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:
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 . 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.