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Checking the Approximations

The preceding discussion considered several possible approximations for nonlinear piano-string synthesis. Other neglected terms in the stiff-string wave equation were not even discussed, such as terms due to shear deformation and rotary inertia that are included in the (highly accurate) Timoshenko beam theory formulation [263,170]. The following questions naturally arise:

To answer these questions, it is helpful to have a truth reference--a ``perceptually exact'' model.

Note that there are software tools (e.g., from the world of perceptual audio coding [62,474]) that can be used to measure the audible equivalence of two sounds [459]. For an audio coder, these tools predict the audibility of the difference between original and compressed sounds. For sound synthesis applications, we want to compare our ``exact'' and ``computationally efficient'' synthesis models.


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``Physical Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2010, ISBN 978-0-9745607-2-4.
Copyright © 2014-03-23 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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