History of Variations
Although the first isolated example emerged in the 14th century, works in theme-and-variation form first emerge in the history of classical music in the early sixteenth century. Possibly the earliest published example is the diferencias for vihuela by Luis de Narváez (1538). A favorite form of variations in Renaissance music was divisions, a type in which the basic rhythmic beat is successively divided into smaller and smaller values. The basic principle of beginning with simple variations and moving on to more elaborate ones has always been present in the history of the variation form, since it provides a way of giving an overall shape to a variation set, rather letting it just form an arbitrary sequence.
Keyboard works in variation form were written by a number of 16th century English composers, including William Byrd, Hugh Aston and Giles Farnaby. Outstanding examples of early baroque variations are the "ciaccone" of Claudio Monteverdi and Heinrich Schütz. Two famous variation sets from the Baroque era, both originally written for harpsichord, are George Frideric Handel's The Harmonious Blacksmith set, and Johann Sebastian Bach's Goldberg Variations, BWV 988.
In the Classical era, Wolfgang Amadeus Mozart wrote a great number of variations, such as the first movement of his Piano Sonata in A, K. 331, or the finale of his Clarinet Quintet. Joseph Haydn specialized in sets of double variations, in which two related themes, usually minor and major, are presented and then varied in alternation; outstanding examples are the slow movement of his Symphony No. 103, the Drumroll, and the Variations in F minor for piano, H XVII:6.
Ludwig van Beethoven wrote many variation sets in his career. Some were independent sets, for instance the Diabelli Variations, Op. 120. Others form single movements or parts of movements in larger works, such as first movement of the Piano Sonata No. 12, Op. 26, or the variations in the final movement of the Third Symphony (Eroica). Variation sets also occur in several of his late works, such as the slow movement of his String Quartet No. 12, Op. 127, the second movement of his final Piano Sonata No. 32, Op. 111, and the slow movement of the Ninth Symphony.
Franz Schubert wrote five variation sets using his own lieder as themes. Amongst them is the slow movement of his string quartet Death and the Maiden D. 810, an intense set of variations on his somber lied (D. 531) of the same title. Schubert's Piano Quintet in A (The Trout, D. 667) likewise includes variations on his song The Trout D. 550. The second movement of the Fantasie in C major comprises a set of variations on Der Wanderer; indeed the work as a whole takes its popular name from the lied.
In the Romantic era, the variation form was developed further. In 1824, Carl Czerny premiered his Variations for piano and orchestra on the Austrian National Hymn Gott erhalte Franz der Kaiser, Op. 73. Frédéric Chopin wrote four sets for solo piano, and also the Variations on "La ci darem la mano" from Mozart's opera Don Giovanni, Op. 2, for piano and orchestra (1827). A further example of the form is Felix Mendelssohn's Variations sérieuses.
Johannes Brahms wrote a number of sets of variations; some of them rely on themes by older composers, for example the Variations and Fugue on a Theme by Handel (1861; piano), and the Variations on a Theme by Haydn (1873; orchestra). The latter work is believed to be the first set of variations for orchestra alone that was a work in its own right, rather than part of a symphony, suite or other larger work. Karl Goldmark's Rustic Wedding Symphony (1875) starts out with a set of variations as its first movement. Antonín Dvořák's Symphonic Variations (1877) and Edward Elgar's Enigma Variations (1899) are other well-known examples. Anton Arensky's Variations on a Theme by Tchaikovsky (1894) is among his most popular compositions.
Variation sets have also been composed by notable twentieth-century composers, including Sergei Rachmaninoff (Rhapsody on a Theme of Paganini for piano and orchestra, and his variations for solo piano on themes by Chopin and Corelli), Charles Ives (Variations on America, 1891), Arnold Schoenberg (Variations for Orchestra, Op. 31, and Theme and Variations, Opp. 43a and 43b), Igor Stravinsky (Pulcinella: XV Gavotta con due variazioni, 1920; Octet: II Tema con variazioni, 1922; Ebony Concerto: III, 1945; and Variations: Aldous Huxley in memoriam, 1963–64), Anton Webern (Variations, Op. 27 for piano, and Variations, Op. 30 for orchestra), Alban Berg (Act 1, Scene 4 and the beginning of Act 3 scene 1 of Wozzeck), Paul Hindemith (Symphonic Metamorphosis of Themes by Carl Maria von Weber, 1943), Olivier Messiaen (Thème et variations for violin and piano, 1932), Benjamin Britten (including the Variations on a Theme of Frank Bridge, 1937, and The Young Person's Guide to the Orchestra (Variations and Fugue on a Theme by Purcell), 1946), Reinhold Glière (Harp Concerto in E-flat: II, 1938), and Frederic Rzewski, Thirty-six Variations on "The People United Will Never Be Defeated!", 1975.
A significant sub-set of the above consists of variations on a theme by another composer.
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