A Piano Note
A piano note is produced by a hammer striking a metal string, or striking a group of two or three identical strings. The sonic character of the resulting note depends on the string diameter and tension, where it is struck, the hammer construction, the soundboard, lid position, and even the type of surface under the piano (not to mention the room it is in). As an indication of the complexity involved, Russell and Rossing demonstrate that the "voicing" of the felt covering the piano hammer, and the force of hitting the key, have a significant effect on the spectra of the notes. Among their findings are that the felt behaves in a non-linear manner, and striking the key harder shifts the excitation spectrum upward in frequency. This implies a brighter sound for a fortissimo note. There is also a wide variation of overtone production between the bass, middle, and treble ranges.
The overtones give a piano its characteristic sound, and make the difference between a Bösendorfer and a tinny upright. Compare the sound of a real piano note [42 kb] and a tone [42 kb], both with a fundamental frequency of 662 Hz. The envelope of the tone has been contoured to have approximately the same shape (attack and decay) as the note, but it completely lacks overtones. The spectrum of the note shows a rather complex structure [52kb]. The red circles are at integer multiples of the fundamental frequency. Everest states (page 83) that due to the stiffness of piano strings, the overtones are not strictly harmonic. But this particular note seems to follow the harmonic pattern pretty closely. An interesting feature is that the piano note actually has multiple peaks around the fundamental, separated by a few Hz. This is probably due to the three strings, which form this note, having slightly different tensions. The consequence is that there is a beat in the note. I suspect that the piano tuner intentionally introduces this effect, but I don't know for sure.
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1. D. Russell and T. Rossing, "Testing the Nonlinearity of Piano Hammers Using Residual Shock Spectra, Acta Acustica, Vol 84 (1998), pp967-975. Also see Dan Russell's web site.