A form in which successive statements of a theme are altered or presented in altered settings. In the 18th and 19th centuries the theme was usually stated first, followed by a number of variations - hence the expression ‘theme and variations’.
In the 16th century, dances were much used as frameworks for instrumental variations. The art reached a high stage of development in 16th-century Spain in works for vihuela and keyboard by Cabezón and others. The English virginalists late in the century, notably Bull, Farnaby, Gibbons and Byrd, also excelled and influenced continental composers, especially Sweelinck and Scheidt.
In 17th-century Italy, Frescobaldi, continuing to write traditional framework-variations such as the romanesca and folia, tended to place the framework notes on strong beats, changing the framework into a repeating scheme. Later (e.g. with Pasquini) variation of the melody became more important, a trend continued in the variations of G. B. Martini, Platti, Alberti and above all J. C. Bach. The insertion of a minor variation in a major set began to appear about this time.
In north and central Germany chorale variations were developed in the 17th century, first by Sweelinck and Scheidt and then by Weckmann and Tunder, who varied each verse of organ chorales, often with motifs related to the text. Free variations became characteristic of north German usage, leading to the chorale fantasia as perfected by Buxtehude. By contrast, in south Germany, with Pachelbel, strict forms were preferred and the final variation of a set is often a fugue. J. S. Bach used nearly all types: passacaglia and chaconne in works for organ and solo violin; grounds in several vocal movements, including the ‘Crucifixus’ of the Mass in B minor; chorale partitas for organ in the style of Böhm and Buxtehude; and canonic variations for organ on Vom Himmel hoch. The Goldberg Variations represent the highest artistic development of the bass-framework variations.
C. P. E. Bach and Haydn continued to cultivate the thoroughbass type, but from c1770 melodic variations predominate in their works and those of others. Haydn wrote few independent sets, but included variation movements in several chamber and orchestral works, often varying two themes alternately (e.g. the second movements of Symphonies nos.53 and 63, and the variations in F minor for piano). Sometimes he combined variations with rondo or ternary form. Mozart's independent sets of variations for piano, akin to his improvisations, were popular in his lifetime and well into the 19th century. He also used variation form in divertimentos, serenades and concertos, occasionally in string quartets and piano sonatas, but never in a symphony. Nearly all are of the melodic type with fixed harmony. The penultimate Adagio variation (usually highly embellished), a contrasting minor-key variation and a fast final variation (often in 6/8 metre) are features. In his earliest variations he echoed Baroque practice by repeating the theme at the end, but later he composed expanded final variations.
A climactic final variation, in effect a developmental coda, is a feature of most of Beethoven's sets. His early ones are mainly based on songs and popular operatic melodies. Between 1800 and 1812 he often used variations within a larger form (e.g. in the finale of the ‘Eroica’ Symphony and in the slow movements of the Fifth and Seventh Symphonies, the Piano Trio op.97 and the ‘Appassionata’ Sonata op.57); from 1818 variations became the spiritual centrepiece of several important works, including string quartets, the piano sonatas and the Ninth Symphony. The Diabelli Variations represent a microcosm of late Beethoven variation style and technique.
Variations of the early 19th century fall into two groups: ‘formal variations’ of the Viennese Classical type and ‘character variations’ determined by the new ideals and imagery of Romanticism. The first category is represented by Hummel, Cramer and Spohr, the second by Weber, Schumann and Mendelssohn. Schubert used both types; Chopin and Liszt brought high virtuosity to their character variations. The greatest master of variations in the late 19th century was Brahms. His Handel Variations for piano represent the metrically strict continuous variation type with final fugue; the bass is the sustaining element, as in the finales of the Fourth Symphony and the St Antony Variations. The Paganini Variations are examples of the Romantic virtuoso type as a series of ‘studies for piano’. Brahms also combined variations with other forms.
During the late 19th century and early 20th fantasia variations, incorporating free material, took precedence. Examples include Tchaikovsky's Variations on a Rococo Theme for cello and orchestra, the Symphonic Variations of Dvořák and Franck, and Strauss's Don Quixote. Elgar's Enigma Variations, while containing programmatic elements, are more conventional in form, but the most important representative of older traditions is Reger. He and Brahms influenced Schoenberg, Berg and Webern. Schoenberg acknowledged Brahmsian precedents in his Variations op.31 for orchestra. Webern's treatment of variations deserves special study, and subsequent composers, including Dallapiccola and Nono, have used the variational possibilities offered by serialism. Among non-serial composers, Hindemith and Britten have made conspicuous use of variation techniques.
