Whenever you get a bunch of musicians together, usually someone shares a revelation related to the music. The trombonist Richard Baker told me about an improvisation technique that the tenor saxophonist George Garzone has been working on for decades. He calls it the Triadic Chromatic Approach.
Here's what George says in a master class:
"I took the four groups of triads—major, minor, augmented and diminished—and figured out a way how to improvise with them using random inversions with a half-step coupling in between each triad. By doing that, you borrow from the 12-tone row. If you repeat yourself by playing two first position, two root position or two second inversions, you will cause the triad to shut itself down, and you start to cause repetition."
In its simplest form, if you play a triad on C (C E G) you can then play a semitone up or down from the G. The new note is part of a different triad, but can't be the root note (because the same inversion cannot be repeated). So no Ab or Gb triads allowed. There's more explanation on the JodyJazz website.
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