Fractal Dimension and Musical Complexity: From Bach to the Blues

A "musical coastline" can be derived from an instrumental solo by plotting pitch against time. The result is a discrete approximation to a (possibly) fractal curve. The fractal dimension of the curve yields some measure of the complexity of the musical phrase. Examples are taken from a violin sonata by J.S. Bach and from solos by three blues guitar players. To establish the reliability of the programming code, mathematical curves of known dimension are included in the analysis.