Computer synthesis of a piano tone
Mindy L. Garber, Jont B. Allen · The Journal of the Acoustical Society of America · 1982
Attempts to simulate piano tones by summing sine waves of inharmonic frequenices have not been totally successful in the past. The physical understanding of what happens to a string inside a piano has never been fully modeled in all detail. A program has been developed to synthesize a piano sound by creating a model of vibrating string. The model is formed by using a differential equation to describe the motion of the string. The terms in the equation account for both the inharmonicity due to the string's stiffness and the decay rates for each harmonic due to the string's internal damping. The model is obtained by solving the differential equation in discrete time steps using fast Fourier transforms in the spatial domain. The waveform of the string is then determined and can be sampled at each step in time.