Multifractal analyses of music sequences

Multifractal analysis is applied to study the fractal property of music. In this paper, a method is proposed to transform both the melody & rhythm of a music piece into individual sets of distributed points along a one-dimensional line. The structure of the musical composition is thus manifested & characterized by the local clustering pattern of these sequences of points. Specifically, the local H¨older exponent & the multifractal spectrum are calculated for the transformed music sequences according to the multifractal formalism. The observed fluctuations of the H¨older exponent along the music sequences confirm the non-uniformity feature in the structures of melodic & rhythmic motions of music. Our present result suggests that the shape & opening width of the multifractal spectrum plot can be used to distinguish different styles of music. In addition, a characteristic curve is constructed by mapping the point sequences converted from the melody & rhythm of a musical work into a two-dimensional graph. Each different pieces of music has its own unique characteristic curve. This characteristic curve, which also exhibits a fractal trait, unveils the intrinsic structure of music