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1A Musical Form found mostly in ClassicalMusic in which there is a theme, for which embellished, simplified, complexified, or otherwise altered versions are composed. Generally speaking, it is customary to perform the theme first, followed by the variations, in an order specified by the composer.
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3Related Classical forms include the Ground Bass form, Passacaglia form, Chaconne form[[note]]where varying melodies are played on top of a repeating bass/harmonic line. You're unlikely to get a consistent answer if you ask a music historian what the difference between the three are, so you shouldn't bother.[[/note]], the Fugue[[note]]a contrapuntal piece where a single theme called the "subject" is introduced in a single voice, and then is repeated and varied in the other voices throughout the piece[[/note]], and Isorhythm[[note]]where a repeating rhythmic pattern is used, sometimes with a repeating melodic pattern often of a different length[[/note]], which all predate the Classical-era "Theme and Variations" form (though the idea of having a central "theme" that a piece is built around predates all of them).
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5Sometimes, an entire soundtrack is built off of this concept: see ThemeAndVariationsSoundtrack.
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7Very common in ClassicalMusic.
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9!!Examples:
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11[[AC:Music]]
12* Music/JohannSebastianBach: Goldberg Variations. Since Bach was symmetry-obsessed, the original aria is repeated after the last variation.
13* Music/LudwigVanBeethoven: [[https://www.youtube.com/watch?v=BBXX9xP7xXs Six Variations]], 32 Variations in C minor, ''Eroica Variations'' (so called because the theme had also been used in his ''Eroica'' symphony), and most famously the ''Diabelli Variations''.
14* Benjamin Britten: ''The Young Person's Guide To The Orchestra'' (subtitled "Variations and Fugue on a theme by Purcell")
15* Music/FryderykChopin: Variations on "La ci darem la mano"
16* Music/EdwardElgar: ''Enigma Variations'' on an original theme; Elgar also claimed that the theme is linked to another theme, but it is never played and Elgar [[RiddleForTheAges refused to say what it is]].
17* Music/JohannesBrahms: ''[[https://www.youtube.com/watch?v=BRu7CMg6wSs Variations on a Theme by]] Music/JosephHaydn''
18* Music/GeorgeFredericHandel: ''The Harmonious Blacksmith'' (video [[https://www.youtube.com/watch?v=ABLb3ls2m_g here]])
19* Music/WolfgangAmadeusMozart: Variations on "Ah! Vous dirai-je, Maman" (better known to English-speakers as the tune for ''Twinkle, twinkle little star''.)
20* Paganini: ''Caprice XXIV'', one of the most famous virtuosic violin pieces, which Music/SergeiRachmaninoff famously turned into a [[https://www.youtube.com/watch?v=HvKTPDg0IW0 Rhapsody for symphony orchestra and piano]], and inspired variations by several other composers including Brahms.

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