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 subst.i.tute 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.
RESONANCE OF COLUMNS OF AIR.
Why does a tube closed at one end, such as the shank of a key, emit a note when we blow across the open end? The act of blowing drives a thin sheet of air against the edge of the tube and causes it to vibrate. The vibrations are confused, some "pulses" occurring more frequently than others. If we blew against the edge of a knife or a piece of wood, we should hear nothing but a hiss. But when, as in the case which we are considering, there is a partly-enclosed column of air close to the pulses, this selects those pulses which correspond to its natural period of vibration, and augments them to a sustained and very audible musical sound.
[Ill.u.s.tration: FIG 136.--Showing how the harmonics of a "stopped" pipe are formed.]
In Fig. 136, _1_ is a pipe, closed at the bottom and open at the top. A tuning-fork of the same note as the pipe is struck and held over it so that the p.r.o.ngs vibrate upwards and downwards. At the commencement of an outward movement of the p.r.o.ngs the air in front of them is _compressed_.
This impulse, imparted to the air in the pipe, runs down the column, strikes the bottom, and returns. Just as it reaches the top the p.r.o.ng is beginning to move inwards, causing a _rarefaction_ of the air behind it. This effect also travels down and back up the column of air in the pipe, reaching the p.r.o.ng just as it arrives at the furthest point of the inward motion. The process is repeated, and the column of air in the pipe, striking on the surrounding atmosphere at regular intervals, greatly increases the volume of sound. We must observe that if the tuning-fork were of too high or too low a note for the column of air to move in perfect sympathy with it, this increase of sound would not result. Now, when we blow across the end, we present, as it were, a number of vibrating tuning-forks to the pipe, which picks out those air-pulses with which it sympathizes.
LENGTH AND TONE.
The rate of vibration is found to be inversely proportional to the length of the pipe. Thus, the vibrations of a two-foot pipe are twice as rapid as those of a four-foot pipe, and the note emitted by the former is an octave higher than that of the latter. A one-foot pipe gives a note an octave higher still. We are here speaking of the _fundamental_ tones of the pipes. With them, as in the case of strings, are a.s.sociated the _overtones_, or harmonics, which can be brought into prominence by increasing the pressure of the blast at the top of the pipe. Blow very hard on your key, and the note suddenly changes to one much shriller. It is the twelfth of the fundamental, of which it has completely got the upper hand.
We must now put on our thinking-caps and try to understand how this comes about. First, let us note that the vibration of a body (in this case a column of air) means a motion from a point of rest to a point of rest, or from node to node. In the air-column in Fig. 136, _1_, there is only one point of rest for an impulse--namely, at the bottom of the pipe. So that to pa.s.s from node to node the impulse must pa.s.s up the pipe and down again. The distance from node to node in a vibrating body is called a _ventral segment_. Remember this term. Therefore the pipe represents a semi-ventral segment when the fundamental note is sounding.
When the first overtone is sounded the column divides itself into two vibrating parts. Where will the node between them be? We might naturally say, "Half-way up." But this cannot be so; for if the node were so situated, an impulse going down the pipe would only have to travel to the bottom to find another node, while an impulse going up would have to travel to the top and back again--that is, go twice as far. So the node forms itself _one-third_ of the distance down the pipe. From B to A (Fig. 136, _2_) and back is now equal to from B to C. When the second overtone is blown (Fig. 136, _3_) a third node forms. The pipe is now divided into _five_ semi-ventral segments. And with each succeeding overtone another node and ventral segment are added.
The law of vibration of a column of air is that the number of vibrations is directly proportional to the number of semi-ventral segments into which the column of air inside the pipe is divided.[29] If the fundamental tone gives 100 vibrations per second, the first overtone in a closed pipe must give 300, and the second 500 vibrations.
THE OPEN PIPE.
A pipe open at both ends is capable 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 pa.s.s from A or A^1 to B and back again in half the time required to pa.s.s from A to B and back in Fig. 136, _1_; therefore the note is an octave higher.
[Ill.u.s.tration: 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 cla.s.s 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 compa.s.s of the instrument.
THE ORGAN.
From the theory of acoustics[30] we pa.s.s 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.
[Ill.u.s.tration: 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 keyboard, for not only do pipes of different shapes give different qualities of tone, but it is found desirable to have ranks of pipes with their bottom note of different pitches. The length of an open pipe is measured from the edge of the lip to the top of the pipe; of a stopped pipe, from the lip to the top and back again. When we speak of a 16 or 8 foot rank, or stop, we mean one of which the lowest note in the rank is that produced by a 16 or 8 foot open pipe, or their stopped equivalents (8 or 4 foot). In a big organ we find 32, 16, 8, 4, and 2 foot stops, and some of these repeated a number of times in pipes of different shape and construction.
THE ARRANGEMENT OF THE PIPES.
We will now study briefly the mechanism of a very simple single-keyboard organ, with five ranks of pipes, or stops.
[Ill.u.s.tration: FIG. 139.--The table of a sound-board.]
It is necessary to arrange matters so that the pressing down of one key may make all five of the pipes belonging to it speak, or only four, three, two, or one, as we may desire. The pipes are mounted in rows on a _sound-board_, which is built up in several layers. At the top is the _upper board_; below it come the _sliders_, one for each stop; and underneath that the _table_. In Fig. 139 we see part of the table from below. Across the under side are fastened parallel bars with s.p.a.ces (shown black) left between them. Two other bars are fastened across the ends, so that each groove is enclosed by wood at the top and on all sides. The under side of the table has sheets of leather glued or otherwise attached to it in such a manner that no air can leak from one groove to the next. Upper board, sliders, and table are pierced with rows of holes, to permit the pa.s.sage of wind from the grooves to the pipes. The grooves under the big pipes are wider than those under the small pipes, as they have to pa.s.s more air. The bars between the grooves also vary in width according to the weight of the pipes which they have to carry. The sliders can be moved in and out a short distance in the direction of the axis of the rows of pipes. There is one slider under each row. When a slider is in, the holes in it do not correspond with those in the table and upper board, so that no wind can get from the grooves to the rank over that particular slider. Fig. 140 shows the manner in which the sliders are operated by the little k.n.o.bs (also called stops) projecting from the casing of the organ within convenient reach of the performer"s hands. One stop is in, the other drawn out.
[Ill.u.s.tration: FIG. 140.]
In Fig. 141 we see the table, etc., in cross section, with a slider out, putting the pipes of its rank in communication with the grooves. The same diagram shows us in section the little triangular _pallets_ which admit air from the _wind-chest_ to the grooves; and Fig. 142 gives us an end section of table, sliders, and wind-chest, together with the rods, etc., connecting the key to its pallet. When the key is depressed, the _sticker_ (a slight wooden rod) is pushed up. This rocks a _backfall_, or pivoted lever, to which is attached the _pulldown_, a wire penetrating the bottom of the wind-chest to the pallet. As soon as the pallet opens, wind rushes into the groove above through the aperture in the leather bottom, and thence to any one of the pipes of which the slider has been drawn out. (The sliders in Fig. 142 are solid black.) It is evident that if the sound-board is sufficiently deep from back to front, any number of rows of pipes may be placed on it.
[Ill.u.s.tration: FIG. 141.]
PEDALS.
The organ pedals are connected to the pallets by an action similar to that of the keys. The pedal stops are generally of deep tone, 32-foot and 16-foot, as they have to sustain the ba.s.s part of the musical harmonies. By means of _couplers_ one or more of the keyboard stops may be linked to the pedals.
SEPARATE SOUND-BOARDS.
The keyboard of a very large organ has as many as five _manuals_, or rows of keys. Each manual operates what is practically a separate organ mounted on its own sound-board.
[Ill.u.s.tration: FIG. 142.]
[Ill.u.s.tration: FIG. 143.--General section of a two-manual organ.]
The manuals are arranged in steps, each slightly overhanging that below. Taken in order from the top, they are:--(1.) _Echo organ_, of stops of small scale and very soft tone, enclosed in a "swell-box." (2.) _Solo organ_, of stops imitating orchestral instruments. The wonderful "vox humana" stop also belongs to this manual. (3.) _Swell organ_, contained in a swell-box, the front and sides of which have shutters which can be opened and closed by the pressure of the foot on a lever, so as to regulate the amount of sound proceeding from the pipes inside.
(4.) _Great organ_, including pipes of powerful tone. (5.) _Choir organ_, of soft, mellow stops, often enclosed in a swell-box. We may add to these the _pedal organ_, which can be coupled to any but the echo manual.