This thesis proposes banded waveguide synthesis as an approach to real-time sound synthesis based on the underlying physics. So far three main approaches have been widely used: digital waveguide synthesis, modal synthesis and finite element methods. Digital waveguide synthesis is efficient and realistic and captures the complete dynamics of the underlying physics but is restricted to instruments that are well-described by the one-dimensional string equation. Modal synthesis is efficient and realistic yet abandons complete dynamical description and hence cannot used for certain types of performance interactions like bowing. Finite element methods are realistic and capture the behavior of the constituent physical equations but on current commodity hardware does not perform in real-time.

Banded waveguides offer efficient simulations for cases for which modal synthesis is appropriate but traditional digital waveguide synthesis is not applicable. The key realization is that the dynamic behavior of traveling waves, which is being used in waveguide synthesis, can be applied to individual modes and that the efficient computational structure can be utilized to achieve an approximate dynamical description in the neighborhood of modes. Secondly this realization is connected to related work on the theory of asymptotics and periodic orbits and hence shown to apply to higher dimensions also.

This theoretical approach is studied in applications to bowed bar percussion instruments, complex stroke patterns on Indian Tabla drums as well as rubbed wine glasses and Tibetan singing bowls. None of these instruments and performance types has been synthesized efficiently before. The simulations are compared to experiments.