Single-Reed Instruments

Figure 15 illustrates an overall schematic for a single-reed woodwind instrument, such as the clarinet, and Fig. 16 shows a particular digital waveguide synthesis model [152,162].

Figure 15: A schematic model for woodwind instruments.

Figure 16: Waveguide model of a single-reed, cylindrical-bore woodwind, such as a clarinet.

The control variable is naturally chosen to be mouth pressure $p_m$ (or more specifically in this case, half of the mouth pressure, $\hm=p_m/2$). A kind of ``incoming pressure difference'' across the mouthpiece is computed as $h_{\Delta}^{+}=\hm-p_b^{+}$, and this is used to index a look-up table. (Specifically, $h_{\Delta}^{+}$ is half of the pressure drop seen across the reed when the reed turns out to be closed.) The table look-up can also be implemented as a nonlinear function that switches between a third-order polynomial (reed open) and a constant (reed closed). The result of the reed-table look-up is multiplied by $h_{\Delta}^{+}$ and subtracted from $\hm$ to form the outgoing traveling-wave component into the bore. The cost of a table look-up implementation such as this is only two subtractions, one multiplication, and the look-up itself, per sample of sound. It is possible to eliminate the multiplication by appropriately reformulating the table, but this requires additional resolution in the table for a given sound quality. Further details of this particular synthesis model for the clarinet are given in [162]. STK software implementing a model as in Fig. 16 can be found in the file Clarinet.cpp.