Numerical simulation and optimization algorithms for the sound design of organ pipes with tuning slots

In the present paper numerical simulation and optimization techniques are examined in order to attain optimal scaling of labial organ pipes. This paper mainly focuses on modeling the geometrical irregularity introduced by tuning slots. To characterize the pipe in the frequency domain, the acoustic input admittance function is calculated using a one-dimensional waveguide model. To be able to take the geometrical irregularities into account with sufficient accuracy, an equivalent circuit of the tuning slot is constructed and inserted into the waveguide. Analytical approximations and numerical techniques are examined and compared in order to obtain the appropriate model of the tuning slot. By means of the waveguide model, the transfer function of the pipe's acoustic resonator can be calculated and the eigenfrequencies obtained. Using these characteristics, the steady state sound spectrum and its envelope can be predicted and used as the basis of the optimization process. The methodology is validated by laboratory measurements performed on experimental organ pipes.