SOUND AND MUSIC.
Our discussion of waves and ripples in the air would be very incomplete
if we left it without any further reference to the difference between
those motions in the air which constitute noise or sound, and those
to which we owe the pleasure-producing effects of musical tones. I
propose, therefore, to devote our time to-day to a brief exposition of
the properties and modes of production of those air-vibrations which
give rise to the class of sensations we call music. Sufficient has
already been said to make it clear to you that one essential difference
between sound or noise and music, as far as regards the events taking
place outside of our own organism, is that, in the first case, we
have a more or less irregular motion in the air, and, in the second,
a rhythmical movement, constituting a train of air waves. The greater
pleasure we experience from the latter is, no doubt, partly due to
their rhythmic character. We derive satisfaction from all regularly
repeated muscular movements, such as those involved in dancing,
skating, and rowing, and the agreeable sensation we enjoy in their
performance is partly due to their periodic or cyclical character.
In the same way, our ears are satisfied by the uniformly repeated and
sustained vibrations proceeding from an organ-pipe or tuning-fork in
action, but we are irritated and annoyed by the sensations set up when
irregular vibrations of the air due to the bray of a donkey or the
screech of a parrot fall upon them. Before, however, we can advance
further in an analysis of the nature of musical sounds, two things must
be clearly explained. The first of these is the meaning of the term
_natural period of vibration_, and the second is the nature of the
effect called _resonance_. You see before you three small brass balls
suspended by strings. One string is 1 foot long, the second 4 feet, and
the third 9 feet. These suspended balls are called _simple pendulums_.
Taking in my hands the balls attached to the 1-foot and the 4-foot
strings, I withdraw them a little way from their positions of rest and
let them go. They vibrate like pendulums, but, as you see, the 1-foot
pendulum makes two swings in the time that the 4-foot makes one swing.
Repeating the experiment with the 1-foot and the 9-foot pendulum, we
find that the short one now makes three swings in the time the long
one makes one swing. The inference immediately follows that these
pendulums, whose respective lengths are 1, 4, and 9 feet, make their
swings from side to side in times which are respectively in the ratio
of 1, 2, and 3.
Again, if we withdraw any of the pendulums from its position of rest
and let it swing, we shall find that in any stated period of time, say
1 minute, it executes a certain definite number of oscillations which
is peculiar to itself. You might imagine that, by withdrawing it more
or less from its position of rest, and making it swing over a larger or
smaller distance, you could make these swings per minute more or less
as you please. But you would find, on trying the experiment, that this
is not the case, and that, provided the arc of vibration is not too
great, the time of one complete swing to and fro is the same whether
the swing be large or small.
In scientific language this is called the _isochronism of the
pendulum_, and is said to have been discovered by Galileo in the
Cathedral at Pisa, when watching the swings of a chandelier die away,
whilst counting their number by the beats of his pulse. This periodic
time of vibration, which is independent of the amplitude of vibration,
provided the latter is small, is called the natural time of vibration
of the pendulum, or its _free periodic time_.
In the case of the simple pendulum the free periodic time is
proportional to the square root of the length of the pendulum.
Accordingly, a short pendulum makes more swings per minute than a long
one, and this rate of swinging is quite independent of the weight of
the bob. We can, of course, take hold of the bob with our hand and
force it to vibrate in any period we please, and thus produce a _forced
vibration_; but a _free_ vibration, or one which is unforced, has a
natural time-period of its own.
In order that any body may vibrate when displaced and then set free,
two conditions must exist. In the first place, there must be a
controlling force tending to make the substance return to its original
position when displaced. In the second place, the thing moved must
have mass or inertia, and when displaced and allowed to return it must
in consequence overshoot the mark, and acquire a displacement in an
opposite direction. In the case of the pendulum the elastic control or
restoring force is the weight of the bob, which makes it always try
to occupy the lowest position. We can, however, make a pendulum of
another kind. Here, for instance, is a heavy ball suspended by a spiral
spring (see Fig. 53). If I pull the ball down a little, and then let it
go, it jumps up and down, and executes vertical vibrations. The elastic
control here is the spring which resists extension. In this instance,
also, there is a natural free time of vibration, independent of the
extent of the motion, but dependent upon the weight of the ball and the
stiffness of the spring.
[Illustration: FIG. 53.]
A good illustration of the above principles may be found in the
construction of a clock or a watch. A clock contains a pendulum
which vibrates in a certain fixed time. The arrangements we call the
“works” of a clock are only a contrivance for counting the swings,
and recording them by the “hands” of the clock. Owing, however, to
the friction of the “works,” the pendulum would soon come to rest,
and hence we have a mainspring or “weights” which apply a little push
to the pendulum at each swing, and keep it going. In a watch there
is no pendulum, but there is a “balance-wheel and hair-spring,” or
a wheel which has a spiral spring attached to it, so that it can
swing backwards and forwards through a small angle. The so-called
“escapement” is a means by which the swings are counted, and a little
impulse given to the wheel to keep it swinging. The watch “keeps time”
if this hair-spring is of the right degree of stiffness, and the
balance-wheel of the right weight and size. Thus a clock can be made to
go faster or slower by slightly altering the length of its pendulum,
and the watch by slightly changing the stiffness of its hair-spring.
It may be noted in passing that our legs, in walking, swing like
pendulums, and every particular length of leg has its own natural time
of vibration, so that there is a certain speed at which each person can
walk which causes him or her the least amount of fatigue, because it
corresponds with the natural free or unforced period of vibration of
the leg considered as a pendulum.
We now pass on to notice another very important matter. If we have any
pendulum, or mass suspended by a spring, having therefore a certain
natural period of vibration, we can set it in motion by administering
to it small repeated blows or pushes. If the interval between these
impulses corresponds with the natural time-period of oscillation,
it will be found that quickly a very large swing is accumulated or
produced. If, on the other hand, the interval between the blows does
not correspond with the natural time of vibration, then their effect
in producing vibration is comparatively small. This may be illustrated
with great ease by means of the ball suspended by a spring. Suppose
that by means of an indiarubber puff-ball I make a little puff of air
against the suspended ball. The small impulse produces hardly any
visible effect. Let this puff be repeated at intervals of time equal
to that of the natural free period of vibration of the suspended ball.
Then we find that, in the course of a very few puffs, we have caused
a very considerable vibration or swing to take place in the heavy
ball. If, however, the puffs of air come irregularly, they produce
very little effect in setting the ball in motion. In the same manner a
pendulum, consisting of a heavy block of wood, may be set swinging over
a considerable range by a very few properly timed taps of the finger.
We may notice another instance of the effect of accumulated impulses
when walking over a plank laid across a ditch. If we tread in time with
the natural vibration-period of the flexible plank, we shall find
that very soon we produce oscillations of a dangerously large extent.
Whereas, if we are careful to make the time of our steps or movement
disagree with that of the plank, this will not be the case.
It is for this reason that soldiers crossing a suspension bridge are
often made to break step, lest the steady tramp of armed men should
happen to set up a perilous state of vibration in the bridge. It is not
untruthful to say that a boy with a pea-shooter could in time break
down Charing Cross Railway Bridge over the Thames. If we suppose a pea
shot against one of the sections of this iron bridge, there is no doubt
that it would produce an infinitesimal displacement of the bridge.
Also there is no question that the bridge, being an elastic and heavy
structure, has a natural free time of vibration. Hence, if pea after
pea were shot at the same place at intervals of time exactly agreeing
with the free time-period of vibration of the bridge, the effects would
be cumulative, and would in time increase to an amount which would
endanger the structure. Impracticable and undesirable as it might be
to carry out the experiment, it is nevertheless certainly true, that a
boy with a pea-shooter, given sufficient patience and sufficient peas,
could in time break down an iron girder bridge by the accumulation of
properly timed but infinitely small blows.
The author had an instance of this before him not long ago. He was at
a place where very large masts were being erected. One of these masts,
about 50 feet long, was resting on two great blocks of wood placed
under each end. This mast was a fine beam of timber, square in section,
and each side about 2 feet wide. The mast, therefore, lay like a bridge
on its terminal supports. Standing or jumping on the middle of this
great beam produced hardly any visible deflection. The writer, however,
placed his hand on the centre of the log and pressed it gently.
Repeating this pressure at intervals, discovery was soon made of the
natural time-period of vibration, and by repeating the pressures at the
right moment it was found that large oscillations could be accumulated.
If he had ventured to proceed far with this operation, it is certain
that, with properly timed impulses, it would have been possible, by
merely applying the pressure of one hand, to break in half this great
wooden mast.
We have constant occasion in mechanical work to notice that whereas one
pull or push of great vigour will not create some desired displacement
of an object, a number of very small hits, or properly timed pushes
or pulls, will achieve the requisite result. We might summarize the
foregoing facts by saying that it is a maxim in dealing with bodies
capable of any kind of free vibration that impulses, however small,
will create oscillations of any required magnitude, if only applied at
intervals equal to the natural free period of vibration of the body in
question.
We can illustrate these principles by a few experiments which have
special reference to musical instruments. If we fasten one end of a
rope to a fixed support, we find we can produce a wave or pulse in the
rope by jerking the free end up and down with the hand. The speed with
which a pulse or wave travels along a rope depends upon its weight per
unit of length, or, say, on the number of pounds it weighs per yard,
and on the tension or pull on the rope. The tighter the rope, the
quicker it travels; and for the same tension the heavier the rope, the
slower it travels.
It is not difficult to show that the speed with which the pulse
travels is measured by the square root of the quotient of the tension
of the rope by its weight per unit of length, or, as it may be called,
the density of the rope.
We have already explained that, in a medium such as air, a wave of
compression is propagated at a speed which is measured by the square
root of the quotient of the air-pressure, or elasticity, by its
density. In exactly the same way the hump that is formed on a rope by
giving one end of it a jerk, runs along at a speed which is measured by
the square root of the quotient of the stretching force, or tension, by
the density. The propagation of a pulse or wave along a string is most
easily shown for lecture purposes by filling a long indiarubber tube
with sand, and then hanging it up by one end. The tube so loaded has a
large weight per unit of length, and accordingly, if we give one end a
jerk a hump is created which travels along rather slowly, and of which
the movement can easily be watched. We may sometimes see a canal-boat
driver give a jerk of this kind to the end of his horse-rope, to make
it clear some obstacle such as a post or bush.
If we do this with a rope fixed at one end, we shall notice that when
the hump reaches the end it is reflected and returns upon itself. If
we represent by the letter _l_ the length of the rope, and by _t_ the
time required to travel the double distance there and back from the
free end, then the quotient of 2_l_ by _t_ is obviously the velocity of
the wave. But we have stated that this velocity is equal to the square
root of the tension of the rope (call it _e_) by the weight per unit of
length, say _m_. Hence clearly—
2_l_/_t_ = √(_e_/_m_); or _t_ = 2_l_ · √(_m_/_e_)
Supposing, then, that the jerks of the free end are given at intervals
of time equal to _t_, or to the time required for the pulse to run
along and back again, we shall find the rope thrown into so-called
_stationary waves_. If, however, the jerks come twice as quickly, then
the rope can accommodate itself to them by dividing itself into two
sections, each of which is in separate vibration; and similarly it
can divide itself into three, four, five, or six, or more sections in
stationary vibration. The rope, therefore, has not only one, but many
natural free periods of vibration, and it can adapt itself to many
different frequencies of jerking, provided these are integer multiples
of its fundamental frequency.
The above statements may be very easily verified by the use of a large
tuning-fork and a string. Let a light cord or silk string be attached
to one prong of a large tuning-fork which is maintained in motion
electrically as presently to be explained. The other end of the cord
passes over a pulley, and has a little weight attached to it. Let the
tuning-fork be set in vibration, and various weights attached to the
opposite end of the cord.
It is possible to find a weight which applies such a tension to the
cord that its time of free vibration, as a whole, agrees with that of
the fork. The cord is then thrown into stationary vibration. This is
best seen by throwing the shadow of the cord upon a white screen, when
it will appear as a grey spindle-shaped shadow. The central point A of
the spindle is called a ventral point, or anti-node, and the stationary
points N are called the nodes (see Fig. 54). Next let the tension of
the string be reduced by removing some of the weight attached to the
end. When the proper adjustment is made, the cord will vibrate in two
segments, and have a node at the centre. Each segment vibrates in time
with the tuning-fork, but the time of vibration of the whole cord is
double that of the fork. Similarly, by adjusting the tension, we may
make the cord vibrate in three, four, or more sections, constituting
what are called the harmonics of the string.
The string, therefore, in any particular state as regards tension and
length, has a fundamental period in which it vibrates as a whole, but
it can also divide itself into sections, each of which makes two,
three, four, or more times as many vibrations per second.
[Illustration: FIG. 54.]
In the case of a violin or piano string, we have an example of the
same action. In playing the violin, the effective length of the string
is altered by placing the finger upon it at a certain point, and then
setting the string in vibration by passing along it a bow of horsehair
covered with rosin. The string is set in vibration as a whole, and also
in sections, and it therefore yields the so-called fundamental tone,
accompanied by the _harmonics_ or _overtones_. Every violinist knows
how much the tone is affected by the point at which the bow is placed
across the string, and the reason is that the point where the bow
touches the string must always be a ventral point, or anti-node, and it
therefore determines the harmonics which shall occur.
Another good illustration of the action of properly intermittent
small impulses in creating vibrations may be found in the following
experiment with two electrically controlled tuning-forks: A large
tuning-fork, F (see Fig. 54), has fixed between its prongs an
electro-magnet, E, or piece of iron surrounded with silk-covered wire.
When an electric current from a battery, B, traverses the wire it
causes the iron to be magnetized, and it then attracts the prongs and
pulls them together. The circuit of the battery is completed through
a little springy piece of metal attached to one of the prongs which
makes contact with a fixed screw. The arrangement is such that when
the prongs fly apart the circuit is completed and the current flows,
and then the current magnetizes the iron, and this in turn pulls the
prongs together, and breaks the circuit. The fork, therefore, maintains
itself in vibration when once it has been started. It is called an
electrically driven tuning-fork. Here are two such forks, in every way
identical. One of the forks is self-driven, but the current through its
own electro-magnet is made to pass also through the electro-magnet of
the other fork, which is, therefore, not self-driven, but controlled by
the first. If, then, the first fork is started, the electro-magnet of
the second fork is traversed by intermittent electric currents having
the same frequency as the first fork, and the electro-magnet of the
second fork administers, therefore, small pulls to the prongs of the
second fork, these pulls corresponding to the periodic time of the
first fork. If, as at present, the forks are identical, and I start the
first one, or the driving fork, in action it will, in a few seconds,
cause the second fork to begin to sound. Let me, however, affix a
small piece of wax to the second fork. I have now altered its proper
period of vibration by slightly weighting the prongs. You now see
that the first fork is unable to set the second fork in action. The
electro-magnet is operating as before, but its impulses do not come at
the right time, and hence the second fork does not begin to move.
If we weight the two forks equally with wax, we can again tune them in
sympathy, and then once again they will control each other.
[Illustration: FIG. 55.—An experiment on resonance.]
All these cases, in which one set of small impulses at proper
intervals of time create a large vibration in the body on which
they act, are said to be instances of _resonance_. A more perfect
illustration of acoustic resonance may be brought before you now.
Before me, on the table, is a tall glass cylindrical jar, and I have
in my hand a tuning-fork, the prongs of which make 256 vibrations
per second when struck (see Fig. 55). If the fork is started in
action, you at a distance will hear but little sound. The prongs of
the fork move through the air, but they do not set it in very great
oscillatory movement. Let us calculate, however, the wave-length
of the waves given out by the fork. From the fundamental formula,
_wave-velocity_ = _wave-length_ × _frequency_; and knowing that the
velocity of sound at the present temperature of the air is about
1126 feet per second, we see at once that the length of the air wave
produced by this fork must be nearly 4·4 feet, because 4·4 × 256 =
1126·4. Hence the quarter wave-length is nearly 1·1 foot, or, say, 1
foot 1 inch.
I hold the fork over this tall jar, and pour water into the jar until
the space between the water-surface and the top of the jar is a little
over 1 foot, and at that moment the sound of the fork becomes much
louder. The column of air in the jar is 1·1 foot in length and this
resounds to the fork. You will have no difficulty in seeing the reason
for this in the light of previous explanations. The air column has a
certain natural rate of vibration, which is such that its fundamental
note has a wave-length four times the length of the column of air.
In the case of the rope fixed at one end and jerked up and down at
the other so as to make stationary vibrations, the length of the rope
is one quarter of the wave-length of its stationary wave. This is
easily seen if we remember that the fixed end must be a _node_, and
the end moved up and down must be an _anti-node_, or ventral segment,
and the distance between a node and an anti-node is one quarter of a
wave-length. Accordingly the vibrating column of air in the jar also
has a fundamental mode of vibration, such that the length of the column
is one quarter of a wave-length. Hence the vibrating prongs of the
256-period tuning-fork, when held over the 1·1 foot long column of air,
are able to set the air in great vibratory movement, for the impulses
from the prongs come at exactly the right time. Accordingly, the loud
sound you hear when the fork is held over the jar proceeds, not so
much from the fork as from the column of air in the jar. The prongs of
the fork give little blows to the column of air, and these being at
intervals equal to the natural time-period of vibration of the air in
the jar, the latter is soon set in violent vibration.
We can, in the next place, pass on now to discuss some matters
connected with the theory of music. When regular air-vibrations or
wave-trains fall upon the ear they produce the sensation of a musical
tone, provided that their frequency lies between about 40 per second
and about 4000. The lowest note in an organ usually is one having 32
vibrations per second, and the highest note in the orchestra is that of
a piccolo flute, giving 4752 vibrations per second. We can appreciate
as sound vibrations lying between 16 and 32,000, but the greater
portion of these high frequencies have no musical character, and would
be described as whistles or squeaks.
When one note has twice the frequency of another it is called the
_octave_ of the first. Thus our range of musical tones is comprised
within about seven octaves, or within the limits of the notes whose
frequencies are 40, 80, 160, 320, 640, 1280, 2560, and 5120.
These musical notes are distinguished, as every one knows, by certain
letters or signs on a _clef_. Thus the note called the middle C of a
piano has a frequency of 248, and is denoted by the sign
[Illustration]
The octave is divided into certain musical _intervals_ by notes, the
frequencies of which have a certain ratio to that of the fundamental
note. This ratio is determined by what is called the _scale_, or
_gamut_. Thus, in the major diatonic natural scale, if we denote
the fundamental note by C, called _do_ or _ut_ in singing, and its
frequency by _n_, then the other notes in the natural scale are denoted
by the letters, and have frequencies as below.
_do_ _re_ _mi_ _fa_ _sol_ _la_ _si_ _do′_
C D E F G A B C^1
n ⁹⁄₈n ⁵⁄₄n ⁴⁄₃n ³⁄₂n ⁵⁄₃n ¹⁵⁄₈n 2n
Hence if the note C has 248 vibrations per second, then the note D will
have 9 × 248 ÷ 8 = 279 vibrations per second. On looking at the above
scale of the eight notes forming an octave, it will be seen that there
are three kinds of ratios of frequencies of the various notes.
(1) The ratio of C to D, or F to G, or A to B, which is
that of 8 to 9.
(2) The ratio of D to E, and G to A, which is that of
9 to 10.
(3) The ratio of E to F, or B to C^1, which is that of
15 to 16.
The first two of these intervals or ratios are both called _a tone_,
and the third is called _a semitone_. The two tones, however, are not
exactly the same, but their ratio to one another is that of ⁸⁄₉ to
⁹⁄₁₀ or of 80 to 81. This interval is called a _comma_, and can be
distinguished by a good musical ear.
Several of these intervals or ratios of frequencies have received
names. Thus the interval C to E, = 4:5, is called a _major third_, and
the interval E to G, = 5:6, is called a _minor third_; the interval
C to G, = 2:3, is called a _fifth_, and that of C to C^1, = 1:2,
is called an _octave_. For the purposes of music it has been found
necessary to introduce other notes between the seven notes of the
octave. If a note is introduced which has a frequency greater than any
one of the seven in the ratio of 25 to 24, that is called a _sharpened_
note; thus the note of which the frequency is ³⁄₂_n_ × ²⁵⁄₂₄ would be
called _G sharp_, and written G♯. In the same way, if the frequency
of any note is lowered in the ratio of 24 to 25, it is said to be
_flattened_. Then the note whose frequency is ³⁄₂_n_ × ²⁴⁄₂₅ would be
called _G flat_, and written G♭.
It is obvious that if we were to introduce flats and sharps to all the
eight notes we should have twenty-four notes in the octave, and the
various intervals would become too numerous and confusing for memory
or performance. Hence in keyed instruments the difficulty has been
overcome by employing a _scale of equal temperament_, made as follows:
The interval of an octave is divided into twelve parts by introducing
eleven notes, the ratio of the frequency of each note to its neighbours
on either side being the same, and equal to the ratio 1 to 1·05946.
The scale thus formed is called the _chromatic scale_, and by this
means a number of the flats and sharps become identical; thus, for
instance, C♯ and D♭ become the same note. The octave has therefore
twelve notes, which are the seven white keys, and the five black ones
of the octave of the keyboard of a piano or organ.
Every one not entirely destitute of a musical ear is aware that
certain of these musical intervals, such as the fifth, the octave,
or the major third, produce an agreeable impression on the ear when
the notes forming them are sounded together. On the other hand, some
intervals, such as the seventh, are not pleasant. The former we call
_concords_, and the latter _discords_. The question then arises—What is
the reason for this difference in the effect of the air-vibrations on
the ear? This leads us to consider the nature of simple and complex air
vibrations or waves.
Let us consider, in the first place, the effect of sending out into
the air two sets of air waves of slightly different wave lengths.
These waves both travel at the same rate, hence we shall not affect
the combined effects of the waves upon the air if we consider both
sets of waves to stand still. For the sake of simplicity, we will
consider that the wave-length of one train is 20 inches, and that
of the other is 21. Moreover, let the two wave-trains be so placed
relatively to one another that they both start from one point in the
same phase of movement; that is, let their zero points, or their humps
or hollows, coincide. Then if we draw two wavy lines (see Fig. 56)
to represent these two trains, it will be evident that, since the
wave-length of one is 1 inch longer than that of the other—that is, a
distance equal to twenty wave-lengths—one wave-train will have gained
a whole wave-length upon the other, and in a distance equal to ten
wave-lengths, one wave train will have gained half a wave-length upon
the other. If we therefore imagine the two wave-trains superimposed,
we shall find, on looking along the line of propagation, an alternate
doubling or destruction of wave-effect at regular intervals. In other
words, the effect of superimposing two trains of waves of slightly
different wave-lengths is to produce a resultant wave-train in which
the wave-amplitude increases up to a certain point, and then dies away
again nearly to nothing, as shown in the lowest of the three wave-lines
in Fig. 56.
[Illustration: FIG. 56.—The formation of beats by two wave-trains.]
We must, then, determine how far apart these points of maximum
wave-amplitude or points of no wave effect lie. If the wave-length of
one train is, as stated, 20 inches, then a length of ten wave-lengths
is 200 inches, and this must be, therefore, the distance from a
place of maximum combined wave-effect to a place of zero wave-effect.
Accordingly, the distance between two places where the two wave trains
help one another must be 400 inches, and this must also be the distance
between two adjacent places of wave-destruction. If, therefore, we look
along the wavy line representing the resultant wave, every 400 inches
we shall find a maximum wave-amplitude, and every 400 inches a place
where the waves have destroyed each other. We may call this distance
_a wave-train length_, and it is obviously equal to the product of
the constituent wave-lengths divided by the difference of the two
constituent wave-lengths.
It follows from this that if we suppose the two wave-trains to move
forward with equal speed, the number of maximum points or zero points
which will pass any place in the unit of time will be equal to the
_difference_ between the frequencies of the constituents. Let us now
reduce this to an experiment. Here are two organ-pipes exactly tuned
to unison, and when both are sounded together we have two identical
wave-trains sent out into the air. We can, however, slightly lengthen
one of the pipes, and so put them out of tune. When this is done you
can no longer hear the smooth sound, but a sort of waxing and waning
in the sound, and this alternate increase and diminution in loudness
is called _a beat_. We can easily take count of the number of beats
per second, and by the reasoning given above we see that the number
of beats per second must be equal to the difference between the
frequencies of the two sets of waves. Thus if one organ-pipe is giving
100 vibrations per second to the air, and the other 102, we hear two
beats per second.
Now, up to a certain point we can count these beats, but when they
come quicker than about 10 per second, we cease to be able to hear them
separately. When they come at the rate of about 30 per second they
communicate to the combined sound a peculiar rasping and unpleasant
effect which we call a discord. If they come much more quickly than 70
per second we cease to be conscious of their presence by any discordant
effect in the sound.
The theory was first put forward by the famous physicist, Von
Helmholtz, that the reason certain musical intervals are not agreeable
to the trained ear is because the difference between the frequencies of
the constituent fundamental tones _or the harmonics present in them_
give rise to beats, approximately of 30 to 40 per second.
In order to simplify our explanations we will deal with two cases only,
viz. that of the _octave_ interval and that of the _seventh_. The first
is a perfect concord, and the second, at least on stringed instruments,
is a discord. It has already been explained that when a string vibrates
it does so not only as a whole, but also in sections, giving out a
fundamental note with superposed harmonics. Suppose we consider the
octave of notes lying between the frequencies 264 and 528, which
correspond to the notes C and C^1 forming the middle octave on a piano.
The frequencies and differences of the eight tones in this octave are
as follows:—
FREQUENCIES OF THE NOTES OF THE MIDDLE OCTAVE OF A PIANO.
Notes. Frequency. Difference.
C 264
33
D 297
33
E 330
22
F 352
44
G 396
44
A 440
55
B 495
33
C^1 528
It will thus be seen that the differences between the frequencies of
adjacent notes are such as to make beats between them which have a
number per second so near to the limits of 30 to 40 that adjacent notes
sounded together are discords.
Suppose, however, we sound the _seventh_, viz. _C_ and _B_, together.
The frequencies are 264 and 495, and the difference is 231. Since,
then, the difference between the frequencies lies far beyond the
limit of 30 to 40 per second, how comes it that in this case we have
a discord? To answer this question we must consider the harmonics
present with the fundamentals. Write down each frequency multiplied
respectively by the numbers 1, 2, 3, 4, etc.—
C. B.
Fundamental 264 495
First harmonic 528 990
Second ” 792 1475
Third ” 1056 1980
Fourth ” 1320 2475
Fifth ” 1584 2970
On looking at these numbers we see that although the difference
between the frequencies of the two fundamentals is too great to
produce the disagreeable number of beats, yet the difference between
the frequencies of the fundamental of note B (495) and the first
harmonic of note C (528) is exactly 33, which is, therefore, the
required number. Accordingly, the discordant character of the seventh
interval played on a piano is not due to the beats between the primary
tones, but to beats arising between the first harmonic of one and the
fundamental of the other. It will be a useful exercise to the reader
to select any other interval, and write down the primary frequencies
and the overtone frequencies, or harmonics, and then determine whether
between any pairs disagreeable beats can occur.
The presence of harmonics or overtones is, therefore, a source of
discord in some cases, but nevertheless these overtones communicate a
certain character to the sound.
Helmholtz’s chief conclusions as regards the cause of concord and
discord in musical tones were as follows:—
(1) Musical sounds which are pure, that is, have no harmonics mixed up
with them, are soft and agreeable, but without brilliancy. Of this kind
are the tones emitted by tuning-forks gently struck or open organ-pipes
not blown violently.
(2) The presence of harmonics up to the sixth communicates force and
brilliancy and character to the tone. Of this kind are the notes of the
piano and organ-pipes more strongly blown.
(3) If only the uneven harmonics, viz. the first, third, fifth, etc.,
are present, the sound acquires a certain nasal character.
(4) If the higher harmonics are strong, then the sound acquires great
penetrating force, as in the case of brass instruments, trumpet,
trombone, clarionet, etc.
(5) The causes of discord are beats having a frequency of 30 to 40 or
so, taking place between the two primary tones or the harmonics of
either note.
The pleasure derived from the sound of a musical instrument is
dependent, to a large extent, on the existence of the desirable
harmonics in each tone, or on the exclusion of undesirable ones.
In the next place, let us consider a little the means at our disposal
for creating and enforcing the class of air-waves which give rise to
the sensations of musical tones. Broadly speaking, there are three
chief forms of musical air-wave-making appliance, viz. those which
depend on the vibrations of columns of air, on strings, and on plates
respectively.
One of the oldest and simplest forms of musical instrument is
that represented by the _pan-pipes_, still used as an orchestral
accompaniment in the case of the ever-popular peripatetic theatrical
display called _Punch and Judy_.
If we take a metal or wooden pipe closed at the bottom, and blow gently
across the open end, we obtain a musical note. The air in the pipe is
set in vibration, and the tone we obtain depends on the length of the
column of air, which is the same as the length of the pipe. The manner
in which this air-vibration is started is as follows: On blowing across
the open end of the pipe closed at the bottom a partial vacuum is
made in it. That this is so, can be seen in any scent spray-producer,
in which two glass tubes are fixed at right angles to each other.
One tube dips into the scent, and through the other a puff of air is
sent across the open mouth of the first. The liquid is sucked up the
vertical tube by reason of the partial vacuum made above it. If we
employ a pipe closed at the bottom and blow across the open end, the
first effect of the exhaustion is that the jet of air is partly sucked
down into the closed tube, and thus compresses the air in it. This air
then rebounds, and again a partial vacuum is made in the tube. So the
result is an alternate compression and expansion of the air in the
closed tube. The column of air is alternately stretched and squeezed,
and a state of stationary vibration is set up in the air in the tube;
just as in the case of a rope fixed at one end and jerked up and down
at the other end. The natural time-period of vibration of the column of
air in the tube controls the behaviour of the jet of air blown across
its mouth, the energy of the jet of air being drawn upon to keep the
column of air in the tube in a state of oscillation. Thus a flutter is
excited in the air in the tube, which is maintained as long as there
is a blast of air across its mouth, and this communicates to the air
outside a wave-motion. We have, therefore, a musical note produced, the
wave-length of which is four times the length of the closed tube across
the mouth of which we are blowing. Accordingly, a very simple musical
instrument such as the pan-pipes consists of a row of tubes closed at
the bottom, the tubes being of different lengths. A current of air from
the mouth is blown across the tubes taken in a certain order, and we
can obtain a simple melody by that process of selection.
[Illustration: FIG. 57.—A closed organ-pipe.]
An organ-pipe is only a more perfect means for doing the same thing.
Organ-pipes may be either open or closed pipes. Also they have
either a reed or a flute at one end for the purpose of establishing
air-vibrations when a current of air is blown into the pipe. The form
of organ-pipe most easy to understand is the closed flute pipe. This
consists of a wooden tube closed at the upper end, and at the lower end
having a foot-tube and mouthpiece as shown in section in Fig. 57. When
a gentle current of air is blown in at the foot-tube, it impinges on
the sharp edge or chamfer of the mouthpiece, and it acts just as when
blown across the open end of a simple closed pipe. That is to say, it
sets up a state of alternate compression and expansion of the air in
the pipe. At the closed end, period-changes in density in the air are
established, but no great movement takes place. At the open end or
mouth there are no great changes of density, but the air is alternately
moving in and out at the mouthpiece. The steady blast of air against
the chamfer, therefore, sets up a state of steady oscillation of the
air in the pipe, the air being squeezed up and extended alternately
so that there is first a state of compression, and then a state of
partial rarefaction in the air at the closed end of the pipe. In this
case, also, the wave-motion communicated to the surrounding air has a
wave-length equal to four times the length of the pipe.
If we open the upper end of the pipe, it at once emits a note which has
a wave-length equal to double the length of the pipe. Hence the note
emitted by an open-ended organ-pipe is an octave higher than that given
out by a closed organ-pipe of the same length.
The action of an open organ-pipe is not quite so easy to comprehend
as that of a closed pipe. The difficulty is to see how stationary air
waves can be set up in a pipe which is open at both ends. The easiest
way to comprehend the matter is as follows: When the blast of air
against the lip of the pipe begins to partially exhaust the air in it,
the rarefaction so begun does not commence everywhere in the pipe at
once. It starts from the mouthpiece end, and is propagated along the
pipe at a rate equal to the velocity of sound. The air at the open
ends of the pipe moves in to supply this reduced pressure, and, in so
doing, overshoots the mark, and the result is a region of compression
is formed in the central portions of the pipe (see Fig. 58). The
next instant this compressed air expands again, and moves out at the
two open ends of the pipe. We have thus established in the pipe an
oscillatory state which, at the central region of the pipe, consists
in an alternate compression and expansion or rarefaction of the air,
whilst at the open end and mouthpiece end there is an alternate rushing
in and rushing out of the air. Hence in the centre of the pipe we have
little or no movement of the air, but rapid alternations of pressure,
or, which is the same thing, density; and at the two ends little or no
change in density, but rapid movement of the air in and out of the pipe.
[Illustration: FIG. 58.—An open organ-pipe.]
An analogy between the vibration of the air in a closed and open
organ-pipe might be found in considering the vibration of an elastic
rod—first, when clamped at one end, and secondly, when clamped at the
two ends. The deflection of the rod at any point may be considered
to represent change of air-pressure, and the fixed point or points
the open end of the pipe at which there can be no change of density,
because there it is in close communication with the open air outside
the pipe. It is at once evident that the length of the open organ-pipe,
when sounding its fundamental tone, is one-half of the length of the
air wave it produces. Accordingly, from the formula, _wave-velocity_ =
_frequency_ × _wave-length_, we see that, since the velocity of sound
at ordinary temperature is about 1120 feet per second, an approximate
rule for obtaining the frequency of the vibrations given out by an open
organ-pipe is as follows:—
_Frequency_ = 1120 _divided by twice the length of pipe_.
We say _approximate_, because, as a matter of fact, for a reason rather
too complicated to explain here, the wave-length of the air-vibrations
is equal to rather more than double the length of the pipe. In fact,
what we may call the effective length of the pipe is equal to its real
end-to-end length increased by a fraction of its diameter, which is
very nearly four-fifths.
[Illustration: FIG. 59.]
We can confirm by experiments the statements made as to the condition
of the air in a sounding organ-pipe. Here is a pipe with three little
holes bored in it at the top, middle, and bottom (see Fig. 59). Each of
these is covered with a thin indiarubber membrane, and this, again, by
a little box which has a gas-pipe leading to it and a gas-jet connected
with it. If we lead gas into the box and light the jet, we have a
little flame, as you see. If, then, the indiarubber membrane is pressed
in and out, it will cause the gas-flame to flicker. Such an arrangement
is called a _manometric flame_, because it serves to detect or measure
changes of pressure in the pipe. The flicker of the flame when the
organ-pipe is sounded is, however, so rapid that we cannot follow it
unless we look at the image in a cubical revolving mirror of the kind
already used. When so regarded, if the flame is steady, we see a broad
band of light.
If we sound the organ-pipe gently and look at the bands of light
corresponding to the three flames, we see that the flames at the top
and bottom of the pipe are nearly steady, but that the one at the
middle of the pipe is flickering rapidly, the band of light being
changed to a saw-tooth-like form (see Fig. 60).
This shows us that rapid changes of pressure are taking place at the
centre of the pipe.
Again, if we prepare a little tambourine (by stretching parchment-paper
over a wooden ring), and lower it by a string into the sounding
organ-pipe, we shall find that grains of sand scattered over this
tambourine jump about rapidly when the membrane is held near the top or
the bottom of the pipe, but are quiescent when it is at the middle.
[Illustration: FIG. 60.]
This shows us that there is violent movement of the air at the ends,
but not in the centre, thus confirming the deductions of theory.
It should be noted that if the pipe is over-blown or sounded too
strongly, harmonics will make their appearance, and the simple state of
affairs will no longer exist.
The celebrated mathematician, Daniel Bernoulli, discovered that an
organ-pipe can be made to yield a succession of musical notes by
properly varying the pressure of the current of air blown into it.
If the pipe is an open one, then, if we call the frequency of the
primary note 1, obtained when the pipe is gently blown, if we blow
more strongly, the pipe yields notes which are the harmonics of the
fundamental one, that is to say, have frequencies represented by 2, 3,
4, 5, etc., as the blast of air increases in force.
Thus, if the pipe is one about 2 feet in length, it will yield a note
near to the middle C on a piano. If more strongly blown, it gives
a note, C^1, an octave higher, having double the frequency. If more
strongly blown still, it yields a note which is the fifth, G^1, above
the last, and has three times the frequency of the primary tone; and so
on.
If the pipe is closed at the top, then over-blowing the pipe makes it
yield the odd harmonics, or the tones which are related in frequency to
the primary tone in the ratio of 1, 3, 5, etc. Hence, if a stopped pipe
gives a note, C, its first overtone is the fifth above the octave, or
G^1.
It is usual, in adjusting the air-pressure of an organ-bellows, to
allow such a pressure as that some of the overtones, or harmonics,
shall exist. The presence of these harmonics in a note gives brilliancy
to it, whereas an absolutely pure or simple musical tone, though not
disagreeable to the ear, is not fully satisfying. Any one with a good
ear can detect these harmonics or overtones in a single note sounded
on a piano or organ due to the subdivision of the vibrating string or
air-column into sections separated by nodes.
It will be seen that the acoustic action of the organ-pipe depends
essentially upon some operation tending at the commencement to make an
expansion of the air in the pipe at one end, and subsequently to cause
an increase of air-pressure in it.
This can be effected not only by blowing into the pipe, but in another
way, by introducing a hot body into a pipe open at both ends. We can
show here as an illustration of this an interesting experiment due to
Lord Rayleigh. A long cast-iron water-pipe about 4 inches in diameter
and 8 feet long is suspended from the ceiling. About 1 foot up the
tube from the lower end a piece of iron-wire gauze is fixed (see Fig.
61). By means of a gas-burner introduced into the tube, we heat the
gauze red hot, and on withdrawing the lamp the tube suddenly emits a
deep organ-like note for a few moments. The heated metal creates an
up-draught in the tube at the lower end, and, as in the case of the
open organ-pipe, causes also an in-suction of air at the upper end.
The column of air is thus set vibrating with a point of alternate
condensation and rarefaction in the centre, and in-draughts and
out-rushes of air at the ends. Indeed, this rush of air into and out of
the pipe at the lower end during the time it is sounding its note is so
violent that if the hands are placed just below the bottom end of the
tube they will feel chilled, as if placed near an electric fan, by the
blast of air. Closing the bottom end of the pipe with a sheet of metal
at once stops the air-movement, and with it the musical note.
[Illustration: FIG. 61.]
[Illustration: FIG. 62.—Singing flame.]
In another form the experiment has long been known under the name of a
_singing flame_. A small jet of burning hydrogen gas is introduced into
a glass tube about 3 feet in length. The jet must consist of a long
narrow brass tube, and the proper position for the jet must be found by
trial (see Fig. 62). When this is done, however, the tube emits a clear
musical note, due to the tube acting as an open organ-pipe. If the
flame is examined in a revolving mirror when the tube is singing, it
will be found to be in vibration in sympathy with the movement of air
in the tube. The tube often refuses to start singing, but may be made
to do it by giving it a little tap. The actions taking place in the
tube are something as follows: When the flame is introduced, it heats
and rarefies the air around it. This causes an in-rush of air both
at the top and bottom of the tube. A state of steady oscillation is
then established, in which the air at the centre undergoes periodical
expansions and compressions, and the pressure of the air round the
flame changes in the same manner. The flame is therefore alternately
expanded and contracted. When it expands, it heats the air more. When
it is compressed, it heats it less. This variation of the flame causes
air to be sucked in or expelled from both open ends of the tube, and
establishes the state of steady vibration in accordance with the length
of the tube. The flame and the air-column act and react on each other,
and establish a state of stationary aerial oscillation in accordance
with the natural time-period of the column of air. The tube can be made
to give out not only its fundamental note, but a series of harmonics,
or overtones, with frequencies 2, 3, 4, 5, etc., times the fundamental
note, by varying the position of the flame, which must always be just
under the place where a node, or place of alternate condensation and
rarefaction, occurs.
We may, in the next place, with advantage briefly examine the
principles of construction of one musical instrument, and allude to
some recent improvements. One of the most interesting of all the
musical appliances devised by human ingenuity is the violin, comprising
as it does in its construction an art, a science, and a tradition. In
principle the violin is nothing but a wooden box, along the top of
which are stretched four strings, which are strained over a piece of
wood called a bridge. These strings have their effective length altered
in playing by placing the finger of the performer at some place on
them, and they are set in vibration by drawing over them a well-rosined
bow made of horsehair. The vibrating string communicates its vibrations
to the surface of the box or body by means of the bridge, and this
again to the air in the interior. The body thus serves two purposes.
It acts as a resonating-chamber, and also it affords a large surface
of contact with the surrounding air, whereby a greater mass of air is
set simultaneously in wave-motion. The four strings are normally tuned
in _fifths_, so that the fundamental note of each is an interval of a
fifth above the next.
The performer varies the note given by each string by shortening its
vibrating length by pressing the finger upon it. The skilled violinist
has also great control over the tone, and can determine the harmonics,
or overtones, which shall accompany the fundamental by altering the
point on the string at which the bow is applied, and lightly touching
it at some other point.
The great art in the construction of the violin rests in the
manufacture of the wooden body. Its form, materials, and minute details
of construction have been the subject of countless experiments in past
ages, and until quite recently no essential improvement was made in
the instrument as completed by the masters of violin construction
three centuries ago. In classical form the violin consists of a wooden
box of characteristic shape, composed of a back, belly, and six ribs.
These are shaped out of thin wood, the belly being made of pine, and
maple used for the rest. A neck or handle is affixed to one end, and a
tail-piece, to which the gut-strings are fastened, to the other.
The strings are strained over a thin piece of wood which rests on two
feet on the belly. One of these feet rests over a block of wood in
the interior of the box called the sound-post, and this forms a rigid
centre; the other foot stands on the resonant part of the belly. The
belly is strengthened in addition by a bar of wood, which is glued to
it just under the place where the active foot of the bridge rests. The
ribs or sides of the box are bent inwards at the centre to enable the
playing-bow to get at the strings more easily. The selection of the
wood and its varnishing is the most important part of the construction.
The wood must be elastic, and its elasticity has to be preserved by the
use of an appropriate hard varnish, or else it will not take up the
vibrations imparted by the strings. The old makers used wood which was
only just sufficiently seasoned, and applied their varnish at once.
An essential adjunct is a good bow, which is of more importance than
generally supposed. Something may be got out of a poor violin by a good
player, but no one can play with a bad bow.
The process of eliciting a musical tone from the violin is as follows:
The player, holding the instrument in the left hand, and with its tail
end pressed against the left shoulder, places a finger of the left hand
lightly on some point on a string, and sweeps the bow gently across
the string so as to set it in vibration, yielding its fundamental note,
accompanied by the lower harmonics. The purity and strength of the
note depend essentially upon the skill with which this touch of the
bow is made, creating and sustaining the same kind of vibration on the
string throughout its sweep. The string then presses intermittently
on the bridge, and this again turns, so to speak, round one foot as
round a pivot, and presses intermittently on the elastic wooden belly.
The belly takes up these vibrations, and the air in the interior is
thrown into sympathetic vibration by resonance. The sound escapes by
the _ƒ_-holes in the belly. The extraordinary thing about the violin
is that the shape of the box permits it to take up vibrations lying
between all the range of musical tones. The air-cavity does not merely
resonate to one note, but to hundreds of different rates of vibration.
The peculiar charm of the violin is the quality of the sound which
a skilled player can elicit from it. That wonderful pleading,
sympathetic, voice-like tone, which conveys so much emotional meaning
to the trained musical ear, is due to the proper admixture of the
harmonics, or overtones, with the fundamental notes. The string
vibrates not merely as a whole, but in sections. Hence the place at
which the bow touches must always be an anti-node, or ventral point,
and the smallest change in this position greatly affects the quality of
the tone.
Quite recently an entirely new departure has been made in violin
construction by Mr. Augustus Stroh, a well-known inventor. He has
abolished the wooden body and bridge, and substituted for them an
aluminium trumpet-shaped tube as the resonant chamber, ending in a
circular corrugated aluminium disc, on the centre of which rests an
aluminium lever pivoted at one point. The strings are strained over
this lever, and held on a light tube, which does duty as a point of
attachment of all parts of the instrument. The strings are the same,
and the manipulation of the instrument identical with that of the
ordinary violin. The vibrations of the strings are communicated by
the pivoted lever over which they pass to the corrugated aluminium
disc, and by this to the air lying in the trumpet-tube. This tube
points straight away from the player, and directs the air waves to
the audience in front. The tone of the new violin is declared by
connoisseurs to be remarkably full, mellow, and resonant. The notes
have a richness and power which satisfies the ear, and is generally
only to be found in the handiwork of the classical constructors of
the ordinary form of violin. One great advantage in the Stroh violin
is that every one can be made perfectly of the same excellence. The
aluminium discs are stamped out by a steel die, and are therefore
all identical. The element of chance or personal skill in making has
been eliminated by a scientific and mechanical construction. Thus
the musician becomes possessed of an instrument in which scientific
construction predominates over individual art or tradition in
manufacture, yet at the same time the musical effects which skill in
playing can produce are not at all diminished.
Whilst our attention has so far been fixed on the external operations
in the air which constitute a train of music-making waves, it seems
only appropriate to make, in conclusion, a brief reference to the
apparatus which we possess in our ears for appreciating these subtle
changes in air-pressure with certainty and pleasure. The ear itself is
a marvellous appliance for detecting the existence of waves and ripples
in the air, and it embodies in itself many of the principles which
have been explained to-day.
[Illustration: FIG. 63.—Diagram of the human ear.]
The organ of hearing is a sort of house with three chambers in it,
or, rather, two rooms and an entrance hall, with the front door
always open. This entrance passage of the ear is a short tube which
communicates at one end with the open air, being there provided with a
sound-deflecting screen in the shape of an external ornamental shell,
commonly called the ear. In many animals this external appendage
is capable of being turned into different positions, to assist in
determining the direction in which the sound wave is coming. The
entrance tube of the ear is closed at the bottom by a delicate membrane
called the tympanum, or drum. Against this drum-head the air waves
impinge, and it is pressed in and out by the changes of air-pressure.
This drum separates the outer end from a chamber called the middle ear,
and the middle ear communicates, by a sort of back staircase, or tube
called the Eustachian tube, with the cavity at the back of the mouth
(see Fig. 63).
Behind the middle ear, and buried in the bony structure of the skull,
is a third, more secret chamber, called the inner ear. This is
separated from the middle ear by two little windows, which are also
covered with delicate membranes. In the middle ear there is a chain
of three small bones linked with one another, which are connected at
one end with the tympanum, or drum, and at the other end with the
so-called oval window of the inner ear. Helmholtz has shown that this
little chain of bones forms a system of levers, by means of which the
movements of the tympanum are diminished in extent, but increased in
force in the ratio of 2 to 3.
The internal ear is the real seat of audition, and it comprises the
parts called the labyrinth, the semicircular canals, and the cochlea.
These are cavities lined with delicate membranes and filled with fluid.
In the cochlea there is an organ called Corti’s organ, which is a
veritable harp of ten thousand strings. This consists of innumerable
nerve-fibres, which are an extension of the auditory nerve. The details
of the organic structure are far too complicated for description
here. Suffice it to say that air waves, beating against the tympanum,
propagate vibrations along the chain of bones into the fluids in the
inner ear, and finally expend themselves on these nerve-fibres, which
are the real organs of sound-sensation.
Helmholtz put forward the ingenious hypothesis that each fibre in the
organ of Corti was tuned, so to speak, to a different note, and that a
composite sound falling upon the ear was analyzed or disentangled by
this organ into its constituents. Although this theory, as Helmholtz
originally stated it, has not altogether been upheld by subsequent
observation, it is certain that the ear possesses this wonderful power
of analysis. It can be shown by mathematical reasoning of an advanced
kind that any musical sound, no matter what its quality, can be
resolved into the sum of a number of selected pure sounds such as those
given by a tuning-fork.
Consider now for one moment the physical state of the air in a
concert-room in which a large orchestra is performing. The air is
traversed by a chaos of waves of various wave-lengths. The deep notes
of the violincello, organ, and trumpets are producing waves 10 to 20
feet in wave-length, which may be best described as billows in the air.
The violin-strings and middle notes of the piano, harp, or flute are
yielding air waves from 6 or 8 feet to a few inches long, whilst the
higher notes of violins and flutes are air ripples some 3 or 4 inches
in length.
If we could see the particles of the air in the concert-room, and
fasten our attention upon any one of them, we should see it executing
a most complicated motion under the combined action of these
air-wave-producing instruments. We should be fascinated by the amazing
dance of molecules to and fro and from side to side, as the medley of
waves of compression or rarefaction embraced them and drove them hither
and thither in their resistless grasp.
The tympana of our ears are therefore undergoing motions of a like
complicated kind, and this complex movement is transmitted through the
chain of bones in the middle ear to the inner ear, or true organ of
sensation. But there, by some wondrous mechanism not at all yet fully
understood, an analysis takes place of these entangled motions.
The well-trained ear separates between the effect due to each kind of
musical instrument, and even detects a want of tuning in any one of
them. It resolves each sound into its harmonics, appreciates their
relative intensity, is satisfied or dissatisfied with the admixture.
In the inner chamber of the ear physical movements are in some wholly
inscrutable manner translated into sensations of sound, and the
confused aggregation of waves and ripples in the air, beating against
the tympanic membrane there, takes effect in producing impulses which
travel up the auditory nerve and expend their energy finally in the
creation of sensations of melody and tune, which arouse emotions,
revive memories, and stir sometimes the deepest feelings of our minds.