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 ~~supports~~ [[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 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 is the 31st [[prime_numbers|prime]] edo.

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