The Mathematical in Music Thinking
Rudolf Wille, Renate Wille-Henning, Fachbereich Mathematik · 2008
Abstract. “The Mathematical in music thinking ” is based on Heidegger’s understanding of “the Mathematical ” as the basic assumption of the knowledge of the things. Heidegger’s ideas are combined with Peirce’s classification of sciences, in particular, to distinguish between the Mathematical mathematical thinking. The aim of this paper is to make understandable the role of the Mathematical in music. The paper concentrates on three domains: the rhythmic of music, the doctrine of music forms, and the theory of tonal systems. The theoretical argumentations are assisted by musical examples: the Adagio of Mozart’s string quartet C major (KV 465), the second movement of Webern’s Symphony op.21, and a cadence illustrating the problem of the harmony of second degree. 1 Music Thinking and The Mathematical ”Musica est exercitium arithmeticae occultum animi ” (”Music is a hidden arithmetical exercise of the soul”)- this statement was written by the philosopher,