49edo: Difference between revisions

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== Theory ==

49edo is very much on the sharp side of things, with sharp tunings of [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]]. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7- and 11-limit, [[Archytas family #Archytas|archytas]] ([[7-limit]]), and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments, being almost exactly equal to {{frac|3|10}}-comma superpyth. It [[tempering out|tempers out]] [[64/63]], [[245/243]], and [[3125/3087]] in the 7-limit, and [[100/99]], [[540/539]], and [[1375/1372]] in the 11-limit. In the 13-limit, its [[patent val]] {{val| 49 78 114 138 170 181 }}, has a ~~very~~ flat harmonic [[13/1|13]], which leads to inconsistent mappings; but using the 49f val {{val| 49 78 114 138 170 182 }} improves 13-limit consistency, and in this val it tempers out [[364/363]] and [[847/845]].

49edo is very much on the sharp side of things, with sharp tunings of [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]]. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7- and 11-limit, [[Archytas family #Archytas|archytas]] ([[7-limit]]), and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments, being almost exactly equal to {{frac|3|10}}-comma superpyth. It [[tempering out|tempers out]] [[64/63]], [[245/243]], and [[3125/3087]] in the 7-limit, and [[100/99]], [[540/539]], and [[1375/1372]] in the 11-limit. In the 13-limit, its [[patent val]] {{val| 49 78 114 138 170 181 }}, has a rather flat (by relative error) harmonic [[13/1|13]], which leads to inconsistent mappings; but using the 49f val {{val| 49 78 114 138 170 182 }} improves 13-limit consistency, and in this val it tempers out [[364/363]] and [[847/845]].

=== Harmonics ===

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 == Theory ==
-edo is very much on the sharp side of things, with sharp tunings of [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]]. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7- and 11-limit, [[Archytas family #Archytas|archytas]] ([[7-limit]]), and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments, being almost exactly equal to {{frac|3|10}}-comma superpyth. It [[tempering out|tempers out]] [[64/63]], [[245/243]], and [[3125/3087]] in the 7-limit, and [[100/99]], [[540/539]], and [[1375/1372]] in the 11-limit. In the 13-limit, its [[patent val]] {{val| 49 78 114 138 170 181 }}, has a very flat harmonic [[13/1|13]], which leads to inconsistent mappings; but using the 49f val {{val| 49 78 114 138 170 182 }} improves 13-limit consistency, and in this val it tempers out [[364/363]] and [[847/845]].
+edo is very much on the sharp side of things, with sharp tunings of [[harmonic]]s [[3/1|3]], [[5/1|5]], [[7/1|7]], and [[11/1|11]]. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7- and 11-limit, [[Archytas family #Archytas|archytas]] ([[7-limit]]), and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments, being almost exactly equal to {{frac|3|10}}-comma superpyth. It [[tempering out|tempers out]] [[64/63]], [[245/243]], and [[3125/3087]] in the 7-limit, and [[100/99]], [[540/539]], and [[1375/1372]] in the 11-limit. In the 13-limit, its [[patent val]] {{val| 49 78 114 138 170 181 }}, has a rather flat (by relative error) harmonic [[13/1|13]], which leads to inconsistent mappings; but using the 49f val {{val| 49 78 114 138 170 182 }} improves 13-limit consistency, and in this val it tempers out [[364/363]] and [[847/845]].
 === Harmonics ===