The impact of improvisation on creativity: A fractal approach

Abstract

This is an investigation of musical creativity. Improvisation is a complex system for understanding musical creativity. Improvisation is often expressed through jazz music. This chapter focuses on the measurement of jazz improvisation in order to better understand musical creativity. The science and art of music analysis are discussed. Improvisation can be a measure for musical creativity; however, there are limitations with existing measurement methods. Instead, fractal analysis offers an approach that addresses such limitations. In a case study approach, the work of John Coltrane and his relevant biographical events are discussed along with a fractal analysis examining the sequential structure of pitches in his saxophone solos. 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 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 (Mandelbrot 1998). In addition, average mutual information analyses revealed various dominant regular rhythmic patterns in several of the pieces. Eighth-note patterns were dominant in his 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 a different pitch encoding technique have previously identified in performances of both classical and jazz music (e.g., Boon and Delcroly 1995). These fractal patterns quantify the concepts of order and complexity addressed in the Birkhoff’s Theory of Aesthetic Value. Fractal analysis offers another approach toward understanding the dynamics of improvisation and musical creativity.