; this is called the first overtone. When
the string is made to move as in Figure 183, three distinct motions
are called forth, the motion of the entire string, the motion of the
portion plucked, and the motion of the remaining unplucked portion of
the string. Here, naturally, different tones arise, corresponding to
the different modes of vibration. The note produced by the vibration
of one third of the original string is called the second overtone.

The above experiments show that a string is able to vibrate in a
number of different ways at the same time, and to emit simultaneously
a number of different tones; also that the resulting complex sound
consists of the fundamental and one or more overtones, and that the
number of overtones present depends upon how and where the string is
plucked.

[Illustration: FIG. 185.--A string can vibrate in a number of
different ways simultaneously, and can produce different notes
simultaneously.]

269. The Value of Overtones. The presence of overtones determines
the quality of the sound produced. If the string vibrates as a whole
merely, the tone given out is simple, and seems dull and
characterless. If, on the other hand, it vibrates in such a way that
overtones are present, the tone given forth is full and rich and the
sensation is pleasing. A tuning fork cannot vibrate in more than one
way, and hence has no overtones, and its tone, while clear and sweet,
is far less pleasing than the same note produced by a violin or piano.
The untrained ear is not conscious of overtones and recognizes only
the strong dominant fundamental. The overtones blend in with the
fundamental and are so inconspicuously present that we do not realize
their existence; it is only when they are absent that we become aware
of the beauty which they add to the music. A song played on tuning
forks instead of on strings would be lifeless and unsatisfying because
of the absence of overtones.

It is not necessary to hold finger or pencil at the points 1:3, 1:4,
etc., in order to cause the string to vibrate in various ways; if a
string is merely plucked or bowed at those places, the result will be
the same. It is important to remember that no matter where a string of
definite length is bowed, the note most distinctly heard will be the
fundamental; but the quality of the emitted tone will vary with the
bowing. For example, if a string is bowed in the middle, the effect
will be far less pleasing than though it were b