73edo: Difference between revisions
Jump to navigation
Jump to search
m word dedup. |
m marrakesh link now via redirect page |
||
| Line 1: | Line 1: | ||
'''73-EDO''' divides the octave into 73 equal parts of 16.438 [[cent]]s each. It tempers out 78732/78125 and 262144/253125 in the [[5-limit]], [[126/125]] and [[245/243]] in the [[7-limit]], 176/175, 441/440 and 4000/3993 in the [[11-limit]], and 91/90, 169/168, 196/195, [[325/324]], [[351/350]] and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[ | '''73-EDO''' divides the octave into 73 equal parts of 16.438 [[cent]]s each. It tempers out 78732/78125 and 262144/253125 in the [[5-limit]], [[126/125]] and [[245/243]] in the [[7-limit]], 176/175, 441/440 and 4000/3993 in the [[11-limit]], and 91/90, 169/168, 196/195, [[325/324]], [[351/350]] and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for [[marrakesh]] temperament. 73et has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp, see following table. | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
Revision as of 15:53, 25 October 2020
73-EDO divides the octave into 73 equal parts of 16.438 cents each. It tempers out 78732/78125 and 262144/253125 in the 5-limit, 126/125 and 245/243 in the 7-limit, 176/175, 441/440 and 4000/3993 in the 11-limit, and 91/90, 169/168, 196/195, 325/324, 351/350 and 352/351 in the 13-limit. It provides the optimal patent val for marrakesh temperament. 73et has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp, see following table.
| Prime number | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | |
|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +4.89 | +8.21 | +1.04 | +7.59 | -2.17 | -6.33 | -1.62 | -3.62 |
| relative (%) | +29.8 | +49.9 | +6.3 | +46.1 | -13.2 | -38.5 | -9.9 | -22.0 | |
| Degree (reduced) | 116 (43) | 170 (24) | 205 (59) | 253 (34) | 270 (51) | 298 (6) | 310 (18) | 330 (38) | |
73edo fits in mavila scale, by the 9;5 relation in the superdiatonic scheme.
73edo is the 21st prime edo.