The fractal correlation dimension is a computational method to calculate musical density. The algorithm is counting the amount of harmonic overtonespectra, and therefore the amount of musical notes played. It calculates this from the soundfile, not from a score. Additional features, like sudden amplitude raise or popps are counted, too. Inharmonic sound components enter beyond an amplitude thresold, where each inharmonic component raises the fractal dimension by one.

Many analysis of musical pieces have shown excellent correspondence between musical form and the fractal correlation dimension. This is especially useful with complex music, like free improvisation and free jazz or contenporary classical music. It also works very good with soundscapes and sound installations.


Fractal dimension of a seven-minute free improvisation piece Broken Wings by Even Parker. The aural development of the pieces density is accordingly.

Related publications

Bader, R.: Fractal Worlds. Fractal dimension analysis in free improvisation. Chapter in David Borgo´s Book ‘Sync or Swarm’ on Free Improvisation, 2006.

Bader, R.: Characterization of guitars through fractal correlation dimensions of initial transients. J. of New Music Research, 35 (4), 323-32, 2008.

Bader, R.: Fractal correlation dimensions and discrete-pseudo-phase-plots of percussion instruments in relation to cultural world view. Ingenierias, Octubre-Diciembre 2002, Vol. V. No 17, p. 1-11.