Trajectory of fifths in tonal vs. atonal music differentiation

The article presents a tonal vs. atonal music discrimination technique. The essence of the discussed idea renders down to the representation of the content of a musical work in the form of the trajectory of fifths. The structure of the trajectory of fifths depends on the scale of the examined composition. The conducted experiments show that the trajectories of fifths corresponding to tonal music are considerably different from the trajectories representing atonal works. The differentiation of tonal and atonal music can be achieved via calculation of basic coefficients quantifying the trajectory of fifths, such as the coordinates of the center of the trajectory, or the distance of the center of the trajectory from the center of the coordinate system. The article presents examples of trajectories of fifths obtained for a selection of tonal and atonal music compositions. The plots illustrating the differences in distributions of values of the considered coefficients obtained for tonal and atonal music pieces are also presented.