SELF-SIMILARITY OF THE 1/F NOISE CALLED MUSIC

Suggestions have been made that computer musicians should attempt to compose fractal music, and questions have been raised whether there is such a thing as fractal music. Voss and Clark observed that music is scaling, or 1/f noise, as analyzed on the basis of the amplitude (loudness) of the audio signals; they failed to find a fractal distribution of acoustic frequencies (music notes) in music. Analyzing Bach's and Mozart's compositions, we have shown that the incidence of the frequency intervals, or of the changes of acoustic frequency, has a fractal geometry. Fractal phenomena are characterized by scale-independency. The purpose of this investigation is to demonstrate the self-similarity of music and to explore its implications.