The theme chosen by the composer may be borrowed from various sources, including folk music, popular music, or something written by another composer. The basic theme is typically a short binary or ternary part form. A set of variations follows, based on some features of the thematic material. Analysis of a set of variations entails determining which musical elements of the theme are varied, and how they differ. Here is a list of some of the important elements that may be varied:
Sound: changing textures, figures, accompaniments, instruments, registers, and dynamics
Melody: varying intervals, motivic structures, and figures
Harmony: altering keys, modes, or progressions
Rhythm: changing tempos, meters, articulations, or patterns
Form: using different structural designs
In a fixed variation, the melodic and/or harmonic features are retained from the theme. Some variations have neither the melody nor harmony fixed, but the form may be fixed. Free variations have none of these elements retained, which is more common in contemporary music. A set of variations often ends with a Finale movement that brings the overall structure to a close. The Goldberg Variations by J. S. Bach are discussedAmong the Counterpoint lessons and materials.
Also known as continuous variations, this style is based on a repeated melodic, rhythmic pattern. This pattern often appears in the bass part, and the instrumental forms of these variations are called a ground, passacaglia, or chaconne. During the Baroque period, movements of instrumental pieces as well as vocal forms found in arias and choruses were commonly based on the ostinato principle. A well-known example is J. S. Bach’s Passacaglia in C Minor, which is comprised of continuous variations based on an 8-measure ground bass. It is included in the Materials below.
Johannes Brahms: Variations on a Theme of Haydn, Op. 56a.