Digital Waveguide Single-Reed Implementation

A diagram of the basic clarinet model is shown in Fig. 6.2. The delay-lines carry left-going and right-going pressure samples $p_b^{+}$ and $p_b^{-}$ (respectively) which sample the traveling pressure-wave components within the bore.

Figure 6.2: Waveguide model of a single-reed, cylindrical-bore woodwind, such as a clarinet.

The reflection filter at the right implements the bell or tone-hole losses as well as the round-trip attenuation losses from traveling back and forth in the bore. The bell output filter is highpass, and power complementary with respect to the bell reflection filter [475]. Power complementarity follows from the assumption that the bell itself does not vibrate or otherwise absorb sound. The bell is also amplitude complementary.^7.1

At the far left is the reed mouthpiece controlled by mouth pressure $p_m$. Another control is embouchure, changed in general by modifying the reflection-coefficient function $\rho(h_{\Delta}^{+})$, where $h_{\Delta}^{+} \isdeftext p_b^{-}/2 - p_b^{+}$. A simple choice of embouchure control is an offset in the reed-table address. Since the main feature of the reed table is the pressure-drop where the reed begins to open, a simple embouchure offset can implement the effect of biting harder or softer on the reed, or changing the reed stiffness.