A Historical and Fractal Perspective on the Life and Saxophone Solos of John Coltrane

John Coltrane's relevant biographical events are discussed along with a fractal analysis examining the sequential structure of pitches in his saxophone solos. Eighteen solos were examined, two songs on two different album releases for each year from 1959–1967. Saxophone solos were transcribed from sheet music into a format that represents an absolute pitch numerically. The pitch sequences were examined using power spectral analysis. Results indicate that all 18 Coltrane saxophone solos display sequences of successive pitches that are consistent with anti-persistent fractional Brownian motion having 1/f α power spectra with scaling exponent α between 1.6 and 1.8. Brownian motion is a type of statistical pattern that is symptomatic of self-similar or fractal patterning across time. In addition, average mutual information analyses revealed various dominant regular rhythmic patterns in several of the pieces. Eighth-note patterns were dominant in Coltrane's earlier work while greater irregularity was present in rhythmic patterns of his later work. Thus, Coltrane's improvised solos, including his later avant-garde compositions, are comprised of Brownian fractal patterns, which others using different pitch encoding techniques have previously identified in performances of both classical and jazz music. These fractal patterns quantify the concepts of order and complexity addressed in the Theory of Aesthetic Value.