The Color, Power Spectrum, and Hurst Exponent Associated with the Linear and chaotic Nature of Changes in Pitch of Selections of Music By Philip Glass

Abstract

White noise is what we call random or white colored noise. It is a simple measure of the frequency at which the system changes over time. The color of noise is a measure of the instability (white noise) or probabilistic nature of a system’s dynamics (i.e. white noise is the most unstable random colored noise), whereas, red noise is the most stable, non-random colored noise. In all types of music, changes in the pitch of the music is a proxy for measuring change in the color of noise, and hence, the stability of noise over time. In the following paper, I hypothesize that particular pieces of Philip Glass’s music can be used to measure (qualitatively and quantitatively), linear and chaotic or fractal (unstable) dynamic change in pitch, which can best be qualitatively and quantitatively explored by determining the color and chaotic (or fractal) nature of a particular measure within a composition. I use statistical models and analysis of those models using computer software to test my hypothesis. The models presented here are analogs, which do not explicitly model the pitch patterns ingrained in a measure from a particular Glass composition. Rather, these models are meant to generate the types of patterns one expects Glass’s music to generate. Surprisingly, I found that one of the analog models predicted that a measure of one of Glass’s compositions consisted of both linear and chaotic pitch components, resulting in the generation of a measure with an indefinite pitch (blue color) state, one, whose dynamics are in-between a stable and unstable state. Analysis of each individual note of a measure of a particular composition is not the intent of this paper at this moment in time. Future research the explicitly models pitch dynamics is needed. Lastly, I opine about further application of this approach to quantify the color of noise and associated power spectrum in many other disciplines.