Generation of partials due to nonlinear mixing in a stringed instrument

Abstract

Nonlinear mixing appears to account for the production of “phantom partials” in piano tones. “Phantom partials” are those that appear at frequencies exactly harmonic to normal inharmonic string partials, and at frequencies equal to the sums of the frequencies of normal inharmonic partials. Nonlinear mixing can occur because tension varies during transverse vibration. This produces longitudinal string forces of phantom-partial frequency that appear at the soundboard bridge and are coupled to the soundboard. “Phantom partials” were found in piano tones, in the motion of a piano bridge, in the longitudinal vibrations of a monochord string, in the acoustical output of a soundboard coupled to a monochord string, and in the acoustical output of a guitar. Any plucked-string or struck-string instrument having appreciable acoustical response to longitudinal string forces could be expected to produce phantom partials. The relation in frequency between phantom partials and normal partials, which varies with inharmonicity, may play a part in differentiating the timbre of tones at the same fundamental frequency in pianos of different size and design.