duction of several tones.

268. The Freedom of a String. Some stringed instruments give forth
tones which are clear and sweet, but withal thin and lacking in
richness and fullness. The tones sounded by two different strings may
agree in pitch and loudness and yet produce quite different effects on
the ear, because in one case the tone may be much more pleasing than
in the other. The explanation of this is, that a string may vibrate in
a number of different ways.

Touch the middle of a wire with the finger or a pencil (Fig. 182),
thus separating it into two portions and draw a violin bow across the
center of either half. Only one half of the entire string is struck,
but the motion of this half is imparted to the other half and throws
it into similar motion, and if a tiny A-shaped piece of paper or rider
is placed upon the unbowed half, it is hurled off.

[Illustration: FIG. 183.--The string vibrates in three portions.]

If the wire is touched at a distance of one third its length and a bow
is drawn across the middle of the smaller portion, the string will
vibrate in three parts; we cannot always see these various motions in
different parts of the string, but we know of their existence through
the action of the riders.

Similarly, touching the wire one fourth of its length from an end
makes it vibrate in four segments; touching it one fifth of its length
makes it vibrate in five segments.

In the first case, the string vibrated as a whole string and also as
two strings of half the length; hence, three tones must have been
given out, one tone due to the entire string and two tones due to the
segments. But we saw in Section 267 that halving the length of a
string doubles the pitch of the resulting tone, and produces the
octave of the original tone; hence a string vibrating as in Figure 183
gives forth three tones, one of which is the fundamental tone of the
string, and two of which are the octave of the fundamental tone.
Hence, the vibrating string produces two sensations, that of the
fundamental note and of its octave.

[Illustration: FIG. 184.--When a string vibrates as a whole, it gives
out the fundamental note.]

When a string is plucked in the middle without being held, it vibrates
simply as a whole (Fig. 184), and gives forth but one note; this is
called the fundamental. If the string is made to vibrate in two parts,
it gives forth two notes, the fundamental, and a note one octave
higher than the fundamental