73edo: Difference between revisions
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table for illustrating the sharpness |
corrected and expanded table |
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'''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 [[Starling temperaments#Casablanca temperament-Marrakesh|marrakesh temperament]]. 73et has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp | '''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 [[Starling temperaments#Casablanca temperament-Marrakesh|marrakesh temperament]]. 73et has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp, see approximation table. | ||
{| class="wikitable center-all" | {| class="wikitable center-all" | ||
|- | |- | ||
|+ 73-EDO approximation of primary intervals | |||
|- | |- | ||
| | ! colspan="2" | Prime number | ||
! 3 | |||
! 5 | |||
! 7 | |||
! 11 | |||
! 13 | |||
! 17 | |||
! 19 | |||
! 23 | |||
|- | |- | ||
| | ! rowspan="2" | Error | ||
! absolute ([[cent|¢]]) | |||
| +4.89 | |||
| +8.21 | |||
| +1.04 | |||
| +7.59 | |||
| -2.17 | |||
| -6.33 | |||
| -1.62 | |||
| -3.62 | |||
|- | |- | ||
| | ! [[Relative error|relative]] (%) | ||
| +29.8 | |||
| +49.9 | |||
| +6.3 | |||
| +46.1 | |||
| -13.2 | |||
| -38.5 | |||
| -9.9 | |||
| -22.0 | |||
|- | |||
! colspan="2" | Degree ([[octave reduction|reduced]]) | |||
| 116 (43) | |||
| 170 (24) | |||
| 205 (59) | |||
| 253 (34) | |||
| 270 (51) | |||
| 298 (6) | |||
| 310 (18) | |||
| 330 (38) | |||
|} | |} | ||
Revision as of 17:00, 17 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 approximation 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.