Charalampos Saitis - "Physical modelling of the piano: An investigation into the effect of string stiffness on the hammer-string interaction"

The stiff string wave equation has four solutions, two of which are related to the string stiffness. In the case of digital waveguide modelling these are neglected [Bensa et al. 2003]. Current research suggests that all four travelling waves should be considered, at least at the neighbourhood of the excitation point [Ducasse 2005]. This dissertation investigates the effect of omitting string stiffness in the context of sound synthesis of the piano by physical modelling. A stiff, lossy string with a spatially distributed hammer force excitation is implemented using both a finite-difference time-domain scheme and a digital waveguide model. The two models are designed so as to have the exact same features but for the two stiffness-related solutions. The numerical experiments study the contact force signal over time for different initial velocity values. The resulting sounds are also discussed. The results generally confirm that the two fast-decaying waves cannot be ignored during simulation. The effect of string stiffness becomes more audible in the low register of the piano as the initial velocity increases, whereas in the high-frequency region results are more ambiguous. This work constitutes my MA Dissertation at the Sonic Arts Research Centre, under the supervision of Dr. Maarten van Walstijn.