Thursday, July 28, 2011

Polymorphism: theme and variations

In object-oriented programming, polymorphism is the ability to create a variable, a function, or an object that has more than one form.

This, along with encapsulation and inheritance, gives object-oriented languages their power.

In music, polymorphism happens across the centuries: in theme and variation pieces, tone rows and even the abstracted instantiations of contrapuntal rules across modes.

A few favs:

33 Variations on a waltz by Anton Diabelli, Op. 120

Theme and Variations. David Oistrakh (violin), Frida Bauer (piano)

Tema con Variazioni from his Suite No. 3 for Orchestra.

From the Met Opera:

Alban Berg's opera Wozzeck uses a Passacaglia, an old Baroque form of Theme and Variations where a bass ostinato (repeated figure, sometimes known as a “ground bass”) is played again and again with variations, sometimes so complex that the original “ground bass” figure can no longer be obviously discerned.

Berg wrote 21 variations on this passacaglia theme (Ex. #1a). (Note, that each of the 12 tones of the chromatic scale is used once before any other tone returns again. This “tone row” consists of the notes E flat, B, G, C sharp, C, F sharp, E, B flat, A, F, A flat and D. This is the basic concept of “12 tone” music, which Berg used exclusively in his only other opera Lulu.)

The only time this theme can be obviously heard is the very first time, played by a solo cello, first repetitively and toward the end of its first statement in a dotted rhythm (Ex. #1b).

Want to learn more? Check out The Met Opera’s teaching materials on Wozzeck.