74edo: Difference between revisions

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''74edo'' divides the [[Octave|octave]] into 74 equal parts of size 16.216 [[cent|cent]]s each. It is most notable as a [[Meantone|meantone]] tuning, tempering out 81/80 in the [[5-limit|5-limit]]; 81/80 and 126/125 (and hence 225/224) in the [[7-limit|7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit|11-limit]]; and 144/143 and 847/845 in the [[13-limit|13-limit]]. Discarding 847/845 from that gives [[Meantone_family|13-limit meantone]], aka 13-limit huygens, for which 74edo gives the [[Optimal_patent_val|optimal patent val]]; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone.

'''74edo''' divides the [[Octave|octave]] into 74 equal parts of size 16.216 [[cent|cent]]s each. It is most notable as a [[Meantone|meantone]] tuning, tempering out 81/80 in the [[5-limit|5-limit]]; 81/80 and 126/125 (and hence 225/224) in the [[7-limit|7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit|11-limit]]; and 144/143 and 847/845 in the [[13-limit|13-limit]]. Discarding 847/845 from that gives [[Meantone_family|13-limit meantone]], aka 13-limit [[huygens]], for which 74edo gives the [[Optimal_patent_val|optimal patent val]]; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone.

74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.

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	''74edo'' divides the [[Octave\|octave]] into 74 equal parts of size 16.216 [[cent\|cent]]s each. It is most notable as a [[Meantone\|meantone]] tuning, tempering out 81/80 in the [[5-limit\|5-limit]]; 81/80 and 126/125 (and hence 225/224) in the [[7-limit\|7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit\|11-limit]]; and 144/143 and 847/845 in the [[13-limit\|13-limit]]. Discarding 847/845 from that gives [[Meantone_family\|13-limit meantone]], aka 13-limit huygens, for which 74edo gives the [[Optimal_patent_val\|optimal patent val]]; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone.		'''74edo''' divides the [[Octave\|octave]] into 74 equal parts of size 16.216 [[cent\|cent]]s each. It is most notable as a [[Meantone\|meantone]] tuning, tempering out 81/80 in the [[5-limit\|5-limit]]; 81/80 and 126/125 (and hence 225/224) in the [[7-limit\|7-limit]]; 99/98, 176/175 and 441/440 in the [[11-limit\|11-limit]]; and 144/143 and 847/845 in the [[13-limit\|13-limit]]. Discarding 847/845 from that gives [[Meantone_family\|13-limit meantone]], aka 13-limit [[huygens]], for which 74edo gives the [[Optimal_patent_val\|optimal patent val]]; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone.

	74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.		74 tunes 11 only 1/30 of a cent sharp, and 13 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.