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Vade Mecum to Mathematical Music Theory
1 What is Mathematical Music Theory?The present article has two purposes. It shall serve as an introductory guide to readers not being familiar with mathematical approaches to music theoretical problems. To readers already being involved in >mathemusical<1
1.1 Historical and Transdisciplinary AnchorsThe manifold and ramified relations between music theory and mathematics have a long history. During the unfolding and differentiation of science the mystic connection between numbers and music in the tradition of Pythagoras was transformed into several forms of founding, explaining and investigating music with mathematical means. An important aspect of this development was the paradigmatic role of knowledge about music for other domains of knowledge. This was institutionally manifest through the prominent role of music in the medieval organisation of the sciences. Famous researchers of the modern era like Rene Descartes, Galileo Galilei, Johannes Kepler, Marin Mersenne, Gottfried Wilhelm Leibniz, Leonhard Euler, Jean d’Alembert and others still contributed with mathematical investigations into music and its theory in this paradigmatic way. In the early days of modern psychology in the 19th century music gained special interest within quite different approaches to psychological phenomena. Johann Friedrich Herbart considered musical thought as the most reliable empirical source for his mathematical investigations into the »statics and dynamics of the mind«. He attributed an autonomous status to the processes of tone ideas (»Tonvorstellungen«) and in accordance with Leibnizian monadology he rejected the insertion of a physiological hypothesis between the physics of sound and the psychology of music. A few years later Hermann von Helmholtz -- being inspired by Georg Simon Ohm -- investigated the physiological foundations of tone sensations and -- along with Gustav Theodor Fechner -- influenced the Mathematisation of Psychophysics and |
