Variations are the art of transformation. A composer takes a melody and shows it “from every angle”: slow, fast, in minor, in a dance rhythm, in a polyphonic setting.
Outstanding examples: Bach's Goldberg Variations — 30 variations on a simple theme; Beethoven's Diabelli Variations — 33 masterpieces built on a banal waltz; Elgar's Enigma Variations — musical portraits of friends. In jazz, the variation principle underlies improvisation: the theme is stated, then the soloist creates their own version, developing the motifs and harmony.
Variation form is built on an unchanging foundation that the composer lights up anew each time. The oldest type historically is the ostinato variation (passacaglia, chaconne), in which the same ground theme repeats relentlessly in the bass. Classical variations keep the theme's harmonic frame while changing texture, rhythm, or mode, and the free variations of the 19th–20th centuries transform the original material almost beyond recognition.
