DYNAMICAL-SYSTEMS THEORY FOR MUSIC DYNAMICS

We show that, when music pieces are cast in the form of time series of pitch variations, the concepts and tools of dynamical systems theory can be applied to the analysis of temporal dynamics in music. (i) Phas e space portraits are constructed from the time series wherefrom the d imensionality is evaluated as a measure of the global dynamics of each piece. (ii) Spectral analysis of the time series yields power spectra (similar to f(-nu)) close to red noise (nu similar to 2) in the low f requency range. (iii) We define an information entropy which provides a measure of the local dynamics in the musical piece; the entropy can be interpreted as an evaluation of the degree of complexity in the mus ic, but there is no evidence of an analytical relation between local a nd global dynamics. These findings are based on computations performed on eighty sequences sampled in the music literature from the 18th to the 20th century. (C) 1995 American Institute of Physics.