Melodic Differences Between Styles: Modeling Music With Step Inertia

Abstract

A well-known phenomenon in melodic structure is “step inertia”: the tendency for a step to be followed by another step in the same direction. There is strong evidence of step inertia in three corpora of Western common-practice melodies: European folk songs, classical instrumental themes, and English hymn tunes. Surprisingly, modern Western popular music does not reflect step inertia. In Billboard’s Hot 100, and Rolling Stone magazine's list of “greatest songs,” inertial (same-direction) steps are less likely than non-inertial ones. To further explore the role of step inertia in different corpora, we created a generative model that assigns probabilities to melodies, considering just four factors: range, pitch proximity, scale-degree frequency within a key, and step inertia. We optimized the weights of these factors for the Essen Folksong Collection and the Billboard corpus, and compared them with n-gram models. The optimal (normalized) weight of the inertia factor is large and positive for the Essen collection (.51) and small for the Billboard corpus (.02). This is further evidence that step inertia plays a much smaller role in popular melodies than common-practice ones, and that non-inertial steps are slightly favored.