Beating frequency and amplitude modulation of the piano tone due to coupling of tones.

The influence on a piano tone from weak coexcitation of damped adjacent tones due to coupling via the bridge is studied. The frequency and amplitude modulation of the sound resulting from coexcitation of one strong and one or two weak tones is analyzed. One weak tone causes frequency and amplitude modulation of the sound, and two weak tones produce beating frequency and amplitude modulation, where the beatings of the two modulations are of opposite phase. By digital recording of the sound of piano tones, the appearance of these phenomena is verified. The audibility of the observed frequency and amplitude modulation is discussed in terms of previously determined detection thresholds. The beating character of both frequency and amplitude modulations, however, distinguishes the phenomena from those previously studied and prompts further psychoacoustic investigations. It is shown that detuning of unison strings may significantly increase the frequency deviation of the frequency modulation in conjunction with affected amplitude modulation. The modulatory effects of coupling to adjacent tones therefore may possibly be utilized in the tuning process. A coupling of tones analogous to the situation in a piano may arise in other stringed musical instruments transferring string vibrations to a soundboard via a bridge.