There are two very different kind of pieces that are called “variations,” sectional variations and continuous variations. Here is a comparison of them:
In continuous variations, changes in the repeated bass line or chord progression are often insignificant if any occur at all. It is not the bass line or chord progression that captures our attention, but the changing relationships of the upper parts with the bass line and chord progression. The upper parts are often out of phase with the bass/chord progression. They create continuity by pressing forward when the repeated pattern ends. They end, perhaps creating a half cadence, before the repeated pattern is done. Thus, it is the play between parts that constantly casts the recurring bass line or chord progression in a new light.
In sectional variations, by contrast, there is no play with the boundaries between statements of the theme. There is clear separation between each variation of the theme and the next. The theme, which is often binary in form, closes with perfect authentic cadence in the home key. The theme is more substantial then in continuous variations and involves a melody as well as a bass line and chord progression. Here are some common kinds of variations that appear in sets of section variations.
Sonata form is a large-scale rounded and balanced binary form that displays the sonata principle:
Thematic material presented in two main keys–the home key and then in a contrasting key (V in major, III or v in minor)–all returns in the home key. The tonal “conflict” near the beginning is decided in favor of the home key in the end.
The First Theme Group (FTG) and Second Theme Group (STG) may include several themes or just one theme. They may consist of several phrases or just one. Theme groups are set apart from one another by their different keys in the exposition.
The closing theme is a new theme that belongs to the STG (it is in the new key). It starts after a PAC (in the new key). I would say “after the first PAC in the new key” if it weren’t for movements in which a theme and its PAC are reiterated. If the material following the PAC that ends the body of the STG does not qualify as a new theme, then we call that material a codetta, not a closing theme.
The transition gets you to the new key. It may begin in parallel with the FTG (a dependent transition), but it may also begin with new material (an independent transition). It typically ends with a HC in the key of the STG, although in major key movements, it may end with a HC in the first key if the STG is in the dominant key (V becomes I).
The retransition, the final part of the development, extends the dominant chord in preparation for the recapitulation and the return of the tonic after instability (sequencing and/or modulation) in the body of the development. Some movements do not have a retransition.
There are two main kinds of rondo:
5-part rondo: A1 B A2 C A3
7-part rondo: A1 B1 A2 C A3 B2 (or D) A4