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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 [261,169]. The following questions naturally arise:
  • How do we know for sure our approximations are inaudible?
  • We can listen, but could we miss an audible effect?
  • Could a difference become audible after more listening?
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 [62,472]) that can be used to measure the audible equivalence of two sounds [456]. 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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A Stiff Mass-Spring String Model
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Efficient Waveguide Synthesis of Nonlinear Piano Strings