Page  00000001 Proposal for a Roundtable Discussion on the Role of Abstract Mathematics in Computer Music Lawrence Fritts', Guerino Mazzola2, Robert Morris3, John Rahn4, and Moreno Andreatta5 1School of Music, University of Iowa 2MultiMedia Laboratory (MML), University of Zurich 3Eastman School of Music, Univeristy of Rochester 4School of Music, University of Washington 5IRCAM Abstract This one-hour roundtable discussion will examine the role of abstract mathematics in computer music. After considering prior developments in mathematics, musical composition, and theory, the panel will discuss recent research and suggest directions for new research. 1 Introduction Since Pythagoras, music and mathematics have been intricately linked. This has been particularly true during the nineteenth and twentieth centuries, which witnessed enormous revolutions in mathematical thought, with repercussions keenly felt in all the arts. As the most abstract of the arts, music underwent a profound transformation in the twentieth century, as mathematical models quickly found expression in the music of Schoenberg, Babbitt, Boulez, Xenakis, Vieru, and other composers. Still, for the striking success abstract mathematics has had in finding a voice in progressive twentiethcentury music, its impact on recent computer music has been relatively limited, where mathematical issues primarily arise in connection with basic research in timbral analysis/synthesis, physical modeling, interactive performance systems, and other areas that have had an important impact on the development of tools for computer music. Yet, music has a fundamental symbolic structure, and the language of structure is mathematics. 2 Panelists In order to examine the role of mathematical structure in computer music, the following panel of composers and researchers has been formed: * Lawrence Fritts (Chair), University of Iowa. Composer, author of "Group Structures in Twentieth-Century Music." * Guerino Mazzola, MultiMedia Laboratory (MML), University of Zurich. Author of The Topos of Music. * Robert Morris, Eastman School of Music. Composer, author of Composition with Pitch-Classes: A Theory of Compositional Design. * John Rahn, University of Washington. Composer, author of Basic Atonal Theory. * Moreno Andreatta, IRCAM. Author of "M6thodes alg6briques en musique et musicologie du XXe siecle: aspects th6oriques, analytiques et compositionnels." Proceedings ICMC 2004

Page  00000002 3 Topics for Discussion In a brief presentation and extended discussion format, the panel will address the following topics: 1. Developments in abstract mathematics since 1800. 2. Musical applications of mathematics in twentieth-century composition and theory. 3. How these developments in mathematics and music have been extended in the recent research and creative work of the panelists and others. 4. How these new ideas can be applied in computer music to compositional design, algorithmic strategies, structuring and manipulating large data and parameter sets, gestural control, musical analysis, and performance. 5. How to implement the goal of establishing mathematical inquiry as an ongoing computer music research area. Conclusion The creative possibilities offered by recent mathematics have remained largely unexplored in the arts. It is our hope that this discussion will help illuminate new creative avenues and expand the horizons of what mathematics can contribute to computer music. References Andreatta, Moreno. (2002). "Tiling problems in music composition: Theory and Implementation." In Proceedings of the International Computer Music Conference, pp. 156-163. San Francisco: International Computer Music Association.. (2003a). " Implementing algebraic methods in OpenMusic." In Proceedings of the International Computer Music Conference, San Francisco: International Computer Music Association.. (2003b). "Methodes algebriques en musique et musicologie du XXe siecle: aspects theoriques, analytiques et compositionnels." PhD Thesis, EHESS/IRCAM. Cassirer, Ernst. (1944). "The Concept of Group and the Theory of Perception." Philosophy and Phenomenological Research: A Quarterly Journal 5(1), 1-35. Fritts, Lawrence. (1994). "The Musical Image of Mathematical Structure." Abstracts ofPapers Presented to the American Mathematical Society, 15(1), 189.. (1995). "Group Actions in Babbitt's Three Compositions for Piano." PhD Thesis, University of Chicago.. (2000). "Group Structures in Twentieth-Century Music." Systems Research in the Arts, Volume 1: Musicology. George Lasker and James Rhodes, ed. Ontario: The International Institute for Advanced Studies in Systems Research and Cybernetics, 10-14. Gauss, C. F. (1966). Disquisitiones Arithmeticae. New Haven: Yale University Press. Henderson, Linda Dalrymple. (1983). The Fourth Dimension and Non-Euclidean Geometry in Modern Art. Princeton: Princeton University Press. Klein, Felix. (1893). "A Comparative Review of Recent Researches in Geometry." Translation of "Programme on Entering the Philosophical Faculty and the Senate of the University of Erlangen in 1872." Bulletin of the New York Mathematical Society 2, 215-249. Mach, Ernst. (1959). The Analysis of the Sensations. New York: Dover, MacLane, Saunders. (1971). Categories for the Working Mathematician. New York: Springer Verlag. Mazzola, Guerino. (1995). "Inverse Performance Theory." In Proceedings of the International Computer Music Conference, San Francisco: International Computer Music Association. _____. (2002). The Topos of Music. Basel: Birkhiuser. Morris, Robert. (1987). Composition with Pitch-Classes: A Theory of Compositional Design. New Haven: Yale University Press. _____. (2001). Class Notes for Advanced Atonal Theory. 2 volumes. Lebanon, NH: Frog Peak Music. Miuller, Stefan and Guerino Mazzola. (2003). "The Extraction of Expressive Shaping in Performance." Computer Music Journal 27(1), 47-58. Rahn, John. (1980). Basic Atonal Theory. New York: Longman, Inc. _____. (1995). "Some Remarks on Network Models for Music" in Musical Transformations and Intuitions: A Festschrift for David Lewin, ed. Raphael Atlas and Michael Cherlin, Pendragon Press. Proceedings ICMC 2004