Pitch Class Sets Part the Third

First Read: Pitch Class Sets Part the Second and Pitch Class Sets Part the First

So no we've got all these funky chords and we need to name them. Why do we want to name them? For the same reason we name traditional chords: because the sonorities all sound similar. A C major chord sounds like a C major anyway you play it as long as it has even the meaning of C-E-G behind it. With atonal chords, the aural similarities may not be readily apparent to most but the idea is that with a trained ear, you can hear it. Pitch class set theory allows you to talk about it with your music theory nerds. I mean friends.

So let's say you've got this crazy chord that goes C-D#-E-F#. In numbers, that would be 0-3-4-6. Without going into the actual details, let's call that chord "4-5". The first number denotes the cardinality of the chord you're naming (in essence, the number of distinct pitches it contains) and the second number denotes a unique identifier. Some pioneering theorists named Allen Forte looked at every possible chord combination and gave them names back in the day so now us nerds talk about how 3-7 is related to 6-18 and how it's cool that 4-Z15 and 4-Z29 are m5 or m7 related and such. Again, without getting into the craziness, pitch class set theory is, preliminarily, a way to abstractly equate atonal chords.

Once you get the basics of identifying chords down, then you can start analyzing relationship between them. We're trained to hear in a diatonic doe-ray-me-far-sew-la-tea-doe kind of way so hearing progression from C Major to G Major is easy for us. Hearing the change between a a4-Z15 and 4-Z29 chord is pretty much impossible for most of us. Pitch class set theory gives us an edifice, albeit mostly an academic rather than aural one, with which to grapple with atonal music (of the Schoenbergian variety).

That's enough pitch class set theory for now. Perhaps I'll come back later and explain some of the mechanics of it in detail. I know you're just dying to hear that!