74edo
IMPORTED REVISION FROM WIKISPACES
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- This revision was by author genewardsmith and made on 2012-04-16 19:41:26 UTC.
- The original revision id was 321254508.
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Original Wikitext content:
//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]]
Original HTML content:
<html><head><title>74edo</title></head><body><em>74edo</em> divides the <a class="wiki_link" href="/octave">octave</a> into 74 equal parts of size 16.216 <a class="wiki_link" href="/cent">cent</a>s each. It is most notable as a <a class="wiki_link" href="/meantone">meantone</a> tuning, tempering out 81/80 in the <a class="wiki_link" href="/5-limit">5-limit</a>; 81/80 and 126/125 (and hence 225/224) in the <a class="wiki_link" href="/7-limit">7-limit</a>; 99/98, 176/175 and 441/440 in the <a class="wiki_link" href="/11-limit">11-limit</a>; and 144/143 and 847/845 in the <a class="wiki_link" href="/13-limit">13-limit</a>. Discarding 847/845 from that gives <a class="wiki_link" href="/Meantone%20family">13-limit meantone</a>, aka 13-limit huygens, for which 74edo gives the <a class="wiki_link" href="/optimal%20patent%20val">optimal patent val</a>; and discarding 144/143 gives a 13-limit 62&74 temperament with half-octave period and two parallel tracks of meantone.<br /> <br /> 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.<br /> <br /> <a class="wiki_link_ext" href="http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3" rel="nofollow">Twinkle canon – 74 edo</a> by <a class="wiki_link_ext" href="http://soonlabel.com/xenharmonic/archives/573" rel="nofollow">Claudi Meneghin</a></body></html>