It just may, indeed, by our topoi and geometric logic: http://www.birkhauser.ch/books/math/5731.htm Mazzola, G., University of Zurich, Switzerland In Collaboration with Stefan Gvller and Stefan M|ller The Topos of Music Geometric Logic of Concepts, Theory, and Performance 2002. 1368 pages. Hardcover. incl. CD-ROM $ 98.- / CHF 144.- ISBN 3-7643-5731-2 Subscription price $ 98.- / CHF 144.- valid until 31.12.02 Regular Price: $ 128.- / CHF 188.- Since the Greek antiquity it has been a tradition of European thinking to describe musical facts in a mathematical language. This formal apparatus has always mirrored the status quo of mathematical knowledge and the requirements of current sound technology. The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Tvne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Tvne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory of musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples. Contributors: Carlos Agon, Moreno Andreatta, Girard Assayag, Jan Beran, Chantal Buteau, Roberto Ferretti, Anja Fleischer, Harald Fripertinger, Jvrg Garbers, Werner Hemmert, Michael Leyton, Emilio Lluis Puebla, Mariana Montiel Hernandez, Thomas Noll, Joachim Stange-Elbe, Hans Straub, Oliver Zahorka