After hearing a recording and examining the score of William Walton's Variations on a Theme by Paul Hindemith in the summer of 1963, the work's namesake wrote a letter of gratitude to its composer. "We had a half hour of sheer enjoyment," wrote Hindemith. "I am particularly fond of the honest solidity of workmanship in this score—something that seems almost completely lost nowadays." Hindemith's untimely death in 1963 prevented him from fulfilling the letter's promise to program the piece in the following season; thus the Variations stand as a particularly poignant memorial to the friendship and influence shared by the two composers.

The work was composed on commission from the Royal Philharmonic Society to celebrate the 150th anniversary of the society's first concert, and the premiere performance, in fact, took place on the very day of the anniversary (March 8, 1963). In composing the piece, Walton took a slightly different approach to variation writing than is usually encountered. Rather than expounding on a short and memorable theme, or extrapolating a particular musical kernel, Walton begins by intoning an entire passage from the original source. The statement of the theme, taken from the second movement of Hindemith's Cello Concerto from 1940, deviates from the original in the slightest of degrees. Harmonic support remains intact, and the melody stands unaltered, aside from its transference from the solo cello to other instruments. The direct invocation of Hindemith with which the piece begins thus lasts nearly two full minutes. Walton uses another interesting device to organize the theme and its subsequent variations. Exploiting the fact that the first 12 notes of the original theme nearly exhaust the 12 tones of the chromatic scale (except for the absence of G natural and the reappearance of A), Walton uses each consecutive note in the theme as the tonal basis of the theme, its subsequent nine variations, and the finale. (Walton excludes one of the theme's A's from the scheme, which only involves a total of 11 sections anyhow.)

The theme, for the most part, assumes a lyrical contour set within a flowing 9/8 time. This smooth surface is momentarily upset, however, by a terse interjection of staccato sequences. This gesture, though quickly subsumed within the statement of the theme by less tense material, reappears in one form or another in each of the subsequent variations. These take on a variety of characters. The first, a vivace scherzo, is a metrically convoluted reworking of several melodic and accompanimental fragments from the theme, while the second takes a more stable but equally lively tack. The Larghetto of variation 3 is foiled by No. 4's rhythmic drive; similarly, variations 5 and 6 contrast an Andante con moto with a 5/4 scherzo, respectively. Variation 7 invokes Hindemith's Mathis der Maler (the score even places the passage within quotation marks!) within a Lento molto context, followed by the Vivacissimo variation 8, the brief but Maestoso variation 9, and a lively fugato finale.

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