Optimization and simulation algorithms for the sound design of labial organ pipes

In the present contribution optimization and simulation methods are investigated in order to attain optimal scaling of labial organ pipes. The goal is to determine the optimal dimensions of the pipe, by which a desired steady state sound spectrum can be achieved. By modifying the geometry of the pipe body, the eigenfrequencies of the acoustic resonator can be tuned in order to amplify or repress given harmonic partials in the pipe sound. Since the dependence of the eigenfrequencies on the pipe dimensions is quite complex, obtaining the optimal scaling parameters is not trivial. To overcome this difficulty two alternative approaches are suggested and examined. In case of simple pipe forms, such as chimney pipes, the transfer (input admittance) function and the eigenfrequencies of the pipe are calculated by means of a one-dimensional model. However, when the pipe geometry is irregular (e.g. pipes with tuning slot) constructing a simple pipe model is not trivial. Therefore, numerical (finite/boundary element) methods are applied in order to predict the transfer function. These modeling techniques serve as guidelines in the development of an optimization algorithm. The usefulness and applicability of the methodology are proven by validation measurements performed on pipes built with optimized dimensions.