Double variation

The double variation (also known as alternating variations) is a musical form used in classical music. It is a type of theme and variations that employs two themes. In a double variation set, a first theme (to be called A here) is followed by a second theme (B), followed by a variation on A, then a variation on B, and so on with alternating A and B variations. Often there is a coda at the end.

The double variation is strongly associated with the composer Joseph Haydn, who wrote many such movements during his career.

The double variation first appears Haydn's work of the 1770s. 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). Elaine Sisman, an authority on variations, notes "This set of sonatas was advertised in Vienna several times in the period in which Haydn wrote his first [double] variations."

While Haydn's double variations show considerable diversity, there are some general patterns.

As Haydn's career proceeded, he moved toward a very particular type of double variations, having the following additional specific characteristics.

According to Sisman, Haydn wrote 21 double variation movements. Sisman's list is restated below in chronological order. 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. For the keys of the A and B sections, lower case designates minor; upper case major. The structural synopses are taken from Sisman with minor corrections; in Sisman's notation an asterisk means "altered".

Although the double variation is associated strongly with Haydn, Elaine Sisman has pointed out that, provided we adopt a somewhat looser definition of the form, Ludwig van Beethoven also emerges as a major composer of double variations. With the partial exception of the Piano Trio in E flat major, Op. 70 No. 2, which Sisman sees as an homage to Haydn, Beethoven's double variations have a rather different character. For instance, sometimes only the A theme is strongly varied, with B remaining relatively constant. Beethoven also likes to interrupt or truncate one or both themes, producing a less regular structure than Haydn's, seen in the often-complex structural formulae given below.

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