This paper is devoted to a qualitative and quantitative study of topological spaces built on premotif collections of musical scores. These motivic topologies are related to similarity concepts in the American music set theory. Through shapes, imitations and gestalts, and similarity relations between any two shapes, we obtain a motivic hierarchy of a score. This model of motivic analysis is completed by proposing different tools, such as weighted shapes and motivic evolution trees (MEn, for visualizing these non-intuitive topologie~. The concept MET, which is related to a systematic variation of the similarity parameter, is of a highly cognitive flavor.In the light of our approach, the still debated question concerning the length of the main theme in Bach's Kunst der Fuge is addressed. As a result, we can state that the extended 12-tone theme is essentially equivalent to the shorter 8-tone version when viewed from its motivic substance.The rigorous language of mathematics has become a powerful tool in musicology. It typically helps understanding complex mechanisms by making abstraction from secondary qualities of the studied objects. In this spirit, Allen Forte (1973) used set theory to model the structure of atonal music. His theory was later adapted and extended to study morivic structures in music by Robert Morris
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.