Pitch Class Set Theory

There's a technique that occasionally pops up in discussions of post-war serial music that seems to exemplify the idea of "paper music" -- music written to be studied an analyzed but not actually listened to. Let's see if we can make any sense of it.

This post began with this work by Alan Theisen, where he figures out all the ways to combine four triads (major, minor, diminished or augmented) to exactly cover all twelve notes.

It ended up somewhere very different, but let's start there.

In my own practice I've been making less use of scale and arpeggio language lately and looking at more neutral, atonal terminology instead. There's a good chance this will show up in some upcoming posts so here's a primer.

Continuing my look at 3- and 4-note sets that aren't common in diatonic music, we arrive at 1-b2-3, the "Phyrgian major" or "Harmonic minor" triad. first here's the usual full-fingerboard diagrams: chords are formed by playing one note of each colour and dark blue is the root. The top one is 1-b2-3 and the bottom is 1-#5-7, its inversion; these are Forte number 3-3:

More loose, geometric, pattern-based, theory-light 12-tone material. This time we have several ways to break up the total chromatic into two equal-sized parts.

Here's a practical idea I've been experimenting with lately for chromatic improvisation. The idea is to dispense with theory and let visual patterns lead instead.

I've been getting some good results lately from adopting a looser approach to atonal material, working with ideas that cover the 12 notes relatively quickly and don't suggest a tonal centre without too much rigor. Examples of this approach can be found here, hereand here; this is another one.

Under certain assumptions (which I'll talk about in a moment) there are only 12 three-note chords. I'm hoping to dig into some of the more unusual ones in later posts so here's a quick survey of them.

We've looked at basic definitions and set out a numbering system for pitch classes that does what we want. Now it's time to see how powerful these ideas can be from an analytical perspective, and to develop some more ideas and techniques along the way.

This post -- the second in our series on pitch class set theory -- looks at three different ways to number pitch classes. These numbering systems are alarmingly similar, so they can get confusing, but an understanding of them is essential for what follows, so hold onto your hat.