Phantom partials are anomalous overtones in the spectrum of the piano sound that occur at sum and difference frequencies of the natural overtones of the string. Although they are commonly assumed to be produced by forced longitudinal waves in the string, analysis of the sound of a piano produced by mechanically vibrating the soundboard while all the strings are damped indicates that phantom partials can occur in the absence of string motion. The magnitude of the effect leads to the conclusion that nonlinearity in the non-string components may be responsible for some of the power in the phantom partials.
The Journal of the Acoustical Society of America 142, EL344 (2017); doi: http://dx.doi.org/10.1121/1.5006351
The Journal of the Acoustical Society of America