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There are actually two major kinds of binary form: that used during the Baroque Period and the more advanced form used in the Classical Period. The discussion here will use a few harmonic terms which are covered in Lesson 8 of our music theory section.
The Baroque binary form, also called simple binary, is divided
into two sections, which we'll call "a" and "b". The "a" section
begins in I (the tonic) and usually moves to V (dominant) in major or
III (mediant) in minor. This sets up the "b" section, which begins
where the "a" section left off and brings the music back to the tonic.
The "a" and "b" sections usually contain different musical material and
themes.
Both sections are also repeated, so the piece is something like:
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The Classical binary form, called rounded binary, simply adds a
little bit to the simple binary form. Rounding is when, at the
end of the second section, a strong thematic reference is made to the
beginning of the movement. Otherwise, the harmonic shape is just like
that of the simple binary. This would look like:
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Binary form was popular throughout the Baroque and into the early
Classical Periods. It then developed into the
sonata form, which basically dominated
musical form for almost the next two centuries.
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