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.
[Illustration: 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 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.[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 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 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.
[Illustration: 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 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.
[Illustration: 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.
[Illustration: 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 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.
[Illustration: FIG. 142.]
[Illustration: 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.
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.
[Illustration: FIG. 144.--A reed pipe.]
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.
[Illustration: FIG. 145.--The keyboard and part of the pneumatic
mechanism of the Hereford Cathedral organ. C, composition pedals for
pushing out groups of stops; P (at bottom), pedals; P P (at top), pipes
carrying compressed air; M, manuals (4); S S, stops.]
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."[31]
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.
[29] It is obvious that in Fig. 136, _2_, a pulse will pass from A to B
and back in one-third the time required for it to pass from A to B and
back in Fig. 136, _1_.
[30] The science of hearing; from the Greek verb, [Greek: akouein], "to
hear."
[31] "Organs and Tuning," p. 245.