Automatic Motivic Analysis including Melodic Similarity for Different Contour cardinalities: Application to Schumann's of Foreign Lands and People

This paper aims at presenting a topological model of motivic structure and analysis, and its application, via the implementation, to Schumann’s Of Foreign Lands and People in Scenes from Childhood. Our immanent approach importantly includes the concept of contour similarity for different motif lengths making then possible to formalize the germinal motif (or leitmotif) concept. Based on motif, contour, gestalt, and motif similarity concepts, the crucial step in our mathematical model is indeed the introduction of neighborhoods of motives that include (similar) motives of different cardinalities and that yield a topological (T0)-space on the set of all motives of a composition. In this space, the ‘most dense’ motif corresponds to the piece’s ‘germinal motif’. The model implementation (JAVA) constructs the spaces and in particular calculates, for each similarity threshold (neighborhood radius), the germinal motif; this is graphically represented in motivic evolution trees. The application to Of Foreign Lands and People briefly exemplifies our method.