Estimated loudness for the acoustic pressure signals, S, as a function of the average key acceleration 〈A〉. The data are obtained from all considered excitations using the mechanical arm (see Tab. 1). The maximums of S, S_max, produced on each key by the first author (who is also a pianist) with a pressed touch are shown. S is reported in sones on the left-side y-axis and as percentage over S_max on the right-side y-axis. The data have been approximated by a robust non-linear regression with a power law of the form $S=b_1+b_2{\langle A\rangle }^{b_3}$, where 〈A〉 is expressed in cm/s². The coefficients of the estimation are shown in figure. The standard deviation of the estimates is indicated in parentheses as uncertainty on the least significant digit.