The presence of phantom partials in the spectra of the piano sound are well known, and for decades they have been attributed to forced longitudinal vibrations in the string. These vibrations are generally assumed to originate with the stretching of the string, which produces frequency components at the sums, differences and second harmonics of the resonant frequencies of the transverse string motion. Results of recent experiments indicate that phantom partials can be produced in other parts of the piano as well as the string, and in some cases these contributions to the sound can be significant. Measurements of the power in multiple phantom partials produced simultaneously by steady-state excitation are providing insight into the process that creates them.
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.
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