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.

---

Previous: Efficient Waveguide Synthesis of Nonlinear Piano Strings
Next: High-Accuracy Piano-String Modeling

Order a Hardcopy of Physical Audio Signal Processing

---

About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.