73edo: Difference between revisions

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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 [[marrakesh]] temperament. 73et has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp, see following table.
'''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. 73 EDO has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp, see following table.


{| class="wikitable center-all"
{{Primes in edo|73|columns=9|prec=2}}
|-
|+ 73-EDO approximation of prime 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)
|}


73edo fits in mavila scale, by the 9;5 relation in the [[7L_2s|superdiatonic]] scheme.
73 EDO fits in mavila scale, by the 9;5 relation in the [[7L_2s|superdiatonic]] scheme.


73edo is the 21st [[prime edo]].
73 EDO is the 21st [[prime EDO]].


[[Category:Equal divisions of the octave]]
[[Category:Equal divisions of the octave]]
[[Category:Prime EDO]]
[[Category:Prime EDO]]
[[Category:Marrakesh]]
[[Category:Marrakesh]]

Revision as of 08:06, 10 June 2021

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. 73 EDO has a sharp tendency, with the approximations of 3, 5, 7, 11 all sharp, see following table.

Script error: No such module "primes_in_edo".

73 EDO fits in mavila scale, by the 9;5 relation in the superdiatonic scheme.

73 EDO is the 21st prime EDO.

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