The 3-3 Trichords
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.
This time we'll use the trichords known as 3-3A and 3-3B. The first of these is, say, C Db E and the second is, say, C D# E. These don't really suggest any kind of diatonic situation; you can find both in Harmonic Minor and in the Octatonic diminished scales if you want to but here we'll be avoiding tonality so we'll forget about that and treat them as little melodic cells that can be moved around.
Incidentally, 3-3 comes in two flavours, 3-3A and 3-3B, which are inversions of each other. This might seem like a trivial difference and some set theorists ignore it, but the major and minor triads share the same relationship so to my mind that's enough of a clue that we might want to consider them separate entities. They really do sound different, although of course they're also closely related. You can mix them up or keep them separate according to your musical needs.
Today I had fun moving them in major seconds, i.e. in two-fret jumps, which covers off most of the chromatic scale fairly quickly. Here are a few ways to play each one, with each copy of the trichord colour-coded -- you can switch between inversions at will, and even between 3-3A and 3-3B, although you'll definitely hear a change in the music when you do.
I like to play the three notes in one position, then slide the last note up or down to the next position; this produces snaking lines that have a bit of a Schoenbergian quality to them:
As far as I know Schoenberg's Fourth Quartet doesn't make prominent use of 3-3A or B, but it's definitely the sound-world I'm getting when I play around with these*. I may do a follow-up on the trichords his main tone row is made of, which according to this appear to be 3-4, 3-8 and 3-9. However, 3-3A and 3-3B do feature in Webern's "Concerto for Nine Instruments":
I'm attracted to this approach because anything derived from strict serial technique has always seemed too abstruse and precise for improvisation. The composer has to work every detail to a fine polish; we ad-libbers need simple formal materials that are audibly explicit enough for listeners to latch onto. The music is played once and usually heard once, after all. I don't intend by this to demean improvisation, just to say that the challenges and success criteria are quite different. So when an improvisor takes inspiration from composed music, a certain amount of transformation is required. It's not clear to me yet exactly what that is but a pragmatic approach seems likely to be at the heart of it.
* EDIT: I decided to make quick placeholder diagrams for these. All of these are contained in the Major scale and 3-8A and B are also Whole Tone Scale subsets. What's interesting is how Webern uses them, which almost completely removes them from those contexts. That suggests that even these less "exotic" trichords might be applied in interesting ways:
