Direct Simulation for Wind Instrument Synthesis

There are now a number of methods available for generating synthetic sound based on physical models of wind instruments, including digital waveguides, wave digital filters, impedance-based methods and those involving impulse responses. Normally such methods are used to simulate the behaviour of the resonator, and the coupling to the excitation mechanism is carried out by making use of simple lumped finite difference schemes or digital filter structures. In almost all cases, a traveling wave, frequencydomain, or impulse response description of the resonator is used as a starting point—efficient structures may be arrived at when the bore is of a particularly simple form, such as a cylinder or cone. In recent years, however, due to the great computing power available, efficiency has become less of a concern—this is especially the case for musical instruments which may be well-modelled in 1D, such as wind instruments. In this paper, a fully time-space discrete algorithm for the simulation and synthesis of woodwind instrument sounds is presented; such a method, though somewhat more computationally intensive than an efficient waveguide structure, is still well within the realm of real-time performance. The main benefits of such a method are its generality (it is no longer necessary to make any assumptions about bore profile, which may be handled in an almost trivial manner), extensibility (i.e., the model may be generalized to handle nonlinear phenomena directly), ease of programming, and the possibility of direct proofs of numerical stability without invoking frequency domain concepts. Simulation results, sound examples and a graphical user interface, in the Matlab programming language are also presented.