Representations of motivic spaces of a score in OpenMusic

Abstract

This paper proposes a novel stand-alone model implementation, called OM-Melos, for the explicit construction of motivic spaces and visualization using the software OpenMusic and Maple. OM-Melos completely implements our topological model of motivic structure and analysis, including the melodic clustering model extension, unveiling all topological details, such as three-dimensional weight graphs and dynamic clustering tables. Our immanent approach comprises the contour similarity for motives of different cardinalities making it possible to formalize the concept of germinal motive. Neighbourhoods of motives are introduced and yield T 0-topological spaces, based on motive, contour, gestalt and motive similarity concepts. The melodic clustering (i.e. an organization of melodic segments into ‘significant’ categories) is extracted from the space by intersecting some sets corresponding to the formalization of motive variations within the model. We apply our approach to Schumann's Träumerei, and successfully compare our motivic analysis to the cognitive scientist Repp's melodic analysis (Journal of the Acoustical Society of America, Vol. 92, No. 5, 1992, pp. 2546–2568): our melodic clusterings of the soprano voice and leading voices weigh well against Repp's, and the salient ascending E-F-A-C-F-F motive has significant germinal function.

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