  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.
