of emitting a note. But we shall
find, if we experiment, that the note of a stopped pipe is an octave
lower than that of an open pipe of equal length. This is explained by
Fig. 137, _1_. The air-column in the pipe (of the same length as that in
Fig. 136) divides itself, when an end is blown across, into two equal
portions at the node B, the natural point to obtain equilibrium. A pulse
will pass from A or A^1 to B and back again in half the time required
to pass from A to B and back in Fig. 136, _1_; therefore the note is an
octave higher.

[Illustration: FIG. 137.--Showing how harmonics of an open pipe are
formed, B, B^1, and C are "nodes." The arrows indicate the distance
travelled by a sound impulse from a node to a node.]

THE OVERTONES OF AN OPEN PIPE.

The first overtone results when nodes form as in Fig. 137, _2_, at
points one-quarter of the length of the pipe from the ends, giving one
complete ventral segment and two semi-ventral segments. The vibrations
now are twice as rapid as before. The second overtone requires three
nodes, as in Fig. 137, _3_. The rate has now trebled. So that, while
the overtones of a closed pipe rise in the ratio 1, 3, 5, 7, etc.,
those of an open pipe rise in the proportion 1, 2, 3, 4, etc.

WHERE OVERTONES ARE USED.

In the flute, piccolo, and clarionet, as well as in the horn class of
instrument, the overtones are as important as the fundamental notes. By
artificially altering the length of the column of air, the fundamental
notes are also altered, while the harmonics of each fundamental are
produced at will by varying the blowing pressure; so that a continuous
chromatic, or semitonal, scale is possible throughout the compass of the
instrument.

THE ORGAN.

From the theory of acoustics[30] we pass to the practical application,
and concentrate our attention upon the grandest of all wind instruments,
the pipe organ. This mechanism has a separate pipe for every note,
properly proportioned. A section of an ordinary wooden pipe is given in
Fig. 138. Wind rushes up through the foot of the pipe into a little
chamber, closed by a block of wood or a plate except for a narrow slit,
which directs it against the sharp lip A, and causes a fluttering, the
proper pulse of which is converted by the air-column above into a
musical sound.

[Illustration: FIG. 138.--Section of an ordinary wooden "flue" pipe.]

In even the smallest organs more than one pipe is actuated by one key on
the