Binary form is a musical form in two related sections, both of which are usually repeated. Binary is also a structure used to choreograph dance. In music this is usually performed as A-A-B-B
Binary form was popular in the Baroque period, often used to structure movements of keyboard sonatas. It was also used for short, one-movement works. Around the middle of the 18th century, the form largely fell from use as the principal design of entire movements as sonata form and organic development gained prominence. When it is found in later works, it usually takes the form of the theme in a set of variations, or the Minuet, Scherzo, or Trio sections of a Minuet and Trio or Scherzo and Trio movement in a sonata, symphony, etc. Many larger forms incorporate binary structures, and many more complicated forms (such as sonata forms) share certain characteristics with binary form.
Read more about Binary Form: Structure
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