Pianolike tones of multiple strings having stiffness
William J. Strong · The Journal of the Acoustical Society of America · 1998
The strings on a piano have stiffness which gives rise to inharmonic partials that are stretched in frequency relative to harmonic values. In addition, most notes on a piano are strung with more than one string. Even though the multiple strings of a note are tuned to the same nominal frequency, they are never precisely in tune. When the multiple strings are sounded together the resulting tone has partials that increase and decrease in amplitude which results from their in-plane and out-of-phase action on the bridge. In order to illustrate these phenomena, pianolike tones for the note C4 were synthesized in which the parameters of 15 partials were specified for each of three strings. Each of the 45 partials was represented with a decaying sinusoid whose frequency, initial amplitude, and decay rate were specified. The amount of inharmonicity and out-of-tuneness of the strings were varied over a considerable range in order to make their effects apparent. Audio samples were recorded for various combinations of partial parameters.