The Slope of Correlated Music

The result of our analysis of 57 different pieces are presented in this appendix. The third movement of the Brandenburg concerto and all of preludes and fugues form the Well-Tempered Clavier Part-I, along with a few other pieces, were analyzed. This analysis was an attempt to recreate the results of Voss and Clarke's[50] in their study of music as noise, which is explained in chapter 4. In our study we extracted a simple signal (which we called the ``top voice'') from the MIDI encoding of these pieces. Our methods of extraction and analysis are also explained in chapter 4. A line was interpolated from the data using least squares error^A.1 to find an approximate value for the slope of the power spectrums[32]. The approximated slope for all the power spectrums is shown. The line which corresponds to the (which has a slope of $-1$) spectrum is also printed on all graphs.

The higher the absolute value of the slope, the more correlated the melodies sound. We make no general claim that music in general works like noise, except that these pieces show a uniform relationship between their small and large-scale structures. These pieces are similar to each other and are all from a specific era of Western music. Unfortunately we did not have access to other pieces in MIDI format.