74edo: Difference between revisions

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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.

== Theory ==

74edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[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 13-limit meantone, a.k.a. 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.

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

=== Odd harmonics ===

~~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.~~

== Intervals ==

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== Music ==

* [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}}~~

; [[Claudi Meneghin]]

* ''Twinkle canon'' (2012) – [https://web.archive.org/web/20171009205013/http://soonlabel.com/xenharmonic/archives/573 detail] | [https://web.archive.org/web/20201127015514/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 play]

~~[[Category:74edo| ]] ~~

~~[[Category:Equal divisions of the octave|##]] ~~

[[Category:Meantone]]

[[Category:Listen]]

[[Category:Historical]]

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 {{EDO intro|74}}
-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.
+== Theory ==
+edo is most notable as a [[meantone]] tuning, [[tempering out]] [[81/80]] in the [[5-limit]]; [[126/125]] and [[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 13-limit meantone, a.k.a. 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.
+edo tunes [[harmonic]] [[11/1|11]] only 1/30 of a cent sharp, and [[13/1|13]] 2.7 cents sharp, making it a distinctly interesting choice for higher-limit meantone.
+=== Odd harmonics ===
 {{Harmonics in equal|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.
 == Intervals ==
@@ Line 12: / Line 14: @@
 == Music ==
-* [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}}
+; [[Claudi Meneghin]]
+* ''Twinkle canon'' (2012) – [https://web.archive.org/web/20171009205013/http://soonlabel.com/xenharmonic/archives/573 detail] | [https://web.archive.org/web/20201127015514/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-74-edo.mp3 play]
-[[Category:74edo| ]] <!-- main article -->
-[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
 [[Category:Meantone]]
 [[Category:Listen]]
 [[Category:Historical]]