In music, variation is a formal technique where material is repeated in an altered form. The changes may involve harmony, melody, counterpoint, rhythm, timbre, orchestration or any combination of these.
Variation forms include ground bass, passacaglia, chaconne, and theme and variations. Ground bass, passacaglia and chaconne are typically based on brief ostinato motifs providing a repetitive harmonic basis and are also typically continuous evolving structures. 'Theme and variation' forms are however based specifically on melodic variation, in which the fundamental musical idea, or theme, is repeated in altered form or accompanied in a different manner. 'Theme and variation' structure generally begins with a theme (which is itself sometimes preceded by an introduction), typically between eight and thirty-two bars in length; each variation, particularly in music of the eighteenth century and earlier, will be of the same length and structure as the theme. This form may in part have derived from the practical inventiveness of musicians; "Court dances were long; the tunes which accompanied them were short. Their repetition became intolerably wearisome, and inevitably led the player to indulge in extempore variation and ornament"; however, the format of the dance required these variations to maintain the same duration and shape of the tune.
Variation forms can be written as 'free-standing' pieces for solo instruments or ensembles, or can constitute a movement of a larger piece. Most jazz music is structured on a basic pattern of theme and variations.
Examples include John Bull's Salvator Mundi, Bach's Canonic Variations on "Vom Himmel hoch da komm' ich her, Passacaglia and Fugue in C minor, Violin Chaconne, and (D minor solo violin suite), Corelli's La Folia Variations, Beethoven's Diabelli Variations, the Finale of Brahms's Fourth Symphony, Variations on a Theme of Haydn, Op. 56, Elgar's Enigma Variations, Franck's Variations Symphoniques, and Richard Strauss's Don Quixote. Both Schubert's Death and the Maiden Quartet and Trout Quintet take their titles from his songs used as variation movements.
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), Ernő Dohnányi (Variations on a Nursery Tune for piano and orchestra, Op. 25, 1914), 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), George Gershwin (Variations on "I Got Rhythm" for piano and orchestra, 1934), 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), William Walton (second movement of the Sonata for Violin and Piano, 1947–49, and Variations on a Theme by Hindemith, 1963), Leonard Bernstein (part 1 of his Symphony No. 2: The Age of Anxiety, 1949, is a Prologue and 14 variations), Luigi Nono (Variazioni canoniche sulla serie dell'op. 41 di A. Schönberg, 1950), Frederic Rzewski, Thirty-six Variations on "The People United Will Never Be Defeated!" (1975), Frans Geysen, De grote variatie for organ (1975), Cristóbal Halffter, Variaciones sobre la resonancia de un grito, for 11 instruments, tape, and live electronics (1976–77), Miklós Rózsa, Theme, Variations, and Finale (1933), John Cage, Variations I–VIII (1958–67), Hymns and Variations, for twelve amplified voices (1979), Ben Johnston, String Quartet No. 4 "Ascent" (Variations on "Amazing Grace", 1973), John McGuire, Forty-eight Variations, for two pianos (1976–80), Andrew Lloyd Webber, Variations for cello and rock band (1977), Steve Reich (Variations for Winds, Strings and Keyboards, 1979), and John Williams, Variations on "Happy Birthday" for orchestra (1995). An unusual option was taken in 1952 with the Variations on an Elizabethan Theme, a set of six variations on Sellenger's Round for string orchestra, in which each variation was written by a different composer, Lennox Berkeley, Benjamin Britten, Arthur Oldham, Humphrey Searle, Michael Tippett, and William Walton.
A significant sub-set of the above consists of variations on a theme by another composer.
Skilled musicians can often improvise variations on a theme. This was commonplace in the Baroque era, when the da capo aria, particularly when in slow tempo, required the singer to be able to improvise a variation during the return of the main material.
Musicians of the Classical era also could improvise variations; both Mozart (see Mozart's compositional method) and Beethoven made powerful impressions on their audiences when they improvised. Modern listeners can get a sense of what these improvised variations sounded like by listening to published works that evidently are written transcriptions of improvised performances, in particular Beethoven's Fantasia in G Minor, Op. 77, and Mozart's Variations on an Aria by Gluck, K. 455.
Improvisation of elaborate variations on a popular theme is one of the core genres of jazz.
Improvisation by means of spontaneous variations, ornaments, embellishments and/or alterations to a melody is the basis of most sub-Saharan African music (traditional and pop) extending from melody and harmony to form and rhythmic embellishments.
- Matrix (music)
- Developing variation
- Musical development
- Strophic form
- Composer tributes (classical music)
- Traditional sub-Saharan African harmony
- White (1976), p.63.
- Copland 2002, 115.
- Sisman 2001.
- Raymar 1931, 5.
- Hodeir and Pautrot 2006, 8.
- White 1976, 64–65.
- Apel, Willi (1962) Harvard dictionary of music, p. 784
- Gerald Drebes: ‘‘Schütz, Monteverdi und die „Vollkommenheit der Musik“ – „Es steh Gott auf“ aus den „Symphoniae sacrae“ II (1647)‘‘. In: ‘‘Schütz-Jahrbuch‘‘, Jg. 14, 1992, p. 25-55. online: 
- American Symphony Orchestra: Dialogues and Extensions
- See Donald M. McCorkle, p. 5 in the Norton Scores edition of the Variations (ISBN 0-393-09206-2).
- Irmer 1985, 4.
- Braunbehrens 1990.[page needed]
- Braunbehrens, Volkmar. 1990. Mozart in Vienna. New York: Grove Weidenfeld. ISBN 0-8021-1009-6.
- Copland, Aaron. 2002. What to Listen for in Music. Revised edition of an authorized reprint of a hardcover edition published by McGraw-Hill Book Company. New York: Signet Classic. ISBN 0-451-52867-0.
- Hodeir, André. 2006. The André Hodeir Jazz Reader, edited by Jean-Louis Pautrot. Ann Arbor: University of Michigan Press. ISBN 978-0-472-09883-5.
- Irmer, Otto von. 1986. Preface to Beethoven: Klavierstücke. Munich: G. Henle.
- Raymar, Aubyn. 1931. Preface to Mozart: Miscellaneous Pieces for Pianforte, edited by York Bowen. London: Associated Board of the Royal Schools of Music.
- Sisman, Elaine. 2001. "Variations". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
- White, John David. 1976. The Analysis of Music. Englewood Cliffs, N.J.: Prentice-Hall. ISBN 0-13-033233-X.
- Ehrhardt, Damien. 1998. La variation chez Robert Schumann. Forme et évolution (Diss. Sorbonne 1997). Lille: Presses Universitaires du Septentrion. ISBN 2-284-00573-X
- Nelson, Robert U. 1948. The Technique of Variation; A Study of the Instrumental Variation from Antonio de Cabezón to Max Reger. University of California Publications in Music 3. Berkeley: University of California Press.