Finite difference time domain (FDTD) approaches to physical modeling sound synthesis, though more computationally intensive than other techniques (such as, e.g., digital waveguides), offer a great deal of flexibility in approaching some of the more interesting real-world features of musical instruments. One such case, that of brass instruments, including a set of time-varying valve components, will be approached here using such methods. After a full description of the model, including the resonator, and incorporating viscothermal loss, bell radiation, a simple lip model, and time varying valves, FDTD methods are introduced. Simulations of various characteristic features of valve instruments, including half-valve impedances, note transitions, and characteristic multiphonic timbres are presented, as are illustrative sound examples.

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