parts, which may be further divided by subsidiary nodes. The string, considered as halved by one node, gives the first overtone, or octave of the fundamental. It may also vibrate as three parts, and give the second overtone, or twelfth of the fundamental; and as four parts, and give the third overtone, the double octave.
Now, if a string be struck at a point corresponding to a node, the overtones which require that point for a node will be killed, on account of the excessive motion imparted to the string at that spot. Thus to hit it at the middle kills the octave, the double octave, etc.; while to hit it at a point one-third of the length from one end stifles the twelfth and all its sub-multiples.
A fundamental note robbed of all its harmonics is hard to obtain, which is not a matter for regret, as it is a most uninteresting sound. To get a rich tone we must keep as many useful harmonics as possible, and therefore a piano hammer is so placed as to strike the string at a point which does not interfere with the best harmonics, but kills those which are objectionable. Pianoforte makers have discovered by experiment that the most pleasing tone is excited when the point against which the hammer strikes is one-seventh to one-ninth of the length of the wire from one end.
The nature of the material which does the actual striking is also of importance. The harder the substance, and the sharper the blow, the more prominent do the harmonics become; so that the worker has to regulate carefully both the duration of the blow and the hardness of the hammer covering.
Chapter XV.
WIND INSTRUMENTS.
Longitudinal vibration—Columns of air—Resonance of columns of air—Length and tone—The open pipe—The overtones of an open pipe—Where overtones are used—The arrangement of the pipes and pedals—Separate sound-boards—Varieties of stops—Tuning pipes and reeds—The bellows—Electric and pneumatic actions—The largest organ in the world—Human reeds.
LONGITUDINAL VIBRATION.
In stringed instruments we are concerned only with the transverse vibrations of a string—that is, its movements in a direction at right angles to the axis of the string. A string can also vibrate longitudinally—that is, in the direction of its axis—as may be proved by drawing a piece of resined leather along a violin string. In this case the harmonics "step up" at the same rate as when the movements were transverse.
Let us substitute for a wire a stout bar of metal fixed at one end only. The longitudinal vibrations of this rod contain overtones of a different ratio. The first harmonic is not an octave, but a twelfth. While a tensioned string is divided by nodes into two, three, four, five, six, etc., parts, a rod fixed at one end only is capable of producing only those harmonics which correspond to division into three, five, seven, nine, etc., parts. Therefore a free-end rod and a wire of the same fundamental note would not have the same timbre, or quality, owing to the difference in the harmonics.
COLUMNS OF AIR.
In wind instruments we employ, instead of rods or wires, columns of air as the vibrating medium. The note of the column depends on its length. In the "penny whistle," flute, clarionet, and piccolo the length of the column is altered by closing or opening apertures in the substance encircling the column.