Further Details

• Input mouth pressure is summed with a small amount of white noise corresponding to turbulence, e.g., 0.1% plus more during attacks
• Turbulence level and spectral shape should be computed automatically as a function of pressure drop $p_{\Delta}$ and reed opening geometry (research topic)
• Simple reflection filter:
  $$H(z) = \frac{1+a_1(t)}{1+a_1(t) z^{-1}}$$
  where $a_1(t) = v(t) - 0.642$, $v(t) = A_v\sin(2\pi f_v t)$,
  $A_v$ = vibrato amplitude (e.g., $0.03$), and
  $f_v$ = vibrato frequency (e.g., $5$ Hz)
• Further loop filtering occurs as a result of using a linearly interpolated delay line for the bore

• Only one (double length) delay line is really used in typical implementations
• To avoid finger-hole models, legato note transitions can be managed using two delay line taps and cross-fading from one to the other during a transition

Alternative Reed Models

• A direct signal lookup, though requiring much higher resolution, would eliminate the multiply associated with the scattering coefficient
• Coefficient tables can be quantized more heavily in address and word length than direct lookup of a signal value such as $p_{\Delta}(p_{\Delta}^{+})$
• Piecewise polynomial approximations are also used

Software

clarinet.cpp in the Synthesis Toolkit (STK):
http://ccrma.stanford.edu/CCRMA/Software/STK/