2009/03/20 by Jean Pierre Boon, Boon, Jean Pierre
Computer Science · Physics and Astronomy · #Data Analysis #FOS: Computer and information sciences #FOS: Physical sciences #Physics and Society (physics.soc-ph) #Sound (cs.SD) #Statistics and Probability (physics.data-an) #cs.SD #physics.data-an #physics.soc-ph
paper · pdf · doi:10.48550/arxiv.0903.3545
4 pages with 2 figures
arxiv created 2009/03/20 · arxiv updated 2009/12/01
The concept of complexity as considered in terms of its algorithmic definition proposed by G.J. Chaitin and A.N. Kolmogorov is revisited for the dynamical complexity of music. When music pieces are cast in the form of time series of pitch variations, concepts of dynamical systems theory can be used to define new quantities such as the \em dimensionality as a measure of the \em global temporal dynamics of a music piece, and the Shanon \em entropy as an evaluation of its \em local dynamics. When these quantities are computed explicitly for sequences sampled in the music literature from the 18th to the 20th century, no indication is found of a systematic increase in complexity paralleling historically the evolution of classical western music, but the analysis suggests that the fractional nature of art might have an intrinsic value of more general significance.