- The ``cyclone'' conical bore model is based on a compound cylindrical-conical segment air column model as illustrated at the top of Fig. 19.
- The input cylindrical section roughly models the instrument mouthpiece cavity and its use avoids the complications previously discussed with respect to the non-linear driver.
- In addition, the cylindrical section can be designed to have an equivalent volume equal to the missing conic section volume. Assuming no diameter discontinuity at the cylinder-cone junction, this constraint is met using a cylindrical section length equal to
*x*_{o}/3. - It should be noted that Benade distinguishes between a cavity's physical and equivalent volumes under playing conditions, which are typically not the same. For the simplified reed function used in this implementation, however, it is reasonable to ignore this difference.
- The cylinder-cone junction filter is derived assuming continuity of pressure and conservation of volume velocity and then discretized using the bilinear transform as:

where is the bilinear transform constant,

*c*is the speed of wave propagation in the structure, and*x*_{0}is the length of the truncated conic section. - This expression could just as well have been derived from the parallel combination of the input inertance
*M*_{o}and the wave impedance of the input cylindrical section. - The junction transmittance magnitude response (
) is shown in Fig. 20 for various values of
*x*_{o}. - The ``high-pass'' filter characteristic associated with the conical waveguide input inertance term can vary significantly depending on the frustum dimensions.
- Shorter values of
*x*_{o}correspond to steeper flare rates, which produce greater wave discontinuity at the junction and greater low-frequency attenuation. - While this might appear to imply a preference for less steeply flared conic sections, it should be remembered that larger values of
*x*_{0}correspond to larger values of in Fig. 15 and thus greater mode inharmonicity. The result is a design conflict between junction discontinuity, which destabilizes the lower air column modes, and mode harmonicity. - The cylinder-cone junction can be implemented using a single first-order digital filter, as discussed by Välimäki and Karjalainen (1994); Smith (1991) and others. A block diagram of the resulting digital waveguide model is shown in Fig. 19.
- Figure 21 displays the input impedance and sound spectrum produced by an example ``cyclone'' waveguide model.
- Despite significant inharmonicity of the input impedance peaks, the resulting synthesis spectrum is harmonic and exhibits contributions from ``misaligned'' peaks as a result of the non-linear regenerative process.
- The sounds produced by the ``cyclone'' model have a distinctive saxophone quality, though the instabilities associated with truncated conic frusta as outlined in earlier sections are present and the functional parameter space can be difficult to assess.

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