Modelling the Dynamics of the Piano Action: Is Apparent Success Real?

The kinematics and the dynamics of the piano action mechanism have been much studied in the last 50 years and fairly sophisticated models have been proposed in the last decade. Surprisingly, simple as well as sophisticated models seem to yield very valuable simulations when compared to measurements. We propose here a very simple model, with only 1-degree of freedom, and compare its outcome with force and motion measurements obtained by playing a real piano mechanism. The model, purposely chosen as obviously too simple to be predictive of the dynamics of the grand piano action, appears either as very good or as very bad, depending on which physical quantities are used as the input and output. We discuss the sensitivity of the simulation results to the initial conditions and to noise and the sensitivity of the experimental/simulation comparisons to the chosen dynamical model. It is shown that force-driven simulations with position comparisons, as they are proposed in the literature, do not validate the dynamical models of the piano action. It is suggested that these models be validated with position-driven simulations and force comparisons.