New Models for New Music

Mathematical modeling of sound and music has become essential to the practice of making music with computers. A variety of models for musical sound and higher level musical features like harmony, melody, and rhythm will be surveyed. In all cases special emphasis will be given to the mutability of the underlying representations and the generation and control of musical material in a reactive real-time performance context. Models of sound include sinusoidal track representations for additive synthesis and resonance models based on banks of high Q filters. Control structures for sound synthesis include those based on neural networks, exemplar or memory-based models, and cluster weighted models. Models for harmony and melody include those based on pitch distributions and a variety of graphical models. Rhythmic representations include those that capture metrical organization and expressive timing variations like swing and rubato. Many of these models are data driven and the underlying statistical issues will be exposed. Finally, a number of musical data bases and some associated tools for musical analysis and synthesis will be described.