]] for the 29&71 and 34&37 temperaments.<!-- 2-digit number --> | |||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||
Revision as of 21:27, 16 September 2022
The 71 equal temperament or 71-EDO divides the octave into 71 equal parts of 16.901 cents each.
71edo is the 20th prime EDO.
Theory
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +7.90 | +2.42 | -5.45 | -1.09 | +6.43 | +4.54 | -6.58 | -3.55 | +6.71 | +2.46 | -2.92 |
| Relative (%) | +46.8 | +14.3 | -32.2 | -6.5 | +38.0 | +26.9 | -38.9 | -21.0 | +39.7 | +14.5 | -17.3 | |
| Steps (reduced) |
113 (42) |
165 (23) |
199 (57) |
225 (12) |
246 (33) |
263 (50) |
277 (64) |
290 (6) |
302 (18) |
312 (28) |
321 (37) | |
It tempers out 20480/19683 and 393216/390625 in the 5-limit, 875/864, 4000/3969 and 1029/1024 in the 7-limit, 245/242 and 100/99 in the 11-limit, and 91/90 in the 13-limit. In the 13-limit it supplies the optimal patent val for the 29&71 and 34&37 temperaments.