Haydn may have been inspired by an earlier example of Carl Philipp Emanuel Bach, the sixth of that composer's Sonatas with Varied Reprises, (W. 50/6, H. 140), in C minor (1760).
As Haydn's career proceeded, he moved toward a very particular type of double variations, having the following additional specific characteristics.
Where different authorities provide different dates, both are given; NG = the New Grove (used by Sisman), MH = Maurice Hinson's edition of the piano sonatas.
Thus flexibly construed, the double variation emerges as the musical form for some of the most famous of Beethoven's works.
As Sisman notes, Beethoven placed his double variations in the same genres as Haydn: the piano trio, the string quartet, and the symphony.
The second movement of Anton Bruckner's Seventh Symphony (1883/1885) is described by A. Peter Brown[5] as a set of double variations.
An example of this usage is found in Cedric T. Davie's discussion [7] of the last movement of Beethoven's Piano Sonata Opus 109, in which some but not all of the variations are double in the intended sense.
The full formula for this movement (adapting Davie's verbal description) is: The two kinds of "double variation" are not mutually exclusive.