J.S. Bach wrote his Chorale Variations on "Vom Himmel hoch da komm' ich her" for two-manual organ and pedals in 1746 and 1747. Bach's variations were all in the key of C major; Stravinsky retains this key for the opening chorale and the first and fifth variations but changes the key of the three central variations to G major, D flat major, and G major, respectively.

The individual variations are, of course, pervasively contrapuntal; Stravinsky also added extra lines of counterpoint to the original variations. Canon plays an important role in this work as well: Stravinsky's canons begin at the interval of a fifth (both above and below the original subject) and at the interval of a seventh. In the third variation's canon, as musicologist Eric White notes, small parts of each phrase are distributed throughout the brass, weaving a complex, dense polyphonic texture. Stravinsky composed the Chorale Variations as a companion piece to the Canticum sacrum (1955), and the two works are scored for nearly identical complements of instruments. The Chorale Variations were first performed in St. Mark's Cathedral in Venice in September 1956.

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