Using physical modeling to learn about the piano : New insights into the hammer-string force

One of the most important ingredients in the generation of a piano tone is the interaction between the hammer and string. In this work we consider the form of the hammer force-compression characteristic in light of recent experiments. The experiments suggest that the functional forms that have been used in previous studies do not account for an effective softening of the hammer during playing conditions. We propose a new way of mathematically describing the hammer-string force that captures, at least semi-quantitatively, this effect.