Teias Matemáticas : Comunicações

20th century mathematics have catalyzed a dramatic rewriting process of music theories and the corresponding information technology. We give an overview of models for harmony and counterpoint, as well as rhythmic and melodic analysis. These approaches have been applied with success to model musical composition and performance. Based upon a mathematical theory for unified representation of music objects, such theories have been implemented in computer programs and applied to musical composition, analysis, and performance. In this talk, the theoretical insights are illustrated by numerous audio examples from classical and modern music, including a computer generated performance of Bachís "Kunst der Fuge", modulation architecture in Beethovenís "Hammerklavier" sonata, rhythmic and melodic analysis of Schumannís "Trümerei", and finally applications to jazz and contemporary music compositions.