71edo: Difference between revisions
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The | The '''71 equal temperament''' or '''71-EDO''' divides the octave into 71 equal parts of 16.901 cents each. 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. | ||
71edo is the 20th [[prime EDO]]. | 71edo is the 20th [[prime EDO]]. | ||
{| class="wikitable center-all" | |||
|- | |||
|+ Approximation of primary intervals in 71 EDO | |||
|- | |||
! colspan="2" | Prime number | |||
! 3 | |||
! 5 | |||
! 7 | |||
! 11 | |||
! 13 | |||
! 17 | |||
! 19 | |||
! 23 | |||
|- | |||
! rowspan="2" | Error | |||
! absolute ([[cent|¢]]) | |||
| +7.90 | |||
| +2.42 | |||
| -5.45 | |||
| +6.43 | |||
| +4.54 | |||
| -3.55 | |||
| +6.71 | |||
| -2.92 | |||
|- | |||
! [[Relative error|relative]] (%) | |||
| +46.8 | |||
| +14.3 | |||
| -32.2 | |||
| +38.0 | |||
| +26.9 | |||
| -21.0 | |||
| +39.7 | |||
| -17.3 | |||
|- | |||
! colspan="2" | Degree ([[octave reduction|reduced]]) | |||
| 113 (42) | |||
| 165 (23) | |||
| 199 (57) | |||
| 246 (33) | |||
| 263 (50) | |||
| 290 (6) | |||
| 302 (18) | |||
| 321 (37) | |||
|} | |||
[[Category:Edo]] | [[Category:Edo]] | ||
[[Category:Prime EDO]] | [[Category:Prime EDO]] | ||
Revision as of 18:42, 16 November 2020
The 71 equal temperament or 71-EDO divides the octave into 71 equal parts of 16.901 cents each. 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.
71edo is the 20th prime EDO.
| Prime number | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +7.90 | +2.42 | -5.45 | +6.43 | +4.54 | -3.55 | +6.71 | -2.92 |
| relative (%) | +46.8 | +14.3 | -32.2 | +38.0 | +26.9 | -21.0 | +39.7 | -17.3 | |
| Degree (reduced) | 113 (42) | 165 (23) | 199 (57) | 246 (33) | 263 (50) | 290 (6) | 302 (18) | 321 (37) | |