![]() 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. Eighth-note patterns were dominant in Coltrane's earlier work while greater irregularity was present in rhythmic patterns of his later work. In addition, average mutual information analyses revealed various dominant regular rhythmic patterns in several of the pieces. Brownian motion is a type of statistical pattern that is symptomatic of self-similar or fractal patterning across time. ![]() 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. The pitch sequences were examined using power spectral analysis. Saxophone solos were transcribed from sheet music into a format that represents an absolute pitch numerically. Eighteen solos were examined, two songs on two different album releases for each year from 1959–1967. John Coltrane's relevant biographical events are discussed along with a fractal analysis examining the sequential structure of pitches in his saxophone solos.
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