Modelling the decay of piano sounds

We investigate piano acoustics and compare the theoretical temporal decay of individual partials to recordings of real-world piano notes from the RWC Music Database. We first describe the theory behind double decay and beats, known phenomena caused by the interaction between strings and soundboard. Then we fit the decay of the first 30 partials to a standard linear model and two physically-motivated non-linear models that take into account the coupling of strings and soundboard. We show that the use of non-linear models provides a better fit to the data. We use these estimated decay rates to parameterise the characteristic decay response (decay rates along frequencies) of the piano under investigation. The results also show that dynamics have no significant effect on the decay rate.