Improvisation and the self-organization of multiple musical bodies

Abstract

Understanding everyday behavior relies heavily upon understanding our ability to improvise, how we are able to continuously anticipate and adapt in order to coordinate with our environment and others. Here we consider the ability of musicians to improvise, where they must spontaneously coordinate their actions with co-performers in order to produce novel musical expressions. Investigations of this behavior have traditionally focused on describing the organization of cognitive structures. The focus, here, however, is on the ability of the time-evolving patterns of inter-musician movement coordination as revealed by the mathematical tools of complex dynamical systems to provide a new understanding of what potentiates the novelty of spontaneous musical action. We demonstrate this approach through the application of cross wavelet spectral analysis, which isolates the strength and patterning of the behavioral coordination that occurs between improvising musicians across a range of nested time-scales. Revealing the sophistication of the previously unexplored dynamics of movement coordination between improvising musicians is an important step toward understanding how creative musical expressions emerge from the spontaneous coordination of multiple musical bodies.

Keywords: complex dynamical systems; movement coordination; multiscale analysis; music improvisation; self-organization.

FIGURE 1

Cross wavelet plots of the lateral movements of the musicians’ right forearms, displaying the strength of coherence at each period (red for high coherence = 1, dark blue for low to no coherence = 0), as well as relative phase angle (right arrows equal in-phase coordination, left arrows equal anti-phase coordination). (A) Displays the coordination between two piano players playing the exact same part, in synchrony with the ostinato backing track. (B) Displays coordination while the musicians improvise over the ostinato backing track.

FIGURE 2

Cross wavelet analysis of experimental data from two piano players improvising with an ostinato backing track (Left) and drone backing track (Right). (A,B) display the normalized time series of the lateral movements of the musicians’ left hands. (C) Cross wavelet analysis of these two time series displaying the strength of coherence at each period (red for high coherence, dark blue for low to no coherence), as well as relative phase angle (right arrows equal in-phase coordination, left arrows equal anti-phase coordination).

FIGURE 3

Cross wavelet analysis of experimental data from two piano players improvising with a swing backing track. (A) Displays coordination of the musician’s upward and downward head movements, while (B) displays the coordination of the upward and downward movements of the musicians’ right hands.

FIGURE 4

Macroscopic and microscopic interaction involved in musical improvisation. (A) Structural changes in visual and auditory information about co-performers actions at both local and global levels serve to constrain musical produce. (B) Adapted from Kugler and Turvey (1987), Illustrates the interaction between the micro and macroscopic scales, here the flow field of information refers to a the time-evolving structures of sound and light that are informative about current, future and past actions of the musicians as a group.