All the overtones which depend on this division, those with six times,
nine times, twelve times the rate of vibration of the fundamental one,
are also withdrawn from the clang. Let us now pluck 20, damping 33 as
before. The second harmonic is not extinguished, but continues to sound
clearly and fully after the extinction of the fundamental tone. In
this case the point 33 not being that plucked, a node can form there,
and the string can divide itself into three parts accordingly. In like
manner, if 25 be plucked and then damped, the third harmonic is not
heard; but when a point between 25 and the end of the wire is plucked,
and the point 25 damped, the third harmonic is plainly heard. And thus
we might proceed, the general rule enunciated by Young, and illustrated
by these experiments, being, that when any point of a string is plucked
or struck, or, as Helmholtz adds, agitated with a bow, the harmonic
which requires that point for a node vanishes from the general clang of
the string.
§ 10. _Mingling of Overtones with Fundamental. The Æolian Harp_
You are now in a condition to estimate the influence which these
higher vibrations must have upon the quality of the tone emitted by
the string. The sounds which ring in your ears so plainly after the
fundamental tone is quenched mingled with that note before it was
extinguished. It seems strange that tones of such power could be
so masked by the fundamental one that even the disciplined ear of a
musician is unable to separate the one from the other. But Helmholtz
has shown that this is due to want of practice and attention. The
musician’s faculties were never exercised in this direction. There
are numerous effects which the musician can distinguish, because his
art demands the habit of distinguishing them. But it is no necessity
of his art to resolve the clang of an instrument into its constituent
tones. By attention, however, even the unaided ear can accomplish this,
particularly if the mind be informed beforehand what the ear has to
bend itself to find.
Public-domain text, read in full here on John Shaqi.
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