Modeling of piano sounds using FEM simulation of soundboard vibration

Abstract

Pattern-matching methods for polyphonic transcription of piano sounds require a set of patterns that can be obtained by modeling the piano-sound spectra. The modeling should take into account not only the string stiffness but also the effect of the soundboard impedance on the string vibration. Studies on that effect corresponding to a wide range of impedance values have previously been carried out by the authors. However, actual impedance values for real pianos must be used in the model. Although the impedance value of a few grand-pianos have been measured by the authors, these results are not significative enough to create a model. Thus, a FEM simulation of soundboard vibration is proposed to obtain nearly-actual impedance values. The simulation considers several cases of vibrating plates from the simplest rectangular one and increasing the similarity to real piano soundboards. The quality of the simulation is verified comparing the obtained results with either recognized theoretical results for the simplest cases or measured values for the more complex ones. The complexity of the simulated soundboard is limited to the case that produces only slight variations in the modeled spectrum. [This work has been supported by Spanish National Project TEC2006-13067-C03-01/TCM.]