Coupled piano strings

The admittance of the piano bridge has a crucial effect on piano tone by coupling together the strings belonging to one note into a single dynamical system. In this paper, we first develop theoretical expressions that show how the rate of energy transmission to the bridge as a function of time (including the phenomena of beats and ’’aftersound’’) depends on bridge admittance, hammr irregularities, and the exact state in which the piano is tuned. We then present experimental data showing the effects of mutual string coupling on beats and aftersound, as well as the great importance of the two polarizations of the string motion. The function of the una corda pedal in controlling the aftersound is explained, and the stylistic possibilities of a split damper are pointed out. The way in which an excellent tuner can use fine tuning of the unisons to make the aftersound more uniform is discussed.