127edo: Difference between revisions

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'''127edo''', which divides the [[Octave|octave]] into 127 parts of 9.45 [[cents|cents]] each, is ~~another~~ equal division interesting because of its approximations, defined by the [[~~Comma|~~comma]]s it [[tempering_out|tempers out]]. In the [[~~5-limit|~~5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family|würschmidt temperament]]. In the [[~~7-limit|~~7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the [[~~11-limit|~~11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[~~Optimal_patent_val|~~optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

'''127edo''', which divides the [[Octave|octave]] into 127 parts of 9.45 [[cents|cents]] each, is an equal division interesting because of its approximations, defined by the [[comma]]s it [[tempering_out|tempers out]]:

* In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family|würschmidt temperament]].

* In the [[7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.

* In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.

127edo is the 31st [[prime_numbers|prime]] edo.

=== Harmonics ===

=== MOS Scales ===

[[MOS_Scales_of_127edo|MOS Scales of 127edo]]

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 {{Infobox ET}}
-'''127edo''', which divides the [[Octave|octave]] into 127 parts of 9.45 [[cents|cents]] each, is another equal division interesting because of its approximations, defined by the [[Comma|comma]]s it [[tempering_out|tempers out]]. In the [[5-limit|5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family|würschmidt temperament]]. In the [[7-limit|7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also. In the [[11-limit|11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[Optimal_patent_val|optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.
+'''127edo''', which divides the [[Octave|octave]] into 127 parts of 9.45 [[cents|cents]] each, is an equal division interesting because of its approximations, defined by the [[comma]]s it [[tempering_out|tempers out]]:
+* In the [[5-limit]], it tempers out the würschmidt comma, 393216/390625 and hence [[support]]s [[Würschmidt_family|würschmidt temperament]].
+* In the [[7-limit]], it also tempers out 225/224, and is an excellent tuning for the 7-limit extension of würschmidt which tempers this out also.
+* In the [[11-limit]], it tempers out 99/98, 176/175 and 243/242, and is an excellent tuning for the 11-limit version of würschmidt, as well as minerva, the rank three temperament tempering out 99/98 and 176/175, for which it is the [[optimal patent val]] and the rank four temperament tempering out 99/98, for which it also provides the optimal patent val.
 edo is the 31st [[prime_numbers|prime]] edo.
+=== Harmonics ===
+{{Harmonics in equal|127}}
+=== MOS Scales ===
 [[MOS_Scales_of_127edo|MOS Scales of 127edo]]