Structure
The piece contains four movements, a structure often used by Beethoven, and imitated by contemporaries such as Schubert, in contrast to the more usual three or two movements of Mozart and Haydn sonatas.
In addition to the thematic connections within the movements and the use of traditional Classical formal structures, Charles Rosen has described how much of the piece is organized around the motif of a descending third (major or minor). This descending third is quite ubiquitous throughout the work, but most clearly recognizable in the following sections: the opening fanfare of the Allegro; in the Scherzo's mocking imitation of the aforementioned fanfare, as well as in its trio theme; in bar two of the Adagio; and in the Fugue in both its introductory bass octave-patterns and in the main subject, as the seven-note runs which end up on notes descended by thirds. It is perhaps the first major piano work (if not work of any instrumentation) to so thoroughly incorporate a Baroque contrapuntal style (the fugue) within an originally Classical structure (the sonata form).
Read more about this topic: Piano Sonata No. 29 (Beethoven)
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