Melodic Transformation in George Garzone’s Triadic Chromatic Approach; or, Jazz, Math, and Basket Weaving

Abstract

Abstract The Triadic Chromatic Approach (TCA) is a melodic improvisation technique, created by the saxophonist and jazz educator George Garzone. With the TCA, successive triads are connected by a semitone and must have different inversions. The resulting lines mysteriously resolve to any underlying harmony. This article develops transformational and Markov-chain models of the TCA, showing how this melodic process approaches a probability distribution where every pitch class is equally likely to appear. Nonetheless, theorizing the TCA is different from performing it, and insights from Garzone’s students—and the anthropology of weaving—suggest that goals are less fundamental here than characteristic gestures.