Geometry of Tones is the updated and elaborated version of an interdisciplinary lecture on mathematical music theory at the University of Zurich during the academic year 1986/87. The book is aimed at a broad, interested readership that wants to gain an understanding of the current state of this theory. Therefore, the development of mathematical formalism is approached with the utmost care and restraint. The central concern of the theory – the mediation between musical form and its meaning – remains at the forefront of the presentation. The current state of mathematical music theory (MaMuTh) is the result of a ten-year research period during which the integration and intertwining of systematic musicology with the language, methods, and insights of modern mathematics was pursued. Special emphasis is placed on the Ge.