Artikel,
Representations of motivic spaces of a score in OpenMusic
Journal of Mathematics & Music, 2 (2): 61–79 (2008)
DOI: 10.1080/17459730802312183
Zusammenfassung
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 T0-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 Traumerei, a
