There are many forms in music and all music has structure. Even the absence of order has its method. If you look at a theoretically free “through composed” piece, one which never references a past melody, motif, key, time signature, rhythm, tone, etc. then it is composed in perfect control. Like a single note, the order of chaos has no internal reference; it is exactly what it is.
Form is structure. You will find at least two sonatas, two sets of variations, a few binary forms, perhaps a couple of ABA forms. Though a waltz is not a form, you will find at least two waltzes. I say at least because one might view Schubert’s third variation programmed here as a waltz. If you consider it a waltz, also admit that it is a waltz in search of identity. The left hand waltzes. The right hand dominates in duple time but finds time to waltz from time to time.
The basic single movement sonata-allegro form is an expanded ABA form. The letters refer to sections of a piece with common musical material. The exposition (first A) has two or more themes in two related keys. The development section (B) improvises on some of this musical material and then returns to a modification of the A section where at least two of the original themes are stated in the original (tonic) key.
Beethoven, the master of form, uses this structure in both the first and last movements of his “Appassionata”. The middle movement is a theme and four variations. The theme and its variations are in binary form, that is two sections, each with repeats.
Though Scarlatti wrote over five hundred sonatas, nearly all are in binary form. This form simply requires that there be two sections of approximately equal duration or weight.
The binary forms found in the Schubert variations programmed here, in the K159 Scarlatti sonata, and those found in the middle movement of the Appassionata, modulate to a second theme in a different key. Beethoven, true to form, modulates to the dominant, the most common related key. However, composers sometimes modulate to a non-related key through a chord with common notes. This “unusual” key modulation was a signature aspect of the romantic period. Though Schubert was not born into the “romantic period”, this attribute reflects his musical inclination.
It is important to note the increase in duration between the Scarlatti and Beethoven sonatas. Including all movements, the Beethoven is ten times longer! The first movement is five times longer. And yet the required elements are equal. Expanded form was a signature of Beethoven and the romantics.