Arnold Schoenberg

Today I want to expand our horizons beyond the more traditional aspects of music theory and talk about a more modern convention known as “12 Tone Music.” This fascinating yet little-known area of contemporary classical music composition has also had its share of controversy, which I’ll discuss a bit for the sake of historical context.

But first, we need to give you a little background on what 12-tone music is, the rules (yes, there are rules) in creating music according to 12-tone principles, and at the end I’ll give you an idea of how you can apply this concept to the guitar.

Shall we?

The Basics of 12-Tone Music

Luckily there aren’t many, but we’ll cover the basics. In essence, you use the chromatic scale (12 pitches) to create a “set.” You can put the pitches in any order you want, but the idea is that you can’t repeat any note until all 12 have been used.

For the sake of an example, here is a set:

This set is known as the prime series. It is also notated as P0 (P-zero).

Where it starts to get interesting is how you build a tone grid, from which you get a complete master set of tone rows to play with. Follow me on this, it will make sense in a second.

Creating The First Inversion Set

What we want to do here is figure out what the intervals are between each note, and then invert them to create the first horizontal (“Inversion”) row – called I0 – in our grid. So, the interval from C to F# is a tritone up. We reverse that to get a tritone down and insert that note into the inversion row.

Next, we take the interval from F# to G and invert that as well. F# to G is a 1/2 step up, so we will go 1/2 step down from F#, which is F.

Continuing along with the rest of the intervals from P0 to create I0 gives us this:

Now that we have our first inversion row, we can fill in the rest of the inversion rows by using the exact same interval relationships in P0 but starting on the notes from I0. In order words:

• The first interval in P0 is a tritone – C to F#.
• Start with F# (the first note in the P1 set) and go up a tritone. That gives us C.

• From F# to G in P0 is a 1/2 step up, so now we want to go a 1/2 step up from the C, which is C#

Follow this same formula for all of the notes in set P1, as well as all of the notes in sets P2 – P12. The complete master structure will look like this:

The horizontal rows moving from left to right are called prime sets. Horizontal rows moving from right to left are called retrograde sets. Vertical rows moving from top to bottom are called inversion sets, and vertical rows moving from bottom to top are called retrograde inversion sets.

I don’t know about you, but I think that’s some pretty cool stuff. You now have a crapload of sets to work with. The controversy with 12-tone music lies in the debate of whether or not this makes the music too mathematical and lacking emotion. I can certainly see that side of the argument, but if you’ve listened to the masters of 12-tone composition (Schoenberg, Webern, Berg, etc.) I think you will come to the same conclusion as many others, which is that one thing definitely not lacking from their compositions is emotional content.

But How Does This Apply To Guitar?

Well, certainly it opens up a new way of composing, doesn’t it? That’s one point. But, what I like to do with these tone rows is create an octave displacement exercise. Pat Martino uses this concept with the chromatic scale to create some of his lines. (Though Martino attributes this chromatic displacement concept to his own discovery, he actually learned it from Dennis Sandole.)

Let’s take the first set – P0 – and displace some of the notes by an octave to create a more interesting sound (click to enlarge).

You can now use this as either a very hip line in your solo, or as a gymnastic exercise that you can move up chromatically for fingering practice.

I encourage you all to check out some 12-tone composers and dig into what they are doing. It’s ridiculously hip stuff, and I’m sure it will resonate with some of you.