WIND INSTRUMENTS.

How it Works by Archibald Williams is part of the HackerNoon Books Series. You can jump to any chapter in this book here. WIND INSTRUMENTS.

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.

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.

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 prongs vibrate upwards and downwards. At the commencement of an outward movement of the prongs 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 prong 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 prong 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 associated 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 pass from node to node the impulse must pass 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. 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 pass from a or a1 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.

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 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.

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.

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 spaces (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 passage 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 pass 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 knobs (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.

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.

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 bass 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.

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.

VARIETIES OF STOPS.

We have already remarked that the quality of a stop depends on the shape and construction of the pipe. Some pipes are of wood, others of metal. Some are rectangular, others circular. Some have parallel sides, others taper or expand towards the top. Some are open, others stopped.

The two main classes into which organ pipes may be divided are:—(1.) Flue pipes, in which the wind is directed against a lip, as in Fig. 138. (2.) Reed pipes—that is, pipes used in combination with a simple device for admitting air into the bottom of the pipe in a series of gusts. Fig. 144 shows a striking reed, such as is found in the ordinary motor horn. The elastic metal tongue when at rest stands a very short distance away from the orifice in the reed. When wind is blown through the reed the tongue is sucked against the reed, blocks the current, and springs away again. A free reed has a tongue which vibrates in a slot without actually touching the sides. Harmonium and concertina reeds are of this type. In the organ the reed admits air to a pipe of the correct length to sympathize with the rate of the puffs of air which the reed passes. Reed pipes expand towards the top.

TUNING PIPES AND REEDS.

Pipes are tuned by adjusting their length. The plug at the top of a stopped pipe is pulled out or pushed in a trifle to flatten or sharpen the note respectively. An open pipe, if large, has a tongue cut in the side at the top, which can be pressed inwards or outwards for the purpose of correcting the tone. Small metal pipes are flattened by contracting the tops inwards with a metal cone like a candle-extinguisher placed over the top and tapped; and sharpened by having the top splayed by a cone pushed in point downwards. Reeds of the striking variety (see Fig. 144) have a tuning-wire pressing on the tongue near the fixed end. The end of this wire projects through the casing. By moving it, the length of the vibrating part of the tongue is adjusted to correctness.

BELLOWS.

Different stops require different wind-pressures, ranging from 1⁄10 lb. to 1 lb. to the square inch, the reeds taking the heaviest pressures. There must therefore be as many sets of bellows and wind-chests as there are different pressures wanted. A very large organ consumes immense quantities of air when all the stops are out, and the pumping has to be done by a powerful gas, water, or electric engine. Every bellows has a reservoir (see Fig. 143) above it. The top of this is weighted to give the pressure required. A valve in the top opens automatically as soon as the reservoir has expanded to a certain fixed limit, so that there is no possibility of bursting the leather sides.

ELECTRIC AND PNEUMATIC ACTIONS.

We have mentioned in connection with railway signalling that the signalman is sometimes relieved of the hard manual labour of moving signals and points by the employment of electric and pneumatic auxiliaries. The same is true of organs and organists. The touch of the keys has been greatly lightened by making the keys open air-valves or complete electric circuits which actuate the mechanism for pulling down the pallets. The stops, pedals, and couplers also employ "power." Not only are the performer's muscles spared a lot of heavy work when compressed air and electricity aid him, but he is able to have the console, or keyboard, far away from the pipes. "From the console, the player, sitting with the singers, or in any desirable part of the choir or chancel, would be able to command the working of the whole of the largest organ situated afar at the western end of the nave; would draw each stop in complete reliance on the sliders and the sound-board fulfilling their office; ... and—marvel of it all—the player, using the swell pedal in his ordinary manner, would obtain crescendo and diminuendo with a more perfect effect than by the old way."

In cathedrals it is no uncommon thing for the different sound-boards to be placed in positions far apart, so that to the uninitiated there may appear to be several independent organs scattered about. Yet all are absolutely under the control of a man who is sitting away from them all, but connected with them by a number of tubes or wires.

The largest organ in the world is that in the Town Hall, Sydney. It has a hundred and twenty-six speaking stops, five manuals, fourteen couplers, and forty-six combination studs. The pipes, about 8,000 in number, range from the enormous 64-foot contra-trombone to some only a fraction of an inch in length. The organ occupies a space 85 feet long and 26 feet deep.

HUMAN REEDS.

The most wonderful of all musical reeds is found in the human throat, in the anatomical part called the larynx, situated at the top of the trachea, or windpipe.

Slip a piece of rubber tubing over the end of a pipe, allowing an inch or so to project. Take the free part of the tube by two opposite points between the first fingers and thumbs and pull it until the edges are stretched tight. Now blow through it. The wind, forcing its way between the two rubber edges, causes them and the air inside the tube to vibrate, and a musical note results. The more you strain the rubber the higher is the note.

The larynx works on this principle. The windpipe takes the place of the glass pipe; the two vocal cords represent the rubber edges; and the arytenoid muscles stand instead of the hands. When contracted, these muscles bring the edges of the cords nearer to one another, stretch the cords, and shorten the cords. A person gifted with a "very good ear" can, it has been calculated, adjust the length of the vocal cords to 1⁄17000th of an inch!

Simultaneously with the adjustment of the cords is effected the adjustment of the length of the windpipe, so that the column of air in it may be of the right length to vibrate in unison. Here again is seen a wonderful provision of nature.

The resonance of the mouth cavity is also of great importance. By altering the shape of the mouth the various harmonics of any fundamental note produced by the larynx are rendered prominent, and so we get the different vocal sounds. Helmholtz has shown that the fundamental tone of any note is represented by the sound oo. If the mouth is adjusted to bring out the octave of the fundamental, o results. a is produced by accentuating the second harmonic, the twelfth; ee by developing the second and fourth harmonics; while for ah the fifth and seventh must be prominent.

When we whistle we transform the lips into a reed and the mouth into a pipe. The tension of the lips and the shape of the mouth cavity decide the note. The lips are also used as a reed for blowing the flute, piccolo, and all the brass band instruments of the cornet order. In blowing a coach-horn the various harmonics of the fundamental note are brought out by altering the lip tension and the wind pressure. A cornet is practically a coach-horn rolled up into a convenient shape and furnished with three keys, the depression of which puts extra lengths of tubing in connection with the main tube—in fact, makes it longer. One key lowers the fundamental note of the horn half a tone; the second, a full tone; the third, a tone and a half. If the first and third are pressed down together, the note sinks two tones; if the second and third, two and a half tones; and simultaneous depression of all three gives a drop of three tones. The performer thus has seven possible fundamental notes, and several harmonics of each of these at his command; so that by a proper manipulation of the keys he can run up the chromatic scale.

We should add that the cornet tube is an "open" pipe. So is that of the flute. The clarionet is a "stopped" pipe.

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