50edo: Difference between revisions

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~~'''50edo''' divides the [[octave]] into~~ 50 ~~equal parts of precisely 24 [[cent|cents]] each.~~

== Theory ==

In the [[5-limit]], 50edo tempers out [[81/80]], making it a [[meantone]] system, and in that capacity has historically has drawn some notice. In [http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf "Harmonics or the Philosophy of Musical Sounds"] (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts – 50edo, in one word. Later, W.S.B. Woolhouse noted it was fairly close to the [[Target_tunings|least squares]] tuning for 5-limit meantone. 50edo, however, is especially interesting from a higher limit point of view. While [[31edo]] extends meantone with a [[7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11/8]] and [[13/8]] are nearly pure. It is the highest edo which maps [[9/8]] and [[10/9]] to the same interval in a [[consistent]] manner, with two stacked fifths falling almost precisely in the middle of the two.

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 {{Infobox ET}}
-'''50edo''' divides the [[octave]] into 50 equal parts of precisely 24 [[cent|cents]] each.
+{{EDO intro|50}}
 == Theory ==
 In the [[5-limit]], 50edo tempers out [[81/80]], making it a [[meantone]] system, and in that capacity has historically has drawn some notice. In [http://lit.gfax.ch/Harmonics%202nd%20Edition%20%28Robert%20Smith%29.pdf "Harmonics or the Philosophy of Musical Sounds"] (1759) by Robert Smith, a musical temperament is described where the octave is divided into 50 equal parts &ndash; 50edo, in one word. Later, W.S.B. Woolhouse noted it was fairly close to the [[Target_tunings|least squares]] tuning for 5-limit meantone. 50edo, however, is especially interesting from a higher limit point of view. While [[31edo]] extends meantone with a [[7/4]] which is nearly pure, 50 has a flat 7/4 but both [[11/8]] and [[13/8]] are nearly pure. It is the highest edo which maps [[9/8]] and [[10/9]] to the same interval in a [[consistent]] manner, with two stacked fifths falling almost precisely in the middle of the two.