Creating Musical Variation

Here is a clip from a very interesting perspectives piece on approaches to creating musical variation, by Diana S. Dabby in the April 4 issue of Science:

In the 21 letters that Mozart wrote to his friend Michael Puchberg between 1788 and 1791, there exist at least 24 variants of the supplication "Brother, can you spare a dime?" Mozart ornaments his language to cajole, flatter, and play on Puchberg's sympathies. He varies his theme of "cash needed now" in much the same way an 18thcentury composer might dress a melody in new attire by weaving additional notes around its thematic tones in order to create a variation. Such ornamentation could enliven and elaborate one or more musical entities, as can be heard in the Haydn F Minor Variations (1793) (mp3 file of theme, mp3 file of variation). The Haydn represents one of the most popular forms of the 18th and 19th centuries--variations on original or borrowed themes. Yet myriad variation techniques existed besides ornamentation, including permutation and combination, as advocated by a number of 18th-century treatises. More recently, fields such as chaos theory have allowed composers to create new kinds of variations, some of which are reminiscent of earlier combinatorial techniques.

In a broad context, variation refers to the technique of altering musical material to create something related, yet new. Recognizing its importance to composers, the 20th-century composer and teacher Arnold Schoenberg defined variation as "repetition in which some features are changed and the rest preserved". He wrote numerous examples showing how a group of four notes, each having the same duration, can be varied by making rhythmic alterations, adding neighboring notes, changing the order of the notes, and so on (see the figure, panels A to C). Changing the order of the notes reflects the 18th-century practice of ars combinatoria. Joseph Riepel advocated a similar approach (see the figure, panel D).


Figure - Idea and variations. Variation techniques illustrated by Schoenberg, Riepel, and a chaotic mapping example. Schoenberg offers numerous ways to vary a given four-note group, shown in the first measure of each line. (A) Rhythmic changes. (B) Addition of neighboring notes. (C) Changing the original order. (D) One of many examples given by Riepel of ars permutatoria, a branch of ars combinatoria, where six permutations of the notes A B C are given (15). Note that Riepel writes above the staff the German musical spelling of the notes so that "B" translates to B-flat. (E) The first measure of a Bach prelude (pitches only) followed by the first measure of a variation generated by the chaotic mapping.