49edo: Difference between revisions

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'''49-EDO''', or '''49 equal temperament''' divides the octave into 49 equal parts of 24.490 [[~~Cent|cents~~]] each.

'''49-EDO''', or '''49 equal temperament''' divides the octave into 49 equal parts of 24.490 [[cent]]s each.

== Theory ==

49edo is very much on the sharp side of things, with sharp tunings of 3 (it is the first square equal division with a "real" 3 of ~~size~~ coprime to its cardinality), 5, 7, and 11. It is the [[~~Optimal_patent_val|~~optimal patent val]] for [[~~Superpyth|~~superpyth ~~temperament~~]] in the 7 and 11 limits, archytas ([[7-limit]]) and [[~~Archytas_clan~~|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.

== Intervals ==

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[[Category:49edo]]

[[Category:Superpyth]]

[[Category:Archytas]]

[[Category:Ares]]

@@ Line 1: / Line 1: @@
-'''49-EDO''', or '''49 equal temperament''' divides the octave into 49 equal parts of 24.490 [[Cent|cents]] each.
+'''49-EDO''', or '''49 equal temperament''' divides the octave into 49 equal parts of 24.490 [[cent]]s each.
 == Theory ==
-edo is very much on the sharp side of things, with sharp tunings of 3 (it is the first square equal division with a "real" 3 of size coprime to its cardinality), 5, 7, and 11. It is the [[Optimal_patent_val|optimal patent val]] for [[Superpyth|superpyth temperament]] in the 7 and 11 limits, archytas ([[7-limit]]) and [[Archytas_clan|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.
+edo 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.
 == Intervals ==
@@ Line 320: / Line 320: @@
 [[Category:49edo]]
 [[Category:Superpyth]]
+[[Category:Archytas]]
+[[Category:Ares]]