A chaotic mapping provides a technique for generating musical variations of an original work. Thistechnique, based on the sensitivity of chaotic trajectories to initial conditions, produces changes inthe pitch sequence of a piece. A sequence of musical pitches $pi%, i.e., any piece ranging from Bach~or earlier! to contemporary music, is paired with the x-components $xi% of a Lorenz chaotictrajectory. Each pi is marked on the x axis at the point designated by its xi . In this way, the x axisbecomes a pitch axis configured according to the notes of the original composition. Then, a secondchaotic trajectory, whose initial condition differs from the first, is launched. Its x-componentstrigger pitches on the pitch axis ~via the mapping! that vary in sequence from the original work, thuscreating a variation. There are virtually an unlimited number of variations possible, many appealingto expert and nonexpert alike.