An investigation into the linear and nonlinear correlation of two music walk sequences

In order to investigate the features of a multiple-part musical score which enhance its appeal to the listener's ear, this study performs a robust analysis of the correlation between two musical sequences. In the proposed approach, a series of notes are extracted from seven well-known classical pieces of music and are converted into one-variable "music walks". The linear correlation between pairs of music walks is assessed using the conventional linear correlation coefficient, while the nonlinear correlation is examined using the mutual information concept. The results show that even though two musical time walks may exhibit virtually no linear correlation, they invariably have a certain degree of nonlinear correlation. In other words, to truly understand the correlation between two musical sequences, it is necessary to consider not only the linear correlation between them, but also the nonlinear correlation. In addition, it is shown that the normalized mutual information coefficient between musical sequences has a relatively low value and varies significantly over the course of the musical score. Thus, it can be inferred that the appeal of a musical score stems at least in part from significant variations in both the melody and the rhythm of the constituent parts such that the overall score has a rich and unpredictable property.