Digitizing via the centered second-order difference [Eq.(7.5)]
Note that requiring three adjacent spatial string samples to be in contact with the piano hammer during the attack (which helps to suppress aliasing of spatial frequencies on the string during the attack) implies a sampling rate in the vicinity of 6 megahertz . Thus, the model is expensive to compute! However, results to date show a high degree of accuracy, as desired. In particular, the stretching of the partial overtones in the stiff-string model of Fig. has been measured to be highly accurate despite using only three spring attachment points on one side of each mass disk .
Nonlinear Piano-String Equations of Motion in State-Space Form