49edo: Difference between revisions
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== Theory == | == Theory == | ||
49edo is very much on the sharp side of things, with sharp tunings of harmonics 3 (it is the first square equal division with a "real" 3 of step coprime to its cardinality), 5, 7, and 11. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7 and 11 limits, [[Archytas family #Archytas|archytas]] ([[7-limit]]) and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments and almost identical to the e-based analog of [[Lucy tuning]]. It [[tempering out|tempers out]] [[64/63]], [[245/243]] and [[3125/3087]] in the 7-limit, and [[100/99]] and [[1375/1372]] in the 11-limit. | 49edo is very much on the sharp side of things, with sharp tunings of harmonics 3 (it is the first square equal division with a "real" 3 of step coprime to its cardinality), 5, 7, and 11. It is the [[optimal patent val]] for [[superpyth]] temperament in the 7 and 11 limits, [[Archytas family #Archytas|archytas]] ([[7-limit]]) and [[Archytas family #Ares|ares]] ([[11-limit]]) planar temperaments and almost identical to the e-based analog of [[Lucy tuning]]. It [[tempering out|tempers out]] [[64/63]], [[245/243]] and [[3125/3087]] in the 7-limit, and [[100/99]] and [[1375/1372]] in the 11-limit. | ||
{{primes in edo|49}} | |||
== Intervals == | == Intervals == | ||
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== Just approximation == | == Just approximation == | ||
=== Temperament measures === | === Temperament measures === | ||
The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 49et. | The following table shows [[TE temperament measures]] (RMS normalized by the rank) of 49et. | ||