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:

• 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?

Note that there are software tools (e.g., from the world of perceptual audio coding [62,475]) 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.