05829695

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05829695 Adilo\^elu, Kamil Obermayer, Klaus Topological features of the two-voice inventions. Klouche, Timour (ed.) et al., Mathematics and computation in music. First international conference, MCM 2007, Berlin, Germany, May 18--20, 2007. Revised Selected Papers. Berlin: Springer (ISBN 978-3-642-04578-3/pbk). Communications in Computer and Information Science 37, 67-77 (2009). 2009 Berlin: Springer EN

doi:10.1007/978-3-642-04579-0_7

Summary: The similarity neighbourhood model is a mathematical model making use of statistical, semiotical and computational approaches to perform melodic analysis of given music pieces. This paper is dedicated to the investigation of topological features and conditions in connection with the model on the one hand and concrete analyses on the other. Therefore, checking the topological features of the model as well as the analysis results is a good practice not only for theoretical but also for practical reasons. The topological features of the similarity neighbourhood model are investigated from a theoretical viewpoint, in order to figure out under which conditions the collection of the results yielded by the model define a topology. These topological features are then tested practically on the two-voice inventions. These investigations and tests have shown that the similarity neighbourhood model defines a topology not for all cases, but depending on the analysed musical piece.