We have presented a computationally efficient modeling framework
applicable to flaring horns and piecewise conical bores. The horn
models use tail-canceling IIR filters to implement finite exponential
and constant impulse response segments, with periodic replacement of
unstable filter components used to avoid indefinite build-up of
round-off errors. The piecewise conical models follow analogous
principles with replacing the FIR filter length. Compared
with previous practical approaches to modeling these musical acoustic
elements computationally, the TIIR approach offers compelling
advantages.