Tuesday, November 29, 2005

Pitch Class Sets Part the First

Advanced Music Theory is often compared to mathematics but the resemblance is superficial at best. Both involve systems of discrete units, true, but at that level of abstraction, mathematics is similar to far more things than music theory (like social sciences or even linguistics). And for those not in the know, I think one specific branch of modern music theory is responsible for giving lay people the impression that music theory requires math: pitch class set theory.

Most of the music that we listen to, whether classical or popular, is scalar, meaning that pitches and their functions are derived with an implicit scalar structure in the background. By far the most popular in recent memory (say from 1700 onwards for the Western World) are the major and minor scales. For people who remember the sound of music, "Homer: Doh! Marge: A deer! Lisa: A female deer!" teaches you how to sing the major scale. The scale gives the tones one sings a field with guideposts. Some tones are more important and stable, other are more tense and create interest, while others serve as signs to lead you from one tone to the next. Without a scalar structure that differentiates pitches, one could imagine a flat musical landscape which generates little or no possiblities at all for interesting music.

Pitch class set theory came about when the scale was in essence obliterated by Arnold Schoenberg and his 12-tone system. Schoenberg did flatten the musical landscape by putting all 12 chromatic tones in the Western equal-temperament system on equal footing. His music harmonic, not scalar, and focuses on pitch sonorities rather than pitch stability. Calling something C and something else C# made no sense in this context because C# was no longer an embellishment of C by rising a half step higher. C# was the same as Db, which is the same as B double sharp, and so on and so forth. So what's an analyst to do? Assign the pitches numbers!

Part II in the next post...

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