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]] into 74 equal parts of size 16.216 [[cent]]s each. It is most notable as a [[meantone]] tuning, tempering out [[81/80]] in the [[5-limit]]; 81/80 and [[126/125]] (and hence [[225/224]]) in the [[7-limit]]; [[99/98]], 176/175 and 441/440 in the [[11-limit]]; and [[144/143]] and 847/845 in the [[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]]; 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.

[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 Twinkle canon – 74 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] [[Category:~~edo~~]]

[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 Twinkle canon – 74 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] {{dead link}}

[[Category:~~meantone~~]]

[[Category:Edo]]

[[Category:74edo| ]]

[[Category:Meantone]]

[[Category:Listen]]

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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&amp;74 temperament with half-octave period and two parallel tracks of meantone.
+'''74edo''' divides the [[octave]] into 74 equal parts of size 16.216 [[cent]]s each. It is most notable as a [[meantone]] tuning, tempering out [[81/80]] in the [[5-limit]]; 81/80 and [[126/125]] (and hence [[225/224]]) in the [[7-limit]]; [[99/98]], 176/175 and 441/440 in the [[11-limit]]; and [[144/143]] and 847/845 in the [[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]]; and discarding 144/143 gives a 13-limit 62&amp;74 temperament with half-octave period and two parallel tracks of meantone.
 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.
-[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 Twinkle canon – 74 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin]      [[Category:edo]]
+[http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 Twinkle canon – 74 edo] by [http://soonlabel.com/xenharmonic/archives/573 Claudi Meneghin] {{dead link}}
-[[Category:meantone]]
+[[Category:Edo]]
+[[Category:74edo| ]] <!-- main article -->
+[[Category:Meantone]]
+[[Category:Listen]]