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The UNIVERSITY of ML OMU
KDMONI) I, GOOLD
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•f^4r
VV - W>-
•o
WONDERS
OF
ACOUSTICS;
OR, THE
PHENOMENA OF SOUND.
FROM THE FRENCH OF RODOLPHE QADAU.
THE ENGLISH REVISED tf*
ROBERT BALL, <M.
With
NEW
CHARLES SCRIBNER & CO.
1870,
Hustraied pbrary of Wonders.
PUBLISH Kl> BY
(paite jlrrtbiw &
654 BROADWAY, NEW YORK.
Bach one volume 12mo. Price per volume, $1.50
Titles of Books. Ao. of Itluxtraiin-n*
THUNDER AND LIGHTNING, .... . . ;:;>
WONDERS OP OPTICS, ... . .70
WONDERS OP HEAT. ..... . t>0
INTELLIGENCE op ANIMAL*, ...... 54
GREAT HUNTS, . ....... '22
EGYPT 3,3-0 YKARS AGO, ....... 40
WONDERS OP POMPEII, . . . . . :•>
THE 8 UN, BY A. GUII/LEMIN, ...... ,\s
SUBLIME IN NATURE, ....... f o
WONDERS OP GLASS MAKING, . . .... e:',
WONDERS OP ITALIAN ART, ....... '28
WONDERS OP THE HUMAN BODY, ..... 45
WONDERS OP ARCHITECTURE. . 5.1
LIGHTHOUSES AND LIGHTSHIPS, ...... 6')
BOTTOM OP THE OCEAN, . . . . . f.8
WONDERS OP BODILY STRENGTH AND S^KILL, TO
WONDERFUL BALLOON ASCENTS, .... . . 30
ACOUSTICS ......... 114
WONDERS OP THE HEAVENS, ....... 48
THE MOON, BY A. GUILLEMIN. . . . . . 6 >
WONDERS OP SCULPTURE. . . . . . . .61
WONDERS OP ENGRAVING, ...... 32
WONDERS or VEGETATION, . . ..... 46
WONDERS OP THE INVISIBLE WORLD, . . . . ;»7
CELEBRATED ESCAPES ....... 26
WATER ......... 77
HYDRAULICS . . . ... . . .40
ELECTRICITY, ........ 71
SUBTERRANEAN WORLD, ....... 2T
* In Press for early Publication.
The above works sent to any address, postpaid, upon receipt of the price by the
publishers.
CONTENTS.
CHAPTER L PACH
SOUND IN NATURE i
CHAPTER II.
EFFECTS OF SOUND ON LIVING BEINGS . . 23
CHAPTER III.
PROPAGATION OF SOUND BY DIFFERENT MEDIA . . 42
CHAPTER IV.
INTENSITY OF SOUND 48
CHAPTER V.
VELOCITY OF SOUND 68
CHAPTER VL
REFLECTION OF SOUND 78
CHAPTER VIL
RESONANCE 99
CHAPTER VIII.
SOUND is A VIBRATION 113
CHAPTER IX.
PITCH OF SOUNDS 143
viii CONTENTS.
CHAPTER X. FAG*
THE NOTES 157
CHAPTER XI.
TIMBRE OR QUALITY OF SOUND 180
CHAPTER XII.
INTERFERENCE OF SOUND 212
CHAPTER XIII.
THE VOICE 226
CHAPTER XIV.
THE EAR 236
CHAPTER XV.
Music AND SCIENCE 244
ACOUSTICS;
OR,
THE PHENOMENA OF SOUND.
CHAPTER I.
SOUND IN NATURE.
Noise and Musical Sound — Voices of Animals — Language of Animals
— M. L and the Monkeys — The Sloth or Ha-ou — Singing
Birds — Insects — Reptiles and Fish — Nocturnal Life in the Forests.
SOUND is movement. Repose is dumb. All sound, all
noise, tells of motion; it is the invisible telegraph which
Nature uses.
Sound is an appeal to sense. It cannot be understood
without the attentive ear, just as light cannot be understood
without the eyes which it enlightens. In voice, and word,
and song it becomes the chief and dearest tie to social life.
Every one knows that the blind, who hear and speak, are
better off than the deaf and dumb, who have only their eyes
to learn by. It is by the voice, that offspring of the air, that
living beings tell most clearly their thoughts, their needs,
and their desires. The voice invites, attracts, or repulses,
excites or soothes, implores or curses. As speech in man's
mouth, it expresses all that mind can conceive, or heart
can feel. Marvellous incarnation ! which lends an invisible
form to thought — which carries from soul to soul passions
B
2 ACOUSTICS.
of emotion, faith or doubt, trouble or peace. To imagine a
dumb humanity is impossible.
We propose to study sound from different points of
view, without, j,t f.rst, discussing the exact nature of the
phenomena to which it gives rise. It will be seen afterwards
that these phenomena may be explained as clearly as can be
desired by the theory of vibrations, and that even the rules
of music arise in a large measure from a certain number of
physical and physiological facts which belong to the domain
of the experimental sciences. Let not the reader feel
alarmed at this, however ; we will touch but lightly on this
side of our subject, and we will confine- ourselves for the
most part to a description of the results which have been
obtained, without entering into a detailed proof of the laws
which we shall have occasion to lay down. This book may,
therefore, be read without great effort by all who wish to
understand the phenomena in the midst of which our life is
spent.
The sensations that the ear experiences are generally
distinguished as "musical sounds" and noises. The dis-
tinction is vague ; we cannot admit any essential difference
between them. All noises consist of sounds of short dura-
tion, almost instantaneous, and more or less discordant.
So, also, musical sounds — or, to speak more correctly, the
sounds employed by musicians — are often exceedingly short
in duration, and the combination in which they are placed
may be perfectly discordant. Where, then, lies the limit
which separates a musical sound from a noise ? It is fixed
by the degree of pleasure or of pain with which it impresses
an organ, whose delicacy varies with different individuals.
The most striking characteristic of noise is the irregu-
larity and abruptness of the impressions made. The rolling
SOUND IN NATURE. 3
of a carriage on the pavement is formed of a series of dis-
cordant explosions ; the noise of falling water in a fountain is
also a rapid succession of jerked or unfinished sounds.
In the soft murmur of a river, in the rustling of the
leaves, the transitions are less abrupt; while in other noises,
such as the long moans of the wind in the chimney, the
notes rise and fall by insensible degrees. In all these cases,
however, we have an irregular succession of heterogeneous
sounds, which follow too rapidly to allow time for musical
feeling to grow, whilst the impressions which constitute
musical sound are sufficiently prolonged to be distinctly
recognised. In this same fact lies the difference between
spoken language and songs. Usually a confused medley of
sounds, which we cannot blend in a single homogeneous
sensation, is also called noise. Thus, a noise is produced
by pressing the palm of the hand on the keys of a piano,
and striking all the notes of the scale together. It is
clear from these examples that the distinction between
noise and sound is only a matter of opinion, and that we
may pass by a thousand gradations from, the one to the
other, although the distance between the two extremes is
great.
The clatter made by falling blocks of wood is called
" noise " by everybody, yet here is an experiment which is
often made : — We take seven pieces of hard wood of the
same length and breadth, but of a thickness decreasing
according to a certain law. One of these dropped alone
upon a plank makes a noise seemingly without a particle of
music in it, but throw them down one after another regularly,
in the order of their diminishing thickness, and the seven
notes of the scale are perfectly heard.
The Chinese get sounds pleasant enough for a melody
B 2
4 ACOUSTICS.
by striking upon flint stones, properly chosen and suspended
by threads. Many instruments used in the orchestra really
produce nothing but harmonious noises, which blend with
the music to sustain the rhythm. Such are the cymbals,
castanettes and triangles, &c.
Inorganic nature produces only noises. The voice of
the thunder, of the storm, and of the sea are but confused
noises. Yet from the wind we may win most musical notes,
by presenting to it an Eolian harp, whose strings can only
vibrate in a certain manner.
In the animal world we meet with an infinite variety of
noises, and of musical sounds ; these noises and songs con-
stitute the language of brutes. " Birds, dogs, and other
animals," says the Pere Mersenne, " have quite a different
cry when they are angry, or complaining, or ill, to when they
are happy and well ; the voice is more shrill in sorrow or
anger than at other times, for bile makes the voice sharp,
while melancholy and phlegmatic humour render it grave,
and a sanguine temperament modulates it to softness.
But the voice of animals is involuntary, while that of man
is free — that is to say, men speak freely, and animals cry,
sing, and use their voices according to a settled law. Many
say ti.j.t animals are not thus restricted, urging that nothing
could be more free than the song of birds like the nightingale,
the goldfinch, and others ; nevertheless, it must be admitted
that they only sing from necessity. It may be that delight
or sorrow forces them to sing, or they may be excited by
some natural instinct, which leaves them no possibility of
keeping silent or of ceasing their song. And when they
listen to a lute, or some other harmonious sound, and sing
in imitation one to another, the sounds which they imitate
so strike their imagination that they cannot be silent ; for
SOUND IN NATURE. 5
their sensitive affection, being warmed by the impression on
the imagination, compels the creative faculty to move the
organ of the voice."
This theory of an involuntary or necessary noise is some-
what arbitrary, for it cannot be denied that many animals
contrive to hold real conversations amongst themselves.
We must here quote G. E. Wetzel's interesting book,
called "A New Discovery of the Language of Animals,
founded upon Reason and Experience." (Vienna, 1800.)
The frontispiece represents a group of superior animals,
with this motto, " They never lie : truth is their language."
The author endeavours to prove that animals make them-
selves understood by combinations of sounds, which con-
stitute the simplest language — a language full of repetitions ;
that they try to make themselves understood by man, and
in their turn understand his language; in a word, that it
would be possible to study the idioms of different animals,
and from them determine the forms and the variations of
their speech.
We actually find in Wetzel's book the rudiments of a
dictionary of the beasts' language filling twenty pages. The
author has even tried to translate into German several
dialogues of dogs, cats, chickens, and other birds in illustra-
tion of his principles. He recounts a conversation composed
of little abrupt cries that he overheard between some captive
frogs, the purport of which was to arrange means to facilitate
their escape. It may be surmised that the drift of the con-
versation was not altogether clear to our linguist, for the
three frogs succeeded in escaping. There is no doubt that
by the careful watching of animals we may come to under-
stand their mysterious language to a certain point, and even
to speak it
O • ACOUSTICS.
Apropos of this is an amusing story from M. Jules
Richard. " Going to visit an invalid friend in a military
hospital/' he says, "I had made the acquaintance twelve
years ago of an old Government official named L . He
was a Southerner, somewhat of a boaster but brave at
bottom, who swore like a heathen, and loved animals. He
had grown familiar with all the cats in the hospital ; and at
the hour when rations are distributed, his ' Mi-aou-ou' would
bring them running from the most distant part of the building,
round the old soldier's porringer. I had always supposed
that the cats, deceived by the perfect imitation of their mew,
or accustomed as the soldiers were to the dinner hour, came
mechanically to gather round their friend. ' They under-
stand me,' insisted the old man — 'they understand me
perfectly. I know cat's speech and dog's speech, but
monkey speech I know better than the monkeys themselves/
" As I smiled with an expression of incredulity, ' Will
you/ said M. L , * come with me to-morrow to the
Jardin des Plantes,* and I will show you something re-
markable. That's all I have to say.'
" I took good care not to miss the appointment, and
M. L was as punctual. He led the way to the
monkey-house, and no sooner had he leant upon the outer
balustrade, than I heard close beside me his guttural cry —
1 Kirrouu ! kirrikiou ! courouki ! courrikiou ! ; I tried to
imitate the sounds that came from my neighbour's mouth :
"'Kirrouu!'
" Throe monkeys fell into place before L .
"'Kirrikiou!-'
" Four monkeys followed their companions.
* Zoological Gardens.
SOUND IN NATURE. 7
"'Courouki!'
"Tli ere were twelve.
"'Courrikiou!'
" All of them were there. L *s discourse lasted for
ten minutes, during which the monkeys — ranged in several
rows, seated on the ground, their front paws crossed on
their knees — laughed, nodded, listened, and replied. Yes
indeed, they answered, and L went on in fine style
with his ' Kirrouu ! kirrikiou ! courouki ! courrikiou !' We
stayed for twenty minutes, and I assure you the monkeys
were not tired. Suddenly L made a move to go : his
auditors became uneasy ; then as L left the balustrade
they uttered cries of distress. We went off, but from a
distance could still see the monkeys, who climbing up the
wires of their cage made signs of farewell. It seemed to me
that they wanted to say, * If you do not come again, write to
us at least.' "
We sometimes hear of a cats' concert. There was a
time when that might have been talked of without metaphor.
There used to be cats' concerts (I do not mean those held
upon the tiles at midnight), pigs' concerts, bears', monkeys',
donkeys', and little birds' concerts, that sang not from
gaiety of heart.
This, according to the Chronicles, is what happened at
Brussels in Ascension week, 1549, in honour of a miraculous
image of the Virgin : — A bear played the organ. This organ
was composed of twenty cats, shut in narrow boxes ; their tails
were tied to cords connected with the notes of the organ.
Each time that the bear struck the keys, he pulled the
tails of the poor cats, and forced them to mew in tune.
Musical historians also speak of organs with pigs and
cats together. Conrad von der Rosen, jester to the
8
ACOUSTICS.
Emperor Sigismond, succeeded, they say, in curing his
master of a deep melancholy, by playing an organ of
cats, arranged in scales, whose tails he pinched by striking
the keys.
Father Kircher devotes one of the most curious chapters
of his " Musurgie " to the voices of animals. First of all he
*&$<':£,
Fig. i.— The Ha-ou, or Sloth.
places the " Sloth" (in Latin called Pigritia, or the Ha-ou
animal). He gives a description of it, together with an
illustration, which he professes to have received from a pro-
vincial of his order, returned from Brazil. We give it for
the sake of its curiosity.
According to this account, the sloth only makes him-
self heard at night: his cry is a ha-ha-ha-ha-ha, running
six notes up and down the scale — doh, re', mi, fa, sol, la,
sol, fa, md, ri, doh. These notes are "tittered at regular
SOUND IN NATURE. 9
intervals, each one being separated from the following by a
short pause. When the Spaniards settled in the country,
they took these nocturnal cries for the singing of men in the
forests. Kircher does not stint his admiration for the voice
of the sloth. " If music had been invented in America,"
he says, " I should not hesitate to say that it was derived
from the song of this creature."
But Father Kircher has other wonders in store for us.
He interprets the voices of men in a most singular fashion.
Those who speak with a strong, deep voice, he classes with
donkeys, after Aristotle's example. The ass truly possesses a
voice strong and deep enough, and he is rash, obstinate, and
rude; so those who have the same voice are rash, obstinate,
and rude. Father Kircher finds no difficulty in explaining the
reason of this phenomenon, and he finishes by saying that
the owners of bass voices are cowardly, avaricious, unbearably
arrogant in prosperity, but more timid than hares in time of
danger. "Such," he says, "was Caligula." Those whose
voices begin their utterance in a low key, but grow shrill
before they finish, are sad, morose, and passionate like oxen.
A weak, shrill voice betrays an effeminate character. With
those who speak fast, a low-pitched voice bespeaks strength
and courage. A shrill and piercing voice is peculiar to the
goat : it indicates a petulant and wantonly nature. Never-
theless, these bad natural dispositions may be overcome by
education and by the will !
Of all animals, birds are the most highly gifted as to
voice. To the parrot nothing is wanting for the mimicry
of human speech ; but this is quite mechanical, and the
wonderful faculty that we admire in the parrot indicates no
advantage or superiority over other animals ; in repeating
the words he hears, he simply proves his utter stupidity.
10 ACOUSTICS.
The starling, the blackbird, the jay and jackdaw, who all
have the thick round tongue of the parrot, are more or less
clever in mimicking speech. Then why do these birds
remain for ever without the expression of intelligence which
speech would give them ? BufTon accounts for the fact by
their rapid growth in infancy, and by their early separation
from their parents, who do not continue the education of
their children long enough to form durable and reciprocal
impressions, which are the sources of intelligence.
Those birds who have the tongue forked whistle more
easily than they talk. When this natural aptitude is joined
with a musical memory, they learn to repeat airs. The canary,
linnet, siskin, and bullfinch are noted for their readiness to
learn. The parrot, on the contrary, does not learn to sing,
but imitates the cries of any animals that he hears : he mews
and barks as easily as he talks.
The nightingale is the true songster of our forests. By
the wonderful variety of its intonations, by the deep passion
of its voice, it bears the palm from all its comrades. The
nightingale's song usually begins with an uncertain, timid
prelude ; by degrees it becomes animated, eager, and soon
we hear the brilliant, thrilling notes pour forth heavenward.
The full, clear warbling alternates with low murmurs, scarcely
audible ; the trills and rapid runs so clearly articulated, the
plaintive cadences, the long-drawn notes, the passionate
sighs, give place from time to time to a short silence ; then
the warbling begins once more, and the woods resound with
the soft and stirring accents which fill the soul with sweet-
ness. The voice of the nightingale reaches as far as the
human voice : it can be heard at a distance of upwards of a
mile when the air is calm, and so much the more clearly
because the nightingale only sings at night, when all
SOUND IN NATURE.
IT
is silent around. In general, it is only the male who sings,
but females have been known to sing as well. In captivity
the nightingales sing during nine or ten months of the year;
when at liberty they only begin in April, and end in June ;
after this month they have a hoarse cry. To make them
Fig. 2.— The Nightingale.
sing in a cage, it is necessary to treat them well, and cheer
their captivity by surrounding them with foliage. Then they
will sing even better than the wild nightingales. The im-
prisoned nightingale will vary its natural song with such
passages as please it from the songs of other birds which
it has heard. Musical instruments, or a melodious voice,
excite and stimulate its talent ; it tries to sing in unison, or
1 2 ACOUSTICS.
to eclipse its rivals, or to drown, all the noises round.
Nightingales have even been seen to drop down dead in the
struggle against a rival singer.
Father Kircher, in his " Musurgie," analyses the song of
the nightingale at some length. " This bird," he says, " is
ambitious and eager for praise ; he makes as much parade
of his song as a peacock of his tail. When alone, he sings
simply; but no sooner is he sure of an audience than he
displays with delight the treasures of his voice, and invents
the most varied modulations."
Barrington has also tried to note the song of the night-
ingale, but, as he himself confesses, without success. The
written notes executed by the most skilful flute-player do
not recall the natural song.
Barrington says that the difficulty lies in the impossibility
of exactly estimating the value of each note. But, though
we have not succeeded yet in transcribing this wonderful
song, it has sometimes been well imitated in whistling.
Buffon tells of a man who could, by his song, so charm
the nightingales, that they would come to perch upon him,
and suffer him to take them in his hand.
As to the compass of the nightingale's voice, it seems
not to be beyond an octave. Very occasionally some shrill
sounds can be heard which mount to a higher octave, but
they pass like lightning, and it is by an exceptional effort
that the bird reaches such a height.
It is by no means proved that the nightingale can learn
to speak, though Pliny tells of one belonging to the
Emperor Claudius, who spoke Greek and Latin. Father
Kircher inclines to believe that this bird could be taught
to imitate human speech, " but," says he, " the story that
Aldrovande relates of three nightingales who told one to
SOUND IN NATURE.
another during the night all that had happened in the day,
at a certain hotel in Ratisbonne, has appeared fabulous to
many people, or at least inexplicable without some signal
imposture, or help of the devil."
Fig. 4. —The Coc::.
He has also arranged in notes the songs of the cuckoo,
the quail, the cock, and of the hen when she is about to lay,
and when she calls her little ones. We reproduce the
ACOUSTICS.
curious plates where he gives the result of these observations,
only omitting the parrot, whose natural cry is expressed
by the Greek word xaLP€i which signifies "Good morning!"
It may be said of most birds that their song is a love-
call. The lark is almost the only one that can be heard
from spring time to winter, and that is because it alone
is faithful to its love throughout the summer. The lark
Fig. 5.— The Cuckoo.
Fig. 6.— The Quail.
sings while flying; the higher it rises the louder it sings. We
can hear it even when it has disappeared in the blue of the
sky. Nothing is so joyous as the exquisite notes of this
song.
There is a species twice the size of the ordinary lark
common in Italy and the south of France. Gifted with
a strong and pleasant voice, it varies its song by counter-
feiting the warble of the goldfinch, the canary, and the
linnet, and even the chirp of young chickens, or the cry of
a cat.
The little birds whose gay song fills the woods, orchards,
SOUND IN NATURE. 15
gardens, and thickets during the summer, belong for the
most part to the tribe of wrens. One of the most remarkable
families is that of the " pewets," who imitate the song of all
the other birds so as to be mistaken for them. They might
be called the mocking-birds of France.
The campanero has a clear bell-like voice, which can, it is
said, be heard at a distance of more than eight miles in the
Fig. 7.— The Common Lark.
region it inhabits. Each morning it raises its song, and
again at noon, when the heat has silenced all its feathered
colleagues, it enlivens the solitude. There comes first
a piercing cry, followed by a pause, and once more a cry
that ends in a silence of six or eight minutes, which is
again broken by a fresh series of cries.
Among the ancients, the swan was also reckoned with
the birds gifted with the power of song, but he only sang
at the hour of death. This fable was long believed, and
to the present day it serves as a comparison for the last
effort of a dying genius. But the voice of the swan is only
i6
ACOUSTICS.
a kind of croak. It is however true, according to Buffon,
that we can distinguish in the cries of the wild swan
a kind of modulated song, composed of clarion-like
notes.
The ancients had very different ideas in the matter of
harmony from our own. They adored the song of the grass-
hopper. Anacreon dedicated an ode
to it. " Happy grasshopper !" says he,
" who, on the highest branches of trees
moist with dew, singest like a queen,
cherished by the Muses and Phoebus,
who has given thee thy sweet song."
Homer compares the eloquence of the
old men of Troy to the song of cicadas,
and a legend relates that a trial of skill
between Eunomus and Ariston, two
players on the cithara, was decided by
a grasshopper; for one of the former's
strings snapping, the gods sent a grass-
hopper, which, perching on the instru-
ment, filled so well the place of the
broken string, that Eunomus was pro-
claimed the victor. In modern times
we cannot recognise music in this insect's monotonous and
piercing notes.
Its musical apparatus consists in two scaly valves placed
below the abdomen, and found only in the male ; these
valves cover two cavities containing two membranes like dry
parchment, the rapid motion of which produces a sharp,
resonant, screeching noise. The other parts of the appa-
ratus intensify and prolong the sound.
The common grasshopper is very common in Provence,
Fig. 8.— The Locust.
SOUND IN NATURE. I/
and is found also pretty far to the north ; it is met with at
Fontainebleau. " In singing," says M. Maurice Gerard, " it
moves its abdomen rapidly, so as to cover and uncover the
openings of the sonorous cavities. Its sound is strong and
sharp, and consists of one note frequently repeated, and
dying away into a hiss like " st," or like air coming from a
narrow aperture nearly closed. If caught it emits strong
Fig. 9.— The Hearth Cricket
cries, which differ perceptibly enough from its song when at
liberty. By whistling to a grasshopper to imitate its song,
you can please, attract, and easily catch it.
In northern countries the green grasshopper is often
taken for the cicada, its cry being much the same. In the
old editions of La Fontaine, the fable of the cicada and
the ant has a grasshopper as illustration. But the two
animals belong to distinct orders. Among the tribe of
crickets and grasshoppers, the male calls the female by a
cry produced by rubbing the elytra (wing-cases); but the
c
iS
ACOUSTICS.
mechanism that produces this monotonous noise differs a
little in different species. The field-cricket rubs the whole
elytra, furnished with strong, hard nerves, projecting like
cords, one against the other. Travellers say that in some
parts of Africa they are kept in little transparent cages : their
monotonous song charms the natives to sleep
The note of the hearth-cricket is slower, more mono-
tonous, less shrill, resembling the cry of the screech-owl.
Fig. 10. — The Grasshopper.
The grasshoppers produce a cry by striking two trans-
parent membranes, furnished with nerves placed at the base
of the wing-cases, like cymbals. Their monotonous singing
is heard in the evening, and all night in damp meadows.
The " dectique " sings by day in the ripe wheat.
Finally, the small cricket produces sounds less musical,
but more varied, than the preceding species. Their thighs
and wing-cases (elytra) have hard projecting nerves, and
they strike the thighs on the wing-cases, as the bow touches
the chords of a violin, generally both at once, but sometimes.
SOUND IN NATURE. 19
left and right alternately. A kind of drum, covered with a
very fine skin, placed near the base of the abdomen on each
side of the body, seems intended to increase the sound.
The cricket's cry is something like a rattle, but of
different quality in different species. One can distinguish
many notes, and the sound changes when calling a female,
or provoking a rival.
Yersin tried to note down the song of these insects.
Charles Butler, the author of the " Feminine Monarchy,"
tried in the same way to note the murmur of the wings that
is heard in a hive of bees about to swarm. "He has
fixed," says Reaumur, "all the accents of the song of the
bee who aspires to lead a swarm, the different keys in which
it is composed, and even the song of the queen-mother
herself." The drones produce with their wings a humming
noise, of which their name is an imitation.
The Death-watches, moving backwards and forwards on
their six feet, strike the wood of old furniture with their
closed jaws, and so cause the noise heard at night.
Reptiles are not silent. The voice of crocodiles and
alligators may be compared, in infancy, to the mewing
of a cat, and at a riper age to broken sobs, or bellowing,
which travellers have sometimes mistaken for the cries of a
child. The lizard of Birmania, M. Thomas Anquetil tells
us, foretells an earthquake by its frequent and piercing cries.
Serpents have only a shrill whistle to serve as voice,
excepting the rattle-snake, who carries at the end of his tail
a curious instrument formed of scaly horns, fitting one into
another, which become more numerous as he grows older.
The croaking frogs are renowned for their talkativeness,
which, according to La Fontaine, once brought them into
trouble ; for, in consequence of their clamour, they were
C 2
20 ACOUSTICS.
deprived of their free democracy and put under a monarchy.
The fish, who pass for dumb creatures, are not so by any
means. Several of them give very peculiar sounds. This
power, which belongs to both male and female, is great at
the time for spawning. When the " maigres " assemble in
shoals, such a noise is heard to come from the water that
they have gained the name of " living organs." M. Dufosse,
who is specially interested in the subject, discovered that the
noise is caused by the quivering of certain muscles; in some
species it is sustained and strengthened by air-bladders.
Thus, by day and by night, a thousand voices join to swell
the grand concert of nature. Even when we imagine our-
selves in complete silence, we are still surrounded by noises.
Try at such a time to listen to some very faint sound, and
you will find that these noises prevent your hearing it dis-
tinctly. To feel what real silence is, one should climb the
lonely summit of a high mountain. Every region has, so to
say, an acoustic physiognomy. In the neighbourhood of
great towns a thousand confused noises are heard, which
betray human activity, as the humming of bees in a hive
tells us it is inhabited.
At Paris this hoarse murmur rolls on through the night.
There are streets where, in the day, a passenger cannot hear
his own voice for the noise of the wheels. The rumbling is
increased by the firm and elastic nature of the soil, which
covers the catacombs like the sounding-board of a violin.
In Europe there are small singing birds who lead the
orchestra of the forest. In America there are stronger
voices to take the lead. Listen to the account Alexander
von Humboldt gives of the nocturnal life, or rather the
voices of the animals, in a tropical forest at night : —
He was passing the night under the spreading heavens,
SOUND IN NATURE. 21
having chosen a sandy plain on the banks of the Apure,
bordering on a thick virgin forest. The night was cool and
moonlight. A deep silence reigned on plain and river, only
broken from time to time by the gentle play of the dolphins in
the water. "Soon after eleven there began in the neighbour-
ing forest such a hubbub, that any thought of sleep for the
remainder of the night was out of the question. All the
thicket resounded with wild cries. Amongst the many voices
which mingled in this concert, the Indians could only recog-
nise those which paused for a moment, to gather fresh
vigour, and began again in a lull of the general chorus.
There were the guttural and monotonous growls of the
alouates, the sweet and plaintive voice of the little mar-
moset, the snore of the monkey, the abrupt cries of the
American jaguar, of the puma, or maneless lion, of the
peccary, the sloth, and a swarm of parrots. When the
jaguars approached the edge of the forest our dog, who had
hitherto barked incessantly, crept whimpering to find an
asylum under our hammocks. Sometimes the roar of the
jaguar was heard from the top of the trees, and then it was
always accompanied by sharp cries of distress from the mon-
keys, who tried to escape this new danger."
If you ask the Indians the cause of this continued
tumult, they answer, laughing, that the animals love to see
the moon shine in the forest, and hold a festival at full moon.
But it is not the moon which excites them most; it is during
a violent storm that their cries are loudest, or when, in the
midst of a peal of thunder, the lightning flashes in the
forest.
These kind of scenes afford a strange contrast to the
calm which reigns in the tropics towards noon in the time of
the great heat, when the thermometer stands at 104° (Fahr.)
22 ACOUSTICS.
in the shade. At this time the larger animals are buried in
the depths of the forest, and the birds hide themselves under
the foliage of the trees, or in the crevices of the rocks, and
so escape the burning rays of the sun, which pour from the
zenith. To make up for this, however, the smooth rocks
and stones are covered with iguanas, geckos, salamanders,
who rest motionless, and with lifted head and gaping mouth
seem to breathe the fiery air with delight. " But," says Hum-
boldt, "during this apparent calm of nature, an attentive
listener for almost imperceptible sounds could distinguish
along the surface of the ground, in the air, a confused
rustling, caused by the buzzing and humming of insects.
Everything betokens a world of organic forces in motion. In
each bush, in the bark torn from the trees, in the earth
furrowed by the insects, life works and manifests itself. It
is as one of the thousand voices of nature speaking to the
thoughtful and pious soul of man."
CHAPTER II.
EFFECTS OF SOUND ON LIVING BEINGS.
rower of Music — Legends and Anecdotes — The Remedial Effects of
Music — Influence of Music on Animals.
As the painter uses light for a messenger of his thought, the
musician bids sound convey his feelings. Music is a lan-
guage, and the sweetest of languages, inasmuch as it is less
formed than any other : it is the ideal of speech.
Music is generally defined as an agreeable combination
of sounds ; but the ancients gave it a far wider meaning.
With them music included the dance, gymnastics, poetry, and
almost all the sciences. Hermes declares that music is the
knowledge of the order of all things, while Pythagoras and
Plato teach that everything in the universe is music. Hence
the phrases "celestial music," "harmony of worlds," &c.,
which were used by ancient writers.
In all probability music was the first of the arts, for
man had a singing master in the bird. Wind instruments
must have come after. Diodorus attributes the invention of
them to some shepherd, who had studied the whistling of
the wind among the reeds. Lucretius holds the same
opinion :
" Et Zepnyri cava per calamorum sibila primura
Agresteis docuere cavas inflare cicutas."
Stringed instruments, and those from which sound is
ACOUSTICS.
produced by percussion, are also very old. The ancients
attribute the invention of music to either Mercury or Apollo.
Cadmus, who brought Hermione the musician to Greece,
Fig. 15.
Cithare.
Fig. 16.
Cithare.
Dou
able Flute.
Fig. 18.
Flute of Pan.
Amphion, Orpheus, and others, are spoken of as the fathers
of instrumental music. According to the book of Genesis,
the players on the harp and organ are descended from
Jubal, the son of Lamech and Adah, of the race of Cain.
EFFECTS OF SOUND ON LIVING BEINGS. 25
The influence of music on the manners of a people, and
its power over the mind, are recognised by the philosophers
of antiquity. Plato supposes that we can distinguish the
sounds which incite sordid or mean feelings, as well as these
which call into action the opposite virtuous feelings. With
Fig. 19. - Pastoral Pipes, or Flutes of Pan.
him it seems that a change in the popular music would be
simultaneous with a change in the constitution of the state.
Polybius tells us that in Arcadia, a dull and cold country,
music was necessary to soften the manners of the people, and
that in no place were so many crimes committed as in
Cynetus, where it was neglected.
26 ACOUSTICS.
Formerly Divine and human laws, precepts and morals,
legends and history, were set to music, and sung in chorus
publicly. The Israelites had similar customs. Music lent a
peculiar charm to abstract things, and fixed them on the mind
of the hearer. Is it some memory of this sort which has
recently inspired a Yankee Meyerbeer with the absurd notion
of putting the American constitution into a symphony?
The Pythagoreans said that the human soul is in some
way formed of harmony. They believed it possible to re-
establish, by means of music, that pre-existing and primitive
harmony of our intellectual faculties, too often troubled by
contact with this lower world. The old writers are full of
stories bearing on the miraculous power of sounds. The
song of Orpheus subdued wild beasts, arrested the course
of the waves, and made the trees and the rocks dance.
When death had bereaved him of his Eurydice, he de-
scended to Hades. The infernal gods, charmed by the
sweetness of his music, granted him the return of his wife,
whom he would have brought to earth again, if he could
have abstained from looking behind during their journey.
Amphion " the divine " built the walls of Thebes. At the
sound of his lyre the stones came and ranged themselves
one upon another :
" agitataque saxa per ortem
Sponte sua in mud membra coisse ferunt."
In the Old Testament we find music connected in a certain
sense, with the destruction of a city. At the trumpet-blasts
of the priests cf Israel the walls of Jericho fell down.
In the songs of Finland we see the river sands change to
diamonds, the haycocks run to stow themselves in barns, the
sea calmed, the bears tamed by the lyre of Wainamoinen ;
EFFECTS OF SOUND ON LIVING BEINGS. 2J
and he himself, falling at last under the spell, sheds in his
ecstacy a torrent of pearls instead of tears.
The holy books of the Hindoos are not behind-hand in
celebrating the power of music. Men and animals move in
harmony with the musician's wand, while inanimate Nature
obeys the influence of music composed by the god Mahedo
and his wife Parbute'a. In the reign of Akbar, the cele-
brated singer Mia Tousine once sang a " raga " consecrated
to the night, in open day. Immediately the sun was eclipsed,
and darkness spread as far as the voice was heard.* There
was another " raga " which burned him who dared to sing
it. Akbar, desiring to make a trial of it, ordered a musician
to sing this song while plunged up to the chin in the river
Jumna. It was of no use : the unfortunate singer became a
prey to the flames.
Every one knows how David played before Saul, when
the evil spirit troubled the king. When Farinelli came to
Spain in 1736, the accents of his voice aroused Philip V.
from a deep melancholy. The king kept the musician
henceforth near him, forbade him to sing in public, and
loaded him with honours. He retained the same position
with Ferdinand VI. This power of music on the passions
has furnished material for numberless legends. They say
that Alexander the Great was roused to fury by the Phrygian,
and calmed by the Lydian melodies of Timotheus. There
is q, story too of a young man whom Pythagoras found so
maddened by jealousy, wine, and a Phrygian air which had
turned his head, that he was about to set fire to the house
of his mistress. The philosopher of Samos simply caused
* It seems that these marvels are renewed no\v-a-days, for a Paris
newspaper announced lately that Dreyschock had played the piano so
divinely, that the wax lights shone with unwonted brilliancy.
28 ACOUSTICS.
a calmer melody to be played upon the flute, and the young
maniac was brought to his senses. On another occasion, a
terrible insurrection which had broken out in Lacedeemon
was quelled by Terpander, who sang to the accompaniment
of his harp. It might have succeeded in that age, but I
doubt whether in the present day the same end could be
gained by arming the police with flutes and guitars.
The Celtic priests used music for softening the manners
of the people. Among the Gauls, their bards could abate
the fury of combatants. St. Augustine tells how a simple
flute-player excited such enthusiasm in a certain tribe that
he was elected king.
There is another legend which recalls the story of
Alexander the Great and Timotheus. Eric the Good,
King of Denmark, heard a musician boast that he could
at pleasure excite in his hearers emotions of joy, sorrow,
or anger. Eric wished to put him to the proof. The
musician was unwilling, and represented to the king the
danger of such a trial. But the more he drew back,
the more the king insisted. Seeing that it must be,
the musician had all weapons removed, and arranged
that some spectators should be placed outside the door,
beyond the sound of his harp. They were to wait at
a distance, and at a given signal to run and seize the
instrument, and strike him with it. Then he shut him-
self up with the king and a few trusty servants, and
began to play on his harp — first of all a melancholy air,
which plunged the listeners in deep sadness; then changing
to a joyous tone, he set them leaping and dancing. But
suddenly the music became wild and fierce — they were
excited beyond measure, and the king appeared in a
fury. Immediately his attendants who waited outside ran,
EFFECTS OF SOUND ON LIVING BEINGS. 29
snatched the harp from the hands of the player, and struck
him with it ; but the king was difficult to subdue, and dealt
many heavy blows before they managed to quell him under
heaps of pillows. Another version tells how Eric broke
open the door, seized a sword, and killed four people; of
which crime he repented so bitterly that he abdicated, and
afterwards set out for Jerusalem as an expiation, but died at
Cyprus.
Under Henry III. the musician Claudin. playing at
the wedding of the Duke de Joyeuse, excited a courtier
to such a degree, that he forgot himself so far as to seize
his weapons in the presence of the king ; but Claudin quickly
calmed him by changing the measure.
The troubadour Pierre de Chateauneuf, who lived in
the thirteenth century, had a marvellous power over the
feelings of his audience. Here is a story told of him
by Nostradamus, in his "Lives of the Troubadours."
This poet, passing through the wood of Vallongue, on
his way from Roquemartine to visit the lord of the place,
fell into the hands of robbers, who, after taking his money
and stripping him, were about to kill him. The poet
prayed them to hear a song he wished to sing before he
died, and they consented. He improvised a song in praise
of the brigands, and when he had finished they gave him
back his horse, his money, and accoutrements, in their
delight at the sweetness of his voice and verse.
A celebrated German legend tells of a wonderful magi-
cian with an enchanted flute. In the year 460 there came
to Hameln, in Saxony, a man who offered to rid the town of
the rats which infested it. The corporation promised him a
large reward. He set himself to play upon his flute an air,
which brought the rats streaming out of the houses by thou-
30 ACOUSTICS.
sands. He drew them by his enchantment to the river
Weser, where all were drowned, and he returned to claim
his promised payment. But, the rats being gone, the towns-
folk thought to escape their bargain, and offered him a petty
sum, which he refused. He said no more, but the next
day appeared with another flute, which when he played, all
the children followed him. He led them to a cavern in the
mountains, and they were never seen again. Then the
people repented their broken faith ; and since that time
they date their years from " the emigration of the children,"
as the Turks do from the flight of the Prophet. There is a
picture of the tragedy in the church at Hameln.
Without going to legends, we may find in modern history
abundant notice of the power of music. Who has not
heard of the "Ranz des Vaches," that air which brings
home-sickness to the Swiss engaged in foreign service ? At
last it was forbidden, under pain of death, to play it in the
army ; for when they heard it the soldiers would burst into
tears, or desert, or even die. " One seeks in vain," says
J. J. Rousseau, " anything in this air to account for such an
effect. It has no power over foreigners, and only acts on
the Swiss by memory and custom — a thousand circumstances
which, recalled by this music, bring to mind their native
land, their old pleasures, their youth, and former ways of
life, exciting sad thoughts of times gone by. The music
then does not act as music, but as an aid to the memory.
Although unchanged, this air has not the same power as for-
merly upon the Swiss, for having lost the taste for their early
simplicity, they do not regret it when it is recalled. So true
it is that we must not seek for the effect of music on the
human heart simply in its physical action."
Military music plays an important part in the history of
EFFECTS OF SOUND ON LIVING BEINGS. 31
battles. A quick, brilliant measure, composed of short
notes, stirs the blood and incites to action. Shakespeare
speaks of the "spirit-stirring" drum. How the Marsellaise
has set the pulses beating !
Men are not equally sensitive to the effect of music.
Some are indifferent, and some even averse to it. St. Augus-
tine anathematises such. In his eyes a dislike for music is
a sign of reprobation. This is going too far, for such an
exception can only be explained by some defect in physical
organisation, and one could mention many great men who
suffered from this infirmity. Boyle speaks of women who
were moved to tears by a tone which did not a.Tect the rest
of the audience. Rousseau mentions a lady, known to him,
who could not listen to any piece of music without being
seized with convulsive laughter. In the History of the
Academy of Sciences we read of a musician being cured of
a violent fever by a concert given in his bedroom.
It is certain that music will serve in many cases as a
means of cure. Doctors of the insane often use it to calm
their patients. In the Middle Ages it was believed that
epilepsy, hysterics, nervous fevers, and idiotcy could be
cured by music. According to Batiste Porta, a flute of
hellebore cured dropsy; a flute of poplar wood, sciatica ; and
a pipe of cinnamon weed was a sovereign remedy for faint-
ing fits.
Father Kircher tells us that music is the usual cure for
St. Guy's dance. The sufferers in this malady dance and
leap till they fall exhausted. They are cured by a strongly
marked music, which excites them more and more, till it
brings them to a crisis. When the disease wa.s raging in
Italy, musicians roamed the country to offer their assistance.
Tha rapid dance they played was known by the name of
32 ACOUSTICS
" Tarantella," a name which reminds us that the malady was
supposed to be produced by the bite of the " tarantula," a
large and venomous spider.
Father Kircher affirms that the spider himself has a great
desire to dance when he hears that air. The experiment
was tried in Andria, before the duchess and her court. They
placed a tarantula on a straw, and saw him jump in time to
the music.
Under the title "Phonurgia latrica," Father Kircher
devotes a long chapter to the employment of music as a
therapeutic agent. This idea should be developed, and
might receive a wider application than hitherto. It is
undeniable that music maybe used as an exciting or calming
agent, according to the rhythm of the air employed.
It is known that with children the nervous system is
always excitable. The most trifling thing frightens them, or
excites their imagination to great joy or sudden terror,
laughter or astonishment. Their nurses quiet them by a
soft lullaby. Cradled in melody, the children sleep. A
joyous tune puts them in a merry mood. For this reason
Montaigne always had his son awakened by music, that he
might be kept in a quiet and happy temper.
Music rests or excites the mind, calms or inflames the
senses, saddens or rejoices the heart. It acts even as medi-
cine. Every one knows how a strongly-accented air helps
one to walk without fatigue. The workman at the crane,
and sailors at the capstan, help themselves by singing in
time to their movements ; and a merry, spirited waltz will set
the feet tingling for a dance.
Many animals are sensitive to music, and if all the stories
told may not be depended on, there are plenty well authen-
ticated. At the head of these stand the singing birds, who
t
1
4
EFFECTS OF SOUND ON LIVING BEINGS. 35
form an orchestra of professionals. Besides these are some
simple amateurs. The horse easily learns to regulate his
motions to music. It is told how the Sybarites employed
special musicians to train their horses to dance to the sound
of flutes. One of these musicians, having a quarrel against
the Sybarites, went over to the Crotonites, and excited
them to war. He marched before the army with a band of
musicians, and on seeing the cavalry in the distance he
played familiar airs, which threw them into a confusion that
ended in defeat.
It has been fancied that cattle graze more heartily to the
sound of the flageolet or some other instrument, and the
Arabs say that music fattens them. In the desert, when the
camels are ready to drop from fatigue, the drivers encourage
them with cheerful songs. Vigneul Marville, of Argonne,
tells an interesting anecdote of the effects of music on dif-
ferent animals. While some one was playing on a marine
trumpet (a kind of stringed instrument invented by Marino),
he watched a cat, a dog, a horse, an ass, a doe, some cows,
some birds, a cock, and some chickens which were in the
court below. " The cat," he says, " seemed perfectly indif-
ferent to the sound of the trumpet, and I judged, from her
appearance, that she would have willingly exchanged all
the music in the world for a mouse; she gave no sign of
pleasure, but slept on in the sun. The horse stopped short
under the window, and raised his head from time to time as
he fed. The dog sat up on his hind legs like a monkey,
with his eyes fixed on the performer; he stayed so above
an hour, and seemed to delight in it. The ass gave no sign
of emotion, but ate his thistles in peace. The doe pricked
up her beautiful ears, and seemed very attentive. The cows
stopped a little, and after having looked at us as if we were
D 2
36 ACOUSTICS.
acquaintances, passed on their way. Some birds in a ca^e,
as well as those on the trees, sang as if they would split their
throats. But the cock, thinking only of his hens, and the
hens, caring only for scratching and grubbing, gave me to
understand that they cared nothing at all for a marine
trumpet."
Buffon says that dogs are easily touched by musical
sounds. " I have seen some dogs with a decided taste for
music, who would come to the court-yard while a concert
was going on within, and wait till the end, then return
quietly home. I have seen others take the exact unison
of a tone that was sounded into their ears." But there is
a wide difference among dogs in this respect. Many will
howl at the sound of some particular instrument, while per-
fectly indifferent to all others. We often see poodles show
their repugnance to certain noises by twisting themselves
about in the most ridiculous fashion, and howling piteously.
I knew a white greyhound who always trembled when
her mistress played her scales. One day, after listening
silently for some time to -an air that was being played,
she broke out in little sharp cries, and then accompanied
the piano in harmony. Surprised and pleased at this new
accomplishment, her mistress fondled her, and gave her
some sweetmeats. Lolette remembered the circumstance,
and afterwards, whenever she had danced before the sugar
cupboard in vain, she had recourse to her grand expedient
and sang her song : she knew that would bring her sugar-
plums. Scheitlin, in his "Psychologic Animale," asserts
that dogs may be taught to pronounce certain words. I
cannot tell how far this is worthy of belief.
According to Buffon, the elephant loves music, and easily
learns to move in time to it, and even to join his own voice
EFFECTS OF SOUND ON LIVING BEINGS. 37
to the accompaniment of drum and trumpet To test this
theory, a concert was once given to a pair of elephants in
the Jardin des Plantes. An air on the violin seemed to give
much pleasure to one of them, but to the variations of the
same air he was utterly indifferent. A martial air of
Monsigny's had no effect on him. The thing which seemed
to please him most was " Charmante Gabrielle," played
upon the cornet ; he listened, swinging himself on his huge
legs, and grunting from time to time in unison; and oc-
casionally he stretched out his trunk and blew, so as
to nullify the sound of the cornet. When the piece was
finished he fondled the musician with his trunk as if to
thank him. From this account we may conclude that the
elephant prefers the low notes to the high, melody to
harmony, simple airs to complex, and adagio to allegro.
His tastes are essentially simple.
Plutarch and Pliny add to the stock of anecdotes
bearing on the same subject. We know the story of the
dolphin charmed by the music of Arion — Schiller has a
ballad on it. The authors of the Middle Ages believed that
each animal has its favourite instrument. To the bear
they allot the fife, to the stag the flute, the harp to the swan,
the flageolet to the singing birds, the cymbal to the bees, and
so on. Imagination evidently plays a great part in these
theories. There is a more probable story of a village
musician, who, returning from a wedding where he had been
performing at the dance, fell into a pit in which lay a wolf.
He began instinctively to scrape his violin. The wolf
crouched in the opposite corner howling. He played
on till the morning, frantically, madly. The strings
snapped one after the other. He was at the last string,
when by good fortune some villagers passed by. Their
38 ACOUSTICS.
curiosity was aroused by the strange music that came from
the ground. They proceeded to search out the mystery,
and discovered Daniel in the ditch. He was saved, and
the wolf killed.
The serpent is particularly amenable to the influence
of sounds. Amongst the accounts we have of snake-
charmers, who taught the serpents to dance to soft music,
Chateaubriand gives us his Canadian experience in the
following story : —
"In the month of June, 1796, we were travelling in
Upper Canada, with some families of the tribe of Onon-
tague's. One day, when encamped in a plain on the banks
of the river Jenesie, a rattle-snake made its appearance.
There was a Canadian with us who played the flute; he
wished to exhibit his power, and advanced towards the
animal with the novel weapon. At his approach the reptile
raised itself in a spiral, flattened its head, inflated its cheeks,
and drawing back its lips, displayed its poisonous fangs and
cruel jaws ; its forked tongue glanced like a flame, its eyes
shone like coals, its body swollen with rage rose and fell
like the billows of a furnace, its skin became stiff and
homy, and its tail moved with such rapidity as to look like
a vapour, making the while a horrid sound. Then the
Canadian begins to play on his flute. The serpent draws
back his head with a motion of surprise. As it falls under
the magical influence, its eyes lose their awful glitter, the
vibration of its tail lessens, and the noise dies away.
The coils of the snake relax by degrees, taking a wider
circuit, and at last they lie one by one upon the ground in
concentric circles. The shades of blue and green, of white
and gold re-appear in all their brilliancy on its sensitive skin,
and lightly turning its head it rests motionless, in an attitude
EFFECTS OF SOUND ON LIVING BEINGS. 3Q
of attention and pleasure. At this moment the Canadian
walks a few steps, still playing on his flute a sweet, mono-
tonous air; the reptile lowers his neck, and dividing the
fine grass with his head, crawls on in the footsteps of the
musician who leads him, stopping when he stops, and fol-
lowing when he goes. He was thus led outside the camp,
in the midst of a crowd of spectators, native and Europe
who could scarcely believe their eyes, and with unanimous
voice it was agreed that the wonderful creature should be
allowed to escape."
Lizards are also said to be remarkably alive to the
influence of music. Pere Labat went to a lizard-hunt with a
negro armed with a noose at the end of a pole. They soon
found one stretched in the sun upon the branch of a tree.
The negro began to whistle to the animal, who stretched his
neck to see where the sound came from. Then the negro
quietly approached, still whistling, and tickled the creature's
sides and throat with the end of the rod. The lizard,
in delight, rolled over on his back, stretching his neck for
the caress, and when within reach the noose was slipped
over him.
The love of the spider for music is also well known. M.
Michelet tells the following anecdote : — " Berthome, the
celebrated violinist, owed his early success to the seclusion
in which he was made to work while very young. But in
his solitude he had one companion unsuspected — viz., a
spider. First of all it lived in the corner of the wall, but
gradually it ventured to the corner of the desk, then on to
the child, and at last it would take up its place on the arm
that held the violin, where it listened, breathless with delight
and emotion. It served as an audience; the child-artist
needed no other encouragement — no other sympathy But
40 ACOUSTICS.
the child had a stepmother, and she one day, bringing a
stranger to hear the boy's practice, saw the creature at its
accustomed post, and with a single blow from her slipper
annihilated the audience. The child took it so to heart that
he was ill for three months, and almost died.'*
Whence comes the power that music exercises over the
soul? What is the secret affinity by which sounds excite
passions ?
Music is the image of motion. It employs sounds
arranged in regular intervals, between which the voice
mounts and falls, according to the fancy of the musician.
In varying the duration and the intensity of the different
notes that succeed one another, every shade of expression,
every possible difference of time is given, from the drowsy
meandering of a stream, which loses itself in the sands, to
the stormy impetuosity of a mountain torrent. Now sounds
act directly on the nervous system by the vibration they
impart to the sensitive nerves, and thus they provoke the
disposition of mind agreeing to the kind of movement
expressed by the music. Gaiety is characterised by a
measure quick and light, gravity by a slow and solemn
movement, anger by an abrupt and hasty staccato. These
different characteristics apply equally well to the motions of
the body, and it is in this unanimity of impression and action
in soul and body that we must seek the explanation of the
effects of music. Sorrow paralyses our limbs, while it makes
our speech slower, and stops the flow of ideas. Music com-
posed of notes which painfully climb a slow ascent of semi-
tones disposes to melancholy reverie, while, on the contrary,
notes which leap by fifths and octaves fill us with a flutter of
excitement, which has its symbolic expression in laughter
and the dance. This explanation of the psychological
EFFECTS OF SOUND ON LIVING BEINGS. 4!
effects of music has not escaped Aristotle. " Why," says he,
" do rhythms and melodies adapt themselves to moods of
the mind, and not flavours, or colours, or odours ? Is it
because they are movements corresponding to actions?
Their intrinsic power rests on a certain tone, and also gives
this tone. Flavours and colours do not act so."
There are other movements which produce just the same
effects upon us. The cascade which falls from the height of
a rock, the limpid stream which ripples softly in its sandy
bed, the waves that beat unceasingly on the shore, affect us
like visible music. One could watch the waves for hours
together break upon the level strand. " The rhythm of this
movement," says Helmholtz, "which is not without a con-
tinual change in detail, awakens a feeling of repose without
tedium, and generates an idea of life wide and grand, but in
perfect and harmonious order. When the sea is calm we
can be pleased for a time by watching its beautiful colours,
but this pleasure does not last as when the water is agitated.
The ripples which are found on small sheets of water are too
hurried in their motions, and rather worry than soothe the
spirit"
CHAPTER IIL
PROPAGATION OF SOUND BY DIFFERENT MEDIA.
Effect of Vacuum — Propagation of Sound in Gas— In Water— In the
Earth — Experiments by Mr. Wheatstone — Hearing by the Teeth.
How is sound carried to the ear which hears it ? What is
the invisible bridge by which it travels? The answer is
easy. A light and elastic fluid surrounds us on every hand.
The winds show us that it can produce the most powerful
mechanical effects. Every commotion at once disturbs this
fluid, and is felt at a considerable distance from its starting-
point. Is it not, therefore, natural to admit that the aerial
fluid in like manner propagates the movements which produce
sound ? We see, besides, that any violent explosion is always
accompanied by a sudden displacement
of the air. Hence scientific men have
not hesitated to say that the air is the
material vehicle of sound. There is
no sound without air. Here is the
simple experiment by the aid of which
we may prove the fact : — Hang a small
bell by a silk thread in a glass globe,
from which the air has been exhausted
by means of an air-pump. Ring the
bell by shaking the thread. Nothing
is heard. The tongue strikes the metal, but the blow is in
a vacuum. But if the stop-cock be opened, and the air
Fig. at.
PROPAGATION OF SOUND BY DIFFERENT MEDIA. 43
allowed to enter, the charm is broken and the bell no
longer dumb (Fig. 21). This experiment maybe made with
an alarum introduced into the receiver of an air-pump. At
first it is heard distinctly, but as the air becomes rarified the
sound grows fainter, and at last dies away. You may even
fire a small pistol under the receiver. You see the flash but
hear no report. These experiments will only succeed when
the pistol or alarum is placed upon a wadded cushion, which
deadens the sound. If not, the vibration is transmitted to
the stand of the air-pump, and from that to the surrounding
air, which carries it to the ear. For this reason it is
difficult completely to insulate the sound which is pro-
duced in the interior of the receiver. It is through
having forgotten this means of communication between
the sounding body and the external air, that Kircher thought
he had found in the same experiment a conclusive argument
against the existence of a vacuum. He had exhausted the
air from a hundred feet length of leaden tubing, which
terminated above in a glass chamber, in which were fixed a
bell and a small hammer that could be raised from outside.
When the hammer fell upon the bell, it gave out a clear
ringing sound, and from this Kircher concluded that this
supposed " vacuum " was but a fiction of the philosopher.
According to Kircher, thick and massive bodies such
as walls or rocks do not transmit sound directly. How
is it, he asks, that if one person strikes a wall, another
can hear the noise by placing his ear on the opposite side ?
This transmission he explains by the presence of air in the
pores of all bodies. It is this confined air which conducts
the sound. If a body be very dense it only allows a small
portion of sound to pass, because it contains but a small
portion of air. He states that glass is the least porous of all
44 ACOUSTICS.
substances, and that a mouse shut up in a glass chamber
heimetically sealed would hear nothing in his prison, what-
ever noise was made outside. Kirch er adds that there is in
Scotland a rock called " The Deaf Rock," hiding behind
which one cannot hear even the firing of a cannon. The
reason of this phenomenon must be sought in the excessive
density of the rock. It is, he says, opaque as to sound,
just as other bodies are opaque to the light.
Although it is true that it is usually by the intervention
of air that sounds reach the ear, it is now known that the
presence of a gaseous fluid is not necessary to their trans-
mission. All elastic bodies — gaseous, liquid, or solid — con-
duct sound. A repeater plunged in water under a glass bell
may be heard distinctly above. The divers can hear under
water what is going on at the surface. It is true the sound
reaches them but faintly ; that is because it loses intensity
by entering into a medium more dense than the air. The
motion which has once passed into the water is carried on
there without hindrance. This is proved by the fact that
sound is as distinct at the depth of several feet as close
to the surface. Were it otherwise the organs of hearing
in fish would be utterly useless. It is certain they can
hear : tame fish have been known to respond to a whistle.
Solid bodies are good conductors of sound. The tick of
a watch held at one end of a hewn trunk is heard perfectly
at the other, not because of the air in the pores of the wood,
but because the wood resounds under the beating of the
escapement wheel. By listening with the ear on the ground,
the report of a cannon can be heard at a distance of twenty-
five miles, and in the same manner the trampling of horses'
feet is audible from a great distance.
" Scuta sonant, pulsuque pedum trerait excita tellus." — VIRGIL.
PROPAGATION OF SOUND BY DIFFERENT MEDIA, 45
This transmission of sound may be rendered visible by
placing a drum, covered with small pebbles, on the ground.
When horsemen pass, even at some distance, these pebbles
are seen to move about. In the Cornish mines they exca-
vate far out under the sea, and there, at this great depth, the
noise of the waves and even the rushing murmur of the
shingle can be heard. In the opposite workings of mines,
too, the miners can hear through the intervening soil,
and are able to direct one another. Such subterranean noises
have given rise, doubtless, to many of the most thrilling
ghost stories.
It appears that wood conducts sound better than any
other solid body. Deal is a better conductor than box, and
box than oak. With four deal rods Wheatstone contrived
to carry the sounds of a concert held in the cellar through
several storeys to the upper room of a house. It was done
in this way : — The rods rested, one upon the sounding-board
of the piano, another upon the bridge of the violin, the third
upon the violoncello, and the fourth touched a clarionet.
They passed through the roof of the cellar, and on to the
upper storey where the audience sat. Each rod ended in a
sounding-board of thin and elastic wood. The whole
structure vibrated considerably when a piece of music was
played below, and the room above was filled with sounds,
which seemed to proceed from witchcraft. Indeed this
experiment has a magical effect. The wood suddenly sings
as if it were alive, and a listener, trusting to his ears alone,
would fancy himself in the presence of a real orchestra.
Mons. Kcenig tried the same experiment with a musical
box shut in a large padded chest. A lath of wood passed
out from the interior, and was surmounted by a sounding-
board. When this shelf was lifted nothing could be heard,
46 ACOUSTICS.
but no sooner was it placed on the free end of the lath
than the tune which was being played inside the chest
became perfectly audible.
The bony parts of the head act as sound-conductors to
the ear. Thus sound can be communicated by the forehead
or by the teeth. Two people holding a thin slit of wood
between their teeth, and talking in an undertone, can hear
one another at a considerable distance. The stethoscope,
invented by Laennec in 1819, is based on the same principle.
It consists of a wooden cylinder, which the doctor places on
the chest of the patient, so as to hear more plainly the noise
from the heart. Wheatstone has proposed an instrument,
to which he gives the name of microphone, also intended
to facilitate the hearing of very faint sounds. It is a small
copper basin, which is placed over the ear, and to the centre
is fixed a long metal stem, a kind of tentaculum, which carries
the sound. Such an apparatus might be fitted to each ear,
the stems uniting into a single tube.
If you strike on a silver spoon, a glass bell, or any other
sonorous body suspended by a thread, the free end of which
is introduced into an ear-trumpet, or held between the teeth,
the ears being stopped, you will hear a deep, full sound, like
a distant bell. A Danish physician, Herhold, tried this
with a spoon fastened to a thread nearly 700 feet in length,
of which one end was fastened to a pole, and the other held
between his teeth.
The deaf and dumb can hear well by their teeth, when
the deafness does not proceed from paralysis of the nerves.
If you make them hold the edge of a musical box, or a rod
of wood resting on the sounding-board of a piano, between
their teeth, they will hear the sound of the instrument.
PROPAGATION OF SOUND BY DIFFERENT MEDIA. 47
One who is partially deaf can understand easily what is
said to him, if the words be spoken into a copper or glass
basin which is applied to his ear or teeth.
Dull bodies, such as hemp, wadding, stuffs of all kinds,
flour, and sawdust, do not sensibly transmit sounds. A
Turkey carpet stifles the sound of footsteps, while a thick
door-curtain prevents the sound of voices passing from room
to room.
CHAPTER IV.
INTENSITY OF SOUND.
Circumstances that Vary the Intensity of Sound— Intensity at Night —
Extent or Reach of Sound — The Inverse Square of Distance —
Speaking Trumpets — Acoustic Tubes — Acoustic Cornets.
THE strength or intensity of sound is determined first of
all by the energy of the movement which produces it, but the
effect on the ear depends on the nature of the medium
by which it is conducted. We have already seen that
under the bell of an air-pump any sound will die away
gradually, as the air becomes rarified. On high mountains,
where the air has not much density, all noises lose their
force, and seem more distant than they really are. At the
summit of Mont Blanc, 15,000 feet above the sea-level,
Saussure found that a pistol report sounded no louder than
a cracker in the plains. In some experiments tried at
Quito between two stations, the one at an altitude of
10,000 and the other 13,000 feet, the report of a nine-
pounder cannon, fired at twelve miles distance, did not
equal that of an eight-pounder heard in the plains of Paris
at a distance of twenty miles. Aeronauts have often told
how feeble their voices become in the high regions of the
air. A railway whistle was heard at a height of three miles
and a half or four miles. That is the greatest distance at
which the human ear has been able to catch sounds from
the earth. At this time the air was unusually damp.
INTENSITY OF SOUND. 49
In thinking of the diminution that all sound is subject
to in the upper air, one is surprised at the intensity of the
noise sometimes produced by an explosion of a thunder-
bolt. A meteor which was observed in 1719, and ac-
cording to Halley's calculation travelled through the air
at a height of more than sixty miles, burst with an explosion
equal to that of a great cannon.
Thunderbolts generally burst with a great noise, and
since we know the explosion is very high above the surface
of the earth, it must be of almost inconceivable violence.
In a confined space sound is exaggerated. In the tunnels
where the workmen laboured at the foundations of the
Pridge of Arcueil, every sound took a metallic ring — even
the voice produced an unpleasing ringing effect in the head.
Priestley made very many experiments, using different
gases in place of air. Having filled a receiver with
hydrogen, and put a bell within it, he found that the sound
ceased almost instantly. The density of hydrogen is only
one-fourteenth that of the air. Pilatre de Rosier, having
breathed great quantities of this gas, found his voice had
become feeble and nasal. Mannoir and Paul did the same
thing at Geneva, and their voices were singularly shrill
and thin.
Sound has much greater force in water. By experiments
tried on the Lake of Geneva, Collaclon estimated that a bell
submerged in the sea might be heard at a distance of more
than sixty miles. Franklin asserts that he has heard the
striking together of two stones in the water half a mile
away.
When sound passes from one medium to another of a
different density, it loses more or less in intensity. As before
stated, divers hear noises from the surface but faintly, while
£
$0 ACOUSTICS.
those outside can hear well what passes under water. For
instance, the stroke of a bell can be heard at a depth of
forty feet. From this we conclude that water gives vibrations
to the air more easily than air to water. If the vibrations
of a solid body, instead of passing directly through the air,
are conveyed through an intermediate liquid, the result is
increased power. Perolle has experimented on this. He
took a watch, carefully sealed with wax, and suspended it
by a thread in a vase, which he filled successively with
different liquids. In the air the tick of the watch became
imperceptible at ten feet distant. Liquids strengthened
the sound. In spirits of wine the watch was heard at
thirteen feet ; in oil, at sixteen ; in water, at nineteen feet :
by all which we see that the force of sound augments with
the density of the fluid through which it passes to the air.
The vibrations of a solid body travel with difficulty
through a gaseous medium ; a large surface is necessary
to increase the sound, and for this reason a sounding-board
heightens the effect of any musical instrument connected
with it, by conveying the vibration to a large mass of air, as
already described in Wheatstone's experiments,
In passing through the air itself, ascending or de-
scending, sound must cross layers, so to say, of varying
density. Saussure and Schultes have stated that sound
travels better up than down a mountain height, and aero-
nauts notice the same thing. This may be explained by
the fact that the voice, and all other sounds, have, even at
the moment of their production, less power in the rarified
air of the higher regions than in the denser air of the
plains.
When the air is unequally heated by the rays of the
sun and other means, sound loses in power, and does not
INTENSITY OF SOUND. 51
travel far.* By this circumstance Humboldt explains the
difference in intensity of sound by night and by day.
Nicholson seeks to account for it by the absence of those
thousand confused noises which during the day disturb the
atmosphere around us. The silence of night, he says,
rests our organs, and renders them more alive to slight
impressions. Silence makes our hearing more acute, as
obscurity tends to sharpen our sight. But Humboldt brings
his observations in America to bear against this opinion.
In tropical countries the animals make more uproar at
night than in the day, and the wind only rises after sunset.
Yet the noise of the cataracts of Orinoco is heard at
Ature's (more than a league distant) three times more plainly
at night. Humboldt has also remarked that this nocturnal
increase in the intensity of sound is more noticeable in the
lower plains than on the table-lands or at sea.
It would, perhaps, be more correct to attribute these
facts to the united influence of the different causes men-
tioned, to which might be added the coldness of night. It
is as true indoors as in the open country, that night inten-
sifies sound. A mouse nibbling at the wainscot sounds
altogether different by night and by day. This cannot be
from any inequality in the density of the air, and we must
account for it by the contrast of silence. Darkness may
also count for something. Many people shut their eyes in
order to hear the better, and the sense of hearing is generally
very acute with the blind.
We have just said that cold is favourable to the propaga-
* At the time when the ventilation of the Houses of Parliament
was under discussion, it was stated that the current of heated air, which
rose from the hall, prevented the voice of the speaker being heard at
the opposite side.
E 2
52 ACOUSTICS.
tion of sound. This is a fact acknowledged by many. In
Polar regions Captain Parry often heard a conversation,
carried on in an ordinary voice, at a mile distance. One of
his comrades at Port Bowen was able to converse with some
of the crew 6,700 feet off, the thermometer standing at the
time 28° below zero. It might be supposed that this
phenomenon is due to the condensation of the air, but the
experiments of Bravais and Martin do not confirm such an
opinion. They ascertained that at St. Cheron a diapason
mounted on a sounding-board was heard at 833 feet distance
soon after midday, and at midnight the sound reached nearly
1,243 feet. On the Faulhorn the sound was heard at above
1,804 feet by night, and even on Mont Blanc at 1,105 feet,
although the air is much less dense on these heights than in
the plains. This unexpected result proves that it is not the
condensation due to the cold which produces an increase in
the intensity of sound ; the phenomenon is evidently more
complex, and it may probably be accounted for in some
degree by the wonderful calm of mountain and Polar
regions.
The wind has much to do with carrying sound. In the
direction of the wind, of course, it travels far. De Haldat
made some experiments near Nancy with a small drum,
from which he concluded that with the wind it travels two
or three times farther than against it. Since then Dela-
roche and Dunal have taken more exact measurements
in the plain of Arcueil. They placed themselves between
two drums of equal size, which were beaten with equal force,
and ascertained the distance at which the two sounds seemed
of the same intensity, when a straight line drawn from one
drum to the other made a given angle with the direction of
the wind. The faintest sound was that which came from
INTENSITY OF SOUND. 53
the nearest drum. In this way they found that for distances
of eighteen or nineteen feet the influence of wind was im-
perceptible ; above that it became appreciable, and increased
with the distance. It was most marked in faint sounds. A
contrary wind deadened the sound, but (and this was the
most important result) all other winds deadened it too,
though to a smaller degree. In still weather, or in a line
perpendicular to the direction of the wind, the sound
extended to its greatest distance. A commotion in the air
is always injurious to the progress of sound, and this is
intelligible if the gusts produce undulations in the air, which
act on those of sound by the principle of interference.
Derham made the same observation at Port Ferajo in Elba,
apropos of the cannon of Leghorn, which was heard better
in calm than in windy weather, even though the wind blew
from Leghorn.
We may quote a remark of the Baron de Zach on this
subject. This astronomer says that at the Seeberg Observa-
tory, which is in a high and lonely situation, the sound of
the neighbouring church bells, the noise of the mills, the
barking of dogs, and the voices of men reached him clearly
during the nights when the stars shone still and bright,
while he could hear next to nothing when the stars trembled
in the field of his telescope. Therefore the force of sound
will indicate to a certain extent the state of the atmosphere.
The great difficulty in all these experiments is the want
of an instrument to measure the intensity of sound ; one is
obliged to trust entirely to the ear. Now the delicacy of
hearing may vary day by day, and it is never the same in
two different persons, and even the same person often hears
better with one ear than the other, and, which is worse than
all, the ear is more impressed by shrill tones than by deep.
54 ACOUSTICS.
One would have thought that the apparent intensity of a
sound must be proportioned to the mechanical power em-
ployed to produce it, but it is not so. When a siren is
turned by pressure of air from the bellows, the deep musical
notes that it emits at first are far less piercing than the shrill
notes produced as the velocity of rotation increases. The
ear becomes more sensitive as the pitch of the note is raised,
and it has been demonstrated that the high treble notes
resound in the ear with a force beyond all others. There-
fore it is certain that by the ear we can only compare
sounds of the same quality. Should an exact measure
for the intensity of sound be attempted, this is how it
must be done: — The phonometer should be an instrument
giving always an equal force to the sounds produced, by
means of a constant pressure from a bellows. The distance
must then be ascertained at which a sound from the phono-
meter would appear as powerful as that of which the intensity
is to be tested. This intensity would be to that of the
standard in the inverse proportion of the square of the
distances of the phonometer and the sonorous source.
All movement which radiates freely — such as light,
electricity, heat, and sound — spreads from its starting-point
in concentric spheres. Thus, the surface of these spheres
increasing always in proportion to the square of the radius,
it follows that the intensity of force emanating from the centre
must diminish in the same proportion as it is distributed
over successive spheres. Hence the intensity of radiation
decreases with the distance from the centre, in inverse ratio
to the square of the distance. This law also governs
gravitation ; all the forces of attraction or repulsion submit
to it Theorv would suggest that it should equally apply
to sound Delaroche and Dunal verified it in the following
INTENSITY OF SOUND. 55
manner : — Having procured five bells, perfectly identical in
tone, they placed one bell at one end of a straight line
measured along the ground ; the other four they hung at the
opposite end. Standing midway between the bells, the
sound emitted by the four ought to be four times as strong
as the sound emitted by the one. Standing at one-third
of the distance which separated the bells — that is to say,
twice as far from the group as from the single bell — the
observer found the sounds were equal. The law then was
exact. The square of 2 being 4, and its inverse square j,
the law requires that at a distance of 2 feet a sound should
have only a fourth of the intensity which it possesses at the
distance of i foot. Thus the sound of the four bells to-
gether being equal to 4, at the distance of i foot, ought to
be no more than J of 4, that is to say i, at the distance of
2 feet. This the experiment proved, since at such a distance
the four bells gave a sound equal to that of the single bell,
at half the distance.
The distance at which the ear can distinguish sounds
represents in some degree the measure of their intensity.
The human voice is sometimes heard at a great distance.
We have already told how in the Polar regions Foster was
able to converse at a distance of 6,700 feet from his
companion. Nicholson relates how, standing one night on
Westminster Bridge, he heard the voices of workmen at Bat-
tersea, more than three miles off. The voices of the sentinels
at Portsmouth may be heard at night in the Isle of Wight,
five miles distant. The laughter of the sailors of an English
man-of-war, stationed at Spithead, reached Portsmouth. It
is hardly possible to credit Derham's affirmation that at
Gibraltar the human voice has been heard above ten
miles distant. Hinrichs assures us that a brass band may
5 6 ACOUSTICS.
be distinguished at four miles, and the drum beating
a retreat at Edinburgh Castle has been heard at nineteen
miles. The report of a cannon travels very far, because it
communicates a vibration to the soil. The cannonade
of Florence was heard beyond Leghorn — that is to say, to
a distance of about 56 miles — and that of Genoa to about
100. In 1/62 the cannon of Mayence was heard at
Timbeck, a small village about 148 miles off. In 1809
the booming of the cannon in Heligoland reached Hanover
— 157 miles; and on December 4th, 1832, the cannon of
Antwerp was heard on the Erzgebirge mountains, 370 miles
Fig. 28.— Speaking-Trumpet.
distant The eruption of St. Vincent in 1815 was heard
at Demerara, 341 miles distant.
To increase the natural range of voice an instrument is
often used, called in English a speaking-trumpet, in Latin
tuba stentorea. ft is formed of a conical tube, furnished
with a mouthpiece, and terminating in a wide-spreading
cup ; and is much used at sea to surmount the noise of
wind and wave; and formerly the watchman used it to give
warning of fires, or to call the labourers to their work in
the fields.
It appears that the speaking-trumpet was invented by
Samuel Morland in 1670. He had several models made in
glass and copper, which were exhibited before King
INTENSITY OF SOUND.
57
Charles II. and Prince Rupert. In one experiment made
at Deal, with an instrument about 5 feet in length and a
diameter of 2 and 20 inches at its respective openings, the
voice was carried over three miles.
When Morland's invention was made public, Fathei
Athanasius Kirch cr claimed it on the pretext that he had
Fig. 23.— The Horn of Alexander.
already employed tubes of a conical form ; but it is easy to
see, from his earlier writings, that the learned Jesuit was
speaking only of ear-trumpets. He gives in this connection
a description of "The Horn of Alexander," from an old
MS. entitled " Secreta Aristotelis ad Alexandrum Magnum,"
to be found in the Library of the Vatican. According to
this unknown author, the horn enabled Alexander to call
his soldiers from a distance of ten or twelve miles. The
t.
58 ACOUSTICS.
diameter of the ring must have been about eight feet.
Father Kircher conjectures that it was mounted on three
poles. Towards the end of the last century, a German, Pro-
fessor Huth, wished to try the effect of such an instrument.
He had a model constructed of thin iron plates, but on
a somewhat smaller scale than that indicated by Kircher ;
and he found that a horn of this kind served as a powerful
speaking-trumpet, especially when furnished with a widely
spreading cup. In 1654, an Augustine monk named Salar
made a similar trial, but no record was kept of the
result.
Shortly after the invention of Morland, Cassegrain pro-
posed that a hyperbolic form should be given to the
speaking-trumpet. Conyers changed it to a paraboloid, and
Jean Matthieu Hase made an elliptic mouth-piece, and a
parabolic cup. All these plans (which have not stood the
test of experience) suppose the increase of sound in
the speaking trumpet is due to the interior reflection of the
sonorous waves. This idea was enlarged on by Lambert
in his theory of the speaking-trumpet, published in 1763,
and quoted in almost all treatises on physics. It is laid
down as a principle that the object of the instrument is to
render the sonorous radiation parallel to the axis of the
tube, wherefore the most suitable form must be chosen for
realising this parallelism. Nothing could be more at
variance with ascertained facts. According to the theory
of reflections a cylindrical tube would be useless. Now,
Hassenfratz has proved the contrary. The tick of a
watch that in ordinary circumstances would be indis-
tinguishable at a distance of about three feet, when placed at
the end of a cylindrical tube twenty inches long, may be
heard at a distance of six or seven feet A cylindrical tube,
INTENSITY OF SOUND. 59
furnished with an open cup or bell, would make a very
good speaking-trumpet. Lambert thought the cup unneces-
sary. Experience proves the contrary : it contributes very
sensibly to the increase of sound. Finally, Hassenfratz
found that lining the interior of the trumpet with woollen
stuff scarcely deadened the sound. Now, this lining must
have prevented any reflection from the inner walls of the
tube.
It results from these facts, that the augmentation of
sound depends entirely on the geometrical form given to
the column of air by the first impulsion. How is this
influence exerted? No theory has yet explained the
mystery. All that can be said is that the speaking-trumpet
confines the sonorous waves, and keeps them from too soon
dispersing, and as it were concentrates them. This notion
makes us instinctively use our hands as" a speaking-trumpet.
The ancients used to fit a kind of cup or mouth-piece
to the masks worn by their actors, to serve the same
purpose.
Notice, still further, that sound is not augmented by a
speaking-trumpet in the direction of its axis only. It is
equally observable in every direction. Thus, if you speak
through a trumpet at a certain distance from a high wall,
the echo is almost equally powerful whether the mouth be
turned towards the wall or in the opposite direction.
The tubes used on board ship are seldom more than six
feet in length, and eleven inches in diameter. One was made
in England of twenty feet or more, which carried words
two miles. When used only for an inarticulate cry, a good
speaking-trumpet will carry the sound three or four miles.
Further experiments on this subject would be interesting.
In England and America they are trying many different
60 ACOUSTICS.
means for warning vessels at sea, when the lighthouses are
invisible through fog. The common method is a bell.
There is one on the Isle of Copeland, in the Irish Sea, rung
by machinery, which may be heard at a distance of fourteen
or fifteen miles. At Boulogne, a bell is fixed in the focus of
a parabolic reflector, and struck alternately by three ham-
mers, which are set in motion by a falling weight. On
board some of the floating lighthouses they use drums or
cannons. At New Brunswick they have a steam whistle.
In a small island off Holyhead they protect the sea-gulls,
that their cry may warn vessels; but, unfortunately, in 1856
the Regulus was wrecked in this part of St. George's
Channel, and some rats escaping from the sinking vessel
found their way to the island, and have multiplied to such a
degree as seriously to affect the bird population. A cat was
introduced to work havoc among the rats, but she made
common cause with them, showing quite as great a partiality
for the birds as they did.
The principal difficulty in this kind of signal is that the
fog interferes with the propagation of sound — at least, it
would seem so from Cunningham's experiments, but positive
proof is wanting. To distinguish the signals of different
stations they can employ intermittent sounds, or a succession
of different notes. Cowper and Holmes have proposed
steam trumpets for this purpose. Captain Ryder would
unite a cannon with a whistle. It might be possible to
propagate a very powerful sound through the water itself, in
which case the sailors must use a long ear-trumpet, like that
which Colladon had for his experiments on the lake of
Geneva. They must fish for the sound. Prsetorius invented
an instrument of the same kind for the solid earth. It was
a sort of shovel, driven into the ground ; the ear, being
INTENSITY OF SOUND. 6 1
applied to the handle, became conscious of a vibration at
the approach of the enemy. The inconvenience of these
contrivances is that they never tell the direction whence the
noise proceeds.
When sound is propagated in a limited space of air, it
loses but little in intensity. Of this, hearing-tubes afford a
striking example. These are long tubes of metal or gutta-
percha, by means of which conversation may be held be-
tween persons at some distance. They are much used in
houses for communicating from the upper to the lower
storeys, and on board ship for speaking to the man aloft, &c.
In the experiments made by Biot in the empty water-
pipes of Paris, he found that the lowest sounds were per-
fectly transmitted through a column of air 3,120 feet in
length. "Indeed," says he, "there was but one way to
avoid hearing, and that was not to speak, even in the faintest
whisper." The firing of a pistol at one end of the tube ex-
tinguished a lighted candle at the other, and blew some
light bodies to a distance of twenty inches. 3 ^ ^^
Once upon a time, in almost every fair might be found a
" Delphic oracle," a Turk's head which answered all ques-
tions whispered into its ear. This was managed by a hear-
ing-tube hidden in the pedestal of the apparatus, and com-
municating with a confederate. The most ingenious thing
of the kind was M. de Kempelen's " speaking woman." This
piece of wax- work was seated on a chair placed alternately
in two different spots of the hall, where spectators were re-
ceived. They spoke in her ear, and the answer seemed to
come from her mouth. The plan of the thing was this : A
tube passed from the hollow of the wax head through one
of the feet of the chair. Two other tubes, connected with
an adjoining chamber, passed under the flooring of the hall
02 ACOUSTICS.
to two points, each marked by a small hole. Round these
points the boards had been planed underneath to a very
thin partition, and pierced with a small hole. They took
care to place the chair so that the hollow foot covered one
of these holes.
The " invisible woman," who created such a sensation at
Fig. 24. — The Invisible Woman.
the beginning of this century in all the principal towns of
the Continent, may be explained as simply. The most striking
part of this machine was a hollow globe (Fig. 24), furnished
with four horns in the shape of trumpets, and suspended by
an iron bar, or more likely by four silk ribands, from the ceiling
of the hall. This globe was enclosed in a cage of open trellis-
work, sustained by four pillars, one of which was hollow.
Through this passed a tube, which was carried also half-
way through one of the upper horizontal cross-bars, whence
INTENSITY OF SOUND. 63
the narrowest possible chink faced the opening of one of the
trumpets. The voice seemed then to proceed from the
globe. Probably the persons who gave the answers from a
neighbouring room had a peep-hole by which they could
watch what was passing in the hall. The questions were
always put at one of the trumpets' mouths.
Sound is wonderfully propagated by means of chimneys,
gas-pipes, heating apparatus, &c. Some chimneys will
convey all kinds of noises from out-doors into the house ;
therefore in prisons and .mad-houses they are specially
careful, in the arrangement of such parts of the building, to
avoid any possibility of communication between the prisoners
or patients by such means.
At Carisbrook Castle, in the Isle of Wight, there is a
well celebrated for its acoustic properties. When a pin is
dropped down its contact with the water is distinctly heard,
and shouting or couching into the well produces a long-
drawn echo. The depth of this well is 210 feet, and its
diameter j 2 feet.
In facts of this kind it is sometimes difficult to determine
how much of the effect is due to the material of which the
walls of the enclosed channel are formed. The same remark
may apply to the transmission of sounds along a smooth
surface. Hutton believed that a person reading aloud upon
the Thames might be heard 118 feet off, while upon solid
ground the distance must be limited to 75 feet. In the
Argentine Theatre at Rome it has been noticed that the
voices of the actors are much better heard since a water-pipe
was carried under the flooring of the hall, and it is natural to
suppose that the water has something to do with this im-
provement.
Most extraordinary acoustic effects may be noticed
64 ACOUSTICS.
under the domes of different churches, that can no more
be explained by theories of the reflection of sound than the
speaking-trumpets. The vaulted dome seems to guide the
sound. It has been noticed that two persons talking in a
whisper at opposite sides of a gallery under the cupola of St.
Peter's at Rome can hear one another distinctly, without
being audible to others. In the Whispering Gallery under
the dome of St. Paul's, the same phenomenon occurs ; the
ticking of a watch even may be heard. In Gloucester Cathe-
dral, a person speaking in low tones in the gallery east of the
choir can be heard at the other end, i6ofeet away. Brydone
says the same thing happens in Girgenti Cathedral. When,
the great door is shut every syllable spoken near it reaches
the other end of the nave, but cannot be heard midway.
These effects are but imperfectly explained by the re-
verberation of sonorous reflections, which accounts for the
phenomena of elliptical vaults, as will be seen in the fol-
lowing chapter. It seems as though the surface guided the
sound. Hutton tells how in a garden at Kingston a whisper
along the wall was heard at a distance of 197 feet. It is
still more striking to notice how a semi-cylindrical channel
will guide sound. Hassenfratz put a watch at one end of a
passage formed by two planks of wood resting edge to edge.
He could then hear the beats at a distance of seventy-five
feet, while in the open air they became inaudible at six feet
Some buildings have an accidental channel of this kind.
There is one in an hexagonal hall of the Paris Observatory,
where the opposite corners are furnished with a means of
communication by a sort of gutter passing round the roof.
A conversation may be carried on there in utter privacy,
though the hall be filled with listeners. At the foot of the
grand staircase in the Conservatory of Arts and Manufac-
INTENSITY OF SOUND. Oj
tures in Paris is a vaulted lobby, where the sound, following
the arches, descends in the corners of the walls.
The same principle explains the mystery of " speaking
chambers." Very often they are but the consequence of an
accidental arrangement of the walls. We have the most
curious of these phenomena in " The Ear of Dionysius," a
cavern in the quarries of Syracuse, in Sicily. In the depths of
this cave the tyrant of Syracuse had a cell formed for his pri-
soners, whence the least sound was carried to the ear of the
sentinel watching at the entrance of the subterranean passage.
Here is Kircher's plan of the cave ; c is the entrance, d
Fig. 25 — Plan of the Ear of Dionysius.
the cell ; //is the projection of a large groove, thirty inches
in diameter, hollowed in the middle of the roof, nearly 100
feet above the pavement, and ending at e, where the sentinel
was stationed ; b is a recess contrived in the side wall. The
groove //acts as a sound-conductor. The opening e has
long been walled up, and consequently at the present day
the cave exhibits most curious effects of echo. Kircher
visited it, and he tells how the faintest sound is exag-
gerated, so that a word pronounced in an undertone becomes
a clamour, and a clap of the hands is like the report of a
cannon. A duet sung by two voices is repeated as a
quartet The length of the cavern is about fifty-two feet.
66 ACOUSTICS.
Kircher has planned numberless imitations of " The Ear
of Dionysius." Some consist of a large twisted tube, with a
wide mouth opening towards the place where the sounds are
produced, and passing into the interior of the room where
the sounds are to be heard. This leads us to speak of the
ear-trumpet, an instrument for gathering sound and con-
densing it in the ear. They are made in various forms, the
simplest and the worst of which is the cone. It is requisite
that the outer opening should be larger than the one
introduced into the ear ; then it is easy to understand how
the movement in that portion of air which filled the wider
mouth of the tube is concentrated in the narrower passage,
and so reaches the ear intensified in power.
Towards the end of the seventeenth century, they tried
ear-trumpets in the form of hunting-horns. One of the
commonest forms is that given as i in the accompanying
plate. No. 2 is another of the most usual. Curtis had
some made to lengthen out like a telescope (No. 3). Ittard
has devised numerous shapes. For instance, No. 4 is a
kind of ellipsoid, furnished with a wide mouth, and a bent
tube to fix in the ear. The dotted line shows a membrane
of gold-beaters' skin, which renders the sound less confused,
though it does not strengthen it. In No. 5 we have a shell,
with a mouth and a tube added, and two membranes of
gold-beaters' skin.
Quite recently Kcenig has constructed an ear-trumpet,
which serves also as a stethoscope (No. 6). A capula,
closed by a membrane, communicates with the ear through
an india-rubber tube terminating in an ivory top. When any
one speaks before this membrane it takes the impression
from the motion of the air, and, carrying it to the air con-
tained in the tube, forces it against the tympanum of the
INTENSITY OF SOUND. 67
ear. When employed as a stethoscope, this simple mem-
brane is replaced by a lens formed of a double membrane,
that can be inflated by means of a cock at the side. The
upper membrane is placed upon the chest of the invalid,
where it moulds itself to the skin, and faithfully transmits
the motion of the air imprisoned in the lens to the ear of the
Fig. 26.— Ear-Trumpets.
doctor. With this apparatus the patient might sound his
own lungs, by pressing the capula against his chest and
introducing the tube into his ear; or a whole class of
medical students might auscultate the same patient simul-
taneously, since several tubes can be introduced into the
capula. The tubes may be lengthened to twelve rr fifteen
feet, without materially weakening the sound; so that a
doctor could sit in his library, and listen to the beating of
his patient's heart in an upper room.
F 2
CHAPTER V.
VELOCITY OF SOUND.
Mersenne — Bureau des Longitudes — Captain Parry— R -gnault — Beu-
dant — Colladon and Sturm — Biot — Wertheim — Distances by
Sound — Depth of a Lake by the Echo from the Bottom.
THAT sound is not propagated instantaneously was noticed
by the first inquirers into its phenomena. Every one knows
that thunder is generally not heard till long after the lightning
flash has passed, and the interval increases according to the
distance of the storm. But what is the exact time that
sound must take to travel a certain distance ? in other words,
what is its velocity ? This was the question that Mersenne
and Kircher set themselves to solve. "Light," says Mer-
senne, " spreads through the sphere of its activity in a
moment ; or, if it takes time, it is so short a time as to be
imperceptible. But sound occupies time in travelling, which
increases with the distance between the place of its produc-
tion and the listener. This has been verified by many
experiments. The axe of the wood-cutter will have struck
a second blow before the sound of the first is heard at a
distance of 600 paces. Repeated experiments are necessary
to ascertain if this delay in sound is proportional to the
distance." He then proceeds to describe the different ex-
periments by which its velocity has been tested, such as
counting the beats of the pulse from the moment when the
flash of a musket or a piece of artillery is seen to the time
VELOCITY OF SOUND. 69
when the report is heard. He records observations of this
kind made at the siege of Rochelle by one of the officers ;
but the results are very inconsistent, and Mersenne there-
fore concludes that the velocity of sound varies according to
local and atmospheric circumstances. Yet in any case he
holds it certain that sound does not travel so fast as the ball
from an arquebus ; indeed he says, " The birds are often
seen to fall from the branches of the trees before the report
is heard, although one may be quite close to the arquebus."
In 1673 Kircher declared that nothing was yet known
certainly as to the velocity of sound, but the Florentine Aca-
demy was instituting experiments for the purpose of throw-
ing light on this interesting subject. These experiments
seem to have taken place in 1660. They reckoned, from the
time elapsing between the flash and the report of a cannon,
that the velocity must be 1,175 ^eet a second. A simple
means of gaining an approximate idea of the velocity of
sound is found in an echo. Mersenne reckoned, with the
help of a pendulum, that seven syllables could be pro-
nounced in a second. Now, an echo at 519 feet distance
will give back seven syllables. It takes one second to pro-
nounce them, and they are heard again the following second.
Therefore the sound travels 519 feet going, and the same
returning — 1,038 feet in all — in one second ; " so that," says
Mersenne, " we may take this as the velocity of reflected
sounds, which I have found always the same, whether pro-
ceeding from trumpets, firearms, stones, or voices." These
experiments, according to which the velocity of sound would
be about 1,038 feet per second (we shall see presently
that this number was pretty near the truth), were disputed
by Kircher, who raised a host of objections against the sup-
posed equality in time for the transmission of sounds of
70 ACOUSTICS.
different kinds. He supposed that a very strong sound
must of necessity be returned more quickly, just as a ball
would rebound from a wall the faster according as the pro-
pelling force was stronger ; but this comparison is altogether
false, for sound does not rebound like the ball, since the
mass of air in which the sound is propagated does not
change its place. The air is not thrown against the obstacle,
neither does it return to the ear ; there is no analogy be-
tween the sonorous motion and that of the ball. Kircher
also fancies that the echo is quicker in the silence of night
than in the noisy day, and that the winds have something to
do with the matter.
The first exact experiments on the velocity of sound in
air were instituted in lyJS by a commission of the Academy
of Science, composed of La Caille, Maraldi, and Cassini de
Thury, who associated several others with them. They
chose for their stations the Paris Observatory, the Pyramid
of Montmartre, the Mill of Fontenay-aux- Roses, and the
Chateau de Lay, at Montlhery. Cannons placed on the
heights of Montlhe'ry and Montmartre were fired alternately,
and the observers at the four stations measured, by help of
pendulums, the time which elapsed between the arrival of
the flash and of the report. They found that on an average
the sound took one minute twenty-four seconds to travel
93,140 feet — that is, about 1,106 feet per second, at a tem-
perature of 6° (Cent). Afterwards, when the influence of
temperature came to be better known (augmenting the
velocity about two feet for every degree Centigrade), they
deduced from this reckoning a velocity of 1,093 feet for o°.
The observations made at the intermediate stations showed
that the velocity of sound is uniform — that is to say, it does
not slacken towards the end of its journey, however great
VELOCITY OF SOUND. fl
the distance. They proved, moreover, that it is the same
by day and by night, in fair weather and foul, and whatever
may be the direction of the cannon-mouth; but that it is
influenced by the wind, according to its force, and the angle
that it makes with the direction of the sound. A contrary
wind retards, while a favourable one accelerates its trans-
mission. These experiments were repeated with some modi-
fications by Kaestner, Benzenberg, Goldingham, and others,
but their conclusions were not altogether satisfactory. A
new measurement was taken in 1822, at the request of
Laplace, by the members of the Bureau des Longitudes.
Two pieces of cannon were placed, one on the elevation of
Montlhery, the other at Villejuif: the distance is about
61,067 feet. Prony, Arago, and Mathieu were stationed at
Villejuif; Alexander Humboldt, Gay-Lussac, and Bouvard at
Montlhery. Each was provided with a good stop chro-
nometer, recording at least the tenth of a second. The
cannons fired at Villejuif were all heard at Montlhery, but
the return shots were so faint that few of them were heard
at Villejuif. This singular circumstance prevented their
noting the influence of the wind as accurately as they would
have done. According to their calculation, the velocity of
sound at a temperature of zero is 1,086 feet. For every
degree of heat two feet must be added, so that at 15° the
velocity would be 1,116 feet.
Since these memorable experiments, others have been
made in Germany, Holland, America, and other places.
During Franklin's voyage to the Arctic Seas in 1825,
Lieut. Kendall discharged forty rounds of cannon, the
temperature varying from 2° to 40° below zero. Captain
Parry also made some observations on the propagation of
sound in equally low temperatures. The united results of
72 ACOUSTICS.
these inquiries tend to the conclusion that in calm air the
velocity of sound is somewhere about 1,088 feet per second.
Biot contrived an ingenious plan for ascertaining whether
sounds varying in pitch are equal in velocity. If not, it is
clear that the notes of a musical air heard afar off would
be altogether changed, since certain notes must be heard
either too soon or too late. In ordinary circumstances this
slight inequality would not be noticed, the distance of the
instruments being insufficient to render such delay appre-
ciable. Biot, therefore, arranged that a flute should be
played at one end of the aqueduct of Arcueil (which was
then empty) while he listened at the other. The melody
reached him in perfect time and tune, having lost nothing in
its transit through 3, 1 20 feet of tubing.
About four years ago, M. Victor Regnault resumed these
inquiries with all the appliances of modern science. Nearly
400 discharges of cannon were fired in the plain of Vincennes.
The arrival of the sound was ascertained by means of a
membrane, which, swinging a little pendulum at the arrival
of the shock, thereby interrupted an electric current. The
instant both of the flash and the report were registered on
prepared paper by a Morse telegraph. On the same paper
an electric pendulum marked the second, close by the spot
where a vibrating tuning-fork registered the hundredth part
of a second.
These experiments were terminated last year in the new
sewers of St. Michel, a series of large tubes extending for a
mile or more. The opening being closed the moment that the
sound was thrown into the tube, it was observed that the noise
of a pistol or trumpet rebounded, so to say, going backwards
and forwards as many as ten times, swinging each time the
pendulums placed along its route. M. Regnault also tried
VELOCITY OF SOUND. 73
the effect of a simple shock or impetus given to a column of
air without sound. I was present at some of these experi-
ments, of which the results were curious enough ; but as
nothing has been yet published, it will be understood that I
can say no more.
The velocity of sound in different -gases has only been
tested partially. It is believed that in oxygen, carbonic oxide,
olefiant gas, nitrogen, and sulphuretted hydrogen it is about
the same as in air ; but in hydrogen, four times greater —
that is to say, about 4,167 feet per second.
The velocity of sound in liquids was first experimented
upon by Beudant He had two vessels moored in the
harbour of Marseilles, a certain distance apart. An assistant
on board one of these vessels struck a bell sunk at its side,
at the same time giving a signal which could be seen from
the other boat, where the moment of arrival of the sound
in the water was recorded. The velocity as determined on
this occasion was 4,921 feet; but Beudant thought the result
not worth publishing, on account of the imperfection of
the means employed. It is only to be found in the Memoir
of Colladon and Sturm. These two measured the velocity of
sound in the water of the Lake of Geneva. The depth of the
lake (45 9 feet), and the clearness of its waters, recommended
it in a special manner for experiments of this kind. The
greatest extent of deep water was found between Rolle and
Thonon, a distance of about eight miles. A vessel was moored
off Rolle, carrying a bell of nearly 140 pounds weight, which
was submerged. It was so arranged that when the hammer
struck the bell, a lighted match fell upon a heap of powder
lying on the deck. Another vessel was moored off Thonon,
from which they observed the flash, and noted the arrival of
the sound by means of a curiously shaped hearing-trumpet
74 ACOUSTICS.
(Fig. 27). It was formed of a long tube, opened and bent, and
had a membrane stretched across the mouth. The observer
turned the surface of this membrane
towards the bell, and placing his ear
to the upper extremity of the cone,
watched for the signal. The moment
the flash was apparent he touched the
spring of a " stop watch" (a kind of
watch whose hands can be either
stopped or set at liberty, by a simple
pressure on the spring), stopping it
Fi 2 immediately the sound reached him.
This was invariably nine seconds after
the flash. Dividing the distance between the two vessels
by the interval of time, the velocity is determined to be 4,708
feet per second — more than four times greater than in the air.
These experiments gave rise to many interesting remarks
upon the propagation of sound in water. Instead of the
prolonged resonance that is produced in air, the sound of
the bell was short and flat, like the clashing of two steel
blades. The water, which is but slightly compressible, had
robbed it completely of its ringing tone. At one time the
lake was rough and stormy, and they had great trouble in
keeping the boats to their moorings, but this had not the
slightest influence on their experiment. Wertheim afterwards
determined the velocity of sounds in different liquids, and
of his results, these are the two extremes: in absolute
alcohol, at a temperature of 23° C, the velocity is 3,808
feet per second ; and in a solution of chloride of calcium,
6,496 feet.
Through solids the transmission of sound is much more
rapid than in gases or liquids. The early experimenters who
VELOCITY OF SOUND. 75
tried to measure its velocity by laths of wood, cords, &c.,
found it too great to be appreciable. The efforts of Hassen-
fratz were fruitless. Biot and Martin tried by means of
the iron pipes made to carry the waters of the Seine from
Marly to the aqueduct of Luciennes, and found that from
a small bell hung at one extremity, two sounds reached the
ear in succession. The first was transmitted through the
iron, and after an interval of between two and three seconds
was followed by another through the air. From this ex-
periment they calculated a velocity of 8,859 feet. This
deduction is not correct : the result is too small. This may
be explained by the lead used at the joining of the pipes
interrupting slightly the transmission of the sound. When
Breguet and Wertheim afterwards experimented on the tele-
graph wires of the Versailles Railway, they gave as the result
of their calculation 11,434 feet per second for the velocity of
sound in iron wire. By the method of vibrations (an in-
direct mode) Wertheim determined the velocity of sound in
some metals. In lead it is equal to four times what it is in
air, about 4,265 feet; in silver and platinum, 8,859 feet j in
zinc and copper, 12,140 feet ; in iron and steel, 16,404 feet.
The highest known velocity of sound is that which Chladni
found in the wood of the fir-tree, about 19,685 feet — eighteen
times that of transmission through the air.
To form a comparison of these different results, let
us imagine for a moment that the stone tunnel pro-
jected by M. T. Gamond is constructed under the
English Channel. The distance from Cape Grisnez to East-
ware Point (the proposed stations) is about twenty-one miles.
A cannon fired at Grisnez would be heard at the English
station in ninety-seven seconds, through the air ; the sea-water
would transmit the sound in twenty-three seconds ; by the iron
76 ACOUSTICS.
rails it would come in a little over six seconds, and by the
telegraphic wires probably a little faster. Finally, if there
were a lath of fir-wood long enough to join the opposite
shores it would transmit the sound in five seconds.
The velocity of sound in air being known, we can em-
ploy it as a means of approximately measuring distances.
Every second that elapses between the flash and the report
of a firearm represents a distance of 1,116 feet between the
station where it is fired and the position of the observer.
We have already seen how Mersenne made use of this fact.
M. d'Abbadie measured different sites in Ethiopia by the
same means. In the island of Mocawa, during the Rama-
dam (a religious fast of the Mussulmans), a cannon was
always fired at sunset announcing the end of the day's fast.
M. Antoine d'Abbadie took the opportunity of noting the
time which passed between the flash and the arrival of the
sound on the opposite bank. He took his station on a hill
near the village of Omkullu, and there awaited the report of
the cannon. The sound reached him eighteen seconds after
he saw the flash: the distance he reckoned to be 21,129
feet. Another time he measured in the same way the
distance from the town of Aoua to Mount Saloda. His
brother Arnauld took his stand on the mountain, while
he himself was upon the roof of a house in the town, armed
with a blunderbuss. They fired alternately, and each one
marked the seconds by his watch : the distance was found
to be nearly two miles. But it seems the brothers made too
much noise, for they were both banished from the Tigris.
Newton gives a formula by which to calculate the depth
of a well from the time that passes between the moment
when a stone leaves the margin and that at which it is heard
to strike the water. Ten seconds would give a depth of about
VELOCITY OF SOUND. 77
1,247 feet- ^e might get the depth of a lake, or even of
the sea, if we could note the reflection of a sound strong
enough to be returned from the bottom. Arago proposed
this to Colladon in 1826, but it was never tried till 1838,
when at the request of the Admiralty of the United States
Mr. Bonnycastle made the experiment. The American
professor found that sound was better perceived in the water
than in the air, and that the greatest distance at which a bell
could be heard under the water was two miles. These conclu-
sions were disputed by Colladon, who urged his experiments
made on the Lake of Geneva. In 1826 he had heard a bell of
nearly 1 40 pounds weight at a distance of eight miles. In 1 84 1
a bell of about 180 pounds, lent by one of the churches of
the canton of Geneva, was heard at a distance of twenty-one
miles. It was suspended forty-nine feet under water, and
the hammer which struck it weighed over twenty pounds;
from which Colladon concluded that, under favourable con-
ditions, sound would be propagated under water to a vast
distance. The noise of the paddle-wheels of a steamboat
is not heard beyond 3,000 to 4,000 feet under water ; but
the noise of a chain shaken at a certain depth is so distinct,
that a ship at two miles distance may be heard to weigh
anchor.
It is understood that in these experiments it is always
necessary to use a hydro-acoustic trumpet. During the trial
of the great bell, each blow could be heard in a house built
upon an embankment at a distance of two miles, although
the house was separated from the bell by a promontory : the
sound seemed to come from the foundations and the walls.
Colladon says nothing of the possibility of measuring the
depth of water by an echo from the bottom.
CHAPTER VI.
REFLECTION OF SOUND.
Laws of Reflection — Echo— Polysyllabic Echo— Polyphonic Echo —
Heterophonic Echo — Reflection and Resonance — Celebrated
Echoes— Legends — Refraction of Sound.
THE laws of reflection show a perfect analogy between light
and sound. Sounds are reflected, like luminous rays, from
any obstacle they may encounter ; and just as we find the
polished surface of a mirror giving back more light than a
rough surface, so different substances return the sonorous
waves with more or less force. Hard and solid bodies re-
flect much better than soft and flexible ones, that cannot
easily right themselves after pressure.
The laws of the reflection of sound do not appear quite
so simple as those which govern the movement of luminous
rays, for the sound-waves travel in curved lines, bending
round obstacles. Nevertheless, for the sake of simplifying
our explanation, we may be permitted to speak of sonorous
" rays" just as we speak of luminous rays, meaning thereby
the direction in which a sound arrives in greatest power,
when propagated through the air. Therefore we may say
for sound as for light, that the incidental and the reflected
ray make equal angles with the reflecting surface, and that
they are comprised in a plane perpendicular to this surface.
The same law obtains in the shock of elastic bodies. Bil-
REFLECTION OF SOUND.
79
liard-players know that the ball rebounds from the cushion
in a direction symmetrical with that in which 'the propelling
force was given. It is thus that a voice striking the wall
M, in the direction A, M, is thrown back in the direction
M, B, symmetrical with the first as regards its relation to the
wall, or (which comes to the same thing) to the perpen-
dicular M, N. The angle which this perpendicular makes
N
Fig. 28.— Reflection of Sound.
with A, M, is called the angle of incidence ; that which it
makes with M, B, is the angle of reflection. These two
angles are always equal, and the reflected ray M, B, is
always in the same plane as A, M, and the perpendicular
M, N.
When the point A, whence the sound emanates, ap-
proaches the line M, N, the point B, towards which the
sound is reflected, approaches it also, and these two points
coincide when the sound travels in the direction of the
perpendicular. That is to say, a voice thrown out at N,
8o ACOUSTICS.
and striking the wall in the direction of the perpendicular
N, M, would return by the same path from M to N.
These principles will help us to understand the pheno-
mena of echoes, as we call the repetition of a sound when
reflected by some distant object Let us suppose, to begin
with, that we have but one reflecting surface. If the ob-
server wishes to hear the echo of his own voice, he must
place himself on the line M, N, which is perpendicular to
the reflecting surface. If he wishes to hear the echo of a
noise produced at a point A, he must place himself at a
point B, symmetrical with reference to the perpendicular
M, N. Before hearing the reflected sound, which travels by
the broken line A, M, B, he will of necessity hear the sound
which passes direct from A to B, since this has a shorter
road to travel. We assume, of course, that no obstacle
stands between these two points which could impede its
passages The observer will then, in general, hear two
sounds in succession, if the first has ceased before the
arrival of the second. This is a necessary condition for a
distant echo, and it evidently depends on the distance of
the reflecting surface.
We will first consider a case where the sound returns to
the place of its departure. The observer is then at N ; he
hears his own voice first at the moment of utterance, then
again after the sound has travelled twice the distance M, N.
Now, it takes at least one-tenth of a second to pronounce
one syllable, and that is pretty .quick speaking; on an
average we do not pronounce more than five syllables in
a second. If, then, the reflecting obstacle be too near the
observer, the first syllable will return before he has uttered
the last, and there will be confusion, the last syllables only,
or perhaps none at all, being given distinctly.
REFLECTION OF SOUND. 8 1
V7e have seen that sound travels on an average about
1,1 16 feet per second; in the tenth of a second, then, it
would be 112 feet nearly, and 224 feet in the fifth of a
second. An obstacle distant 112 feet in a straight line
would, therefore, send back the sound after one-nfdi of a
second, allowing one-tenth for its journey there and one-
tenth for its return. This distance would suffice for a mono-
syllabic echo — that is to say, for the repetition of a single
syllable. One-fifth of a second it would take to pronounce
it, so that as I pronounce the end of my syllable the begin-
ning has already returned to me. If the obstacle is nearer
than 112 feet, the reflected sound breaks in upon the ar-
ticulated sound and confuses it. If the obstacle is at a
greater distance, a longer or a shorter time will elapse be-
tween the spoken syllable and the echo which repeats it.
All that has been said of the monosyllabic echo will
apply to the polysyllabic, or the echoes of many syllables.
We have only to increase the distance in proportion to the
number of syllables to be repeated. For two syllables w
must allow 224 feet; for three, 336 feet, and so on. Of
course, if more than five syllables are uttered in a second,
the distance allowed may be smaller ; but if less than five,
the distance must be greater. The principle is always the
same. The distance must allow the sound to go and re-
turn during the time taken for the utterance of the phrase.
However, it is true that several syllables spoken in suc-
cession are produced more rapidly than a single one is apt
to be, which explains why Kircher found the distances de-
crease slightly for polysyllabic echoes. Whilst he gave 100
feet for an isolated syllable, he reckoned only 190 for two,
and 600 for the seven syllables —
" Arma virumque caao."
G
S3 ACOUSTICS.
He states elsewhere that the distances allow of a great lati-
tude. The echo of a trumpet is distinct from 90 to no
feet, and the distance for an echo of seven syllables may be
reduced to 400 feet, while sometimes 600 feet is not
sufficient for the repetition of seven syllables. When too
many syllables are given for the echo to repeat distinctly,
the first which return are drowned by the last uttered, and
only a mutilated edition of the phrase is obtained. From
this circumstance it is easy to hold a conversation with the
echo, by question and answer, remembering only that the
end of the question must serve as reply.
Cardan tells a story of a man who, wishing to cross a
river, could not find the ford. In his disappointment he
heaved a sigh. " Oh !" replied the echo. He thought him-
self no longer alone, and began the following dialogue : —
"Onde devo passar?"
« Passa."
« Qui ?"
« Qui."
However, seeing he had a dangerous whirlpool to pass,
he asked again —
" Devo passar qui ?"
" Passa qui."
The man was frightened, thinking himself the sport of
some mocking demon, and returned home without daring
to cross the water. He told his adventure to Cardan, who
had little trouble in explaining it.
We have supposed hitherto that the observer heard the
echo of a sound produced by himself, returning by reflec-
tion to its point of departure. The same reasoning applies
in cases where the sound rises at a certain distance from the
observer, as in Fig. 28, where the listener is placed at B and
REFLECTION OF SOUND. 83
the sound comes from A. We only have to consider the
difference of the direct road A, B, and of the indirect A, M, B.
This difference represents the circuitous route by which the
reflected sound has travelled, or the advance gained by that
sound which has travelled direct ; and it must be equal to
twice 112 feet — that is, to 2 24 feet — fora monosyllabic echo ;
double that for an echo of two syllables, and so on.
Lastly, there are multiplied or polyphonic echoes — those
29 — The Hcptaphonic Echo.
which reproduce several times consecutively the same sound
or phrase. They are caused when several obstacles placed at
different distances, acting either alone or together, send back
the sound in successive echoes. The accompanying figure
represents a heptaphonic echo, that is, of seven voices. The
projecting pieces of the wall, A, B, c, D, E, F, G, which throw
back the .jimd, are at nearly equal distances; it returns
first from A, then from the others in succession. If the
echo have to repeat a single syllable seven times, the succes-
sive distances must differ by at least 112 feet ; for two syllables,
G 2
84
ACOUSTICS.
224 feet, and so on. The farther the distance, the feebler the
echo, as the sound is scattered and lost ; thus the voice dies
gradually until it completely ceases. When the obstacles
which produce the echo, instead of being placed at equal
distances, are nearer together in proportion as they recede
from the observer, the echoes mingle, the second arriving
before the end of the first, the third before the second is
completed, and so on. Kircher shows how this law may be
used to produce a sentence from a word. Suppose a five-voiced
echo so disposed (Fig. 30) that the first repeats distinctly the
word clamors (voice) : if the second obstacle be at double
the distance, the third at triple, and so on, a trisyllable in
five sounds would be produced. But put the second so near
that the sound of the consonants c I is lost in the first echo,
only the word amore would be heard ; and by placing the
succeeding obstacles at properly arranged intervals, the
third would repeat more, the fourth ore, the last re. So
REFLECTION OF SOUND. 85
that, in asking in a loud voice the question, Tibi vero gratias
agam, quo damore ? the echo replies, Clamore — amore — more
— ore — re. The word constabis would divide into stabis —
obis — bis — is, but without giving a sentence of any meaning.
Fig 31. — The Heterophonic Echo.
Ivircher also tried to construct an heterophonic echo-
one that should reply in a different word — which he con-
trived thus : At the salient angle of a wall was an obstacle
(Fig. 31) which, instead of throwing the voice back to the spot
from whence it had come, sent it round to the other side
of the building, where an accomplice was concealed ; he
86 ACOUSTICS.
replying, his voice followed the same route as the question,
and reached the mystified hearer, who, having heard asked,
Quod tibi no mm ? (What is your name ?) hears the answer,
Constantinus. Kircher relates that he had been much amused
at his friends' expense by this innocent mystification, in the
Campagna at Rome. To render the illusion complete, the
voices of the two actors should be alike.
It would be possible to utilise the echoes of a church, as
ornaments to the singing, by disposing pauses which should
be filled in by their resoundings. Kircher gives several ex-
amples of musical effects thus obtained, and adds that the
churches of St. Peter and St. James of the Incurables at
Rome are particularly adapted for the application of this
artifice.
The Hebrew name for echo is " daughter of the voice;" to
the ancient poets Echo was a nymph who loved the beautiful
Narcissus, whose love being despised, she dissolved in tears,
and remained only a voice which replied to the passion of
another —
"Nee prior ipsa loqui didicit resonabilis Echo."
The echoes which animate a landscape seem to establish a
kind of sympathy between man and nature. The forest par-
takes in our joys, and repeats the cries of the hunters and the
notes of the horn.
"Non canimus surdis, respondent omnia silvze." — ViRGIL.
As Mersenne says, God has given a voice to the woods,
rivers, and mountains.
The echoes in towns, and regions of peculiar confor-
mation, are of various qualities : sometimes the response is
muffled and hoarse, sometimes clear and distinctly accented,
REFLECTION OF SOUND. 87
These differences in quality, depending evidently on the
character of the reflecting surfaces, prove that an echo is
something more than mere reflection. It is beyond doubt that
the phenomena of resonance, of which we shall speak sub-
sequently, play a certain part in it. All the facts observed
prove, also, that the reflection of sound can be made clear
and distinct from very irregular surfaces ; an old rampart, a
ruined tower, a tree, a hill, a wooded gorge, are the ob-
stacles which form the best echoes. The luminous image
is perfect in proportion as the surface which reflects it is
uniform ; the sonorous image is not subject to these con-
ditions. We must conclude that in most cases the mode of
action of the surfaces which form an echo has some analogy
with the effects of curved mirrors. Perhaps the resonance
of the obstacles themselves, and of the air confined in them,
contributes largely to the production of the phenomenon.
It is certain that the concurring conditions which should
be regarded as favourable or necessary to the production of
an echo, are far from being known. Theory and experiment
are equally at fault. In some cases the local conditions
which should, according to the theory of reflections, produce
an echo, do really produce it ; but often our expectation
is deceived where no reason for it can be discovered.
The echoes of forests depend much, probably, on the
grouping of the trees, as the following facts may show : —
Gay Vernon, in his youth, had often amused himself by
waking an echo formed by the buildings of a mill. After
passing several years in Paris, he returned to his native
village : to his surprise the echo no longer existed ; yet
nothing had been changed about the mill — only a group of
trees, which formerly shaded it, had been cut down.
In the plain of Montrougc, near Paris, there was for-
88 ACOUSTICS.
merly a remarkable echo produced by a wall, before which
were several rows of trees. Hassenfratz tried to ascertain
on what circumstances the phenomenon depended. He
placed an assistant at a certain distance to call out, and
approached the wall slowly, listening carefully : the echo
died away as he drew near, but there remained a faint
sound, proceeding not from the wall, but from the trees.
Putting his ear to their trunks he perceived a slight tremor,
while in the wall there was no vibration. He also observed
that the walls of certain houses produced an echo when the
windows were shut; or with the windows open, but the
doors shut. In some vaults certain notes only produce the
effect. The echo of the ancient college of Harcourt has
a strange peculiarity : it returns the voice of a man placed
in the middle of the court, but the low notes were heard in
the direction of the Rue de la Harpe, the high notes in a
direction fifty degrees more to the north.
All these facts show that Echo is a capricious being,
whose caprices are not easily divined. Here is a story in
illustration: — An Englishman, travelling in Italy, met
with an echo so beautiful that he determined to buy it.
It was produced by a detached house. This was taken
down, carried to England, and reconstructed on one of his
estates, exactly on its original plan — a place having been
chosen for it at exactly the same distance from his dwelling
as it stood, in Italy, from the place whence the echo was
most distinctly heard. To test the echo he sent for a box of
pistols, charged both the weapons, went to the window, and
fired — no sound was returned ; drawing the trigger of the
second, he shot himself through the brain ! It was never
known what defect in the construction was the cause of this
lamentable disappointment
REFLECTION OF SOUND. 89
Clouds also re-echo terrestrial noises. The members of
the Bureau des longitudes, in the course of their experiments
for measuring the velocity of sound, found that the report
of cannon was always followed by an echo if clouds were
overhead. The rumbling of thunder is owing partly to the
multiplied reflection of sound between the earth and the
storm clouds. Echoes are also produced by excessively high
waves, and the sails of ships, and it is said that words
spoken through a speaking-trumpet come back if they strike
on the convex surface of the sails.
Echoes are especially distinct in the silence of night;
the noises of day prevent their being heard distinctly.
Mersenne relates that the echo of Ormesson, in the valley of
Montmorency, replies fourteen syllables at night, and only
seven in the day-time.
In deep valleys, and the hollowed strands of rivers,
remarkable echoes are found. In one well-known echo,
between Coblenz and Bingen, where the waters of the Nahe
flow into the Rhine, there is an echo which gives seventeen
repeats, the voice seeming alternately far and near. One
day, the steamer not having the usual fire-arms on board to
rouse the echo for the amusement of the tourists, there were
loud cries for a pistol. A Pole, not understanding the case,
rushed on to the bridge, exclaiming, " I have no pistol, but
here is a dagger." Ebell relates that an echo at Derenberg,
near Holberstadt, repeats the twenty-seven syllables of this
sentence — Conturbabantvr Constantinopolitani in/miner a-
bilibus solliritudinibus. It would be as astonishing to find
a mouth capable of pronouncing them quickly ; but as he
says that the distance was only 254 paces, which is not
enough for such an echo, there must be some mistake in
the account
90 ACOUSTICS.
It is said that near Brussels there is an echo of fifteen
repeats ; and at Rosneath, near Glasgow, on the Clyde, one
which repeats an air of music three times. This scarcely
seems credible.
An echo at Woodstock, near Oxford, repeats seven-
teen times by day, and twenty times by night ; the distance
is half a mile.
At Genetay, two leagues from Rouen, in a semi-circular
court, there is a remarkable echo. When crossing the court
singing, the singer hears only his own voice, while those
listening hear only the echo, single or multiplied, according
to their position.
At three leagues from Verdun are two towers, apart, and
isolated from the building to which they belong ; standing
midway between them, the speaker's voice is echoed twelve
or thirteen times with decreasing force, but except from
this spot the echo is lost ; while between one tower and the
building a single echo is heard. Near Heidelberg is an
echo which imitates thunder. To waken it a pistol is
fired from the base of the hill Heiligenberg ; a wooded
gorge in front so reflects the sound, that instead of the
report of the pistol a noise of thunder is heard.
In Bohemia, near Aderbach, there is a circular space six
leagues in diameter, surrounded by bare pointed rocks. At
one spot in the centre is an echo which repeats three times
a sentence of seven syllables, while at a short distance off
no echo is perceived.
In the walls of Avignon, Kircher found the voice re-
peated eight times. In Rome an echo is repeated from
two to seven times. Boissard, in the " Roman Topo-
graphy," gives this description of the tomb of Ccecilia
Metella: It is a round tower, its walls twenty-four feet
1
REFLECTION OF SOUND. 93
thick, and ornamented with 200 heads of bulls in marble,
to commemorate the two hecatombs sacrificed at the funeral
of the daughter of Metellus Crs.ssus. This monument is
situated near St. Sebastian, and called "The Bull's Head."
A sentence spoken at the base of the hill on which it stands
produces a multiplied echo. Boissard says that when he
sang the first line of the ^Eneid, it was repeated eight times
distinctly, and several times more imperfectly. Mersenne,
speaking of this echo, says the place can still be seen
in which the hecatomb was immolated, where the echo would
make the sacrifice seem larger than it was. Whether the
place was chosen to give a greater solemnity to the rite, or
whether it was chosen for the burial-place of the house of
Crassus to immortalise it by multiplying their names to
posterity, he could not tell.
In a private dwelling an echo is not at all pleasant,
as it causes what is said or done to be heard at a dis-
tance. It is only in large halls or places of amusement
that it would be desirable, while in a church, if it makes the
preacher's voice better heard, it also frequently interrupts
him by the re-echo.
The drawing by Kircher (Fig. 32) represents the Hall at
Simonetta, near Milan. Measured from the interior of the
court, the fagade is 121 feet, and the wings 66 feet; the
height of the upper storey, between the gallery and the roof,
32 feet, the gallery 16 feet. When a pistol is fired from
the window in the left wing, it is repeated forty or fifty
times, and the sound of the voice twenty-four to thirty
times. Addison and Monge tried it, and Bernouilli believed
he counted sixty repetitions.
In vaulted buildings there is an echo, owing its peculiarity
to the laws of geometric curves. The ellipse is a lengthened
94
ACOUSTICS.
curve like a flattened circle, and two points in its interior,
//(Fig. 33), are called the foci, because in each of them
are collected the rays of light or sound, which, diverging
Fig. 33-
from the other, are reflected from the interior of the curve.
A person placed at one of the foci of an elliptic curve hears a
whisper from the other focus, so that two persons placed at
34-
these positions could converse in a whisper without being
overheard. There is a building of this kind at Muiden, near
Amsterdam. Parabolic surfaces have one focus, to which
parallel rays converge after reflection, while those diverging
from it become parallel after reflection; so that if two
REFLECTION OF SOUND. 95
parabolic mirrors are placed opposite each other, the slightest
sound made at the focus of one is heard at the focus of the
other, as is shown in Fig. 34. This makes them applicable
in lighthouses, for throwing rays of light or the sounds of
bells to a distance. With less reason they are chosen for
acoustic trumpets. It is supposed that at the focus where the
ear is placed the rays coming from a certain distance are con-
densed, as a parabolic mirror condenses at its focus the sun's
Fig 33-
rays. The sails of a ship sometimes produce this effect
when inflated by the wind. Arnott says that in a coasting
vessel off Brazil, by standing before the mainsail the bells of
Sari Salvador could be heard from a distance of no miles.
Church vaults, caves, and ramparts very often furnish some
curious illustrations of acoustic effects. In an elliptic vault,
sound issuing from one point is heard at another fixed point
by a single reflection from the wall; and between two
opposite parabolic vaults it is heard, though less distinctly, by
means of a double reflection. Other systems of curves might
give the same result by a number of successive reflections.
96 ACOUSTICS.
Thus two parabolas combined with a plare surface, as in Fig.
35, would give it by means of a triple reflection; and it is
possible that the action of multiplied reflections would go
far to explain many curious results.
Sound is much increased by the echoes in a closed vault
In a cave of the Pantheon, the keeper by striking the flap of
his greatcoat makes a noise like the report of a cannon. The
same phenomenon is found in the caves of Kentucky. In the
Cave of Smellin, near Viborg, in Finland, by throwing in a
live animal you hear terrible noises. Olaus Magnus says
that when an enemy approached the inhabitants would
conceal themselves, while the boldest amongst them cast
an animal into the cavern, whose terrible roarings "over-
threw the enemies like oxen at the shambles, when the
Finlanders leaving their hiding-places spoiled the slain."
Pliny tells of a similar cave in Dalmatia, where the falling of
a stone raised a perfect storm. Fingal's Cave, in the island
of Staffa, presents another remarkable phenomenon. The end
of this cavern is dark and gloomy, and may be compared
to the chancel of a church, while the basaltic columns may be
likened to the organ-pipes. At the extremity of the grotto,
and near the level of the water, is a small opening, whence
come harmonious sounds, which are produced by the swell
rising and falling.
St. Clement of Alexandria relates that in Persia were
three mountains in an open country, so situated that ap-
proaching the first you heard confused voices and wrangling;
on nearing the second the hubbub increased, but reaching
the third you heard sounds of mirth and rejoicing.
The panic terror which overcame the Gauls near the
temple of Delphi, defended by the god Pan, is attributed to
echoes. In the same way, Mersenne says, " The Persians,
REFLECTION OF SOUND. 97
while ravaging Greece and Megara, awaking an echo in the
night, imagined they heard the cries of numerous enemies,
and attacked the resounding rock, on which they spent their
courage and their darts, and were next day taken captive."
Another remarkable analogy between light and sound is
the refraction which both rays undergo in passing from one
medium to another. A spoon put into a glass of water
seems to bend ; this is the effect of refraction. The rays of
light which meet the water in an inclined direction are bent
when they emerge into the air. The effect of prisms and
lenses depends on the successive refractions to which light
is subject on passing from the air into the glass, and back
again ; the glass being so prepared as to give the requisite
deviation. M. Hajech thus proves that the rays of sound
follow the same laws : He had a hole made in the partition
wall of two rooms, and placed in it a tube closed by two mem-
branes. This tube was successively filled with water, carbonic
acid, hydrogen, ammoniacal gas, &c. At one end another
tube was attached, filled with air, and ending in a wadded
box containing an alarum watch. The sound passed through
the tube containing the gas or liquid, and the observer in
the next room noticed where the sound had most force.
When the two membranes were perpendicular to the axis of
the tube, the direction corresponded with the axis, without
deviation ; but when the front membrane was inclined to
the axis, a sensible deviation was perceived, which was
measured by holding a plumb-line to the ear, which traced
the arc of a circle on the floor. These experiments showed
that the rays of sound are refracted by the same laws as the
rays of light : they depend on the angle at which the rays
strike the reflecting body, and the comparative velocity
with which they are transmitted* through the two media.
H
98 ACOUSTICS.
This was the same for water and hydrogen, but different in
the case of carbonic acid.
M. Sondhauss observed the refraction of sound by means
of a lens of collodion filled with carbonic acid. When a
watch was placed in the axis of this lens, the sound was
concentrated at another point of the axis on the opposite
side. This, therefore, was the focus, and the sound of the
watch was distinctly heard ; but when the lens was removed
it was lost. This experiment was made more easily by
means of Helmholtz's sonorous globe; this was moved
slowly before the lens, and the india-rubber tube attached
to it placed in the ear. .
Mersenne has also considered the question " whether
sounds are bent by refraction, as light is when it passes
from one medium into another." But he only explains
how light is affected by refraction, and hence how magni-
fying lenses should be cut ; and then adds, " I do not be-
lieve that these effects can be produced in sounds by human
industry ; as to the angels, if they like to dispose the vibra-
tions of the air as they please, I do not doubt they can do
the same thing with sound as with light."
CHAPTER VIL
RESONANCE.
Resonance— Vitruvian Vases— Harmonic Tablets — Sonorous Globes
— Glasses Broken by the Voice — Acoustics of Churches and
Theatres.
THE assertion that sound passes round an obstacle must not
be taken too literally. Very massive bodies may arrest it,
as an opaque screen does light. Two persons separated by
a rising ground can hear each other, because sound passes
over the obstacle as light cannot ; but it is made fainter, and
they would hear much better if it were removed. It is only
when sound is conducted through a closed tube or passage
that its direction may be changed without diminishing its
force; in open air it grows fainter, as daily experience proves.
To hear a speaker well you should be in front of him, and to
hear an indistinct voice you instinctively turn the ear in the
direction from which it proceeds. When the stream of
sound meets an obstacle it can turn the other way, as a
current checked by an island, but its force is diminished.
A very large and massive object will entirely arrest sound.
Under the arches of large bridges you may place yourself so
that no sound from without can reach you. Behind the
vertical fall of the Rhine at Schaffhausen there is complete
silence. The sounds of bells may often be heard in streets
from an opposite direction to that of the bells ; the houses
arrest their sound, and only the reflected sound from the
opposite walls is audible.
H 2
100 ACOUSTICS.
Elastic bodies of slight density offer little impediment to
the passage of sound, and are of little use in damping it.
It would be as wise to try to keep out light with a glass
screen as to try and intercept sound by a boarded par-
tition. The elastic body becomes itself sonorous and
vibrates to the touch. The same thing is observed when
sound is reflected from an elastic surface, which acts as
a spring-board to return the sound with vigour. By this
means the wonderful intensity of some echoes is to be
explained. At the same time other sounds, arising them-
selves from the reflecting surface, mingle faintly with the
reflected sound. We say then that the surface resounds.
It is analogous to the reflection of the solar rays by a body
which, besides returning the direct rays, becomes heated
and then radiates heat in all directions.
The resonance of arches is a complex phenomenon due
both to resonance and reflection. Sound returns too
quickly from the walls of a high arch to produce a distinct
echo, yet not quickly enough to be blended with the
original sound ; the vibrations of the walls bring in a new
element, and so a thousand confused noises are produced,
which give rise to the remarkable effects we have noticed in
speaking of echoes. We can observe these phenomena
when passing in a steamboat under a bridge, of which the
sides and arches intensify the sound of the paddles. When
a locomotive rushes with great velocity underneath a bridge,
the reflection of the noise produces a sound like violent
explosion, and in a tunnel the uproar becomes deafening.
Sheets of water are very favourable to these effects, by the
facility with which they reflect sound. Thus Cagniard de
Latour, having compared two pits — one dry, the other
containing a little water — found the latter was much more
RESONANCE. IOI
sonorous than the former. Undar the arches of bridges, the
resonance is sensibly weaker when there is no water under-
neath.
Drapery, tapestry, and all fabrics of that class have the
effect of deadening sound ; they destroy sound in a room
which contains them just as gloomy colours render it dark.
It is for this reason that even a good piano is often not well
heard in a room carpeted, hung with curtains, and filled
with cushioned furniture. Empty rooms are always re-
markably sonorous. In churches, or in rooms where
meetings are held, too great resonance is very injurious to
distinct hearing. It is apt to drown the voice of the
speaker and render him unintelligible. But the case is very
different in a concert-hall ; there we endeavour to in-
crease the resonance of the walls by a casing of thin
wood.
In the time of Rousseau the best constructed orchestras
were to be found, it is said, in the Italian theatres. The
platform was made of light and resonant wood, such as pine.
It was supported upon arches with an empty space beneath,
and it was separated from the audience by a railing in the
pit distant a foot or two from it By this arrangement even
the body of the orchestra was supported freely and
could vibrate without obstacle, thus allowing full scope to
the power of the instruments. At the Paris opera, on the
other hand, the orchestra was very badly arranged, being
near the ground and enclosed all around with massive
wood and iron, which destroyed all resonance. At the
present time, the principles of construction so much praised
by Rousseau are adopted in the majority of theatres specially
devoted to music ; but it is true that many competent archi-
tects consider them useless or even injurious.
102 ACOUSTICS.
Vitruvius tells us that the Greeks put inverted brass
bells over conical supports in the niches of the wall, to
increase the resonance in their theatres. They were used
especially in Corinth, from whence Nummius carried them
to Rome. Sometimes vases of baked clay were used for
cheapness. Vitruvius says that the bells were suited to cer-
tain notes of the gamut. He explains at length the way of
making and placing them, as represented in the drawing by
Kircher, Fig. 36. He recommends that the bells should be
so constructed as to give the fourth, fifth, octave, eleventh,
twelfth, and double octave, or the series of notes —
sol, doh, re, sola, doha, rev soly
Kircher thinks this contrary to the laws of harmony, and
Substitutes —
sol, si, re, sola, si,, rea, sol,,
which seems to us correct. Probably the brass bells emitted
no sound, and the resonance was produced by the air con-
tained in them and the niches of the walls. Sounding-
boards in musical instruments are intended to intensify the
feeble sounds emitted from the strings, whose surface is
too small to put a mass of air in motion— they divide it
without making it vibrate ; it is necessary, therefore, to
stretch them across a sounding-board, which receives the
vibrations, and propagates them with more effect. A tuning-
fork becomes very audible when it rests on wood. For
this reason diapasons are attached to a wooden case to
increase the sound ; the case also causes the air in it
to resound, and thus adds to the effect. It is necessary
that the size of the case should be proportioned to the note
to which it belongs, or the effect would not be produced.
RESONANCE. 105
Elastic bodies of a certain form — sticks, chords, mem-
branes, strings, &c. — have their own peculiar notes, which
they give when struck, or which they prefer to reinforce by
resonance. The volume of air contained in the case of a
diapason has its own particular note, which must accord with
the cound which it is capable of reinforcing. M. Helmholtz
applied this principle to make an instrument for analysing
sounds, called the sonorous globe (Fig. 37). It consists of a
Fig. 37. — Sonorous Globe.
hollow sphere of glass or metal, with openings at two oppo-
site points : one of a form to receive the sound, while in the
other a tube is inserted of ivory and india-rubber, to apply
to one ear while the other is closed. The volume of this
globe, and the size of its orifice, determine the note which
it is adapted to reinforce. * If that note exist in any
noise, it will be heard resounding in the globe, but no other
note will produce any effect. In this way, a note can be
distinguished in the midst of confused sounds, which veil it
entirely from the naked ear. A series of these globes, of
different sizes, supplies an apparatus for analysing sounds,
106 ACOUSTICS.
of much importance in acoustic researches. If two dia-
pasons of the same note are placed even at a considerable
distance, with their openings facing each other, then, if one
be struck, and the sound arrested by laying the hand on it,
the note will be heard from a distance carried on by the
other diapason —
" Et sese lampada tradunt."
Here the vibrations are sent through the communicating
column of air, the atmosphere transmitting the vibration in
the air contained in one case to the other, which responds.
A violin or stringed instrument will sound if the note to
which it accords is given at a distance ; but sounds which it
does not render produce no effect on it.
Kircher mentions a large stone which vibrated to a cer-
tain organ-pipe. We have often heard of the famous pillar
in a church at Rheims, which vibrates perceptibly at the
sound of a bell, while all the others are immovable. Boyle
asserts that he has often felt with his hand the pews in
church vibrating at the sound of the organ, or at the human
voice, certain notes producing more intense effects than
others.
A glass may be broken by the voice. Every glass has
its own note, heard when it is tapped or broken ; so that
if a man with a true, strong voice, pronounces the note on
the edge of the glass, it will break in a few seconds. The
octave of the note is said to be equally effectual. Thin convex
glasses are the best for trying the experiment. The sound
of a violin would answer, while the blast of a trumpet would
not. A German physician saw it done in an inn by a man
who made it his trade. Several glasses were ranged before
him; he struck them in succession with a key to get the
RESONANCE. IO7
note, then bending down sounded the same note vigorously,
and the glasses broke. There was no proof that the glasses
had not been prepared : a slight scratch with a diamond
would have made success more certain.
It is curious that the earliest mention of this class of
facts should be in the Talmud. " It was said by Rame,
the son of Jacheskel : If a cock shall put his head into a
vessel, and break it by his crowing, the owner must pay the
whole price. Rabbi Joseph says, ' These are the words of
the Master : If a horse by neighing, or an ass by braying,
break a vessel, the owner shall pay the half of the price.' "
The writers of the Talmud who invented these niceties of
law must have had exuberant imaginations.
We have just seen that the phenomena of resonance are
always produced by vibrations in elastic bod:es. Gene-
ralising from this, we perceive that all sound results from the
vibration of elastic matter, so that sound may be denned
as a vibratory movement, perceptible by the ear. But
before enlarging on this, we have a few words to say on the
acoustics of churches, theatres, &c. — a difficult problem,
which has been but little studied. How should a hall be
constructed, so that the sound emanating from one point
may be transmitted distinctly in all directions ?
The ancients built circular amphitheatres, with the seats
in raised circles, and semi-circular theatres, with the stage, not
extending far back, enclosed in thick, solid walls. But the
only roof was a covering to keep off the sun's rays, which,
though it could not fail to reflect sound, was not taken into
account by the architects. They succeeded in so disposing
the seats that the actor's voice should proceed directly
to all the hearers, numbering often some thousands. Even
in the ruins of such theatres, we can see that this end was
io3
ACOUSTICS.
generally attained. Every word spoken in the arena can
be heard at the farthest seats. The theatre of Hadrian's
villa atTivoli, the circus of Murviedro, and the amphitheatre
at Nismes (Fig. 38) are remarkable in this respect.
The only means employed by ancient architects to aug-
ment sound were the vases or bells already mentioned.
Fig- 38- — Amphitheatre of Nisme*.
Public affairs were transacted in an open building called
a forum. Under the blue heavens they enjoyed their
amusements, took counsel, and listened to harangues. But
now that civilisation has left its cradle to find a home under
ruder skies, for this simple architecture various kinds of
halls, circuses, concert-rooms, theatres, houses of legislation,
&c., are substituted. Platforms, pillars, stalls, boxes,
pews, introduce great difficulties into the propagation of
RESONANCE. IO9
sound, by their powers of resonance and reflection. We
must proceed on a new plan to discover the method of
applying the science of acoustics to modern buildings.
Domes are generally unfortunate in their effect; they pro-
duce a too powerful and too prolonged resonance. Under
the dome of St. Paul's the sound seems to run along the
Avails. In the Rotunda at Rome this resonance produces
such singular effects, that it is said many people go to
church for the sake of hearing them. In the circular con-
cert-room of the Fine Arts Society in Berlin, where the
walls are broken by a large number of deep embrasures,
Fig. 39- Fi«- «*
this inconvenience is not met with. The dome of St. Mary's
at Dresden is remarkable for the same absence of resonance.
There is no advantage in elliptic arches or halls, the
ellipse only serving to concentrate sound at a particular
point. The parabola, which makes diverging rays parallel,
has some recommendation. The speaker's desk should be
at the focus of the curve. Chladni proposes to terminate
a rectangular hall with a parabola. This arrangement
(Fig. 39) is found in some ancient basilicas. It might be
completed by giving a parabolic form to the roof over the
platform. A sounding-board of this nature is sometimes
placed over the pulpit ; its mode of action is the same as
that of the apparatus for reflecting in lighthouses. In a
concert-room or hall it might be an advantage to construct
no
ACOUSTICS.
over the platform a spherical dome, with its axis directed to
the centre of the hall. Another idea of Chladni's is to place
the speaker's platform in a
semi-conical space at the ex-
tremity of the hall (Fig. 40),
but he admits that this arrange-
ment would be unsightly and
difficult of construction. In
theatres, of course, no reflector
could be placed behind the
actors. The only suggestion
deserving attention is to em-
ploy, like the ancients, triangular columns turning on their
axes, instead of the folding screens through which so much
sound is lost (Fig. 41). The arrangement of the seats in
a semi-circular form would not suit the exigencies of the
Fig. 4«.
Fig. 43.
Fifi 43-
modern drama. An advantageous form is given in Fig. 42.
The theatre of Parma, which is celebrated for its acoustic
properties, is given in Fig. 43. The boxes in front of the
stage are the great defect in modern theatres. Zamminer
compares them to monster traps for strangling sound.
RESONANCE. Ill
Unfortunately the architect is compelled to consult the
wishes of those who come not to hear, but to see.
In the construction of our churches and amphitheatres,
the simplest laws of acoustics are neglected, and conse-
quently very imperfect effects obtained. The commonest
defect is an excessive sonorousness, which prevents words
from being distinctly perceived. The semi-circular room
of the Fine Arts School in Paris, though beautifully deco-
rated, is miserable in this respect. The great Amphitheatre
of Physics and Chemistry in the Jardin des Plantes, and the
Amphitheatre of Physics in the College of France, are
inconveniently sonorous. They have tried to remedy it by
using drapery to deaden the walls, and pieces of wood to
impede the vibrations of the raised seats ; but this modi-
fication is of little use. In the church of St. Paul, Boston,
which has the same defect, the preacher's voice can only
be heard once a year, on Christmas Day, when it is deco-
rated in such a way that the arches are less sonorous.
The semi-circular form, so often given to amphitheatres,
produces great inequality between the seats at the centre
and those at the extremities, as in the Amphitheatre of
Physics of the Sorbonne, and that of the Conservatory of
Arts and Trades, but there the inconvenience is lessened
by the chair being differently placed. The most advan-
tageous form is that approaching the quarter of a circle,
because the walls direct the sound to the hearers.
For placing the raised seats, the general rule is to follow
a line direct from the platform to the beginning of the roof.
A concave curve would be more advantageous, as it would
obviously allow of the back rows hearing better. Mr. Scott
Russell, M. Lacheze, and others have proposed several
curves for this purpose.
112 ACOUSTICS.
The most original project for improving the acoustics of
theatres is that suggested to Chladni by Langhaus, of Berlin.
He would direct from the stage to the spectators a slight
current of air, which should carry the words of the actors.
It would be produced by skilful ventilation.
CHAPTER VIII.
SOUND IS A VIBRATION.
Trevelyan's Instrument — Singing Flames — Pendulum — Undulations of
Water — Progressive and Stationary Waves — Vibration of Rods,
Strings, Boards, and Tubes — Graphic Method.
UP to the present we have only considered the phenomena
of sound as affecting the senses. It is now time to consider
what produces them. The phenomena of
resonance point to the conclusion that sound
can only originate in the vibrations of a
ponderable body.
Common experience shows us that a
sound of any force is always accompanied by
vibrations perceptible to the touch. Drums
beaten in the streets shake the window-panes.
The report of a cannon makes the earth
tremble ; those near enough feel a shock in
the chest. In a concert-room, turning the
opening of a hat toward the orchestra, you
may feel the trembling of the air by placing
your finger-ends on the crown. In many
cases it is easily proved that sound cannot
be produced without a concurrent vibratory
movement. A stretched chord when struck
makes oscillations which are visible, and, owing to the per-
sistence of luminous impressions, it takes the form of Fig. 44.
I
H4
ACOUSTICS.
The outline of a diapason becomes indistinct while it sounds,
because of the rapid motion. A glass bell, rung by means of
a fiddle-stick or wooden hammer,
will communicate violent shocks
to a little ivory ball hung beside
it. Each time that it touches
the bell, the ball is thrown away,
returning again and again as by
an irresistible impulse, only to
rebound once more. If the edge
of the bell be touched with a
pencil, it grates against the vi-
brating glass ; or if a horizontal
bar of steel be rubbed between
the thumb and fore-finger with
a little colophony, it gives a
sharp sound ; and if the ivory
pendulum touch either extremity,
it rebounds with great force.
Plates of brass, wood, or glass
give different sounds, according
to the manner of striking them.
Sand sprinkled on the surface
assumes regular curves, marking
the lines of repose. A membrane
stretched upon a cardboard frame,
and hung by three threads in the
pipe of an organ, will throw to
a distance the powder scattered upon it. The better to
show this, a glass pipe can be used for the organ (Fig. 45).
It is always easy to produce sounds by mechanical
action repeated at short intervals. The buzzing of a fly's
Fig- 45-
SOUND IS A VIBRATION. Ilg
wings, the chirp of a cicada or grasshopper, are examples of
this kind of sound. A flexible card pressed against the
edge of a cog-wheel makes a sound, which grows sharper as
the rotation becomes more rapid ; this is the principle of the
rattle. In the siren (an apparatus- that will be described
further on) a stream of air or liquid is directed against a
perforated revolving disc ; this stream either passes or is
arrested alternately, thus giving birth to a remarkable sound.
In the reed stop of an organ the sound is produced by the
vibrations of an elastic tongue. The lips tremble while
playing on the oboe or clarinet.
It sometimes seems as though sound might be produced
by a continuous movement ; the flute and the common whistle
seem influenced by the action of an uninterrupted current of
air. But in these cases the current is broken and divided
into two streams by the orifice, one part entering the
mouth-piece, the other escaping into the outer air. The
current first compresses that portion of the air next the
orifice ; this latter, reacting by its elasticity, resists the
current, then gives place again, repeatedly; so there is,
in reality, a continued series of vibrations. Wertheim suc-
ceeded in playing upon pipes submerged in liquid, by the
injection of a stream of the same liquid. The sounds he
obtained had the same musical character as when the pipes
were played upon by air. Cagniard de Latour had pre-
viously to this made glass tubes vibrate in water by means
of friction, so that the water became sonorous.
We must here mention the "rocker" of Trevelyan, in
which the sound results from the contact of two metals
unequally heated.
In 1805 M. Schwartz, inspector of one of the foundries of
Saxony, having placed a silver cup, still hot, upon a cold anvil,
I 2
1 1 6 ACOUSTICS.
heard, to his great astonishment, musical sounds coming
from the metal. Professor Gilbert, of Berlin, repeated this
experiment, and described how the cup vibrated so long as
the sound was heard, but grew quiet as it cooled and the sound
ceased ; he did not attempt to explain the phenomenon.
About 1829 Mr. Arthur Trevelyan, wishing to melt resin
with an iron, found the iron was too hot, and laid it against a
block of lead to cool. Scarcely had the iron touched the
lead, when a sharp note was heard coining from it, some-
thing like a Northumberland flute ; at the same time he
saw the iron moving in rapid vibration. Mr. Trevelyan set
himself then to study these facts, and he gave an explanation
of them which seems to be the true one. The vibrations he
supposes to be caused by the sudden expansion of a cold
body when brought into contact with a warmer. At the
moment when the hot iron touches the lead at a given
point, the lead expands and repulses the iron ; the iron then
touches at some other point, where the same thing occurs,
whilst the point first touched cools and contracts. By this
play of alternate expansion and contraction the "rocker"
is able to produce music. It is usually made in brass, of
a prismatic bar, the lower angle having a hollow groove.
This is fixed on a round handle. When heated to about the
temperature of boiling water, or a little more, it is placed on
a piece of lead. Mr. Tyndall made the same experiment
with a heated shovel, which he balanced on two pieces of
sheet lead fixed in a vice. It immediately took a see-saw
motion, and gave out a musical sound, which could be
modified by lightly touching the handle.
Sometimes a musical vibration may be obtained by a
simple coin or ring laid upon a piece of lead, after having
been sufficiently heated.
SOUND IS A VIBRATION.
When a current of air is heated and cooled periodically
at a certain point, there results a succession of alternate
dilatations and contractions, which may prove a source of
sonorous vibrations. This is illustrated by the apparatus
of Fig. 46. It is composed of a glass tube, in which is fixed
a small metallic web. This is heated red-hot by a spirit-
lamp. After a few moments a plaintive sound — a sort
of low moaning — seems to float around
the tube ; gradually it swells, increases,
becomes very loud; then, as the web
cools, the sound dies away, and the
tube becomes silent again. The sound
is caused by the ascending current of
air becoming heated as it passes through
the web, and cooling as it leaves it
Indeed, by lowering the tube towards
a horizontal position it may be stopped
momentarily, because of the interruption
of the current of air. The mysterious
sounds which were heard to procee$
from the statue of Memnon at sunrise
were, very probably, caused by the
currents of air in the hollows of the stone being heated by
the sun's rays (Fig. 47),
We often hear the gas sing when the jet is stopped by
an obstacle which prevents the free passage of the current.
The jet, instead of being continuous, is intermittent, and
the gas escapes by pulsations. A current of hydrogen in a
glass tube would produce the same effect. This little cir-
cumstance has given rise to a number of beautiful expert
ments by Count Schaffgotsch and others. Introduced into
a glass tube is a small brass burner, with a gas flame (Fig. 48).
Fig. 46.
u8
ACOUSTICS.
If then a note be sounded at a distance, in harmony with
the glass tube, the air within begins to vibrate, and communi-
cates its pulsation to the flame, which grows tall, and trem-'
bles, and begins to sing in its turn. It may be silenced by
Fig. 47.— Statue of Memnon.
pressing a finger on the opening of the tube, but will sound
again for another call of the voice ; only the true note must
be produced, or the flame will not respond. With four
flames and four tubes, a little organ may be made to give
the chord doh, mi, sol, doh, in perfect harmony, whose
SOUND IS A VIBRATION. II 9
music is sustained as long as the flame continues to burn.
Sometimes, too, it will happen that the flame will begin to
sing spontaneously, if its point be placed at a certain part
of the tube.
It is easily proved that the sound of singing flames is
produced by a pulsation of gas burning in the
tube. The flame changes alternately from yellow
to blue, according to the quantity of gas which
comes to feed it. If the head be moved quickly
from right to left, the flame will seem to separate
into a number of blue and white images, which
being received on different points of the retina,
are not confused in the eye. The result may
be better obtained by using an opera glass
during the experiment The best means of
separating the successive appearances of the
flame is, however, furnished by the revolving
mirror. This is a mirror with two, three, or four
faces, rotating round a vertical axle. It causes
the flame to appear every moment in a new
direction, the result of which is a kind of lu-
minous ribbon, continuous so long as the flame Fig. 48.
remains still, but breaking into a chaplet of
brilliant pearls when it begins to vibrate. There is a suc-
cession of little stars, followed by luminous trails of a rich
blue, such as we see in jets of gas when the wind blows
on them. These trails terminate in spaces of complete
darkness, which seem to indicate that the flame is momen-
tarily extinguished, though immediately rekindled.
Sonorous flames may also be studied by means of a
revolving disc, perforated with a circular row of holes. A
vibrating body, looked at through such an apparatus (called
120 ACOUSTICS.
a stroboscope), appears to move with diminished velocity.
It is as if we had a microscope to magnify time. The
vibratory movement is a motion of going and coming,
reproduced at equal intervals, in a uniform rhythm. The
oscillations of the pendulum give a curious example of this.
Moved from its position of repose, the pendulum imme-
diately returns because of its weight. It falls, but in falling
it acquires an increase of velocity, and passes the starting-
point. It mounts to an equal height on the opposite side.
It cannot mount higher, for the weight
draws it back while it swings, thus
gradually destroying its velocity, which
becomes nothing as at the moment
of first setting it off. Then the pen-
dulum is found exactly in the same
condition as at first ; and the action
recommences in an opposite manner:
it descends, passing the point of equi-
Fig. 49.-The Pendulum. ijbrjum at [ts maximum speed, and
returning to its starting-point with no
velocity. Thus it has accomplished a complete oscillation,
going and returning, or two simple oscillations in a contrary
direction. Should nothing stop it, it will continue indefinitely
to move thus from side to side of its vertical ; but the re-
sistance of the air, and the friction of the thread at the point
of suspension, together with other causes, diminish by degrees
the scope of the oscillations, and so bring the pendulum at
last to rest. It is ascertained that all oscillations are accom-
plished in a definite time. A pendulum a little over a yard
long performs one oscillation in a second.
The motion of the pendulum is kept up by the force of
gravitation. The vibrations of a sonorous body are usually
SOUND IS A VIBRATION. 121
sustained by the force of elasticity. Like the vibrations of
a pendulum, they are finally extinguished by the action of
different resisting forces which are constantly tending to
destroy them. The duration of the vibration of perceptible
sounds varies from the tenth to the twenty-thousandth part
of a second.
As to the- particular nature of these vibratory move-
ments, they may be of different kinds. In the air they form
alternate condensations and dilatations. A prismatic body
may contract and dilate lengthwise, or bend transversely, or
even perform rotatory vibrations.
When sound is propagated the vibrating air-particles do
not sensibly change their place, but only move near their
positions of rest for a short space, and the motion or pulse
only is transmitted to a distance. Therefore it is that water
scarcely seems to be displaced when traversed by an ordi-
nary wave. To prove this, throw a stone into a piece of
quiet water. Around the point of commotion we see con-
centric rings, which are propagated to the shore, describing
larger and larger circles. On their way they meet with
many floating bodies — pieces of wood, withered leaves, and
straws. Light as they are, these are not carried away. We
see them rise at the approach of the wave, and sink as it
passes, but they do not perceptibly change their place. It
is not then a material wave which is carried on the surface
of the water ; that which appears to be carried is merely the
shock or impulse, and the deformation that results from it.
The rings dissolve each moment, and each moment are
formed anew, with fresh particles, which in their turn
quickly come to repose. Let us now imagine, instead of a
single stone, a number thrown in one after another, at
regular intervals, to the same place; the waves that they
122
ACOUSTICS.
excite will also break upon the shore at regular intervals,
but they will not carry the particles of water very far ; they
mount and fall continually, and pass on the impulse they
have themselves received.
The interesting experiments of Ernest Henry and Wil-
liam Weber showed that liquid particles generally move in
Fig. 50.— Undulations of Water.
circles, while the wave travels onwards. To make this
plain, let us suppose that each particle makes a complete
circle in the time that the wave takes to go from the point o
to the point 12 in Fig. 50 : it will make the twelfth part of
a circle as the wave clears each of the twelve spaces
Fig. 51.— The Quarter of an Undulation.
between the points o and 12. At the moment the wave
touches point 3 (Fig. 5 1) the particle o will already have
had time to accomplish three-twelfths or one-quarter of its
circle ; the particle i two-twelfths or one-sixth, and the par-
ticle 2 one-twelfth of the circle, while particle 3 will scarcely
have begun its movement. At this moment the particle o
will have reached the lowest point of its course, and then
will begin to mount the opposite side.
SOUND IS A VIBRATION.
123
The next figure (Fig. 52) represents the situation of the
particles by the time the wave has reached point 6. The
particle o has finished the half-circle, particle 3 a quarter,
and so on. It is now 3 which is at the base of its path,
Fig. 52. — Half of an Undulation.
whilst o is again on the general level. Between o and 6 is
a hollow.
In Fig. 53 the first particle has described three-quarters
of a circle, and is seen on the culminating point of its
course ; the particle 3 has made half its journey, and re-
gained its first level; the whole set from 3 to 9 form a
Fig. 53. — Three-quarters of an Undulation.
hollow undulation, just as the set between o and 6 did
formerly.
Finally, in Fig. 54 the hollow is displaced for three
points — that is, from 6 to 12. The point 3 is now at the
summit of its course ; while point o, having described an
entire circle, has returned to its primary position. Between
o and 6 there is a crest. This elevation, and the depression
124
ACOUSTICS.
which extends from 6 to 12, taken together form an entire
wave, and the interval it fills is called the wave-length. It
will be noticed that at the depth of the hollow the particles
are at a distance from one another, while towards the crest
of the wave they are close together. The same thing is
Fig. 54.— Complete Undulation.
repeated at regular intervals afterwards. When the particle
o has finished its second revolution, the particle 1 2 has only
accomplished its first ; there is one complete wave between
o and 12, and another between 12 and 24 (Fig. 55). When
the particle o has made three turns the waves are propa-
gated up to the point 36 ; when it has made four turns the
Fig. 55-
waves have reached point 48, and so on, advancing a wave-
length at each oscillation.
Particles may travel in ellipses instead of circles, and
these ellipses may become so elongated as to be transformed
into straight lines. Then the liquid particles only rise and
fall vertically ; they simply make transverse vibrations, as we
may see them do in chords, metal plates, and membranes.
SOUND IS A VIBRATION. 125
The general form of the wave remains the same, but the
trough and the crest become symmetrical, the one being
always the reverse of the other, as is shown in the following
curves (Fig. 56), which represent the progress of a trans-
verse vibration. Such are the undulations of the ether
which produce light
Fig. 56.— Progression of a Transverse Vibration.
If the orbits of the particles, instead of becoming ver-
tical lines, changed into horizontal lines (the propagation of
the wave being always supposed horizontal), we should have
longitudinal vibrations, analogous to those of gaseous bodies.
The particles then can only separate and approach by turns,
whence result alternate dilatations and compressions, as may
be seen in the curves in Fig. 57, which represent the pro-
gression of a longitudinal wave.
126 ACOUSTICS.
In a body of cylindrical form another class of vibrations
may be seen — tortuous or revolving vibrations. The par-
ticles circulate round the axis of the cylinder, and the motion
is propagated in the same manner as in other cases. Each
particle begins its excursion a little after the preceding one,
and therefore remains a little behind it, in all the phases of
the oscillations, which they pass through together.
Fig. 57. — Progression of a Longitudinal Vibration.
In this way the progressive waves are propagated in an
unlimited medium. Thus sound is transmitted in the open
air, light through the ether, and undulations in an unbounded
sheet of water. We observe these waves to move along as
if each phase of the movement of the first particle were trans-
mitted successively to all the file. In transverse vibrations
we see the summit of the wave displaced, and travelling
along the chord. In longitudinal vibrations it is the compres-
sions and dilatations which are transmitted (Fig. 57). An
india-rubber tube, fixed at one end and held by the hand at
SOUND IS A VIBRATION.
127
the other, is shown in Fig. 56. A slight stroke at one end
will send a transverse wave undulating along the tube, thus
forming the curve. It may be followed with another wave,
by striking again on the end of the tube the moment it
becomes still ; then with a third, and a fourth, and so on,
till the first has reached the wall against which the tube is
fixed. From this instant the phenomenon changes its aspect ;
die waves being unable to advance are obliged to return,
ii.
in.
B ABA
Fig. 58.-Shock of Elastic Balls.
and the returning waves meet the later, which are still
advancing ; hence the result known as " fixed waves.'
The fixed waves characterise the sonorous vibrations of
elastic bodies, whether they give out their own sounds, or
only resound under the influence of repeated shocks. They
can be easily distinguished from progressive waves. In
the one the particles vibrate one after another, whilst in the
fixed waves they vibrate altogether. These waves do not
travel ; they are born, live, die, and rise again- always in the
same place.
This change is owing to the intervention of reflected
waves. The laws which govern these phenomena are com-
128 ACOUSTICS.
plicated enough. To give an idea of them, let us consider
what happens at the meeting of two elastic bodies. Suppose
A and B (Fig. 58) to be two billiard-balls hung by two parallel
threads. Raise the ball A, and let it fall against ball B ; if
their size be equal (I.), A will remain in repose after the
shock, giving up all its velocity to B, and B will be thrown
forwards. If the ball A be larger than B (II.), it will pass the
vertical line with a velocity scarcely diminished, chasing the
smaller ball before it. Finally, if A be smaller than B (III.),
it will be thrown back with more or less force ; the greater
the resistance opposed by the mass B, the stronger will be
the rebound.
The same thing takes place when a vibration is propa-
gated in an elastic medium. The balls A, B, in Fig. 58 (I.),
represent two neighbouring particles which transmit a pro-
gressive wave. B receives all the velocity from A, and A
remains in repose till another impulse comes to disturb it.
But if A and B are, so to say, the bordering columns of
two media of differing density, we fall into one of the two
cases represented by II. and III. If, for example, the me-
dium B be less resistant than the medium A, the particle A
will pass forward while communicating its velocity to par-
ticle B (II.). If, on the contrary, the second medium be
more resistant than the first — if, for example, B represent a
fixed obstacle — the particle A will be thrown back, and B
will be scarcely stirred.
Now, in these cases what must follow ? The particle A
not being at rest will become a source of movement for all
the particles behind. The result will be a reflected wave,
which will carry back the movement given by A, either in
the direction that A was pursuing before the shock (II.),
or in the contrary direction (III.).
SOUND IS A VIBRATION. 129
These comparisons will serve to give an approximate
idea of the phenomena accompanying the reflection of a
sonorous wave. The first case (II.) represents the re-
flection of a sound in the interior of a solid body which
vibrates in the air, A being a point of the surface, and B a
particle of air.
A reflection of the same nature takes place at the ex-
tremity of a tube filled with air, opening into the atmos-
phere ; for the surrounding air, because it moves more freely,
has less resistance than the air inside. Therefore the sound
which comes from an open tube is partially reflected by the
surrounding air, and returns to the tube. This result, indi-
cated by theory, may be verified by experiment : at the end
of a very long open tube a faint echo is formed. Biot
observed that when he spoke at one end of the water-pipes
of the aqueduct at Arcueil, the sound was echoed back tc
him six times.
The case shown in Fig. 58 (III.) is the same as we have
in fixed obstacles. Sound is reflected in this manner, in the
interior of a closed tube, from one end to the other. A
simple apparatus, which we have not time to notice now,
would show how, in either case, the direct waves and the
reflected combine so as to produce fixed waves, separated
by points of repose, called nodes.
The particles comprised between two consecutive nodes
form what is called a simple wave.* Agitated by a common
motion, they all rush forward in the same direction, and
return in a contrary one. The centre of each wave is also
a centre of vibration. There the commotion is at its
* The simple wave is equivalent to the half of a complete or double
wave, just as a simple vibration is the half of a complete or double
vibration.
'3° ACOUSTICS.
maximum ; from the centre to the nodes it diminishes, the
extent of the excursions decreases, and at the nodes all
movement has ceased.
The particles of two consecutive waves always vibrate in
opposite directions. If they rise in one, they sink in the
other, and vice verscL (Fig. 59) ; if on the one side they
Fig 59.— Nodes and Centres.
approach or depart from the node that separates the two
waves, they approach or depart equally on the other side.
The interval between two nodes or two centres is a
simple wave-length, which is half an entire wave-length.
The length of a fixed wave is equal to that of a progressive
wave ; it is the measure of the advance made during the
time a single vibration lasts ; in other words, it is the space
traversed by sound during one vibration.* Thus when a
* A simple wave-length corresponds to a simple vibration, as a
double or entire wave-length corresponds to a double or complete vi-
bration. Sometimes one and sometimes another of these quantities is
employed, therefore it is necessary not to confuse tl em.
SOUND IS A VIBRATION. 1*1
ta9 o ^
vibration lasts the millionth part of a second, the corre-
sponding wave-length is thirteen inches if the sound be pro-
pagated in the air, and fifty-six in water, &c., since these
numbers represent the spaces traversed in the different
LQ.OO <K. . ,
media during the mi m oath of a second.
In the reflection from a fixed obstacle, a node is formed
close against it, since the direct and the reflected shock,
being in contrary directions, neutralise one another. Nodes
are therefore found at the points of suspension of a
vibrating body — at the ends of a string, for instance, or the
points where a metal plate is held in a vice. The position
of the other nodes depends on the shape of the sonorous
body, and the sound given out by it.
Any elastic body will generally return all the sounds
which meet* it, but the resonance varies greatly in intensity.
It is strong only when the nodes of the fixed waves, resulting
from the interior reflection of sound, follow certain regular
directions, and in this case they continue after the producing
cause has ceased to act. The sounds which develop such
a peculiar resonance in a body are such as are produced by
a mechanical shock — in other words, they are the sounds
properly belonging to a body. Any other sound finds but
a feeble echo.
Let us now consider the fixed vibrations of some
sonorous bodies, and find out the arrangement of the nodes
which characterise their specific sounds. Take first a
string, fastened at both ends. In this case there is a node
at either end, since the extremities are motionless ; there
may be, besides, any number of nodes at intervals from
one end of the string to the other. If it vibrates trans-
versely in all directions, all its points will simultaneously
describe the same kind of orbits, but of different dimensions,
J 2
132
ACOUSTICS.
that of the centre of the chord being the widest. This orbit
may be a right line, vertical or horizontal, an ellipse, a
circle, or any other curve, according to the
mode employed to produce the vibrations.
If it be a right line, the string will vibrate
in a plane ; if it be a circle, it will form a
spindle (Fig. 60). To make it vibrate with
three nodes, we have only to touch the
middle of the string lightly with the finger
while striking one of the two halves with
the bow; the string then divides into two
conical spindles or segments, separated at c
by a node, and vibrating in contrary directions
(Fig. 61). Touching it in the same way at
different points, we may obtain three, four,
or even five segments of the string, in each
case giving a different sound according to
the manner in which it is divided. The
immobility of the starting-points may be
demonstrated by placing slips of paper upon them, which
will remain perfectly quiet while on the nodes, but at any
other point will be thrown off immediately (Fig. 62).
Fig. 60.
6i.
By rubbing the chord lengthways with a little resin
Fig. 63), the longitudinal vibrations are shown, consisting
of alternate dilatations and contractions. When there are
only two nodes at the extremities A, B, the section A, c,
dilates, while B, c, contracts, and vice versa; the middle
SOUND IS A VIBRATION. 133
C becomes a centre of vibrations where the movement
of translation is a maximum, but where the density remains
the same. In the nodes A, B, the density, on the contrary,
changes most, and there is no translation. It could not
possibly be otherwise, for since those particles at C move
more than the others they will trench upon those in front,
forcing them to a compression ; at the same time distancing
those behind, which, consequently, must separate more and
more.
Now the chord may be again subdivided into portions of
an equal length, separated by nodes which will become the
Fig. 63.
centres of successive compression and dilatation. From the
two sides of each node the particles move in contrary di-
rections ; compression takes place when the node be-
comes the meeting-place of two files, and dilatation when
it is the starting-point of two files moving away again (Fig. 64).
It often happens that a string is stirred at the same
time by longitudinal and transverse vibrations, more or
less complicated, to which may be also added rotating
J34 ACOUSTICS.
vibrations. * Each particle then describes an orbit in the
form of a spiral slightly distorted. If you picture a poor
fiddle-string tortured by the bow of the fiddler, who strokes
it and strikes it, pinches and stretches it by turns, you will
Fig. 64.
not marvel to see it execute curves such as no geometer
has ever dreamed of.
To get transverse vibrations from a prismatic metal
plate, it may be either fixed by one end or laid upon two
triangular wedges (Fig. 65). A series of centres and nodes
Fig 65.
will then be seen, whose distribution depends on the
manner in which the rod is supported. The general rule
is that there are always centres at the free extremities, and
nodes at the fixed points. The nodes are shown under the
form of straight lines, which cross the plate, and which
* A chord cannot vibrate transversely without lengthening slightly,
and this occasions longitudinal vibrations. This longitudinal sound is
sometimes recognisable in the la of the violoncello.
SOUND IS A VIBRATION.
135
may be rendered visible by throwing sand upon the plate
while it vibrates. The grains of sand unable to remain at
the centres, where the tumult is at its height, take refuge
at the nodes, which afford them a quiet asylum, and group
themselves in fine right lines, called the lines of repose, or
nodal lines.
Tuning-forks belong to the same category as the pris-
matic metal plates ; they vibrate so that there are two
centres at the extremities of the branches,
which alternately approach and separate,
two nodes close to the base, and a third
centre in the midd'e of the fork. This
lower centre makes the stem rise and fall,
so that when placed upon a wooden table
it causes it to resound by the incessant
vibration (Fig. 66)
The longitudinal vibrations of prismatic
or cylindrical bars develop a wonderful
force. Savart, having secured a steel rod (Fig. 67), placed
a spherometer opposite the free end, not touching.it when
at rest, but near enough to be struck at each vibration.
The shocks were heard when the sphero-
meter was at a distance of Y^^Q- of an
inch ; the total variation in the length
of the rod (dilatation and contraction)
being then at least double, or equal
to -2^- of an inch. It would have
needed a weight of 3,740 pounds, hung to the end of the
rod, to lengthen it to this extent. This proves that
during its longitudinal vibrations, a steel wire is subject
to a traction which might become strong enough to break
it Thus, when a weight is not sufficient to break a metal
Fig. 66.
Fig. 67.
136 ACOUSTICS.
wire, or even lo get a permanent elongation, either of
these results may be obtained by making the wire vibrate
Fig
throughout its length while the weight hangs from it. For
this reason it is always necessary to avoid a regular oscil-
lation of the chains of a suspension bridge. In America,
and other countries where there are great suspension
SOUND IS A VIBRATION.
137
bridges, they forbid regiments of soldiers walking in time,
or even herds of cattle, to pass, fearing the effect of the
vibration on the chains.
To make a thin plate of metal, wood, or glass vibrate
transversely, the edge should be struck with a bow. The
simplest means of holding it during this operation is to take
Fig. 69.— ChladnPs Figures.
it between the thumb and the fore-finger, if it be small
enough, or to let it rest on three fingers. The best way,
however, is to fix it with four screws covered with cork,
at four points, through which the nodes will pass. The
bow is then drawn vertically across the edge of the plate.
If the plate be previously, or during the vibrations,
sprinkled with fine dry sand, the grains of sand will be seen first
to dance tumultuously, and at last to range themselves in
regular and symmetrical figures. The nodal lines on the
138
ACOUSTICS.
plate mark the places where there is no vibration. Each
line separates two vibrating segments, where the vibrations
are opposite, the surface falling in one while it rises in
the other. Figs. 68 and 69 represent some of the nodal
lines which may be seen on plates of different forms —
square, triangular, circular, &c.
Fig. 70.- ChladnL
These beautiful phenomena were discovered and pub-
lished by Ernest Florens Frederic Chladni, Doctor of Phi-
losophy, in 1767. He passed the greater part of his life
in illustrating acoustics in the different towns of Germany,
France, and Italy, wherever his erratic humour led him.
To him we are also indebted for the first catalogue of ae'ro-
ites, and the earliest affirmation of their ex-terrestrial for-
SOUND IS A VIBRATION. IJ9
mation. Chladni's figures long puzzled the philosophers,
who looked upon them as an unanswerable enigma. Savart
endeavoured to explain them, but as usual he only involved
the matter in deeper obscurity. The only useful discovery
which he contributed -,vas one made by his assistant, of using
a powder of heliotrope in place of sand, and laying a sheet
of damp paper over the figures, by which means they may
be printed and kept for reference.
Bells, discs, and glasses vibrate with nodal lines which
divide the surface like seams. If the bell or glass be turned
mouth upwards and filled with water, these vibrations will
express themselves in beautiful ripples upon the surface.
On pouring the water in, it will be thrown away from the
vibrating segments, and remain motionless in contact with
the nodes. The nodes may also be discovered by suspend-
ing a little ball by a string, and letting it gently touch the
vibrating surface; when the ball remains still we may know
that it is on a nodal line.
The same experiments may be shown on a drum, or a
sheet of paper or collodion stretched upon a frame. Owing
to its flexibility, a thin membrane will easily resound under
the impression of any sound whatever. The tympanum of
the ear affords a striking instance of this. Therefore we
may ascertain the position of the nodes and vibrating
segments in a vibrating column of air by the ear, or by a
little drum covered with sand.
We have already said that the vibrations of the air are
longitudinal. In the vibrating segments there is agitation;
in the nodes, complete repose ; with alternate compression
and dilatation. The motion of the air in the segments may
be communicated to a membrane, if it be struck perpendi-
cularly; the compressions and dilatations that take place in
MO ACOUSTICS.
the nodes will cause it to vibrate, if they act on one side
only. The ear is especially sensitive to the changes of
density in the nodes.
The flames of Koenig (noticed more fully hereafter)
allow us to make use of this property belonging to mem-
branes, to exhibit the changes in the density of the air.
These flames are supplied by a stream of gas, vibrating under
the pressure of a membrane inserted in the pipe. Observed
in a revolving mirror they have the appearance of a row
of tongues, separated by black spaces (Fig. 71), which
depend upon the nature of the sonorous vibrations. An
admirable means of studying the vibrations of sonorous
bodies is afforded by the " phonography " first conceived by
William Weber. Imagine a pendulum ending in a point,
swinging exactly over a sheet of paper blackened with
smoke. Evidently, the point will clear a white line for
itself through the black powder, in which it will pass from
right to left, and from left to right. But if the paper be
drawn slowly back, it will touch a different point each
moment, and, instead of a straight line, there will appear
an undulating curve.
The same result may be obtained by using a vibrating
SOUND IS A VIBRATION.
141
rod in place of the pendulum, which shall mark its way
upon a piece of smoked glass. If the tube have a fine and
flexible point it will trace every vibration by a zigzag on
the glass. It is still better to use a rotating cylinder for
this purpose, with a sheet of blackened paper fastened to
it. When the tracing is
finished, the paper is taken
off and steeped in alcohol,
which fixes the pattern.
In Fig. 72 we are able to
see how the tuning-fork may
be made to write. Fixed
to one of its prongs is a
bit of pointed copper wire
or a pen-nib. Observing
the direction in which it
vibrates, this is brought up
to the cylinder in such a
way that its oscillations are
parallel to the axis. Be-
fore any vibration takes
place the point will trace
upon the revolving cylinder a fine straight line, but as
soon as the vibration begins the line grows tremulous,
and each sinuous curve corresponds to an oscillation of the
sonorous body. The same experiment may be also tried
with a plate or membrane on to which is fix^d a perpen-
dicular point of some kind — a horse-hair or hog's bristle, or
a bit of tinsel. Fig. 73 represents different curves obtained
in one or other of these ways.
Leon Scott had a very ingenious idea for visibly tracing
the vibrations of the voice, or any other sound transmitted
Fig. 72.
142
ACOUSTICS.
by the air, with a membrane arranged after this manner.
This is the principle of the instrument that Koenig called
the phonautograph : A membrane furnished with a flexible
point is stretched over the end of a kind of ear-trumpet ; it
rig 73-
resounds loudly when a note is sounded at the other end of
the apparatus by the voice or an organ-pipe, and the point
will write its vibrations on a turning roller. Koenig wrote a
musical air of seven notes by this means ; but it is hardly
likely that anything more complicated could be written, for
the tracings are, in general, not very intelligible.
CHAPTER IX.
PITCH OF SOUNDS.
Measure of Notes — Chladni— Mersenne — Pythagoras — Sonometer —
Savart's Rattle — Sirens — Limits of Sound — Extent of the Kcale
of Musical Sounds — Limits of the Human Voice.
WE have seen that the origin of sound must be sought in
the vibrations of elastic bodies. These vibrations are essen-
tially isochronous — that is to say, the same phase con-
tinually returns at the end of the same interval, and
each oscillation lasts exactly the same time as the preceding.
It will be easy now to define the pitch of sounds, or that
which distinguishes a low tone from a sharp one, as the
duration of their vibrations, or the number of vibrations ac-
complished during a certain time.
Sounds of the same pitch, whatever they proceed from,
correspond in the number of their vibrations. Two notes
produced with different instruments are always in unison, if
they have the same number of vibrations. When a note
is higher than another it is because of its more rapid vibra-
tions. Therefore, to appreciate the exact pitch of a note,
the number of variations it executes in a second must be
counted. One of the simplest means of ascertaining this is
as follows : — The sonorous body is furnished with a point
wherewith to write upon and a rotating cylinder covered with
blackened paper, and is then sounded. By the side is placed
a registering chronometer, which marks each second on the
same cylinder. The number of zigzags, counted between
A\VVvV^/<//Vl
144 ACOUSTICS
the two marks, gives the pitch of the note. If the tone of a
tuning-fork were known exactly beforehand, it would answer
instead of the chronometer ; as writing side by side with the
sonorous body, whose vibrations are to be counted, each
bend of its course represents a known fraction of time.
Suppose, for example, that the tuning-fork makes 100 vibra-
tions in a second, and that side by side with 50 of its oscil-
lations 220 are found in the
parallel tracing: from this we
condude that the tracin§ win
give 440 vibrations in the time
.
which the tuning-fork takes to
* *' accomplish 100 — that is to say,
Fis 74- in a second (Fig. 74).
Chladni discovered a clever
plan for ascertaining the number of vibrations, by starting
from oscillations slow enough to be discernible, but too
slow to act upon the ear. He took a metallic bar, long
and thin enough to give only four oscillations a second
— easy to count, watch in hand. According to the theory,
a bar of half the length must give sixteen vibrations ;
a bar one-fourth the length, sixty-four, and so on. Con-
tinually shortening the bar, in the given proportion, we
enter at last the region of sonorous vibrations. But all
this only holds good in theory ; in practice it is full of error.
Mersenne measured the pitch of notes by the length of
the string required to produce them. He had noticed that
when two strings of different lengths, but otherwise identical,
were made to vibrate, the number of the vibrations was
always in the inverse ratio to their length. Thus a chord of
fifteen feet, stretched by a weight of seven pounds, gave ten
vibrations a second ; these were too slow to be heard, but
PITCH OF SOUNDS.
'45
by shortening the chord to one-twentieth of its length Mer-
senne obtained a sound twenty times sharper, or 200 vibra-
tions a second, which he took as the starting-point for his
measurements.
The sonometer or monochord (Fig. 75) acts on this prin-
ciple. Its use is to ascertain the pitch of a note. On a
wooden box are fixed two bridges a, b, over which a string
75-
or wire is passed. One end is firmly attached to a pin;
the other, being carried over the pulley /, is stretched by
a weight. Between the two bridges is a divided scale,
along which passes a movable bridge g, which is used to
reduce the length of the string, if so required, till it is in
unison with the given note ; then the scale will show to a
fraction the length of the chord, and a very simple calculation
gives the corresponding note, provided only the note of the
entire string is first known. This is settled by comparison with
a tuning-fork, and we shall presently see how that is fixed.
146 ACOUSTICS.
By the sonometer it has been demonstrated that the
half of the string gives the upper octave of the note ren-
dered by the whole length of the string ; that if its length is
reduced to two-thirds the sound mounts to the fifth ; that
taking three-fourths we obtain the fourth, &c. When the
entire length gives doh, the three-fourths will give fa, the
two-thirds sol, the half the octave doh, and so forth. These
relations existing between the length of the strings and the
notes of the scale were not unknown to the Pythagoreans ;
and we may interpret them by saying that the octave, the
fifth, and the fourth are intervals characterised by the rela-
tions of -f-, |, -f of the number of vibrations. Hence a
note is the upper octave of another when it makes twice
as many vibrations in the same time; also two notes
have the interval of a fifth when three vibrations of the
one correspond to two of the other; and they form a
fourth when one makes four vibrations while the other
makes three.
The sonometer also gives us a true- idea of the value of
the anecdote told by so many authors. One day, it is said,
Pythagoras passed a forge where four blacksmiths were at
work, and to his surprise he heard that the four hammers
beating in measured time on the anvil gave the intervals of
the fourth, the fifth, and the octave. He had them weighed,
and found that their relative weights were as the numbers
I? 4^ ^ 2. On his return home the great philosopher resolved
to test this result by another experiment. He took a chord,
and strained it successively by four weights equal to these
of the hammers. The four notes produced under these
circumstances gave the intervls of the fourth, the fifth,
and the octave. Unfortunately, however, the notes of
a chord do not vary in true proportion to the weight at-
PITCH OP SOUNDS. 147
tached ; to obtain the octave, for instance, we must not
only double but quadruple the amount of tension. With
the four weights of the hammers Pythagoras would never
have been able to get these intervals from his string. Again,
it would be very difficult to find hammers giving notes pro-
portioned to their weight; the circumstance is merely a
coincidence. Finally, it must be allowed that in a forge
we do not hear the blow of the hammer on the bar so much
as that of the bar on the anvil.
Modern scientific men have applied another principle to
the measurement of the number of vibrations. It consists
in producing sounds by a succession of periodical impulses
given by a wheel, whose turns are registered by a mechani-
cal contrivance. This idea was first put in practice by
Stancari. He took a wheel three feet in diameter, and
fixed on its outer circle 200 iron points. Thus prepared,
the wheel was set on a horizontal axle, and turned with
great rapidity. The points whistled through the air, and
the pitch of the sound thus obtained was in proportion to
the rapidity of its rotation.
About the year 1830, Savart found another method of
illustrating this by a kind of huge rattle. The sounds
were produced, by causing the teeth of a rotating wheel to
strike in quick succession against a flexible metal plate.
The wheel was set in motion by a leather band passing over
a large fly-wheel, which was turned by a handle. A register-
ing apparatus fixed to the axle marked the number of turns
made in a given time. Multiplying this by the number of
teeth, we have the number of the vibrations executed by the
edge of the plate, and consequently the pitch of the note
sounded. The difficulty of turning the wheel with uniform
velocity, and the bad quality of the sounds emitted by
K2
I48
ACOUSTICS.
this cumbrous apparatus, have long ago brought it into
disfavour.
Savart thought to supersede the siren of Cagniard de
Latour by his great rattle. The plan of the siren is as fol-
lows : — A disc, perforated with holes
placed in concentric circles, is rotated
in such a way that a current of air
is directed against a point of the per-
forated circle j the air passes whenever
it meets a hole, and is interrupted
when it strikes upon the plate. If
the disc turns ten times in a second,
and the holes are twelve in number,
the jet of air will pass 120 times in a
second, and this will also 'be the num-
ber of vibrations of the sound produced.
This arrangement, first invented by
Seebeck, is valuable in many re-
searches. By it, for instance, it is
proved that sound can only be engen-
dered by puffs or impulses, succeeding
one another at regular intervals, for
the holes must be equi-distant on the
disc if we want to obtain a sound cor-
responding to their number. Holes
irregularly distributed only give a
noise of high and low sounds.
The disc may be turned by a fly-wheel, or by a kind of
clockwork, which also registers the number of turns. The
improved siren of Cagniard de Latour (Fig. 76) was
worked by the very current of air which caused the sound.
The wind coming from a bellows (Fig. 77) enters through
Fig. 76. -Siren
of Cagniard de Latour.
PITCH OF SOUNDS. 149
0, into a brass cylinder, closed at the top by a perforated disc.
On this disc rests another, perforated in the same manner,
which turns on an axis c\ when the holes coincide the
air passes, but it is periodically intercepted. The per-
forations are made obliquely through the two discs, in
such a way that when the holes meet they are at right
angles one with the other. Thus the current urged from
below suddenly changes its direction in passing from the
lower to the upper hole, and gives an impulse to the
movable disc sufficient to turn it. The velocity of the rota-
tion increases continually, and the note rises in pitch, so
that if the pressure of the bellows were kept up the shrillness
would become almost unbearable. It is true that the speed
and the pitch may be adjusted by arranging the pressure, but
it is very rarely that a perfectly regular note is obtained
from the siren. When the note in unison with the one to
be measured is reached, the pressure is maintained constant,
while the index is consulted for the number of turns. This
reckoner, shown uncovered in the figure, is set in motion
by an endless screw, fixed upon the axis of the moving disc
c\ this works into two toothed wheels, which, by indices
on the dials, mark respectively the hundreds, tens, and
units. If, at the end of five minutes, the first dial points to
66, and the other to 30, the number of turns accomplished
would be 6,630 ; supposing, then, the disc has twenty holes,
that would give 132,600 puffs of the sonorous current in
five minutes, or 300 seconds, or 442 a second ; from which
we conclude that the note obtained corresponds to 442
double vibrations
The siren can sing under water, and therefore gained
its name. Plunged in any liquid, it can be made to sing by
forcing a powerful jet of the same through the aperture.
ACOUSTICS.
Thus water, oil, and mercury will sing. The sounds are
distinguished by a peculiar quality, but the notes are the
same as in the air.
Fig- 77.— The Bellows.
We must plainly confess that the tone of the siren is
not so pleasant to the ear as its name would lead one to
suppose; these shrill and piercing sounds would scarcely
PITCH OF SOUNDS. 151
set us dreaming of the Siren's songs which Homer says
allured travellers by their wondrous spell, and if we stop
our ears, it is certainly not for fear of being bewitched.
To produce the current of air requisite for working these
instruments, an apparatuses used (Fig. 77) composed of a
double pair of bellows, acted upon by a pedal /, a rod ty
and an air compartment c, perforated with a certain num-
ber of holes. By these holes the siren, or the tubes which
are to be sounded, receive the wind. They can be opened
and shut at pleasure by pressing different buttons.
A natural question arises here as to the limit of audible
sound. What are the very lowest and the highest notes
appreciable by the ear ?
In 1700, Sauveur pronounced the lowest sound to be
that produced in a pipe of iorty feet, corresponding to
twenty-five vibrations per second.
The deepest bass-pipe yet constructed by organ-builders
is thirty-two feet in length. It should give the doh-2, cor-
responding to thirty-two simple vibrations. On the other
hand they make very short pipes, which should give 10,000
vibrations, or more. But is it proved that these sounds
actually exist?
The lowest notes of the octave of sixteen feet, the doh
of sixty-five, and the re of seventy-three vibrations, are heard
only as a kind of rumbling, in which the most practised ear
can scarcely distinguish the musical pitch ; and the pipes
that produce these notes can only be tuned by indirect
means. On the piano, where they constitute the lower
extremity of the key-board, their musical character is very
undecided ; and orchestral music but rarely descends
below the mi of the double-bass, which has eighty-two
152 ACOUSTICS.
vibrations. In these regions the ear already begins to
apprehend the vibrations of the air as separate shocks.
This sensation becomes more distinct as we advance to
the octave of thirty-two feet, and as we approach the doh
of thirty-two vibrations we no longer hear a sound, properly
speaking ; that which strikes the ear is only a series of
disconnected explosions. Many people, nevertheless, ima-
gine that they have heard the notes of this octave ; but this
is because the organ-pipes produce, simultaneously with their
fundamental note, other higher notes of which we shall speak
presently; a pipe of thirty-two feet causes the notes be-
longing to a higher octave to resound slightly, and this in
all probability deceives the listener.
The same illusion is doubtless present in the con-
clusions Savart has drawn from his experiments on the
limits of hearing. He arranged a bar of iron to turn round
a horizontal axis in such a manner, that at each half revo-
lution it should pass through a chink hollowed in a plank.
At the moment of its entrance the bar forced the air like
a piston, producing a sort of explosion, and if the wheel
turned fast enough a deep sound was heard, accompanied
by a loud rumbling. Seven or eight revolutions a second
still gave an audible sound, wherefore Savart concluded
that the deepest note distinguishable by the ear might be
fixed at seven or eight double, or fourteen to sixteen simple
vibrations. But Despretz has without difficulty shown
the error of this, for by arranging two chinks instead of one
for the iron bar to pass through, we do not get the octave
as we ought by doubling the number of the explosions.
It must then be admitted that the note of thirty-two vibra-
tions, corresponding to sixteen rotations, has already been
PITCH OF SOUNDS. 153
obtained by eight; and this is not surprising if we remember
that natural sounds are almost always accompanied by
higher notes, called harmonics, as we shall presently see.
At the most, Savart's instrument gives a note of about thirty
semi or simple vibrations a second.
Helmholtz had recourse to another plan. He used a
wooden case closed at both ends, and having a small
opening into which was fitted a gutta-percha tube, in-
tended to be introduced into the auditive canal. On this
sounding-board he stretched a wire, weighted in the middle
by a brass coin with a hole in it ; owing to this precaution
the string could not give the upper octaves of its fundamental
note, which was very deep.
Under these circumstances, the sound of a string which
gives a medium note becomes insupportable through its
strength ; but that employed in these experiments, giving
the re of seventy-three vibrations, produced only a faint and
slightly growling noise. Coming down to si of sixty-one
vibrations, Helmholtz scarcely heard anything. From these
experiments he concluded that audible sounds began at
about sixty semi-vibrations, and took a musical character
at about eighty, in the octave already mentioned of sixteen
feet. But the limits of hearing may perhaps vary in different
persons, and depend in some degree on experience and on
the intensity of sounds.
The higher limit of hearing is certainly not the same for
every one. Many people cannot distinguish certain high
notes that others hear perfectly. Savart tells us that a
sound of 31,000 semi-vibrations, produced by the longi-
tudinal vibrations of a glass cylinder, was heard by the
greater part of his audience, whilst the 33,000 vibrations
154 ACOUSTICS.
of a cylinder a little smaller were scarcely heard at alL
With large toothed wheels he produced a very intense
sound, which was not lost till the moment when it appeared
to perform 48,000 vibrations per second; but it is difficult
to prove in this case that the flexible plate touched all the
teeth of the wheel.
Despretz thought to extend this limit by means of tuning-
forks which should give 73,000 semi -vibrations. There are
some miniature tuning-forks still preserved at the Sorbonne,
and shown on special occasions. But how are the notes
determined ? M. Marloye first adjusted tuning-forks to the
ear. He began by making a scale which passed from
16,000 to 32,000 vibrations, guiding himself by ear; then
in the same manner he tuned a fork to an octave higher
than the last, giving consequently 64,000 vibrations, and cor-
responding to doh10; then he went to re10 of 73,000 vibra-
tions. These tuning-forks can only be heard by very
sensitive ears ; the very shrill notes produce a painful
impression, an indefinable uneasiness which lingers for
some time ; it is very difficult to perceive their musical
relations. Till further light dawns on the subject, we do
not deem these conclusions very important.
Recently Kcenig resumed these experiments. The highest
notes that he could distinguish corresponded to 40,000
vibrations ; but, as we have already said, the limit varies
with different persons. Very high notes cease to be appre-
ciable by many ears. Has not Wollaston told us that many
people are quite incapable of hearing the sharp chirp of
grasshoppers, or even the twittering of sparrows ? Perhaps
there are animals who can distinguish notes beyond the
reach of human ears.
PITCH OF SOUNDS. 155
To resume : appreciable sounds are limited to a range
of from about 60 to 40,000 semi-vibrations per second,
which range may be sometimes passed for ears of excep-
tional power and delicacy. The undulations of the ether
produced by light and heat are infinitely more rapid.
Heat begins at 65,000,000 vibrations, visible colours
range from 400 to 900 trillions, 1lhd chemical rays attain as
much as a quadrillion. Heat is not produced simply by
the vibrations of the fluid ether ; it is certain that ponderous
bodies themselves vibrate when they are heated ; therefore
we must admit that molecules can accomplish vibrations of
wondrous rapidity. But what becomes of those vibrations
which are too rapid to be audible, and too slow to be felt as
heat? Have we senses that can appreciate them, organs
that can be affected by them ? May we seek in these un-
classified vibrations the explanation of galvanism and elec-
tricity, which everything leads us to suppose a form of
motion ? Who can tell ?
It will not be uninteresting to mention here the compass
of the notes given by the commonest musical instruments.
First stands the organ, the grandest and richest of all,
which occupies the whole field of audible vibrations — nearly
ten octaves. The piano has almost seven octaves, com-
prising all the notes from la-a to doh7, or from 54 to 8,400
vibrations.
The sounds of the violin properly extend from 400 to
6,000, along four octaves, but much higher sounds can be
drawn from this instrument. The violoncello, or violone, is
confined to a scale of between 80 and 350 vibrations ; but
the octo-basso of M. Villaume embraced vibrations as low
as 64. The cornet, trombone, and other brass instruments
156 ACOUSTICS.
give very varied sounds. The highest note used in the
orchestra is probably the re7, which corresponds to 9,400
vibrations.
We may take as the extreme limits of the human voice
the fa-, of 87, and the doh6 of 4,200 vibrations —
I
CHAPTER X.
THE NOTES.
Relation of the Notes— Scale— Names of the Notes — Hymn of St.
John— Musical Notation— Major and Minor Keys— The Waves of
the Tempered Scale — Galin and Cheve — Choir and Concert Pitch
— Natural Tuning-fork— M. Lissajous' Method.
Music is not so much concerned with the absolute pitch
of notes, as with their relation one to another, or the inter-
vals between them. The pleasure we derive from the com-
bination of certain sounds depends on this relation. When
two notes are in the mutual relation of two simple whole
numbers, they form a concord or harmony ; discords are
produced by complex relations. In this sense we may say
that music is a matter of numbers.
Pythagoras was aware that a string divided into two
unequal sections would give two perfectly harmonious
sounds, when the lengths of the two sections hold a simple
relation to one another, expressible by whole numbers.
The relation i : 2 corresponds to the octave ; the relation
2 : 3 to the fifth ; 3 : 4 to the fourth, and so on. Most pro-
bably the Greek philosopher had learnt this law from the
Egyptian priests, which is equivalent to saying that it was
known in the earliest times.
Harmonious intervals, therefore, are based on the re-
lations of the pitch of the notes. Take, for example,
the fifth doh, sol. The ear tells us that this harmony
may be found between very high as well as between very
15 ACOUSTICS.
low notes, not at all depending on the absolute number
of vibrations. Measurements show that any two notes
having this interval hold always the mutual proportion of
3 : 2, and consequently this interval is always caught by
the ear when two notes are as 3 : 2. From this it is easy
to see that the more nearly this relation is consummated,
the purer and sweeter will be the harmony ; and therefore
this interval is called a true fifth. We shall presently see
that it is seldom realised in all its purity.
The simple intervals adopted by musicians are charac-
terised by the following relations :—
Octave
Fifth
Fourth
Major third • • . .
Minor third • • • .
Major sixth • • • •
Minor sixth • . . .
A note is said to be the upper octave of another when it
makes twice as many vibrations in a given time, and vice
versa. The successive octaves of a note are distinguished
by figures placed below or in a bracket, thus : doh2 means
the upper octave of doh (we never write doh,) ; doh3 is the
upper octave of doh2, or the double of doh, £c. Descend-
ing to the lower octaves we write them thus : doh-, is the
lower octave of doh, doh-2 the double octave, and so on.
It is easy to see that two, three, or four notes which
harmonise when taken two and two, will still accord when
united altogether. The two chords of three notes most plea-
sant to the ear are the perfect major chord, characterised by
the numbers 4, 5, 6, and the perfect minor chord, represented
by the fractions \, \, {-. They both contain a fifth, a major
third, and a minor third, the only difference being that in
THE NOTES.
159
the major chord the major third is the lower, while in
the minor it is the upper interval. To realise the different
harmonies a musical scale has been adopted, composed
of seven degrees (the octave of the first note making an
eighth), which may be expressed by the following syllables : —
Doh, re, mi, fa, sol, la, si, doh ;
the relation amongst them being as the numbers —
24, 27, 30, 32, 36, 40, 45, 48.
The first scale is followed by another, and so on, each being
formed by raising all the notes of the preceding scale one
octave. We have already described how the successive
octaves are written. The relations which the different notes
of the scale bear to the first, constitute their musical in-
tervals, and are expressed by the following numbers : —
Doh— doh
Doh— re .
Doh — mi.
Doh— fa .
Doh— sol.
Doh— la .
Doh — si .
Doh— doha
Doll— re2 .
Doh — mia
Doh— faa .
Doh — so!2
*
Doh— doh,
unison
i : I
second
8
9
third .
4
5
fourth
3
4
fifth .
2
3
sixth .
3
5
seventh
8
15
octave
2
ninth .
4
9
tenth .
2
5
eleventh
3
8
twelfth
i
3
* *
*
• double octave . I
4
Doh — mi,
&c.
seventeenth
&c.
: 5
&c.
The names of the intervals simply recall the position of
the notes in the scale. The twelfth, the double octave,
and the seventeenth make perfect harmonies, which fact
I Go ACOUSTICS.
presupposes the simplicity of the relations which characterise
them ; it is needless to particularise them further, since they
are but the counterparts of the fifth, the octave, and the third.
Associating the notes of the scale by twos, we do not
always obtain a harmony. A suitable choice must be made.
But even discords are important in music. The interval
from cloh to re, called a major tone ; the interval from re to
mi, called a minor tone ; the intervals mi — fa and si — doh,,,
known as diatonic semitones, are very characteristic discords.
The scale just explained does not suppose any know-
ledge of the absolute pitch of the notes ; it merely depends
upon the relationship they bear one to another. The first
note may be anything ; but its value once determined, that
of all the other notes is fixed also. This may be noticed
in the exercises of solfeggio, which consists in singing the
notes of the scale on the syllables doh, re, mi, fa, sol, la, si.
The sound represented by doh may be chosen arbitrarily ;
but by this choice the pitch of all the notes is decided. If,
for example, the doh has 240 vibrations, the re must have
270, the mi 300. the fa 320, and so on.
The names of the first six notes were introduced in 1026,
by Guido TAretino, or Guy of Arezzo ; they are the beginnings
of words taken from the hymn of John the Baptist: —
" Ut* queant laxis ?rsonare fibris
Jlftra gestorumyfzmuli tuorum,
•Sb/ve polluti /abii reatum,
Sancte loannes."
The air to which this hymn is now sung at St. Jean is not
exactly the same as the ancient air, in which the six syllables
chosen by L'Aretino really fall upon the notes they name.
That air, found in a MS. in the library of the Chapter of
Sens, has been copied in old style, as follows : —
* Ut is the first syllable in French, but is replaced by doh in English.
THE NOTES. l6l
HYMN OF ST. JOHN
Ancient Melody.
Rat que-ant la - xis re-son -a- re fi-bris Mi - ra ges-to-rum fa- mu-H tu
- o-rum Sol - ve pol-ln-ti la - bi - i re - a-tum. Sane - te lo-an-ness.
The seventh syllable, si, was not added till 1684, by
Lemaire. In Italy they soon substituted doh in place of ut,
as being a more vocal syllable. The names proposed by Guy
did not come quickly into general use, for in the time of
Jean de Muris, in the fourteenth century, they still used the
syllables pro, to, no, do, tu, a, in Paris; but at last they
were accepted pretty generally, excepting in England and
Germany, where they kept for the notes the names of the
letters C, D, E, F, G, A, B, or H.
Here is the history of the letter designation. Since the
time of Gregory the Great, perhaps even before the sixteenth
century, a series of scales of fixed notes corresponding to
the limits of the voice and to the sounds of the principal
instruments had been used. They were called after the first
seven letters of the alphabet, in this way : —
A, B, C, D, E, F, G, a, b, c, d, e, f, g, aa, bb, cc, &c.
At a latex date, a note having been added below, it was
designated by the Gamma, or Greek G, whence comes the
common name of the scale, Gamut.
Guido 1'Aretino substituted for these letters points set
upon parallel lines (les portees\ to each of which a letter
served as key. The key fixed the value of the line ; thus,
when F was written upon the beginning of a line, all points
L
l62 ACOUSTICS.
placed upon this line represented the note F. Afterwards
they enlarged these points, and determined to place them
in the intermediate spaces, and multiplied both lines and
spaces, as it was found necessary.
The signs of the notes only served at first to mark the
difference of intonation, without respect to the duration.
Jean de Muris, or Mceurs, invented square figures to dis-
tinguish the relative value or duration of the notes. This
was about the year 1338, and in 1502 the invention was
perfected by Octavio Petrucci, who discovered a way of
printing music with movable type. The longest note accord-
ing to the old notation was called a Long, ^ ; the next in
duration was a Breve, r or M. Of these, the latter is occa-
sionally found in church music, the former but seldom. The
moderns have gradually confined themselves almost entirely
to the following, which, since the fifteenth century, have
been indicated by the accompanying signs : —
o j j ; ; ;
Semibreve. Minim. Crotchet. Quaver. Semiquaver. Demisemiquaver.
We also find Occasionally P Hemidemisemiquaver.
A long is equal in duration to two breves, a breve to two
semibreves, a semibreve to two minims, a minim to two
crotchets, and so on. These notes may be replaced by
equivalent rests : —
EEE ~r~ r * ^ ^
Long Breve Semibreve Minim Crotchet Quaver Semiquaver Demisemiquaver
Rest. Rest Re^t. Rest. Rest. Rest Rest. Rest
To fix the absolute duration of a note, a metronome is
employed. 3-
The letter G has become the key of sol, gj; the letter F,
the key of fa, §i; the letter C, the key of doh, JL &c.
THE NOTES. 163
The syllables doh, re, mi, fa, sol, la did not originally
designate any fixed notes, but only the degrees of a scale ;
they represent the hexachord of Guido I'Aretino. They
used to be written underneath the letters which marked the
fixed scales, beginning with C, F, or G.
CDEFGABcdef...
doh re mi fa sol la
.. .. .. doh re mi fa sol la .. ..
doh re mi fa sol la ..
doh re mi fa
The same fixed note might then occupy different places in
the movable scale, and this was sometimes found to be
incompatible with the preservation of the intervals adopted
for the notes doh, re, mi, fa, sol, la. This led to different
plans for harmonising, and there was a great confusion in
the musical system. The necessity was soon felt of altering
some of the fixed notes, when the movable scale was so
transposed, that the intervals of the fixed corresponding
notes did not realise the intervals first intended by the
notes doh, re, mi, fa, sol, la. Thus, when doh was written
below F, and fa below B, the interval from F to B should
have been a fourth; but as it was in reality greater, it was
lessened by lowering B a semitone. This note then became
B flat, while it remained B natural in the scale beginning
with C. This double part it had to play was indicated by
writing the B in different ways, and it is also the origin of
the signs f ) flat, and (1) natural.*
It was only after a thousand changes and attempts that
the modern musical system took form. The principal rule
which directs it is this : Whatever note be fixed upon for
* This is more clearly shown by the French words bemol and becarre.
L -A
1 64 ACOUSTICS.
beginning the scale, the other notes must all follow in the
intervals already decided on. To provide for this necessity
the sounds are altered, either by raising them a semitone,
which is called sharpening, and this is expressed in the
notation by the sign ft; or by lowering them a semitone,
which is called flattening, and is expressed by the sign °.
For the value of this semitone the ratio ff is used, which
is less than ^-f , the value of the interval from mi to fa.*
The words doh, re, mi, fa, sol, la, si are now used for
the principal fixed notes of the piano and other instruments,
and following the sign " or It they become changed notes,
in such instruments as the organ and pianoforte. In vocal
music and fidicinal instruments, the ratios of the diatonic
scale are preserved in every key. The scales always bear
the name of their first note or tone. All the major scales
are modelled on the scale of doh, formed by the set of
natural notes —
Doh, re, mi, fa, sol, la, si, doh.
The intervals are reproduced with tolerable exactitude,
owing to the alterations applied to certain notes. The
scale of sol is composed of the notes-
Sol, la, si, doh, re, mi, fajf, scl;
the scale of fa, of the notes —
Fa, sol, la, si!?, doh, re, mi, fa ;
and so forth. These scales belong to the major key.
There have been many other scales used in music which,
from having the third minor, have given rise to minor
scales, as, e.g. —
La, si, doh, re, mi, fa, sol, la.
The chief difference between the two scales lies in the
• The semitone is nearer fa than mi.
THE NOTES. 165
introduction of the minor third, la — doh (5 : 6), in place of
the major third, doh — mi (4:5) ; they are each characterised
by a perfect harmony formed with the third and the fifth
of the tonic.
Perfect major chord . . • doh, mi, sol.
Perfect minor chord » . • la, doh, mi, or
doh, mi!?, soL
The minor scale is still further varied by raising the seventh,
and sometimes also the sixth note of the scale a semi-
tone, for certain harmonic reasons.
It would singularly complicate the construction of all
instruments with fixed sounds, if it were attempted to make
them realise the scales in their theoretical purity. It was
necessary to make a compromise, and this was done in the
tempered or adjusted scale. The ear will tolerate a slight
deviation from perfect harmony, and this allows a simplifi-
cation of the scale in instruments with fixed notes, by
employing only one sound for two notes nearly alike, from
the inverse alteration of two neighbouring notes. Thus doh&
and re& have but one pipe or string for both, &c. &c. In this
way it is managed on a keyed instrument to interpolate five
black keys with the seven white of each octave, thus
forming the chromatic scale, which is composed of twelve
equal semitones, adapting themselves to all the exigencies
of the musical system. It follows that we are thereby led
to alter more or less sensibly the natural notes represented
by the white keys, and so to modify all musical intervals.
The adjusted semitones may be approximately rendered
by the relation ~\\ and an adjusted whole tone scarcely
differs from a major tone £. The fifth and the fourth are
only falsified to an inappreciable extent by the adjustment,
but the thirds are so much so that they are painful to an
1 66 ACOUSTICS.
ear educated to pure harmony, which is wonderfully more
exquisite. Some authors of the last century gave the name
of "wolves" to these lost intervals, where the discords
seemed to meet and growl.
A natural voice, guided only by instinct, always gives
true intervals; and violinists whose ears have not been
spoilt by the orchestra will play true thirds and sixths much
more delightful than the adjusted intervals. Unfortunately
the free-toned instruments, which play in the orchestra with
tempered or adjusted instruments, are forced to follow their
lead and acknowledge the false intervals; and thus those
violinists who have all their lives been forced to play
falsely in the orchestra, become accustomed to the change
of tone. Under the overwhelming influence of the or-
chestra the accuracy of the voice also suffers. Singers end
by adapting themselves to the adjusted notes, and lose the
power of singing a simple air with that true intonation which
constitutes its charm. Still, if a singer have true ear and
taste, Nature reasserts her rights as soon as she is relieved
from the requirements of the accompaniment.
The inconveniences arising from the equal adjustment
have given rise to numberless attempts to return to natural
harmony, even in instrumental music. Erard's harp with
a double movement ; Poole's enharmonic organ, and that
of Gen. Perronet Thompson ; the harmonium devised by
Helmholtz — all give the different scales without the aid of
adjusting or tempering. The vocal systems adopted in
France by Galin and Cheve', and in England by the
numerous Tonic Sol-fa Associations, hold to the natural
scales in their purity. The English societies employ the
syllables doh, re, mi, fa, sol, la, ti, doh, and reduce them in
writing to the letters d, r, m, f, s, 1, t, d. Galin and Chev^
THE NOTES. 167
employed the figures i, 2, 3, 4, 5, 6, 7, for this purpose, the
successive octaves being indicated by points placed over or
under the figures. It is only needful to give the absolute
pitch of the first note, or tonic, for all the other notes to be
determined. This plan is believed to give greater facilities
for reading music than the old notation, and has had many
advocates. Rousseau recommended it most highly.
" Music," says J. J. Rousseau, " has shared the fate of
all arts which are only brought to perfection slowly. The
inventors of notes thought merely of the state of the art in
their own day, not looking on to the future ; and, therefore,
the nearer the art draws to perfection, the more defective
are their signs found to be. As it advances, new rules are
established to obviate present inconveniences; in multiplying
the signs, the difficulties also are multiplied; and what with
additions and alterations, they have formed out of a simple
principle a most cumbrous and ill-arranged system. Mu-
sicians, it is true, do not admit this. Custom is everything.
Music is not for them the science of sounds; it is but a
science of crotchets and quavers and minims. As soon as
these are lost to sight, they think that music is done with.
Besides, why should that be made easy for others which
they have acquired with such difficulty ? The musician is
not the one to be consulted on this subject, but a man who
understands music, and has reflected on the art."
When a piece is to be played by several performers,
it is necessary for the instruments to agree ; therefore, in
the orchestra they are tuned by means of a tuning-fork,
whose note remains constant. Formerly, the pitch used to
be given to an orchestra by a kind of whistle, furnished with
a graduated piston, whereby the pipe could be lengthened
or shortened at will, so as to draw different fixed sounds
1 68 ACOUSTICS.
from it. There was the choir-pitch for the plain song and
for secular music, the chapel-pitch, and the orchestra or
concert -pitch. The latter was never fixed: they raised or
lowered it, according to the compass of the voices. The
chapel-pitch, on the contrary, was fixed, at least in France,
and generally higher than concert-pitch. As for the choir-
pitch, which agreed with the organ, it is hard to say whether
it was higher or lower than the chapel-pitch, for authors
contradict one another on this point ; it would seem that
after all they only set the organ to chapel-pitch.
Since the science has been possessed of means for
measuring the absolute pitch of notes, musicians have been
able otherwise to determine the pitch of the different lead-
ing orchestras of Europe, and, very curiously, it has been
discovered that it is everywhere rising rapidly. Sauveur,
who appears to have first studied the question, found in
1700 that the lowest note in the harpsichord, la, made 202
vibrations ; and the low doh of the harpsichord, 244 vibra-
tions, which gave Ia3 810. Other determinations of the
last century vary from 820 to 850. In 1833, Henri Scheibler
examined the tuning-forks of the principal theatres, and
found that at the Opera they had two of 853 and 868 ; at
the Italian and Conservatoire, others of 870 and 88 1 vibra-
tions ; at Berlin he found a la of 883 ; at Vienna they varied
from 867 to 890. In 1857, M. 'Lissajous declared a new
progression in the orchestra-pitch. Here are the results of
his measurements : —
Opera of Paris 896
Opera of Berlin 897
Theatre of San Carlo, Naples . . . 890
Theatre clella Scala, Milan • • • 903
Italian Opera, London .... 904
Maximum in London . « . . . 910
THE NOTES. 169
This increasing elevation in the pitch of instruments is
proved by the ancient organs found in some basilicas.
What is the reason that musicians and authors have made
this change? It is supposed that most instruments show-
greatest brilliancy in their high notes, and therefore the
makers have by little and little heightened the pitch. Singers
generally follow the same inclination, to the detriment of
their voices. But we must not go too far in attributing the
ruin of so many fine voices to this solely ; it would be fairer
to seek the cause, as M. Berlioz does, in the tendency of
modern composers to write higher parts for vocal music than
the ancient composers. Whatever the height of the pitch
may be, it is easy for the composer to keep within reason-
able limits.
It is none the less true, however, that the progressive
variation must at last trouble the musicians, and it is very
important to return to a natural and absolutely settled
pitch. Sauveur insisted on the necessity of this so long
ago as 1700. He first proposed for this purpose the sound
which makes 200 vibrations per second. Finding subse-
quently that his calculation was erroneous, he modified his
views, and so proposed to take a doh of 512 vibrations for
his starting-point. This number is one of the series
i, 2, 4, 8, &c., whose terms may be regarded as the suc-
cessive octaves of unity. Chladni afterwards adopted the
same doh of 512 vibrations, corresponding to the natural
la, 853, and this was generally employed by scientific men.
However, as the pitch of the orchestras continued to rise,
the German philosophers meeting at Stuttgard in 1834
decided on choosing a normal la more in harmony with the
custom of musicians, and they fixed definitively on the la
of 880 vibrations ; this is the German la, most useful for
17° ACOUSTICS.
numerical calculations. Unhappily, this congress could not
reach the rest of the world, and the pitch still mounted in
a very disorderly manner. Then it was that the decree of
February 16, 1859, fixed an official diapason for France.
This pitch gives the normal la with 870 vibrations; it
scarcely differs from the German, yet it is much less useful
for calculations.
Here follow the numbers of the simple vibrations of the
adjusted scale based upon Ia3 (French style), and of the
natural scale beginning with the same doh. The octaves are
obtained by doubling, or by dividing by two.
Notes. Adjusted Scale. Natural Scale. Natutal Ratio
or Relation.
Doh ... 517.3 ... 517.3 ... 24
Re ... 580.7 ... 582.0 ... 27
Mi ... 651.8 ... 6^6.6 ... 30
Fa ... 690.5 ... 689.7 ... 32
Sol ... 775.1 ... 7760 ... 36
La ... 870.0 ... 862.2 ... 40
Si ... 976.5 ... 970.0 ... 45
^\ Doh ... 1034.6 ... 1034.6 ... 48
The middle octave of the piano is represented by ths
following notes : —
Henceforth, in France all musical instruments will be
tuned by a tuning-fork set to the official standard of the
Conservatoire. Concord is thus ensured, and there is no
more to fear from the tendency of orchestras to raise the
pitch.
The piano, violin, and other instruments are generally
THE NOTES. 17 1
timed by ear. One string is set to the note of the tuning,
fork, and the others are regulated by the musical intervals,
chiefly by octaves and fifths. According to Weber's experi-
ments, a very fine ear can appreciate a difference of a
thousandth part, or one vibration in a thousand, but that
is the limit. The study of beats, however (a phenomenon
which we shall soon notice), leads us much further. It is
by this means that organs are tuned. When extreme pre-
cision is required we have recourse to a later method
invented by M. Lissajous. the principle of which will
now be explained.
A prismatic rod can vibrate transversely, so that its free
end describes a right line. If a steel bead be fastened at
this end, the continuance of the luminous impressions will
appear as a line of brilliancy. The eye has the power
of preserving the most fugitive impressions for about the
fifteenth part of a second. If then the luminous point run
its course in less, time than ^ of a second, the whole track
will appear illuminated. Thus a burning stick or piece of
charcoal swung round in the air will make a fiery circle.
When the section of the rod is rectangular, it can be made
to vibrate either in its thickness or its breadth. In either
case the bead will draw a line of light, but in the former
the route will be perpendicular to that which it takes in the
latter. But we may agitate the rod in yet another way by
striking it obliquely. It is then moved simultaneously in
two directions crossing at right angles. Will it decide to
follow one impulse rather than the other? The rod takes
a middle course between the two roads, and follows first
one impulse and then the other, changing momentarily.
The little bead takes a tortuous road, and its luminous track
allows us to follow the rod in its rapid evolutions.
172
ACOUSTICS.
The number of straight vibrations depends on the
direction in which the rod vibrates. When the section of
the rod is square, its thickness and breadth being equal,
the number of vibrations will evidently be the same in
both directions. In this case the little bead will describe
an ellipse, which may either pass into a circle or flatten
to a straight line. Calculation proves this. The line may
be understood a priori by
supposing that the rod
moves diagonally from its
position of repose, always
making little equal steps
forwards and to the right,
forwards and to the right ;
then, in returning, back-
wards and to the left
backwards and to the left,
as shown in Fig. 78. To
explain the ellipses, it
would be necessary to
enter upon some rather abstruse propositions.
When the two dimensions of the rod are as 1:2, the
corresponding numbers of vibrations will evidently be in
the relation of the octave ; if the measurements are as 2:3,
the vibrations will be the fifth, &c. The bead and the
reflected ray then will describe the curves given later on
in Figs. 84 and 85. It may therefore be said that these
figures characterise the musical intervals.
Wheatstone's kaleidophone (Fig. 79) is on this principle.
This is an apparatus composed of several metal rods, to
the end of which are fixed light glass beads, silvered within.
When illuminated by the sun or the light of a lamp, the
Fig. 78.— Vibration of a Square Rod.
THE NOTES.
373
bright spots will describe curves as shown in the figures,
while the rods vibrate. Wheatstone made this known in
1827, and the kaleidophone is now found very frequently in
the studios of scientific men. Let us, then, examine some
other conclusions drawn from the same principle. Imagine
an upright mirror fixed at the end of a horizontal bar, which
can be made to vibrate alternately vertically and horizon-
tally (Fig. 80). On this mirror we throw a luminous ray,
by placing it before a lamp covered with a shade, from
7Q- — The .Kaleidophone.
which a single ray escapes by a small hole pierced for the
purpose. While the mirror remains motionless the reflected
ray will form upon the wall a simple point of light ; looking
straight into the glass for the image of the lamp, we see the
tiny light shining like a fixed star. Now, if the bar be
struck so as to oscillate, the reflected ray shares the move-
ment of the mirror, and the image on the wall is displaced.
As, at first, the bar only vibrates in a vertical plane, we see
upon the wall a luminous track, drawn straight down ; and
looking into the vibrating mirror, we see there also a perpen-
dicular line. If, on the contrary, a horizontal motion be
given to the bar. the reflected line will be horizontal too.
174 ACOUSTICS.
Finally, if the bar be made to vibrate obliquely, we shall see
both upon the wall and mirror the fanciful curves of the
kaleidophone. It will even be sufficient to hold before the
mirror a metal button, a pin's head, or any small bright
object. Its reflection will form a luminous curve as soon as
the bar is set in motion. The form of the curves will
always depend on the rate of the vibrations executed by the
bar in a straight line, if it oscillates first in «. vertical, and
then in a horizontal plane.
Fig. 80.
The same curve may be obtained by a double reflection
on two mirrors, each vibrating in a different plane (Fig. 81).
They are placed opposite one another, so that a ray of
light reflected by the first will fall upon the second, which
throws it back in its turn against the wall. If, then, one
only of the mirrors be made to vibrate, the brilliant point
upon the wall will change into a luminous line, drawn in the
direction of the vibrations, because the reflected ray shares
the motion of the reflecting surface. But if the first mirror
be made to vibrate horizontally, and the second vertically,
the reflected ray will receive from the first a horizontal
movement, to which is added a vertical movement by the
THE NOTES.
'75
second reflection ; the two movements combine, as in the
kaleidophone, to give birth to the different curves already
Fig. 81.
described. They may be seen either by looking directly into
the second mirror, or by receiving the image of the luminous
point upon a screen of any kind. Greater clearness and
Fig. 82.— The Optical Method of M. Lissajous.
brilliancy is given to this experiment by passing the luminous
rays through a lens. A simple inspection of the curves will
shew the n.tio of the respective numbers of the vibrations
!76
ACOUSTICS.
made by the two mirrors. A. straight line or an ellipse
indicates unison, the figure 8 the octave, and so on.
Instead of fixing the two mirrors to horizontal and
Phase
Fig. 83. — Unison i : i.
Pliatc
f i
Fig. 84.— Octave i: a.
vertical rods, they may be fastened against the branches of
two tuning-forks, placed at right angles, one horizontally
and the other vertically, as in Fig. 82. The first gives
to the reflected ray a horizontal movement, the second
imparts to it a vertical impulse, and thus are obtained curves
which reveal at once, by their aspect, the musical relation of
THE NOTES.
I7JT
the two forks. Herein consists the optical method for com-
paring sonorous vibrations, made known by M. Lissajous in
1855. It enables us to ascertain the musical interval of
Fig. 86.— Fourths 3:4.
two vibrating bodies, with a certainty unknown before this
beautiful discovery.
It may be asked why the same ratio should produce
different figures. This is due to the difference of phase. If
one of the two mirrors be slightly behind the other in first
beginning to vibrate, this delay (which is called difference of
178 ACOUSTICS.
phase, or simply phase) modifies the appearance of the
figure resulting from the combination of the two movements.
Thus, when two tuning-forks in perfect unison begin and
end their course together (when there is no phase), the
trajectory of the luminous image is a right line; in any
other case it is an ellipse or a circle. Under each figure
will be found written the difference of phase as a fraction
of the entire vibration.
When the vibrations of two tuning-forks are in the ratio
of two whole numbers, the optical figure drawn at the
beginning of their movement will continue unchanged
as to form, but will diminish slightly in size as the vibrations
die away. In this case, only one of the curves which
characterise the musical interval in question will be seen.
But if there be the slightest discordance between the two
tuning-forks, the figure does not remain steady, but changes
gradually, so as to pass through a complete cycle of the
different curves which correspond to the same interval.
This is because the delay (or phase) continually increases,
and the figure consequently changes in the same way. The
more decided the discord, the more rapid the changes. So
it happens that the ellipse which characterises unison will
pass into an oblique ellipse crossing the line, then narrowing
into the form of a straight line, it passes on to a reversed
obliquity. This variation of the figures betrays the slightest
discord immediately, and also helps to an appreciation of
its value.
By this means the tuning-forks are tested in the Con-
servatoire ; once corrected by the standard there, they
are stamped and fully recognised. But the fork to be tested
has no mirror attached j its own polished surface serves the
purpose.
THE NOTES. 179
M. Lissajous has added to his beautiful inventions
that of the "vibration microscope." The object-glass is
held by one branch of a tuning-fork placed at right angles
with the tube. When the fork vibrates the object-glass
oscillates before the tube, and the objects upon the field
of the microscope seem to oscillate in the same direction.
If, then, one of the objects itself vibrates in a different di-
rection, the real and the apparent vibrations blend, and the
curve thereby formed will show the number of vibrations of
the body under consideration.
M a
CHAPTER XI.
TIMBRE OR QUALITY OF SOUND,
Form of Waves— Simple and Complex Sounds — Harmonics— Timbre
of Voices and Musical Instruments — Musical Sounds — Vowels.
WE have seen that the pitch of a note depends on the
rapidity with which the vibrations succeed one another.
Is that the only difference which can exist between sounds ?
Evidently not ; for we never confuse sounds having a
different origin, even when they are in unison ; they are
distinguished by what has been called timbre. The sounds
of the cornet, for instance, do not resemble those of the
harp, nor does the violin sound like the organ. The same
note, even, has a different character according as it is
sung on a or o\ whence it follows that the vowels only
represent the changing timbre of the human voice. We
may even classify the differences in the timbre of musical
instruments by determining which vowels they seem most
to resemble.
What, then, causes the timbre? How can the same
note produce such different impressions ? These questions
have long occupied philosophers, and it is but latterly
that they have been satisfactorily answered, owing to the
researches of Helmholtz.
It had always been supposed, and with reason, that the
timbre must have some connection with the particular form
of the vibrations of the sonorous body. Their number
TIMBRE OR QUALITY OF SOUND. l8l
simply determined the pitch; no other possible difference
remained than that which might be presented by each
vibration taken separately. Such a difference was easily
discoverable in liquid waves, which may be pointed, crested,
or flattened, while still keeping the same rate of vibration.
A puff of wind ruffling the surface of the water causes
numberless little ripples, which change the form of the
waves without hastening or retarding their motion. But
what is the form of a fixed vibration (like that of a chord),
where each of the points of the vibrating body simply
rises and falls, and therefore always remains in the same
straight line ? Nothing is simpler. Just as a man might go
from one place to another in a thousand different ways
during a quarter of an hour, loitering the first five minutes,
then running a little way, and again dawdling at the end
of the journey, so a vibrating particle may change in more
than one manner during the hundredth part of a second
which it takes to run its course. It can go first slowly,
then very fast, and again slacken its speed ; and it may do
this two or three times along its route. The revolving
mirror enables us to record the alterations of velocity which
take place during one simple oscillation. A sheet of
smoked paper, which is moved rapidly under the vibrating
point, will show in visible tracery all the irregularities of the
oscillating motion; by looking at the curve so obtained,
it may be known at once how many times during each
oscillation the andante alternates with the presto. The
revolving mirror reflects a bead fixed at the end of a hori-
zontal bar, in a series of different perspectives, giving the
appearance of a luminous ribbon ; if, then, the bar vibrate
perpendicularly to this ribbon, the bead rises and falls, and
the shining band changes into a chain of serpentine folds.
1 82 ACOUSTICS.
The curve is exactly analogous to that shown by the graphic
tracery.
When the particular nature of a periodical motion is
known beforehand, the curves may be traced without having
Fig. 87.
been seen. On a horizontal line the successive seconds
must be marked ; at each division an upright line is raised
to the height where the vibrating body should' be found
at this moment ; the extremities of these lines give the curve
of the vibration. Thus Fig. 87 represents the periodic
Fig. 88.
motion of a hammer worked by a hydraulic wheel : first it
rises slowly, then suddenly falls ; at the first point it is quite
low, up to the ninth it lazily rises, between the ninth and
tenth it comes down with a sudden fall. The motion of
the bow-string of an archer is just the same. Fig. 88
shows in like manner the course of an india rubber ball
TIMBRE OR QUALITY OF SOUND. 183
which rebounds vertically after having touched the ground.
A revolving mirro" would show it describing this curve,
which is formed of successive arches.
The simplest or most regular periodical movement is
that of the pendulum. It is represented by a curve having
the sinuous form of Fig. 89. Thus a pendulum ending in a
point will trace its oscillations on a sheet of paper slipped
underneath it. The straight line indicates the direction in
which the paper is drawn ; the oscillations are perpendicular
Fig. 89
to this line, as pointed out by the arrows. It is easy, by
the aid of this curve, to reproduce the remarkable movement
of the well-known simple pendulum. Take a card, and after
cutting a slit in it with a penknife, hold it against the curve
in such a position that the slit shall be vertical ; then move
it slowly from right to left. You will never see more than
one point of the curve, and it will seem to oscillate in the
slit just like a pendulum.
The mathematical law of pendular motion may be in
some degree explained by illustration. Let us imagine a
luminous point — a small lantern, for instance — fastened to
the edge of a vertical wheel revolving with a uniform velo«
I84
ACOUSTICS.
city (Fig. 90). Placing yourself opposite this, you will see the
light describe a perfect circle. The appearance would be
very different viewed sideways. Take a somewhat distant
position, where you see only the edge of the wheel, and the
light will seem to travel up and down exactly in a perpen-
dicular line, only it will have the appearance of going much
faster in the centre of the line than at the top or bottom.
At these two points, indeed, it will seem to stop for a
moment before turning. Now this apparent movement will
Fig. s<x
be the exact imitation of a pendular movement, which
would make the luminous point swing the length of the
vertical diameter of the wheel.
A " pendular vibration " is any periodical movement of
the same character as that of the pendulum, the velocity
being zero at the two extremities, and increasing towards
the middle, where it reaches its maximum. A simple sound
is produced by a pendular vibration. The motion of the
branches of a common tuning-fork approach this type of
vibration ; it gives a note very nearly simple, and so also
does the flute.
All simple sounds at 2 exceedingly sweet, and seem softer
TIMDRE OR QUALITY OF SOUND. 185
than they really are. Their timbre has something mournful,
recalling the timbre of the vowel combination ou; this is
quite independent of the material of the sonorous body.
We shall soon see what is necessary to produce a simple
sound; it is a ram avis of nature, seldom if ever met
with.
The sounds we find in nature are complex, that is to
say, they are composed of several simple sounds differing in
height. Each body forms a little orchestra to itself when it
vibrates freely. The lowest sound gives the pitch, the
others accompany it. This it is that gives the timbre or
tone. A rich, full timbre is like a nest of harmonious
sounds, whose warblings please us, we know not why.
It had long been known that many bodies give fainter
sounds at the same time with the fundamental one ; and
these were called harmonics ; but no one understood the
part they played, nor was it suspected that they are the
principal, if not the only, cause of the tone distinguishing
different instruments, and that the numberless vibratory
curves are explained by their intervention.
Sauveur gave the name of harmonics of a fundamental
sound to those sounds which make 2, 3, 4, 5 vibrations,
whilst the other makes only one ; together they form the
natural series of i, 2, 3, 4, 5. The first harmonic is the
octave of the fundamental sound, and the second is its
twelfth, or the octave of the fifth ; then follow the double
octave ; the seventeenth, or the double octave of the third ;
the nineteenth, or double octave of the fifth, &c.
In order to indicate the ratio of the height of the har-
monics by their designations, the fundamental sound has been
included with them, as the harmonic i ; the octave will be
the harmonic 2 ; the twelfth, the harmonic 3, &c. Taking
1 86 ACOUSTICS.
doha for the fundamental sound, we have the following
series : —
doh, doh, so!3 doh. im\ sol, latf, dohs to. mi, faJt.
8345678 9 10 ii
Notwithstanding their names, these notes do not in-
variably form harmonious chords. The first six, however,
do so; 7 and n, approximately represented by latt and
faj, do not even belong to the musical scale ; they are dis-
cordant notes, and so is 9, the re. When these notes are
perceived in a compound sound they mar its beauty, giving
it somewhat of a harsh or jarring tone.
In 1700, Sauveur thus notices the phenomenon of har-
monics or "overtones :" —
" On striking a harp-string," says he, " besides the funda-
mental sound, a number more may be heard at the same
time by a delicate and educated ear, sharper than that of the
entire chord, produced by some portions of the string which,
freeing themselves in some way from the general vibration,
take one of their own. These complex vibrations may be
explained by the example of a slack-rope, such as dancers
use ; for while the rope-dancer gives the rope a violent
swing, he may with his two hands give two different im-
pulses to the two halves."
" Each half, each third, each quarter of a string has its
own special vibrations, while the general vibration of the
whole string is going on. It is the same with a bell when it
is very good and tuneful."
After enumerating the successive harmonics which ac-
TIMBRE OR QUALITY OF SOUND. 187
company the fundamental sound of a string, he adds :
" It would appear, then, that whenever Nature makes for
herself, as we may say, a musical system, she employs sounds
of this kind ; and yet they have been hitherto unknown
to the theory of musicians. When they were heard, they
were treated as irregular and of no. consequence, the
musicians thinking thereby to prevent a breach in the im-
perfect and limited system then in vogue."
Twenty-five years later, Rameau used these ideas as the
base of a new musical system.
Fig. 91.— Fundamental Sound and Octave.
The fundamental sound and its harmonics, taken singly,
are simple sounds with pendular vibration. Their inter-
mixture constitutes a complex sound, whose vibrations take
a form more or less complicated. Each of these compounded
vibrations is composed — ist, of one vibration of the fundamen-
tal sound ; 2 nelly, of two vibrations of the octave ; 3rdly, of
three vibrations of the twelfth ; 4thly, of four vibrations of the
double octave, and so on. The general form of the curve
which represents this compound vibration, is determined by
the fundamental sound ; but the harmonics make its contour
1 28 ACOUSTICS.
shrink and swell by their vibrations. In Fig. 91, the dotted
line represents the curve of the fundamental sound, and the
white line, the curve resulting from the addition of the
octave. It is a curve of this species which characterises the
timbre or quality of a compound sound ; it changes form
according to the relative intensity of the harmonics ; but
the number of the great curves or periods is always the
same, and for this reason, the pitch of the mixed sound is
that of the fundamental note.
Inversely, a periodical vibration, of whatever form, may
always be separated into a series of simple harmonic vibra-
tions of pendular form. In other words, all complex sound
of a definite pitch may be resolved into an harmonic series
of simple sounds, beginning with the fundamental, which has
the same pitch as the complex sound. This is a theorem
of Fourier's, and one of the most interesting ever drawn
from analysis ; but we cannot make more than a passing
reference to it. From it we conclude, that if quality depend
on the form of vibrations, this form in its turn depends upon
harmonics, so that in reality quality is given by the super-
position of simple sounds. This is no mathematical fiction,
no subtle definition devoid of reality; experience confirms
these deductions in the most striking manner.
In order thoroughly to understand a compound move-
ment, let us refer once more to the undulations of a liquid
surface. Suppose the water be agitated by two stones, in two
different places ; there are then two centres of commotion,
whence two systems of circular and concentric rings spread
out, till they meet and interpenetrate ; but the eye can still
follow their separate circles. It is beautiful to watch this
kind of motion at the sea-side. The waves as they come
in, easily distinguished by their foaming crests, break in a
TIMBRE OR QUALITY OF SOUND. 189
regular succession, and thrown back in different ways, ac-
cording to the form of the coast -line, they intermingle, cross-
ing obliquely in all directions. A steam-boat leaves behind
her in the water two divergent breaks of dancing waves ; a
bird plunging after a fish will make a succession of tiny
circular waves, which work their way across the general
commotion. It is rarely that an attentive observer fails to
follow the differ jnt partial movements which give a special
form and direction to each.
In the same way the ear can perfectly distinguish the
different sonorous movements transmitted to it simultane-
ously by the air. Let us transport ourselves in thought to
the midst of a ball room, at the moment when the orchestra
bursts forth with a merry dance. What a mixture of sounds,
which can nevertheless be disentangled more or less ! The
strings of the bass violin and the mouths of men give out
sonorous waves twelve or fourteen feet long ; the rosy lips
of women give shorter and more rapid undulations ; the
silken rustle of dresses, and the noise of footsteps, produce
small tempests of tiny crowded waves; and all these mingle
without losing their identity, for the ear can still distinguish
their different origin. The auditory canal, however, which
receives all these impressions at once, is but a speck in com-
parison with the mass of air in the room where all these
vibratory motions are going on The ear cannot follow the
sonorous waves throughout their course, as the eye observes
the motions in a sheet of water.
If a stone be thrown into water already agitated by
undulations of a certain extent, little concentric circles will
be seen spreading over the undulated surface, just the same
as in quiet waters. At the moment when the little circular
ring coincides with the crest of one of the great waves, the
I QO ACOUSTICS.
height of this wave is suddenly augmented by the height of the
little one; so too its tiny depression, added for a moment to
the depression already existing between the large waves, will
hollow it yet a little more. On the contrary, when a de-
pression meets with an elevation, the principal effect will
be weakened. Thus the addition of smaller waves to
greater simply increases the height of the hollow ; and if
we can imagine the little wavelets raised out of our vision
for a moment, we shall see nothing but the large waves,
slightly modified. in their outline.
The separation of elementary notes, found associated
in any noise whatever, may nevertheless be effected by the
ear with the aid of the resonant globes already described.
We have seen that these globes each reinforce a particular
note of which they are constituted guardians ; they respond
to, echo, and draw it, so to say, out of the general tumult.
With a set of these globes, each made for a special note,
it will be easy to single out the notes from any medley,
however slight their existing force. Thus also it is proved
that the harmonics of musical sounds, far from being a
fanciful illusion, a merely subjective phenomenon, have a
true existence. With a little practice, they may be caught
by the ear alone.
Once accustomed to listen, the ear listens almost uncon-
sciously. Thus when a drum is heard at some little dis-
tance, a low dull sound is first noticed, which is caused
by the air imprisoned in the hollow ; then a succession of
sharp notes, clearer and more defined, produced by the
stretched parchment or head ; other harsh sounds are due
to. the 'jarring of the strings on the lower parchment ; and
finally there is a metallic ring, coming from the sides of the
cylinder.
TIMBRE OR QUALITY OF SOUND. IQI
The Human voice is very rich in harmonics, taking very
complex timbres. With the sympathetic resonant balls,
sixteen harmonics or overtones can be reckoned in a bass
voice singing a or e, on a very low note. Rameau was
not unaware of this phenomenon, and many musicians have
noticed it since. Seiler tells us how, in listening during
sleepless nights to the voice of the watchmen telling the
hours in Leipsig, he often seemed to hear first the twelfth,
and then the note itself. M. Garcia says that, listening to
his own voice in the silence of night upon a bridge, he has
been able to distinguish the octave and the twelfth of the
note he gave. We seldom notice the existence of these
parasite notes in the sound of the voice, because we do not
look for them ; but we may easily convince ourselves of the
fact in this way. Ask a singer to sing the vowel o on the mil?
in the bass, then gently strike the si* of the middle octave
on the piano, so as to fix attention on this note. You will
continue to hear the sit? after the finger has left the piano
and the string has ceased to vibrate. This is because the
si?, resounding in the mil? of the voice, will replace the
sound of the string. If you wish to tiy the sol of the
following octave, or the seventeenth of mitr, in this way, it
will be better to take the vowel a.
Let us mention here that the notes from mi6 to
so!6, belonging to the last octave of the piano, are always
heightened in tone by a peculiar resonance they excite in
the auditory canal: thus acquiring a fictitious intensity,
which gives a piercing character to the sounds they ac-
company as overtones. To a sensitive ear it is actually
painful. We know that even dogs are very sensitive to this
kind of impression ; a high mi on the violin will make
them howl. This irritability of the ear in regard to very
1Q2 ACOUSTICS.
high notes, renders it particularly sensitive to those disagree-
able dissonances that always strike us in choirs, especially
when the voices are at all forced. Above the lower notes we
really hear a crowd of little screaming notes, accompanying
the harmony like an orchestra of castanets and cymbals.
Fine strings also abound in overtones. Helmholtz has
counted as many as eighteen. The harmonics 7, 9, n, 13,
14, 17, 1 8, are more or less discordant; if they had more
intensity they would produce a most unpleasant effect.
Happily the ear only catches the first upper notes, which
agree with the fundamental note, and even these can only
be seized by close attention.
These facts seem to show that all sonorous vibration,
having a peculiar timbre, is reduced by the ear to simple
sounds which form an harmonious series. This conclusion
may seem at first sight too absolute, and contrary to our
senses, since we are not accustomed to take note of the
existence of several notes in a musical sound. At most,
musicians only distinguish in a chord the notes that form it,
but that are produced separately. The difficulty seems to
augment when the chord is formed with compound intervals,
such as the twelfth, repeat of the fifth, and the seventeenth,
triplique of the third (as Sauveur calls it). Kcenig made
a pretty experiment in this way. On the sounding-board of
an enormous tuning-fork he arranged a whole orchestra of
small ones, which gave amongst them the first four or five
harmonics of their leader. Then with a vigorous stroke he
set the great patriarch in vibration, and afterwards all his
attendants : the air was filled with a deep harmonious sound,
very full, but seeming to the unpractised ear a single note,
the voices of the sharper forks not being heard. He then
suddenly stifled the deepest by placing his hand upon it,
TIMBRE OR QUALITY OF SOUND. 193
and the others were heard immediately — clearly separating
themselves, as soon as the deep tone which had sustained
and bound them together was subdued.
Thus, in ordinary circumstances, the ear seems unable to
accomplish the dissection necessary for reducing the timbre
to its constituent parts. But this is a mistake. It is only
necessary to understand the words we use. Indeed, we
must here distinguish between perception or sensation, which
is complex, and the impression received by the mind, which
is simple. The ear really perceives several notes when fa is
given by the violin, but the whole of these notes only recall
to our mind a fa having a peculiar timbre ; we have no
particular reason for analysing our impression further. The
hearing apparatus dissects the complex sounds that strike it,
but the separate elements are reunited in the nervous im-
pression made on the mind. Physiology gives us many
instances of similar illusions. Thus we take for simple
colours, tin's which the prism divides into numberless tints.
The theory of binocular vision shows how during our whole
lives we see all objects double, and nevertheless it needs a
strong effort of attention to be convinced of it. Few people
know that in the retina there is a little blind spot, the punc-
tum ctcctim, and that consequently in one direction we
cannot see at all. This blank is so large that there would
be room in it for seven lunar images in a row, and at a
distance of a few feet a human face would be lost in it ,
yet it is not inconvenient. When Mariotte illustrated the
fact by experiments in the court of Charles II., he was
greatly amused at the astonishment occasioned among his
illustrious audience. There are some well-authenticated
instances of people who have only discovered by chance
that they had lost the sight of one eye years ago. Such is
N
194 ACOUSTICS.
our indifference to a phenomenon always present with us.
We do not notice the complexity of a sound any more than
the double image of an object that we look at with both
eyes ; yet it is this very duplicity that gives the effect of
relief, as shown by the stereoscope. Timbre is the relief of
sounds.
We manage to distinguish the sounds of different instru-
ments, or the voices of different people ; and in these cases
there are many things to help us besides the timbre — those
little noises which precede and follow the emission of the
sound, its duration and power, its intermissions and varia-
tions. But the ear must be educated to the task of dissecting
the timbre, in order to be conscious of its complexity.
Helmholtz has corroborated these deductions by com-
posing different artificial timbres with the notes they were
supposed to contain. Here is an experiment that any one
can easily try : Raise the hammers of a piano so as to have
all the wires at liberty, then sing loudly the vowel a upon
any note you choose, standing near the instrument. The
resounding of the strings exactly reproduces the a. The
resemblance is much less complete when the hammers are
not all lifted from the strings ; because the vowel a is
characterised by a peculiar timbre, depending on certain
sharp notes ; the strings corresponding to these notes
vibrate through sympathy, and their intervention gives to
the echo of the voice the timbre it had in singing the a.
In the same way the timbre of the clarionet, the cornet, and
so on, may be imitated.
The height of a musical sound, then, is always that of
the dominant note in this harmonic medley, and this is
generally the lowest of all. But the presence of the upper
notes is not without its influence on our judgment of a
TIMBRE OR QUALITY OF SOUND. 1 95
complex sound — it sharpens it, slightly raising the musical
scale. For this reason even practised musicians sometimes
mistake an octave in comparing notes of different timbre.
We have already said that the ear does not depend
solely upon timbre in discerning the origin of sounds, but
is guided by certain accessory noises. In many cases these
characteristic noises are only heard at the first moment, or
as the sound dies away.
The preparation for the emission of a sound is almost as
important as its timbre. With the human voice the noises
preceding the emission of the vowels are so very distinct,
that they are called after the explosive consonants, ^, /, d,
t, £, k. They give to the vowel following a peculiar
character quite apart from its timbre.
In any loud note given by a brass instrument, we can
distinguish between the hautbois, clarionet, &c., without
regard to the timbre. Then, too, the greater or lesser
rapidity with which the fundamental sound and its har-
monics die away, constitutes a sensible difference between
catgut strings and wires, even when they are equally struck.
The vibrations of the first being unsustained, their sound
is somewhat poor and dry ; while, the vibrations of the metal
wires enduring much longer, their sound is fuller, though
less penetrating.
In other cases the sound is accompanied by noises
throughout. Thus, in wind instruments there is a sort
of whistling, caused by the action of the air on the edge
of the opening. The scraping of the bow is always heard
more or less with the violin. Noises of this kind are ex-
pressed by the letters/, v, s, j, z, /, r.
The vowels, too, are constantly accompanied by little
noises, that help us to guess them even when they are
N 2
i96
ACOUSTICS.
whispered. These sounds are heard more in speaking than
in singing, for in singing the timbre or the musical part of
the vowel is most dwelt upon, and this is heard to a much
greater distance. This is why consonants are not heard
so far away as vowels, and why a distant voice may be mis-
taken for a cornet. The consonants n and m, however, by
their mode of formation, have somewhat of the nature of
vowels, and the accessory noises play a very subordinate
part. If you stand at the
foot of a hill and listen to
voices speaking some way
up, you will scarcely catch
any words except those
formed with ;;/ or n.
A few further remarks
may be made about diffe-
rent timbres. In the first
place, we can obtain simple
sounds by strengthening
the fundamental sound of
a tuning-fork by a resounding box (A, Fig. 92), whose upper
notes do not harmonise with those of the fork. The timbre
of simple sounds is sweet and subdued, not brilliant enough
for music.
Sounds accompanied by upper notes that are not harmo-
nious, are not included in our definition of musical sound :
we can only use them in music when the upper notes die
away so quickly that we may forget them, and notice only
the principal note. In this category we place rods, discs,
tuning-forks, bells, parchment skins, &c. Tuning-forks
have very high upper notes, heard at the moment of striking
the metal. The first is at an interval of a twelfth from the
Fig. 92. — Mounted Tuning-fork.
TIMBRE OR QUALITY OF SOUND. 197
fundamental sound. The ear always separates these sharp
quickly passing notes from the principal notes, and has no
tendency to blend them with it, as it does the harmonious
elements of a musical sound.
The sound of common bells can hardly be ranked as a
musical sound : but it appears that a skilful founder is
able to make the first upper notes of a bell harmonious,
and then the timbre is tolerably good. This explains the
pleasant effect of chimes. There are eight at Amsterdam,
one of which numbers forty-two bells, and has a compass
of three octaves and a half (between doh2 and fa.). The
most celebrated is that of Ghent Paris is going to have
one at Saint Germain 1'Auxerrois.
The fundamental sound of bells is lowered by an
increase of weight or diameter. The largest bell in the
world is that cast at Moscow, in 1736. Its weight is about
193 tons. Unfortunately it was cracked before ever it was
rung. Still, there is one at Moscow, weighing 63 tons,
that dates from 1307. The great bells of our cathedrals
seldom weigh more than 10 tons. That of Notre Dame de
Paris, founded in 1680, weighs nearly 13 tons.
Franklin's harmonica is composed of a number of glass
bells, which are sounded by rubbing round the edges with
damp fingers. The effect is rather irritating to the nerves,
the sound being too penetrating, because of the prevalence
of harmonic overtones.
Instruments that are played upon by striking, such as
timbrels, tambourines, castanets, triangles, and cymbals, are
classed together with bells and tuning-forks. They have
discordant upper notes. The tam-tam or gong of the
Chinese is a circular disc with a raised edge, made of well-
tempered and hammered bronze. It is struck with quick
198 ACOUSTICS.
light taps from the rim to the centre, and wonderful effects
are got from the multiplied sounds, which gather and seem
to burst out with great violence. It is as if a struggle were
going on in the metal of sounds which make frantic efforts
to escape from their prison. The sheet iron with which
the sound of thunder is imitated in theatres, produces effects
somewhat similar.
The skins of the drum and tambourine do not give
true musical sounds, but the resistance of the frame or
body stifles the higher notes considerably. All these noisy
instruments are employed chiefly to mark the time, and
they are in high favour among savages. There is not a
nation on the earth that
has not invented a drum
of some kind to beat a
measure, and animate the
dancers. Amongst the Es-
quimaux, the Patagonians
and Hottentots, and the
New Zealanders, they are
to be found. An earthen
Fig. 93.— Sistra of the Ancients. ,. r. „ , ,
pot or bit of hollowed wood,
or a calabash, with an ass's or crocodile's skin, form the
materials of these rough resounding boxes. The tambourine
and the castanets, which Southern nations use so gracefully,
are of very ancient origin. The crotalon of the priestesses
of Bacchus (Fig. 94) was nothing more.
Strings and pipes are pre-eminent as the true source of
musical instruments. Their timbre is harmonious. A
homogeneous string vibrating completely gives, besides its
fundamental sound, the series 2, 3, 4, as harmonics ; but
it may be made to vibrate in such a way as only to give one
FIG. 94.— PRIESTESS Of BACCHUS (from a Bas-relief).
TIMBRE OR QUALITY OF SOUND. 2OI
of its harmonics, dividing itself into different segments,
separated by nodes.
The quality or timbre varies, according as they are
played upon by pulling, as in the harp ; by striking with a
hammer, as in the piano ; by drawing a bow across, as in
the violin ; or by the wind blowing over them, as in the
./Eolian harp.
In the construction of pianos, the experience of two
centuries led to the foundation of a number of rules, which
are now justified by theory. Thus the hammers of the
middle strings have been made to strike them at the
seventh or the ninth of their length, because the best quality
or timbre was thus obtained. Theory shows that by this
arrangement the harmonics 7 and 9, the first which will not
harmonise with the fundamental sound, are suppressed. The
time during which the hammer remains in contact with the
string also influences the timbre.
Strings of cat-gut have very little persistency of sound,
though their harmonics are very high ; so the disagreeable
effect of these is neutralised. In the violin their timbre is
slightly modified by the resonance of the instrument, whose
own proper sound is generally doh3. The first harmonics
are less distinct in the violin than in the piano, but the
sharp harmonics are more strongly marked.
Open pipes are much like strings, having a fundamental
sound, with a timbre comprising the natural series of notes,
i> 2, 3, 4> 5 ; and the fundamental sound can be got rid of,
and nothing left but a harmonic, by forcing the wind. In
the closed pipes some of the harmonics are wanting : they
give only the notes I, 3, 5, 7.
A closed pipe has always the same fundamental sound
as an open one of double the length ; this may be seen by
2C2
ACOUSTICS.
closing an open pipe midway with a slide (/, Fig. 95), so
reducing it to a closed pipe of half its former length, when
the sound will remain the same. In short, the law that ex-
plains the names of the register (or draw-stop) of an organ is
this : The height of the fundamental sound is in inverse ratio
to the length of the pipes. An open pipe of 1 6 feet gives
the lower octave of the open pipe of 8 feet, but
is in unison with the closed pipe of 8 feet ; the
open pipe of 8 feet is the lower octave of the
open pipe of 4 feet, and in unison with the
closed pipe of 4 feet, &c.
In the organ there is a pipe for every note,
each one giving only its fundamental ; but in
other wind instruments there are many plans
for getting all the notes of the scale out of the
same pipe. Thus the horn is made of a very
long brass pipe, curled round : its only harmonics
are 8, 9, 10 ; but these will give the actual scale
by a little modification, which is done by intro-
ducing the hand into the end. In the trombone
the length of the pipe is varied by a slide ; in
the cornet-a-piston, by supplementary pipes. In
Fig. 95. other instruments, like the flute and clarionet,
the pipe is pierced with holes, that are opened
and closed by keys. The column of air in the pipe is made
to vibrate in such a way as to form centres, in relation to
the open holes, wherefore these openings produce the same
effect as if the pipe were cut at the places where they are
situated. Owing to this mechanism, the musician has in
his hands a whole set of pipes of different lengths, from
which he can draw the most varied sounds.
In all wind instruments one of the most important parts
TIMBRE OR QUALITY OF SOUND. 203
is the mouth or opening. The most simple is such as we
find in flutes and the generality of organ-pipes ; it is repre-
sented by the whistle (Fig. 96), which is a simple mouth-
piece without a pipe. The wind strikes upon the lip of the
mouth with a rustling that may be considered as a medley
of feeble sounds. The column of air in the pipe strengthens
some of these by a sympathetic resonance, and these are
the harmonics the pipe will utter. In the reed
mouth-pieces the stream of air first sets in vibra-
tion a metal key, which interrupts it periodically
This trembling of the key gives birth to a num-
ber of notes, among which the column of air
makes its choice ; but the sound is not the same
as when the pipe is played with an ordinary
mouth-piece. To this list belong the reed-stop
pipes of organs, and the notes of the harmonium,
clarionet, hatitbois, bassoon, cornet, and cor
anglais. Our lips act as reed mouth-pieces when playing
upon such instruments as the horn, trumpet, or trombone,
their position and their tension influencing one or other
of the harmonics of the tube of the instrument.
In the production of the voice there are vocal chords
which play the same part, but their mode of action is quite
different from that of the lips. They determine the height of
the note for singing or speaking. In the clarionet and
horn the note depends on the volume of air in the pipe ;
but here, on the contrary, it only depends on the tension of
the vocal chords, and not at all on the volume of air
which is made to resound by their action. But this reso-
nance becomes very important from another point of view.
It modifies the timbre by favouring certain sounds. This
is the origin of vowels.
204 ACOUSTICS.
A vowel is nothing more than the particular timbre
taken by any note, if the resonance of the mouth streng-
thens, amongst the harmonics of this note, that which ap-
proaches nearest to a certain fixed note. Thus, for example,
the vowel a is produced by the resonance of sit?4. To
articulate a, the mouth is placed in such a position as to
sound si&4 ; and whatever be the fundamental of the sound
we emit, it is always the harmonic nearest to sil?., which will
be made prominent.
If when the mouth be opened to articulate some such
vowel a number of tuning-forks of various pitch be passed
before it, one will always be found to answer to it by increase
of sound : its note is the one that answers to the proper
volume of air contained in the mouth. In this way Helm-
holtz found that each vowel is characterised by one or two
notes, usually the same, but sometimes modified, according
to the accent in which the vowel is spoken.
It is easy to understand how this occurs. The defini-
tion of the vowels as five letters of the alphabet is alto-
gether insufficient, as they are indeed numberless, if we take
heed of all shades of pronunciation. We must at least dis-
tinguish seven principal vowel sounds which group them-
selves in this way : —
> e i
Therefore if a vowel be defined by its specific note, the note
varies with the language in which the vowel is spoken. The
notes decided on by Helmholtz for the German vowels, differ
TIMBRE OR QUALITY OF SOUND.
205
from those that M. Bonders attributes to the same vowels
pronounced in Dutch.
The vowels a, o, and ou have always only one single
specific note, but for the others two are found ; and this two-
fold expression is explained if we remember that the mouth
in their case takes the form of a bottle, the wide part being
represented by the mouth, and the narrow neck by the
tongue and the lips. These two cavities vibrate separately.
Here are the notes which, according to Helmholtz, answer
to the vowels spoken in the accent of North Germany : —
f
P "-
s-f-
H- P-
k
M
PI
— U
— f —
1 .
?
e
— j_ —
- 1
— r
|h
T
r
OU O A AI B I EU U
The intensity of the partial sounds of a vowel does not,
then, depend on the place they occupy in the harmonic
scale, but only on their absolute pitch ; and it is this which
distinguishes the timbre of vowels from that of musical
instruments. Take, for example, a flute : whatever note it
gives, it is always the octave which resounds simultaneously.
But if a be sung upon any note whatever, one cannot foresee
what harmonic will be strengthened : sometimes it will be
the octave, sometimes the twelfth or the seventeenth, or
some other note of the harmonic series. Thus if a be sung
upon the note sit>3, the octave will be given, for the specific
note, of the vowel a is the octave of sit>3 ; but if the fun-
200
ACOUSTICS.
damental note be fa%, the ninth harmonic la&4, which is
the nearest to sit>4, will be heard above all. There is ^a
slight analogy here with the violin, which always strengthens
the neighbouring notes of doh3, the sound belonging to the
volume of air imprisoned within it.
Fig. 07.— Vowels observed by the aid of Koenig's Flames.
Kcenig obtained a visible image of the timbre of vowels
by means of his flames, upon which the voice was made to
act by a gutta-percha tube furnished with a funnel (Fig. 97).
They are fed by a jet of gas, which crosses a hollow capsule
closed on one side with a membrane, which is made to
vibrate by the voice. This membrane acts upon the flame
TIMBRE OR QUALITY OF SOUND.
207
as a bellows, which makes it by turns flare up and grow
dim ; if the shocks be too violent, and the flame small, it is
extinguished altogether; even if it be able to resist, it becomes
jfejyj
> A . . J ,
w^, m --'• -f^-s •••-"- y --^^ i -;',^^/'-^^— x^--?^
^^"^^^5a^^B^^^^^^^^»^^^BM^':' -^3i: — '. - /£^gssi^g
Fig. 98.— The Timbre of Vowels.
bluish. A flame palpitating thus would appear in the re-
volving mirror under the form of a serrated ribbon, whose
changing appearance reveals the number and relative
strength of its harmonics, as shown in Fig. 98.
After having accomplished the analysis of timbres,
208 ACOUSTICS.
Helmholtz tried to reproduce them by means of synthesis,
reuniting the notes that had been separated by analysis.
He constructed an harmonic series of eight tuning-forks,
which were mounted between the branches of a set of
electro -magnets, so as to be able to maintain them in
vibration by the action of a periodical current of electricity.
In front of each tuning-fork was placed a sounding-box,
which could be shut more or less completely by pressing
upon the key-board. When the box was closed the tuning-
fork gave hardly any perceptible sound, but it grew stronger
as the box was opened wider. With this apparatus, an o
was distinctly produced by strongly sounding the sit?3, more
feebly sit?2, and fa4; a was obtained by giving sit>2, sii?3, and
fa, moderately, and sifr4 and res with full force. The tuning-
fork having siir2 for its fundamental gives, when sounding
alone, a very faint ou. Kcenig made a like apparatus with
ten tuning-forks. But we must always remember that com-
pared with true vowels the resemblance is generally some-
what doubtful. Once, and only once, we heard a perfect a.
How is it possible to describe the marvellous power
possessed by the ear for separating such complex sounds
into simple vibrations? We have seen that the strings of
a piano effect this dissociation of harmonics, since they
answer to all the notes which are united together in the
sound examined. Imagine a series of musical strings giving
the scale of all possible notes, and then we shall have some-
thing with which to reproduce faithfully all varieties of timbre
or composite sounds.
Helmholtz thinks that the ear possesses just such a
series. This is the wonderful organ discovered by Corti,
and called after him. It is situated in the labyrinth, and
may be described as the terminal fibres of the auditory
TIMBRE OR QUALITY OF SOUND. 209
nerve. There are above 3,000 fibres spread over the mem-
brane of this labyrinth ; and, supposing that each one
answers to a particular note, we have an instrument of 3,000
strings — more than enough to gather and reunite all the
sounds in creation. There must be at least 400 for each
octave.
In the same manner the perception of colours may be
explained by the existence of fibres of the optic nerve, each
appropriated to a simple colour. This hypothesis was put
forward by Thomas Yo:mg. It cannot be denied that by
this ingenious theory all the phenomena of our perception
of colour and sound are explained in a very natural way.
It is now understood that the ear must act as a prism, which
decomposes the timbre into its primary elements, although
the complex impression made upon the brain is seldom
analysed by the mind accustomed to judge of its impressions
only as a whole.
The most pleasant and musical qualities of timbre are
the harmonics i, 2, 3, 4, 5, 6. Compared with simple sounds,
musical sounds are richer, fuller, and more magnificent —
more coloured, so to say ; they seem soft and mellow, too,
so long as the sharp upper notes do not trouble the har-
mony. In this list we may place the sounds of the piano
and organ, the human voice and the cornet, unless they are
forced. The flute belongs rather to simple sounds. With
such sounds only very little music can be produced : they
must be sustained by others. An instrument composed of
tuning-forks (which also give sounds almost simple) would
not be pleasant to listen to alone.
The large pipes of an organ give very faint harmonics
of the fundamental sound, and are therefore very nearly
simple. This is especially true of the closed pipes. When
210
ACOUSTICS.
a sound only contains the odd notes of the harmonic series
(the fundamental, the twelfth, &c), as happens in the
narrow and closed organ-pipes, the clarionet, and strings
Fig. 99. — Voices of Birds.
struck in the middle, the timbre becomes hollow; when the
number of higher sounds increases, it becomes nasal; when
the fundamental sound governs, it is full; when this is too
feeble, it becomes //////. The sound of a string is fuller
when struck with a hammer than when pulled by the
fingers.
TIMBRE OR QUALITY OF SOUND. 211
When the harmonics above 6 are very distinct, the
sound becomes harsh and piercing, because of the discords
caused by these high notes ; but if they are heard in mode-
ration, they rather add brilliancy and colour to the tone of
an instrument.
This subtle and changeful element which we have
spoken of under the name of timbre plays an important part
in the relations of voice and feeling. It is the timbre which
renders a voice sympathetic, persuasive, and loving; or
sharp, quarrelsome, and disagreeable. The timbre of a
bird's song serves instead of speech, expressing ail the
emotions that stir its little heart (Fig. 99).
CHAPTER XII.
INTERFERENCE OF SOUND.
Beats— Resultant Sounds — Sonometers of Scheibler and Koenig — In-
fluence of the Movement of the Source of Sound on its Pitch.
HOWEVER paradoxical it may appear, we shall see in this
chapter how sounds quarrel, fight, and when they are of
equal strength destroy one another, and give place to silence.
The phenomena of resonance revealed a sort of sympathetic
reciprocal bond existing between sounds. The strings of a
violin hanging on a wall resound without being touched
when another violin is tried in the same room. Every
sonorous body harbours a family of notes, which readily
respond to the call of a friend. We are now about to study
the warfare of notes, to spy out their enmities and discords.
We shall see how the whole crowd of harmonics take sides
when two declare war. Often, indeed, we hear them skir-
mishing when as yet the two chiefs are quiet.
Two notes are said to " beat" when their union gives rise
to periodical alternations of strength and weakness. This
phenomenon is well known in organ-pipes. When two
slightly discordant pipes are sounded together there is a
beating effect produced ; the sound alternately swells and
dies away, and when the strong swells follow very quickly
there is quite a little tumult.
Sauveur was also the first to study this curious pheno-
menon, and he found that important deductions might be
made from it From his experiments he had concluded
INTERFERENCE OF SOUND. 213
that the number of beats is always equal to the difference of
height of the two notes ; for each double vibration that
the one accomplishes more than the other there is a beat ;
therefore nothing is easier than to determine the absolute
height of two notes by counting their beats. Suppose, for
instance, that two pipes are tuned for the notes doh and re :
the interval being a major tone, the first will always make
eight vibrations while the other makes nine ; the difference
being one, there will always be one beat for eight vibrations
of one and nine of the other. If we now count four beats
a second, we shall conclude that in the second the first tube
has made four times eight, or thirty-two vibrations, and the
other four times nine, or thirty-six ; and thus the absolute
pitch is at once determined. The beats may be also observed
in tuning-forks, or in any other sonorous bodies, if only
their vibrations be sufficiently slow.
What is the producing cause of this phenomenon of
beats ? According to Sauveur, " the sound of two pipes
must have more power when their vibrations, after having
been separated, reunite and coincide, and strike simul-
taneously upon the ear." " It even seems," he says, " that
the common expression of musicians, that the pipes beat
when their sound is thus redoubled, originates in this idea."
The explanation of beats rests upon the phenomena of
interference. Two vibrations are said to interfere when
they urge the air-particles in opposite directions. This is a
case of "union is strength ;" for when two vibratory motions,
acting on a point, coincide, they assist and strengthen
each other; when they are in opposition they Aveaken, and
even annul the sound of both. In the same way it has
been demonstrated that light added to light will produce
darkness.
214 ACOUSTICS.
We have already seen the composition of vibratory
motions, and how they may be examined by means of curves.
Let us imagine two identical vibrations starting from the
same point at the same time : they pass on uniformly, and
acting together assist one another, and augment the motion
of the particles, the result being a vibration in the same time,
Fig. too. — Coincidence. Fig. 101.— Opposition.
but much more energetic (Fig. 100). If the two vibrations
be so disposed that one generates a condensation where the
other generates a rarefaction, they act against one another,
and if their power be equal, completely neutralise one
another (Fig. 101). Two sounds of the same pitch and
intensity thus meeting produce silence. This startling effect
may be shown with two organ-pipes, exactly similar in all
respects, and mounted side by side on the same bellows.
While one only is played upon it sounds loudly ; when both
are made to sound together there is scarcely any sound,
INTERFERENCE OF SOUND. 215
although they vibrate, as may be proved by placing a feather
near the opening, where the current of air is broken ; but
they vibrate in opposition. When the air on entering one
tube is condensed, it is rarefied in the other ; the surround-
ing air is also urged in contrary directions by the two
different actions ; and since there is no reason why it should
obey one rather than another, it remains motionless, and the
sound is never produced.
This curious fact may be directly proved. A communica-
tion is made between the two pipes with two of Kcenig's
Fig 102. —Interference.
flames, so arranged that the point of one passes a little
mirror which hides its base, but shows by reflection the base
of the other. This produces the illusion of a single flame.
If, now, this flame be seen in the revolving mirror while the
two pipes are played upon, the point will separate from the
base, which proves that the two flames shine alternately
(Fig. 102). If both pipes act on the same flame, the effect is
neutralised, and the flame remains motionless. Two equal
vibrations, then, either strengthen or weaken one another,
according to the manner in which they combine ; but the
same effect, whichever it be, continues throughout the move-
ment. If there be the slightest inequality the case is very
different. In such a case one soon gains on the other, and
passes on, then slackens, and is in its turn overtaken and
passed, and so on. The encounters will take place in all
2l6 ACOUSTICS.
manner of ways. Sometimes there will be an augmentation,
sometimes a falling off, of sound ; the two notes alter-
nating more or less completely between brilliancy and ex-
tinction. If one should make exactly nine vibrations while
the other made eight, and if the two vibrations started in
opposition, they would at first weaken one another ; then as
one took the lead (nine simple vibrations having been ac-
complished on one side to eight on the other), they would
coincide for an instant, thus supporting one another ;
then, after eight or nine simple vibrations more, they would
again be in opposition, and weakened as at first. In the
interval of eight and nine double vibrations, there would
always be an augmentation of power or a beat. This would
occur each time that the more rapid note gained a double
vibration on the other (Fig. 103).
An illustration will explain this. Let us imagine two
Fig. 103.— Beats.
rivers subject to periodical high-tides, rising in one at the
beginning of each month, that is to say twelve times a year,
and in the other every twenty-eight days, or thirteen times
a year. Suppose further that between the high tides there
intervened low ones : a high and a low tide would be equi-
valent to a complete undulation or double vibration. If these
two rivers flowed into the same lake they must cause great
INTERFERENCE OF SOUND. 21 7
commotion at certain times, whilst at others they would
exert scarcely any influence over the state of the waters. It
is indeed clear that if at any given moment the full tides co-
incide, the low tides must also fall together ; and since the
difference between the two rivers is but two days, this must
happen for two or three months ; and at these times their
united action on the open waters would make a sensible rise
and fall. But when the high tide of one happened at the
same time as the low tide of the other, there would be no
variation in the level of the lake. This period of calm
would also last some months. Say that the two rivers rise
together January ist, they fall the i4th or i5th, mount
again towards the end of the month, and fall in the middle
of February. At the end of six months the river which rises
every four weeks will be about fifteen days in advance of
the other, and therefore will have a full tide in the middle
of July, just as the other has a low one. This state of things
will begin about June, and last till August. During this
time there will be no effect. The summer then will be a
period of great calm for the lake. Towards the end of the
year, the second river being a whole month in advance, its
thirteenth tide will coincide with the twelfth of the other,
and the lake will again be agitated by a great flux and reflux.
Thus each winter the lake will be stormy, and each
summer will find it calm. In ten years, the 120 high tides
of the one, combined with the 130 of the other, would
have produced ten periods of maximum agitation. It is
thus that two notes, making respectively 120 and 130
complete vibrations in a second, will give at the same time
ten beats.
This phenomenon may be exhibited in various ways.
By transcribing faithfully the vibrations of the air, the
218
ACOUSTICS.
varying intensity will also be revealed if there have been
any beats. To obtain a tracing with two slightly discordant
tuning-forks, it is only necessary to fasten on one a piece of
blackened glass, and on the other a flexible point ; then
make them vibrate horizontally, and hold them so that the
point rests on the glass (Fig. 104). The curve then drawn
shows the augmentation as often as the one fork has gained
on the other a complete vibration. Fig. 105 shows two
tracings obtained in this way with two notes, which were at
first in the ratio 24:25, and afterwards in that of So:8i.
The flames of Kcenig furnish another means for observing
beats.
The physiological perception of beats seems, at first
sight, irreconcilable with the hypothesis, according to which
the ear always separates notes of unequal pitch. If the
two sounds do not act upon the same fibre, how can their
vibrations combine in the auditory apparatus? The answer
is simple. It must not be forgotten that the nervous fibres,
like all elastic bodies, are influenced, though in a less degree,
by vibrations a little out of unison, so that the sphere of
action of two neighbouring sounds spreads over a large sur-
face of fibres, instead of embracing only two. A note that
is a semitone higher or lower than thf note of a given fibre,
INTERFERENCE OF SOUND.
219
makes it resound ten times less than a note in unison;
still the resonance is percep'ible. Ac-
cording to that, we see that the unison
of two neighbouring notes, which beat,
must be manifested in all the inter-
mediate fibres, and the ear must be
affected by them.
When the augmentations follow
rapidly, the effect of the beats becomes
very disagreeable, like the burr of an
r, or the grating of a scythe on wood.
The harshness is at its height when
there are thirty or forty beats per
second ; beyond that it becomes
difficult for the ear to separate them,
and the impression is not so strong.
Helmholtz declares that he has been
able to distinguish up to 132 beats
per second (between the sis and doh6)
— without counting them, be it un-
derstood. Since the lowest sound
perceptible by the ear comprises about
thirty double vibrations, it is therefore
possible to hear beats at least four
times as rapid as the lowest notes.
This observation contradicts the
common opinion, that very rapid beats
are perceived by the ear as a very
low note. The reason of this hypo-
thesis was, that two notes resounding
forcibly toge'h?r engender a third note, called the resultant
tone, which is expressed simply by the difference of the two
105.
2 20 ACOUSTICS.
primitive notes, or, which comes to the same thing, by the
beats produced by their concurrence.
The resultant sounds were known before they were
understood. The German organist Sorge speaks of them in
a work published in 1745. The celebrated violinist Tar-
tini set himself, nine years later, to found a new musical
system thereupon; but his book is so abstruse that even
D'Alembert admits he could not understand it.
It has long been thought that the resultant sounds must
always be lower than the sounds which cause them ; but
Helmholtz foretold by theory resultant sounds which should
be sharper, and experiment has fulfilled his prophecy.
There are, then, two kinds of resultant sounds : first,
the differential sounds, whose pitch is given by the difference
in the number of vibrations of the primary sounds. These
are the easiest to observe. Secondly, the additive sounds,
the pitch of which is found by adding the vibrations of the
primitive sounds. Let us suppose, for example, that two
pipes are sounded together, giving a fifth. Their notes
will be in the ratio of 2:3, and the difference being unity,
the differential sound will be one, the octave below the lower
of the two sounds. The sum of two and three is five ; one
might, therefore, also hear a note which would be the major
sixth of the sharper of the two sounds. With doh2 and
so!2 we can obtain doht and mi3, but we shall hardly hear
anything beyond the doh — unless, indeed, the generating
sounds are very strong. If (as generally happens) the latter
are accompanied by harmonics, the intermingling of the
respective harmonics, the fundamental notes, and the first
resultant sound, may give birth to new resultant sounds ;
but these superfluities are difficult to observe, on account of
their weakness.
INTERFERENCE OF SOUND. 221
The resultant sounds of a major third are these. The
minims represent the primary, the crotchet the first diffe-
rential, the quavers the cross products, and the barred note
the additive sounds : —
^E
To hear the resultant sounds, it is only necessary to
force the generating sounds. Theory shows that this
phenomenon must be considered as a kind of disturbance
of the vibratory motion, which becomes too violent to follow
the simple laws of ordinary elastic vibrations. * It is by an
analogous perturbation that tuning-forks and bells give the
upper octave of their fundamental sound whenever they are
violently set in motion ; whilst vibrating moderately they
would only produce upper sounds not harmonic.
Resultant sounds and beats render important aid
in tuning organ-pipes, &c., indicating with great precision
the difference in the pitch of two notes. Koenig was thus
enabled to tune a doh9 of 32,000 vibrations, and a re9 of
36,000, by their differential sound — the doh6 of 4,000
vibrations.
Henri Scheibler, a silk manufacturer at Cre'feld, did
much to utilise the employment of beats for tuning
musical instruments. This man, who had a passion for
acoustics, devoted not less than twenty-five years to per-
fecting his method. He constructed, with inconceivable
trouble, considering the state of science at that time, a set
222 ACOUSTICS.
of fifty-six tuning-forks, giving the scale from la of 440 to la
of 880, embracing an entire octave by degrees of eight
simple vibrations. This set of forks formed what he called a
sonometer. Taken two and two in the order in which they
succeed one another, they always give four beats a second.
They are thus tuned by differences, and the last will, of
course, give the exact octave of thi first. If this result has
been attained we are sure that the first made 440, and the
last 880 vibrations per second, for the beats prove a diffe-
r.nce of 440, and we know, on the other hand, that they
are as i : 2. We understand that these fifty -six tuning-forks,
the notes of which are perfectly certain, allow any note
whatever, contained within the limits of their octave, to be
tuned by them with mathematical precision ; we have only
to count the beats that this note gives with the tuning-fork
to which it stands in the nearest relation. If the note be in
another octave it is set by means of a supplementary tuning-
fork, which gives its true octave.
Scheibler published his method in 1834. He also went
to Paris, to try and make his sonometer known ; but the
difficulty of construction frightened the manufacturers.
Thanks to the progress of science, this valuable method is
now within reach of every one. Kcenig made sonometers of
sixty-five tuning-forks, embracing the middle octave of the
piano (from 512 to 1,024 simple vibrations). He even went
beyond this, filling in the same way the whole scale of per-
ceptible sounds. In the bass octaves great forks are used,
furnished with movable weights that slide along the
branches ; according to their position the fork gives different
notes. In the very high octaves Kcenig replaces the tuning-
forks by straight rods. The sonometer that he exhibited in
1867 was composed, first, of eight large tuning-forks, for
INTERFERENCE OF SOUND 223
the four octaves comprised between the doh of 32 and that
of 512 simple vibrations. Each of these could give thirty-two
notes, so that they represented a scale of 2 5 6 notes. Secondly,
the middle octave (512 to 1,024) is represented by sixty-
four; the next octave (1,024 to 2,048) by eighty-six ; and the
next (^2,048 to 4,096) by 172 tuning-forks, making a total of
330. Thirdly, from doh6 of 4.096 vibrations, Kcenig employed
steel rods, the length of which is inversely proportional to
the pitch of their longitudinal sound. Ninety-six rods thus
represent the four octaves from doh6 to doh,0 (64,000).
This last octave is almost beyond the limit of perceptible
sound ; few people can hear the sol9 (48,000) that Kcenig
obtained by transverse vibrations of a rod about three
inches long.
Two tuning-forks with an exact difference of two simple
vibrations will beat the seconds just like a pendulum ; if
they vary more, they will beat a fraction of a second as
small as is wished for. In counting these beats we may
also see another very curious phenomenon — the influence of
a movement of the sonorous source on the pitch of its note.
Kcenig took two tuning-forks, doh4, giving four beats per
second when left in their places ; he placed himself about
two feet distant from the sharper one, and moved the other
backward and forward between it and his ear, keeping his
eyes fixed on a pendulum. When the to-and-fro movement
was synchronous with that of the pendulum, the listener only-
heard three beats in the second when the low tuning-fork
approached his ear; but there were five when it receded.
It follows that the tone of this fork was raised a double
vibration during the first second, and was equally lowered
during the following one. In fact, by moving it two feet
nearer (which represents the length of its wave) a complete
224
ACOUSTICS.
vibration is gained, and by moving it an equal distance the
same is lost — just as navigators who sail round the world
gain or lose a day, accordingly as they travel with the sun,
or in a contrary direction.
Railways often afford opportunities for observations of
this kind. Thus the whistle of the engine-driver seems more
shrill when the train approaches than when it is passing
Fig. 106 — Influence of Motion on the Pitch of Sounds.
away. Taking thirty-one miles an hour as the speed of a
train, we find that it moves about forty-six feet per second,
which is •£•% of the velocity of sound ; a calculation based
upon this shows that for an observer placed on the railroad,
the note of the whistle will be changed in the ratio of
24 : 25 ; he will either estimate it too high or too low
by a semitone, according to the direction of the motion.
If it is a la for the engine-driver, it will be latt for the signal-
man at the approach of the train, aM la^ after it has passed.
A stationary whistle would have the same effect for passengers;
INTERFERENCE OF SOUND. £25
they would only hear the true note at the moment of pass-
ing. If the observer and the whistle were carried in opposite
directions, the effect would be still more striking — the note
would appear alternately a whole tone higher, and a whole
tone lower than the reality. At the moment the trains met
it would leap a major third.
In 1845, M. Buys-Ballot made some experiments of this
kind on the railroad between Utrecht and Maarsen. Three
groups of musicians were placed as close as possible to the
rails, and distant from one another about half a mile. A
musician placed upon the locomotive blew a trumpet, first
on leaving Utrecht, then between the three groups, and
finally after having passed them. The others estimated the
varying pitch of the note, and it was always found conform-
able to theory.
Mr. Scott Russell tells us that the reflection of the noises
of a train on the piles of a bridge should produce the
same effect as the contrary movement of two trains, and thus
the notes which are echoed back, altered by a whole tone,
mix very discordantly with those which are heard directly.
To obtain minor thirds by reflection, the train should move
at a speed of seventy-three miles an hour.
A German philosopher, named Doppler, has inquired
into these facts, applying them to luminous vibrations, and
the explanation of the colours of the stars ; but these are
only speculations.
CHAPTER XIIL
THE VOICE.
Organ of the Voice— Bass — Tenor — Alto — Soprano — Celeorated
Voices— Song and Speech— Vowels and Consonants— Ventrilo-
quism.
THE sublime effects of the human voice are produced by a
very puny instrument. Some cartilages, a pair of ligaments,
a group of muscles — that is all which Nature needed to create
a musical instrument, the sweetness and moving power of
which no human invention has rivalled. This vocal appa-
ratus is a reed with two lips. It is composed of the larynx,
a cartilaginous tube, which forms the " Adam's apple " in
the throat ; the vocal chords, flexible ligaments with only a
narrow slit, the opening of the glottis, between them ;
the lungs, which furnish the wind ; and the cavities of the
^nwiith, where the first rude sound of the voice is fashioned
into vowels and consonants.
The vocal chords can meet and separate, contract and
expand, by the action of certain muscles ; the current of air
proceeding from the lungs makes them vibrate, and this
vibration causes the sound. Thanks to that ingenious in-
strument, the laryngoscope, by means of which the inside
of the mouth is made visible and the formation of the
voice may be observed, the different conditions which
modify it are well known.
For the production of a chest-voice a very complete
action is necessary, and a very close contact of the two
THE VOICE. £27
sides of the glottis ; and the vocal chords vibrate throughout
their whole extent. In falsetto notes they only vibrate
partially, and the glottis opens so as to form an elliptical
orifice. Practised singers can sound the same note alter-
nately in chest-tone and falsetto, without taking breath ; but
as for Garcia's story of the Russian peasants, who sang
an air simultaneously with chest-voice and falsetto, we must
class it among the miracles.
If the voices of women be shriller than those of men,
it is because of the smaller dimensions of the larynx. The
opening of the glottis is nearly twice as large with men as
with women and children. At the age of puberty the
glottis of a man suddenly enlarges, and his voice generally
drops an octave ; it is then said to " break."
Men's voices are divided into bass, barytone, tenor, and
counter-tenor. The last-mentioned is at the present day
extremely rare. Women's voices are contralto, mezzo-
soprano, and soprano. In the following table is shown
the compass usually assigned to these different voices.
fa —
Basse. Bar?ton. Tenor. Cnntral'o. Mezzosonrano. S-i>rano.
(rr lenor.)
This shows that ordinary voices do not compass two full
octaves. The difference between the lower fa in the bass
(174 simple vibrations) and the upper sol of the soprano (1,5 66
vibrations) is a little over three octaves. But these limits
P 2
223
ACOUSTICS.
are passed by exceptional voices. On the one hand we
hear of bass voices reaching the fa of 87 vibrations; and
on the other, of sopranos that can touch fa in the fifth
octave of 2,784 vibrations, and even higher.
i
The voice of Gaspard Forster, a Dane, extended over
three octaves, while that of the youngest of the sisters Sessi
embraced three and a half. Catalani could also command
three octaves and a half.
Forster.
Farioelli.
At the Bavarian Court there were in the sixteenth
century three remarkable basses, who, according to Prae-
torius in his " Syntagma Musicum," reached the fa-x.
Christine Nilsson and Carlotta Patti attain a mar-
vellous height. When acting the Queen of Night in The
Magic Flute, Mdlle. Nilsson gives the fa5. But the
highest voice ever known seems to have been that of
Lucrezia Ajugari, whom Mozart heard in Parma, 1770. In
a letter addressed to his sister Marianne, he transcribes
THE VOICE. 229
several passages that she sang before him. We only quote
the last, which ends in dohfl.
Trills were given on the rec, and other adornments of a
similar kind. The father of Mozart adds that La Bastar-
della sang these passages with a little less power than the
lower notes, but her voice remained pure as a flute. She
descended easily as low as sol .
Oulibicheff tells of a Madame Becker, who astonished
St. Petersburg in 1823 by her wonderful roulades. Kuhlau
composed the part of Adelaide, in his opera Le Chateau des
Brigands, for her. The grand air in the third act goes up to
las. On one occasion, at the moment of giving this dan-
gerous note, the leader of the orchestra looked so fixedly at
her that she was frightened, and gave doh6.
The quality of the voice depends, as before explained,
on the number and force of its harmonics. A " true voice "
is one that passes without hesitation from one note to
another. Practice will do much to produce it, but a musical
memory is also necessary. The absolute pitch of the notes
is difficult to fix in the memory ; but it is by no means un-
common to find people, especially professional musicians,
who can give any note as it is asked for by name.
The difference between the singing and the speaking
voice consists in this : the first bounds from interval to
interval, while the conversational voice rises and falls by a
230 ACOUSTICS.
continuous motioii. The singing voice is sustained on the
same tone, as on an indivisible point, which is not the case
in simple pronunciation, where the sounds are not sufficiently
united to be appreciated from a musical point of view.
The dramatic declamation of the ancients was an approach
to song, and often had an accompaniment on the lyre. We
find a relic of it in the peculiar intonation of the Italian
orators, and in the monotone recitation heard in cathe-
drals. Recitative forms the link in modern music between
speech and song. It might even be said that up to a certain
point song is but an idealised imitation of the accents of im-
passioned speech. One may cry and complain without
singing, but both may be imitated by song. With a little
attention, too, we may find the vestiges of musical intona-
tion in common speech. The accented syllables and the
fall of phrases are marked by a change of tone. In an
affirmative German sentence, Helmholtz says, the point is
indicated by a fall of a fourth, while in an interrogation it
rises a fifth. Indications of this kind are to be found in
the Gregorian chant.
Sic can - ta com - ma , sic du - pun - eta :
FZi*~*^^*_.*__.f_-,_* '
i r i r-i3r-f-H
f
sic ve- ro punctum Sic signum in-ter-ro- ga- ti- o- nis?
In Chinese, intonation is a grammatical element
" If," said M. Ch. Beauquier, " we could translate into
musical sounds all the most singing sentences, such as in-
THE VOICE. 231
terrcgations, menaces, ironical sayings, &c., we should find
a national similarity, amongst different individuals, in accent-
ing the same phrases. The Italian modulates much, the
German less, the Englishman not at all."
The sounds of speech are divided into vowels and
consonants ; the timbre of the vowels varies according to
the resonance of the mouth, but the consonants are, as we
have explained already, little more than noises. The lips,
the tongue, the palate, the teeth, bear a part in the pro-
duction of these characteristic sounds, which make up the
framework or scaffolding of speech, and which are alone
written by the Orientals, to the utter neglect of the vowels.
The child commences with the vowels, only gradually learn-
ing the consonants, and only when he does so can his
speech become intelligible.
The letters of the alphabet have been thought by some
to have certain physiological characters. Listen to Mer-
senne. He writes as follows : —
" The vowels a and o signify what is grand and full ; and
because a is pronounced with a widely opened mouth, it
signifies clear things, and actions which are used in opening
or beginning some work. Therefore it was that Virgil com-
menced his '^Eneid' by the word Anna.
" The vowel e expresses something subtle, and is pro-
perly used in mourning and sorrow :
' Heu quoe miserum tellus, quoe me zequora possunt !'
"The vowel / means very small and slight things.
Thence comes the word minim. It expresses also something
penetrating.
"O is expressive of strong passions : O patria / O tern-
232 ACOUSTICS.
pora ! O mores ! and to represent rotundity, because the
mouth must form a circle while uttering it.
"£/ belongs to things secret and hidden."
Then he proceeds to classify the consonants. He makes
the / indicate a breath, a wind (flatus) ; s and x, bitter
things (stridor) ; r, rough, hard, disorderly things, violent
and impetuous actions, which have earned it the title of
the canine letter ; m, all that is great (magnus, monstre) ;
n, things dark, hidden, and obscure, and so on.
Boiste, in his " Observations on Pronunciation," says the
f is the soul of the French language ; it is the most variable
of all the letters, the one most capable of modulation, and
having most shades. According to the same author, " the
doubling of the f denotes either sharpness or vanity,
pedantry or satire ; it irritates, it domineers, it bites; in such
words as en cffct, qu'ai-je affaire, cela suffit, c'est affreux.
None but a born and educated Frenchman can truly pro-
nounce this." Words formed by onomatopreia imitate
natural noises ; the great poets often get very happy effects
from the different characters of consonants and vowels. In
the well-known verse of Virgil the clatter of horses' hoofs
is rendered by a succession of vigorous dactyls :
" Quadrupedante putrem sonitu quatit ungula campum."
It has been remarked that each of the vowels has its
favourite place in the musical scale. Helmholtz says that
the vowels which belong to a given note are, first, those
whose characteristic is a little higher than the note in
question, and afterwards those whose characteristic is the
octave or twelfth of the same note. The ou, whose charac-
teristic is fa.,, is produced with greatest ease on the notes 163,
THE VOICE. -33
mi2, fa2, and fa. The e prefers re3, mi^ fa, : then again fa,
and sifr, because of its characteristic fa^
This affinity of the vowels for certain fixed notes is prin-
cipally verified in the limits of falsetto and chest-voices. A
woman's voice giving a lower note than doh3 turns involun-
tarily to the o or on. Above mi4, the most easy note to
sound is a. Passing si4, i takes the ruling place. Such
facts are very important to composers, and to those who
write words intended for a musical setting.
Jean M filter and other physiologists have studied the
mechanism of the human voice, by means of the artificial
larynx, made of india-rubber bands fixed to the end of a
tube, and acted upon by pincers, which give a variable
tension. By blowing into tlvs apparatus, sounds can be
produced closely resembling those of the human voice.
To imitate the vowels, the theory of timbre shows that
it is necessary to strengthen certain fixed notes in these
sounds. Thus it is that Mr. Willis produces the vowels by
the help of a whistle mounted on a tube, which he could
lengthen or shorten at pleasure. By adding to such an
apparatus sensitive membranes to produce the characteristic
sounds of consonants, it is possible to imitate speech. We
have all heard of the dolls who say papa and mamma. Mr.
Wheatstone had a kind of bag-bipe which could pronounce
short phrases. Mersenne tells us of an organ that gave
vowels and consonants. In 1791 Van Kempelen exhibited
234 ACOUSTICS.
a speaking automaton, but the spectators did not speak very
enthusiastically of the resemblance of the artificial sounds
to the human voice.
The vocal apparatus found in birds is placed very low in
the throat. This is the reason that Cuvier was able to cut
the neck of a singing bird without preventing its song.
With men an accidental opening in the larynx renders the
formation of the voice impossible. Magendie tells us of a
man he knew who was always obliged to wear a cravat
with a valve, to stop a leakage in his throat.
The organ-stop called vox humana is only a set of very
short zinc pipes, which often give a harsh and screaming
sound, and is seldom effective.
Ventriloquists only talk like ordinary mortals, but they
avoid opening the mouth so as to be seen to speak, and
they scarcely move their lips, and breathe as little as possible.
Their voice then appears changed, and as if coming from a
great distance. This is not done without a great effort of
the lungs, which fatigues the chest, and obliges the ventrilo-
quist from time to time to resume his natural voice ; there-
fore dialogue is easy to them, while at the same time it
helps to mislead the audience. They speak also while
breathing, and the stifled sound thus produced seems to
come through a thick wall. The illusion is completed by
an imitation of the inflexions used when people call from a
distance. But when one becomes familiar with the voice of
a ventriloquist the illusion is dispelled. Robertson proved
this with a servant of his, who was a famous ventriloquist.
Ventriloquists generally find it very easy to imitate the
voice of a child ; but they can rarely sing in a borrowed
voice.
This art was known in the earliest ages ; the sorcerers
THE VOICE. 235
made use of it. Amongst the celebrated ventriloquists we
may mention Louis Brabant, valet-de-chambre of Francis I.,
Saint Gille, Baron van Mengen, Charles, Comte, &c. Of
this last they tell a number of odd stories. Once at Tours
he made them break open a closed shop, in which, from the
groans they heard, they supposed some one was starving.
At Nevers an ass suddenly declared, with strong invectives,
that he would carry his rider no further. He cured people
possessed with devils, exorcising the demons, who were
heard to fly away howling. In a church invaded by revolu-
tionists greedy of destruction, he made the statues speak,
reproaching the iconoclasts for their Vandalism ; and they
took to flight, wild with terror. Once he saved himself from
the peasants of Fribourg, who were going to burn him as a
sorcerer, by making a voice of thunder come from the
furnace towards which they led him, whereupon they fled in
disorder.
CHAPTER XIV.
THE EAR.
The External and Internal Ear — The Ossicles— The Mechanism of
Hearing — The Fibres of Corti — Inequality of the Two Ears —
Perception of the Direction of Sound.
ON either side of the head Nature has placed the ears,
commissioning them to receive and introduce to the presence
of the mind tlie sounds which arrive as invisible messengers
from Nature. It is not because there is no other way in
which the auditory nerve can be reached. We have seen
that it is possible to hear through the teeth. Deaf people
have even been known to hear by the epigastrium ; but the
natural road for sonorous impressions is by the auditory
canal.
With men and all the mammalia, the hearing organ
comprises three successive compartments — the external
orifice, the middle ear, and the inner ear. The external ear
is composed of a passage c (Fig. 107), opening out at the
base of the temporal bone, and a cartilaginous funnel.
This is a sort of hearing-trumpet, for gathering and con-
centrating the sonorous waves. When this is wanting, or is
flattened against the head, the hearing loses much of its
delicacy. In many animals this concha is movable ; horses
and dogs prick their ears, in order to hear better. The
motion is produced by the cutaneous muscle of the head.
It is a very rare faculty among men, though individuals
possessing it are occasionally met with.
THE EAR. 237
The middle ear is separated from the external by the
tympanic membrane, which closes a kind of hollow cavity
in the hardest part of the temporal bone. This membrane
receives the sonorous vibrations, and transmits them to the
interior. With birds and reptiles it is placed near the
crown of the head. The passage E forms a free communica-
tion between the membrane and the back of the mouth,
Fig. 107. -The Ear.
by which means an equilibrium is maintained between the
outer air and that imprisoned in the cavity. One can easily
experience the reality of this communication, by stopping
the mouth and the nose, and then blowing. The tympanic
membrane swells under the pressure of the imprisoned air,
and one who tries to breathe under these conditions feels it
to be drawn inwards. This explains why we should open
the mouth when standing near a cannon as it is fired. The
pressure upon the tympanum caused by the detonation is
thm diminished, by being equalised on both sides.
238 ACOUSTICS.
The bony partition opposite the tympanum is perforated
by two small holes, the one round and the other oval ;
they are both closed by fine membranes. The oval orifice,
which is above the other, communicates with the tympanic
membrane by a series of little bones. These are— the
hammer (m, Fig. 1 08), which is fastened to the middle of the
tympanum ; the anvil (ri}, resembling a molar tooth, and
supporting the head of the hammer; the little lenticular
bone (/) joining the anvil to the stirrup-bone, which adheres
by its base to the membrane of the oval
orifice. Some tiny muscles attached to the
sides of the concha can act upon the hammer
and anvil, making them turn together round
a horizontal axis ; the end of the hammer
then either draws or pushes the tympanic
Fig 108 —Ossicles membrane, and the end of the anvil acts on
the stirrup.
The internal ear, or labyrinth, is composed of the
vestibule v (Fig. 107), surmounted by three semi-circular
canals R, and the cochlea L, which has the form, both outside
and inside, of a turbinated shell. The vestibule opens on
the oval orifice, the cochlea on the round one ; but they
communicate by means of a pretty large opening. The
bony labyrinth has a lining membrane, which takes nearly
the same form, and is generally a counterpart of the ex-
ternal surfaces. It is filled with a liquid called the
vitreous fluid, and over it are spread the terminations of the
acoustic nerve N.
The process of hearing is as follows : — The vibrations
of the tympanum are communicated by the air in the
concha to the round orifice, and by the ossicles to the oval
orifice. The membranes which close these orifices make
THE EAR. 239
the fluid in the labyrinth vibrate, and consequently the float-
ing filaments of the acoustic nerve ; and thus the sensation
of sound is produced.
The hammer, probably, serves also to give a variable
tension to the tympanic membrane when we listen atten-
tively. The movement of the muscles which control it may
be voluntary. Fabrice d'Aquapendente could produce a
little noise in his ear by acting on the hammer, and Miiller
could make his ossicles crack, so as to be heard by another
person. M. Daguin observed, when he was handling some
veiy small objects in perfect silence, and let one fall by
accident, a slight tinkling, due in all probability to the same
cause. These facts prove that the hammer strains the tym-
panic membrane when one " gives ear," just as the pupil
adjusts itself to look fixedly at an object.
The tympanum is not absolutely necessary to hearing.
When it is torn the hearing is impaired, but not destroyed,
since the surrounding air then acts directly upon the mem-
branes of the two orifices.
The inner membrane of the cochlea is lined with elastic
fibres, discovered by the illustrious Corti, and bearing his
name. They apparently form the terminations of the
filaments of the auditory nerve. Helmholtz thinks that
each one is attuned to a special note, and as they are above
3,000 in number, there must be above 400 for each octave.
The interval from one to another would be ^ of a tone,
and so they form a wondrous instrument for reproducing
every note that the ear can distinguish. We have already
seen its bearing on timbre, and the analysis of harmonics.
The cochlea may, then, be called an ^Eolian harp of 3,000
strings, that move in sympathy to all the sounds of creation.
This idea has been unexpectedly confirmed by the
240 ACOUSTICS.
recent researches of M. V. Hensen on the hearing of the
decapod crustaceans. Having placed some of these animals
in sea-water, charged with strychnine, in order to intensify
the action of the nervous centres, he has seen them thrown
into convulsions at the slightest noise ; from which experi-
ment he concludes that with them audition takes place
through the medium of auditory hairs, each hair vibrating
in unison with a certain note. When he examined the point
of attachment between a nervous cord and one of these
hairs under the microscope, whilst a horn was being loudly
sounded, the point became indistinct through the rapid
motion of the hair each time certain notes were given, the
neighbouring hairs remaining motionless. One of the hairs
answered to reik and to re&3, a little more faintly to so!2, and
still less to sol. Probably it had for its fundamental tone an
harmonic common to these four notes, and situated between
re4 and re$4. Another hair vibrated under the influence of
the notes la&3, rett2, and lafl, which indicated the fundamental
tone lajfv
In the vestibule and semi- circular canals, the termina-
tions of the nerves are found to be under other conditions.
There we find some little crystalline particles, called otolithes,
and some fine elastic bristles, which seem meant to sustain
the vibrations of the nervous filaments. Scarpa and Trevi-
ranus believed this different formation of the various ramifi-
cations of the acoustic nerve must be for the purpose of
enabling us to distinguish the pitch and timbre of sounds ;
but our present knowledge of the matter does not allow us
to define everything in the wonderful organisation of the
auditory apparatus.
Paralysis of the auditory nerve causes incurable deaf-
ness. Atrophy of certain parts of the plexus, or " Corti's
THE EAR. 241
organ," explains the partial deafness which prevents
sounds of a certain pitch being heard. Many ears are
incapable of hearing very high sounds. Wollaston found
that several people were deaf to the chirping of crickets,
and some even to that of sparrows. Why may there not be
animals to whom sounds beyond the range of the human
ear are still perceptible? There are certain kinds of insects
that vibrate, just like our well-known crickets, without making
the faintest audible sound : may it not be that there is, in
truth, a delicate music audible only to its proper listeners ?
Musicians have been known to play in the orchestra,
and to be aware of the slightest falsity in tune, who yet could
not join in a common conversation without the help of an
ear-trumpet. Mr. Willis describes a singular phenomenon
under the name of paracousis. Some people who have
imperfect hearing, and cannot in general hear faint sounds
at all, hear them at once when they are accompanied by a
great noise. Mr. Willis knew a lady who made her servant
beat a drum whenever she wanted to listen to anything, for
then she could hear very well. Another person could only
hear when the bells were ringing. Holder mentions two
similar cases : one of a man who was deaf except when
they beat a large drum close beside him, and another of
one who never heard so well as when he was rattling over
a stony road in a carriage. There was a shoemaker's ap-
prentice, too, who only heard while his master was beating
the leather on the stone. Such facts may perhaps be
explained by the habitual relaxation of the muscles of the
hammer, which would render them incapable of acting on
the tympanic membrane, except under the excitement of
very strong vibrations.
With many people the ears are unequal in their power
Q
£42 ACOUSTICS.
of hearing. From M. Fechner's experiments it seems that
the left ear generally hears better than the right. He
thinks that the reason may be the common habit of sleeping
on the right side. Ittard mentions a remarkable instance of
a man he knew, whose two ears heard different notes at
the same time when a single one was given. M. Fessel,
of Cologne, lately discovered the same peculiarity in
himself. In setting some tuning-forks — first by his ear,
and then by a more exact process — he noticed that all which
he had set by his right ear, while holding the normal or
pattern tuning-fork to his left, were too low, while the
others, set in the opposite way, were too sharp. It follows
that the same sound is sharper for his right ear than for
his left. Much struck by this circumstance, he examined
the hearing of many persons, and found it a much more
common thing than could have been imagined. So that
we might ask a musician for the right la or the left. M.
Fessel even supposes that the phenomenon is objective, and
that the same tuning-fork really gives a higher note when
it vibrates before the ear to which it appears sharper.
This note of resonance is heard in the same way by an on-
looker. He asked different persons of his acquaintance to
carry alternately to the right and left ear two duplicate
tuning-forks; and according to the notes they heard, he
could tell by which ear they heard too high or too low. But
such facts need verification.
As the two eyes serve to give us the impression of the
geometrical relief of a body, so the two ears allow us to
judge of the direction of sounds. When the eyes are blind-
folded, and one ear stopped, all sound seems to come in the
direction of the free ear; or, at least, our inference as to its
direction is very uncertain.
THE EAR. 243
It is the concha of the ear that specially helps to arrest
attention, and to recognise the direction of sonorous waves.
Diderot tells us of a blind man who, when disputing
with his brother, took up something and threw it very neatly
at his head, his aim being guided by his ear.
The hearing of the blind is generally very acute and
delicate, because it has to serve them for. the most part
instead of sight. Ittard invented an instrument, which he
called an acoumeter^ to measure the delicacy of hearing. It .is
a brass ring, hung upon a thread, and struck by the ball of
a pendulum which falls from a given height. The distance
at which different persons cease to hear it is accurately
measured. Freycinet used this instrument for studying the
hearing of savages. In nocturnal birds and timid animals,
such as the hare, the external ear is largely developed. The
ears of the lower animals are incomplete. The cavity of
the tympanum is entirely wanting in fish, the round and
oval orifices being at the top of the head. The articulata
do not show any visible auditory apparatus. Amongst the
molluscs, the cephalopods are the only creatures that possess
a vestige, and there it is of the simplest form, consisting
merely of a cavity and acoustic nerve.
CHAPTER XV.
MUSIC AND SCIENCE.
Principles of Music — Euler — Rameau — Sauveur — Helmholtz — Har-
mony and Discord Explained by Beats — Chords — Major and Minor
Keys.
THE disdain with which the majority of musicians reject all
attempts of the exact sciences to invade their domain is, up
to a certain point, justifiable.
The help that mathematics has hitherto given to musical
science is very slight ; it has scarcely done more than point
out a few vague analogies which explain nothing. It has
travelled in a defective circle ; the pleasure of the ear has
been exalted into a principle, and made the foundation of
all systems.
It was known that harmonious chords correspond to the
relations of whole numbers. The Pythagoreans propounded
and repropounded this theory, without deducing from it any
other conclusion than some aphorisms upon the harmony of
the world, and the occult power of numbers. Philosophers have
attempted to find the seven notes of the scale repeated in
the movements of the celestial bodies, and even the great
Kepler abandoned himself to such mystical speculations.
In the first half of the eighteenth century, towards 1740,
the great mathematician, Leonard Euler, endeavoured to
explain the relations of musical intervals by considerations
drawn from physiology. He reasoned thus : That which
pleases us is always that which to our feeling possesses a
MUSIC AND SCIENCE. i*45
certain perfection ; and wherever there is perfection there is
necessarily also order — that is to say, some law which
governs. A song will please us if we recognise the order of
the sounds of which it is composed ; and it will please us so
much the more in proportion as we are able to understand
that order. Now, there are in sounds two ways in which
order may manifest itself — by their pitch, as represented by
high notes or low notes, and by their duration. Pitch is
reckoned by rapidity of the vibrations, and duration by the
length of time during which a sound is heard. Order with
regard to duration consists in rhythm or time ; order in
pitch is simple proportion amongst the vibrations. The
degrees of accord in these proportions — that is to say, in the
musical intervals — depend upon their simplicity, for the ear
appreciates them so much the more easily as they are ex-
pressed by the most simple numbers, and the pleasure is
greatest when it costs us least. In developing these principles
Euler succeeded in establishing the laws of harmony.
That which is wanting in his theory is, that it is not
based upon any certain fact. Nothing warrants us in
admitting that the ear can judge of the relations of vibra-
tions which depend on the thousandth part of a second.
The observations of astronomers show that the ear separates
at the most two strokes of a pendulum which vibrates in
a tenth parth of a second. How can it be supposed that it
can compare the proportion between two vibrations num-
bering, for example, 5,000 and 5,050 ? And nevertheless it
easily recognises this relation in so many musical intervals.
Ideas analogous to these of Euler had been already put
forward in 1701 by Sauveur. "The mind," he says, "by
its very nature loves, at the same time, simple perceptions
because they do not weary it, and varied perceptions because
246 ACOUSTICS.
they spare it the ennui of uniformity. .... Every
variety which pleases the mind is then confined in certain
limits ; it must be guarded from becoming difficult to per-
ceive, confused, complicated . . ." He then explains
how chords are rendered agreeable to the ear by the more
or less frequent concurrence of vibrations. When these
concurrences become rare, as in thirds where they occur
only once in five or six vibrations, the perception of the
sound becomes less simple, but it is nevertheless pleasant
because it is slightly varied, the discords putting the har-
monies in still stronger contrast.
But there is a point at which the harmony of this variety
stops, and this point is given by the ratio 5 : 6. Sauveur
afterwards remarks that harmonies do not make beats, and
that discords do. Unfortunately, he has not developed this
idea as it deserves.
In 1726, Rameau started another theory, which D'Alem-
bert thought worthy of notice. It seems, at first, to account
for the pleasure that music gives us. It is very curious to
see the means that this celebrated artist has taken to dis-
cover what he calls the principle of harmony.
" I saw," said he, " that I must follow in my researches
the same order that exists in the things themselves ; and
as, to all appearance, there must have been song before there
was harmony, I asked myself in the first place how song
was obtained.
" Enlightened by the method of Descartes, which I
had happily read, and with which I had been struck, I began
with myself. I tried some songs, like a child who is
practising singing ; I watched what took place in my mind
and in my voice, and it always seemed to me that there was
not any reason that decided me, when I had uttered a sound.
MUSIC AND SCIENCE. 247
to choose one more than another of all the multitude of
sounds that might come next. There were certainly some
for which my voice and my ear seemed to me to have a
predilection, and that was the first thing I noticed ; but this
predilection appeared to me purely a matter of habit. I
imagined that in a different system of music from ours, with
another kind of song, the predilection of the voice and sense
would have been in favour of another sound ; and I con-
cluded that, since I found in myself no good reason to
justify this predilection and to regard it as natural, I must
not take it as a principle in my researches, nor even sup-
pose that it would exist in another man who was not in
the habit of singing or of hearing it."
He declares, however, that the sounds which had seemed
to him to succeed each other most naturally were the fifths
and the thirds, or the sounds which correspond to the
relations of 2 to 3, and of 4 to 5. But this simplicity of
relations appeared to him to be only a sort of convenient
arrangement, and insufficient to account for a phenomenon
such as that which he sought to explain.
" I began," continued he, " to look around me, hoping
to find in nature that which I could not discover in myself
so surely or so clearly as I desired. The search was soon
rewarded : the first sound which struck my ear was a clap
of thunder. I suddenly perceived that it was not one, and
that the impression which it made upon me was complicated.
'That, said I, is the difference between noise and sound.
Everything that produces a simple impression upon my ear
is noise, and everything that produces an impression com-
posed of several others is sound.' I called the primitive
sound a fundamental tone ; its concomitants, harmonics."
He afterwards discovered that harmonics are very sharp
248 ACOUSTICS.
and very transient, so that they cannot strike equally a
musical ear, and one lacking in musical sensibility. Then
he decided that the complementary sounds of the funda-
mental tone must be its twelfth and its seventeenth — that is,
the octave of the fifth and the double octave of the major
third. Then, as he knew by experience, as he says, that
the octave is only a repeat, he thought it quite natural that
his voice and his imagination should lower the harmonics
to the last point ; and that, therefore, his fancy should be
taken by the third and the fifth of the fundamental tone,
and not by their repeats, when he took the notes that his
ear suggested to him after the fundamental tone.
Thus the multiple resonance of the sonorous body be-
comes the base upon which is built the musical system.
Rameau deduces from it the formation of the diatonic scale
and the principal rules of harmony. But his fertile imagi-
nation led him afterwards to attempt to draw from the same
source the principle of geometry; and it is here that
D'Alembert, to whom is due the merit of developing and
simplifying Rameau 's system, ielt himself obliged to place
his veto, and to circumscribe clearly the range of the musi-
cian's discovery. D'Alembert continually asserts that the
demonstration which Rameau pretends to have given of the
principles of harmony is no demonstration, and that there
will always enter into the theory of musical phenomena a
sort of metaphysics, which introduces into the science an
obscureness natural to itself. "But," says he, "if it be un-
just to demand here the unshaken complete assurance which
is produced only by the clearest light, we doubt at the same
time whether it would be possible to throw upon these
matters a stronger light than that which we have already."
The judgment that D'Alembert passes upon Rameau's
MUSIC AND SCIENCE. 2-49
system proves sufficiently that the illustrious mathematician
understood perfectly well its weak points, or, to speak more
correctly, its insufficiency. It is not enough to say that the
octave is a repeat ; the word does not sufficiently account
for the important part that this interval plays in musical
compositions ; and, on the other hand, the phenomenon of
harmonic resonance is not so general as Raineau supposes.
A large number of sonorous bodies produce in reality en-
tirely dissonant simultaneous sounds. It is therefore not
right to lay it down as a principle that harmonics are found
by natural resonance ; and even if it were true, we must
remember that the ugly has quite as much a place in nature
as the beautiful, which proves that a thing may be at the
same time natural and disagreeable.
It must then be acknowledged that this theory has not a
rational foundation, since it does not explain in any way the
origin of discords. Nevertheless, we cannot but admire
the ingenuity with which Rameau has deduced his system
from data so incomplete ; and it may be said, without exag-
geration, that he has inaugurated a new era in the theory of
music.
The celebrated Tartini published in 1754 a treatise on
Harmony, in which he took as his starting-point resultant
tones, which he thought he had discovered, and which he
had observed when he played two chords at once. Tartini
calls such tones of the series i, 2, 3, &c., monad harmonics y
from the concurrence of which results a sound All har-
mony, he says, is comprised between the monad, or com-
ponent unison, and the full sound, or compound unison.
He then enumerates the resultant tones of musical in-
tervals, always mistaking the octave, and finds that the
different intervals may be so arranged as to give the same
250 ACOUSTICS.
resultant tone, which may be considered, therefore, their
common base, &c. &c.
At this time the theory of music had not emerged
from a circle of ideas completely estranged from natural
philosophy and physiology. Generally, the propounders of
systems have lost themselves in mystical speculation. The
German philosopher Herbart travelled in this track ; ac-
cording to his views any two sounds suggest to the mind two
ideas, which exercise at once an attractive and repulsive
force. In the soul of the fifth, hate has just overcome
love ; in the major third, the two powers keep an armed
neutrality. The most curious conclusion is, that the
adjusted scale is that which satisfies most fully the musical
ear! and that Herbart was the first to lay the foundations
of a mathematical psychology.
Aristoxenus had eagerly combated the arithmetical sub-
tleties of the Pythagorean school. He has found many
imitators among musicians of modern times. The Spaniard
Eximeno published, towards the end of the last century, a
work in which he demonstrates that music has no manner
of connection with mathematics. This must still be the
opinion of M. Fetis, to judge from the preface to his " Traite
d' Harmonic."
This learned theorist describes in the following terms his
discovery of the principles of harmony — a discovery which
he made one day in May, 1831, as he was travelling from
Passy to Paris, and which caused him such emotion that he
was obliged to seat himself at the foot of a tree : — " Nature
furnishes us, for elements of music, with only a multitude of
sounds, which differ among themselves in intonation, dura-
tion, and intensity, in a greater or less degree.
"Amongst these sounds, those which differ sufficiently to
MUSIC AND SCIENCE. 25 1
affect the sense of hearing distinctly become the objects of
our attention ; the idea of the relations which exist between
them becomes present to the intelligence, and under the
action of sensitiveness on the one hand, and will on the
other, the mind arranges them in different series, of which
each one corresponds to a particular order of emotions, of
feelings and ideas.
"These series become then the types of tones and rhythms
which have necessary consequences, under the influence of
which the imagination comes into exercise, in the creation
of the beautiful."
After such assertions, ought he not to have made the
scale ?
There appeared in Germiny, in 1863, a book which
made immediately a great sensation. It was " La Theorie
de la Perception des Sons," by Helmholtz.* The illustrious
author has succeeded in reducing to physical phenomena,
susceptible of being submitted to calculation, the secret re-
lations of sympathy and antipathy which exist between
natural tones, and explaining the cause of the sensations
which we experience from them.
M. Helmholtz is Professor of Physiology at the Univer-
sity of Heidelberg, which boasts also Kirchhoff and Bunsea
Already illustrious by the discoveries with which he has
enriched physiological optics — it is to him that we owe the
ophthalmoscope — and by other scientific researches, he was
the man who was needed to find the answer to an enigma
two thousand years old.
We have already spoken at length of the researches to
which M. Helmholtz devoted himself, with the object of
* Die Lehre von den Tonenipfindungen.
252 ACOUSTICS.
discovering the true nature of tone, and we have mentioned
his experiments on beats and resultant tones. It was in
that way that he discovered the key to harmony, the true
principle of concords and discords.
It is necessary to fully understand his ingenious argu-
ments, and with that view we first consider beats. The
disagreeable sensation that they give us is easily explained.
All intermittent excitement of the nerves tires us. We know
the unpleasantness of unsteady light like that of a flame
blown by the wind. A strong steady light soon dulls the
irritability of ths retina, just as continued pressure hardens the
skin ; a flickering light, on the contrary, or a rapid and oft-
repeated pressure, allows the nerves to retain their sensibility,
and becomes for that reason a source of pain. Tickling
excites the epidermis in the same way an intermittent sound
irritates the ear, and hence it is that beats are felt to be a
source of discord.
Sauveur had divined the same reason. "Beats," he
says, "do not please the ear, because of the inequality of
the sound, and it is very probable that it is the absence of
these beats which renders octaves so agreeable. Following
out this idea, it appears that the chords in which the beats
are not heard are just those that musicians call harmonies,
and that those in which the beats are perceived are discords;
also that when a chord is discord in a certain octave, and
harmony in another, it is because it beats in one and not in
the other ; it is then called an imperfect concord. If this
hypothesis be true it will reveal the true source of the rules
of composition, till now unknown to philosophy, which
referred almost entirely to the judgment of the ear. Natural
judgments of this kind, however foolish they may some-
times appear, are not in reality so ; they have some very
MUSIC AND SCIENCE: 253
real causes, the knowledge of which belongs to Philosophy,
provided she were able to put herself in possession of it."
Sauveur (or rather Fontenellc, the historian of the
Academy) adds afterwards, in returning to this idea, that
what is real harmony of chords has probably not been
fixed by Nature, and that what is called a fine ear is quite
as much the result of long custom, of old habits, and of
arbitrary prejudices, as of an inborn faculty. He would
thus explain the great difference that is found between
nations in their taste for music.
These ideas were not further developed, and they fell
into oblivion. It is only recently that M. Helmholtz has
entered upon the same investigation with all the resources
of modern science, and has unravelled the physical principles
of harmony.
In studying beats, M. Helmholtz first proves that the
degree of roughness which they give to a musical interval
does not depend solely upon their frequency; they become
less irritating in the bass octaves, where the same number of
beats correspond to a larger interval. Thus, the minor
second, si3 — doh4, is very discordant, while the fif.h, doh — sol,
is a harmony ; and yet these two intervals give alike thirty-
three beats in a second. This circumstance is explained by
the greater difference of the strings, which answer to a larger
interval. The sol does not vibrate the string allotted to
doh, and the doh does not vibrate the string sol, whence it
follows that resonance is powerless to unite the two notes on
the same string, and to give rise to beats ; on the contrary,
the notes si and doh make a great number of strings vibrate
in common, which renders their beats perceptible to the
acoustic nerve.
When the beats are observed in two tones between
254 ACOUSTICS.
which the interval is very great, the phenomenon is due to
the harmonics, or rather to the resultant tones. Thus doh^
the harmonic of doh, will beat with all the notes which it
may happen to approach ; for instance, with re2 or si, even
when these notes occur as harmonics of another fundamental
tone. Two tones, too far removed to touch each other
directly, may then be in opposition through the medium
of their satellites; thus, mi3, the harmonic of doh, will
beat with mit?3 which carries the colours of lat>. But the
struggle may even take place under the same roof; when
two harmonics of the same note find themselves too close
together they quarrel. Thus, the harmonics 8 and 9,
or 9 and 10, which differ only by a tone, always beat,
and disturb the internal harmony of the tone, wherever they
are at all prominent. Their presence explains the harshness
of the trumpet, and of strained bass voices.
When two sounds of whatever tone make exactly the
octave, the harmonics of the sharper note are superposed
upon the harmonics of the flat
Doh ... i 2 3 4 5 6 7 8 9 10 ...
Dohs... 2 4 6 8 ip . . .
doh doh, sol, doh, mi, sol#3 las doh« re« mi4 ...
From that time there are no more beats ; but however little
the chord may be disturbed, we become aware of it by the
great tumult that the divided harmonics produce. The
doha will beat with the untrue doh2, the doh3 with the untrue
dohv and so on.
The reason why the octave is the consonant interval par
excellence of which the ear has the most correct appreciation
is easily seen. The virtual or eventual beats of the harmonics
MUSIC AND SCIENCE. 255
distinguish it by their energy, the least discord betraying itself
by a great cacophony. The other concords are much less
characteristic, as we shall see. Take, for instance, the
twelfth 1:3, and the following will be the order of the two
series : —
Doh... I 23456789..*
I I I
Sol ... 3 6 9 • • •
doh doh, sola doh, mis sol, . . . doh4 re* . • •
The coincidence of the harmonics again takes place
here ; but it is less important. If the doh be a little untrue,
the harmonics 3, 6, 9, which it has in common with the sol^
are divided and beat ; but they are weaker than the har-
monics of a less elevated order, which divide when the
interval of the octave is adjusted; their beats are not so
perceptible, and then the concord is less distinct.
The other concords — fifths, fourths, thirds, &c. — contain
already elements of discord ; here the harmonics are super-
posed only partially, but there remains the germ of discord.
Thus, for example, in the fifth : —
Doh... 2 4 6 8 10 12 . . .
I I
Sol ... 3 6 9 12 ...
doh sol doh, sol, doh, re, tnis sol, ...
The so!2 and the so!3 are, at the same time, the harmonics
of doh and sol, and coincident when the fifth is exact ; but
the re3 of the series of SOL can beat with the doh3 and the
mi3 of the series of DOH. The concord of the fifth is then
not absolutely pure, besides which it is less characteristic
than the octave; for a false fifth only makes those harmonics
256 ACOUSTICS.
beat which are of the same class as those that beat a false
twelfth.
The same may be said of the other harmonious chords.
The more slightly raised the harmonics are which form
the coincidence, the purer is the interval, and the better dis-
tinguished by the eventual beats of these harmonics.
In the intervals where there exist harmonics which have
the power to disturb the chord, it is necessary to take
account of the juxtaposition more or less close of these
notes, for the beats will be so much the more slow in pro-
portion to their nearness. We have already said that the
impression made by thirty-three beats in the second is very
disagreeable ; beats much more rapid than this cease to be
perceptible ; and very slow beats, instead of annoying the
ear, give to the music a solemn character, or an expression
of trembling emotion like that produced by the tremulo of
the voice.* It follows that an interval will be so much the
more discordant, as it supplies a larger number of less
elevated harmonics which are able to produce beats of a
certain rapidity.
On these principles it is easy to calculate a priori the
degree of purity of different intervals considered in all parts
of the musical scale. M. Helmholtz calls an interval in which
one of the two given notes coincides with a partial tone of
the other, an absolute or free consonance, for in that case
there is also coincidence between all the respective har-
monics. To this category belong unison, successive octaves,
the twelfth, seventeenth, &c. The intervals which imme-
diately follow in point of purity are, first the fifth, then the
* There is found in modern organs, in fact, a regular arrange-
ment for making beats. The effect of the register called nnda marts is
made also ty slow beats.
MUSIC AND SCIENCE.
fourth, which may be called perfect
concords ; the major sixth and third
are medium concords ; the minor sixth
and third are but imperfect ones. Yet
the beats of the thirds are very sensible
in the deep notes of the scale, and
they were not admitted into the group
of imperfect concords until the end
of the twelfth century. The employ-
ment of minor sixths and thirds is never
justified except by necessities in the
formation of chords.
If the intervals be split, the major
fifth and third are improved (they
change into the major tenth and
twelfth) ; the fourth, the minor third,
and the sixth, on the contrary, become
more discordant.
M. Helmholtz tried to make these
phenomena, and the laws which regulate
them, evident by means of a figure,
which represents in a very irregular
curve the relative degree of discord or
any two notes of a violin, calculated
according to the intensity and frequency
of the beats of the superior tones of
those notes, supposing that the highest
effect would be thirty-three beats in a
second. Upon a straight line, by which
is represented a note which, starting
from doh3, rises by insensible degrees to
the double octave dohs, stand the Cor-
257
258 ACOUSTICS.
dillera of displeasure (Fig. 109). Valleys mark the position
of unison of the fifth, the octave, the twelfth, and the double
octave. The Chimborazo of discord occurs quite close to
unison, where the least discord produces the most percep-
tible beats. More or less distinct unevenness distinguishes
the other discordant regions ; and more or less deep depres-
sions, the various degrees of concord.
The influence of resultant tones is in every way analogous
to that of superior or harmonic tones. The union, then, of
two tones accompanied by their harmonics, the first differen-
tial sounds, produces only the beats pointed out as being
those of harmonics ; and, as they are in general much more
feeble than harmonics, the consideration of them is less
important for practical purposes, where we have to do
only with musical tones that have harmonics; but in treating
of simple tones, it is necessary to have recourse to the beats
of resultant tones, to account for discords, and to characterise
harmonics. Thus the first differential sound of the octave
coincides with the deepest of two given notes, and can
therefore beat with it, since the chord is disturbed; and
this is one means of judging of the accuracy of an octave
formed by two simple notes. The fifth again, and perhaps
also the fourth, are characterised by resultant tones; but
the other intervals lose all clearness and decision when
only simple tones are employed. And this is, in fact,
the reason why empty harmonic tones are improper in
musical harmony: they can only be used to strengthen
richer tones. This remark applies, for instance, to the large
closed pipes of an organ. If a piece of music be played
upon an organ with the register closed, it has neither
character nor energy ; the absence of harmonics makes it
very difficult to distinguish harmonies from discords, and
MUSIC AND SCIENCE. 259
this want of clearness renders the music so weak and soft
as to be tedious.
The sound of the flute contains, besides the fundamental
tone, its sharpened octave, and sometimes the twelfth ; the
intervals of the octave and the fifth are well denned ; the
thirds and sixths only very indistinctly. It is a common
saying that the worst thing in the world after a flute solo is
a duet on two flutes ; yet this instrument becomes very
useful when it is played in concert with others which have
more energy. The same thing may be said of harmoniums
with diapasons. Therefore we see that the quality of
musical intervals varies necessarily with the tone of the
instruments.
The most extended analysis of the sound of instruments
has shown that the ear delights, above all, in tones in which
the two first harmonics (octave and twelfth) are strongly
accentuated, the two following somewhat modified, and the
others less and less perceptible. Taking this as a starting-
point, it is easy to explain the particular effect of each
instrument, and to establish a priori a number of practical
rules known to musicians.
It is clear that the consideration of beats helps to the
understanding of the part that whole numbers play in the
fixing of musical intervals. Fourier's law, in virtue of which
every sonorous movement is an accumulation of simple
notes, becomes thus the true base of counterpoint, since
concords are derived from the superposition of partial sounds,
and discords from their antagonism.
We have now to speak of sounds with respect to their
effect produced when they are combined in music ; this
subject encroaches upon the domain of aesthetics, where we
have no longer fixed and invariable principles to guide us
R 2
260 ACOUSTICS.
like those of purely physical sciences. Musical scales,
modes, &c., have been developed, step by step, in the course
of centuries; and the changes that the tastes of different
nations have wrought in them are a sufficient proof of the
instability of their foundations. The science of counter-
point is based, in part at least, upon laws capable of improve-
ment, and it would be rash to affirm that it has yet reached
its last point of development. Nevertheless, here again we
find some general laws which seem to have guided artists
unknown to themselves, and which spring naturally from
those which we have already established. These laws prove
the philosophical necessity of rules to which ignorant
groping has led.
Thus the formation of multiple chords rests upon the
same principles as that of consonant intervals. It is necessary
that the three intervals between the three notes which com-
pose a triple chord should be separately consonant, in order
that the chord may be so. Intervals which exist in dif-
ferent chords may be classified under different degrees of
consonance.
The difference between major and minor modes may
consist in the resultant tones which are formed by the com-
bination of three notes. In major chords the resultant
tones are only repetitions of notes given in lower octaves.
It is found that in minor chords this does not happen ; the
resultant tones there are formed by the harmony, and
form major chords which accompany the minor. This
intervention of a strange element, and probably also the
very feeble beats of resultant tones of the second order,
give to the minor chord something mysterious and un-
decided, that all musicians have felt without being able
to account for.
MUSIC AND SCIENCE.
26l
In the accompanying example the major and minor
chords are printed in minims; the resultant tones of funda-
mental notes, in crotchets ; the resultant tones due to the
combination of fundamental notes and harmonics, by quavers
and semiquavers. A rest placed after a note denotes that it
is slightly higher than the sound it ought to represent.
Passing on to the melodious combination of sounds, we
find that melody depends like harmony upon the phenome-
non of superior tones, inasmuch as these tones determine the
affinity of sounds, just as the affinity of chords results from
the notes which are common to them. Melody is the
succession of notes following each other in an order pleasant
to the ear. According to Rameau and D'Alembert, it springs
262 ACOUSTICS.
from harmony, and the effect of it will be found expressed
or unexpressed in the harmony, and especially in the un-
expressed fundamental bass. But as homophonous song
existed long before polyphonous music, or music in har-
mony, we are compelled to seek an independent origin for
melody.
We notice first that melody is a movement which is
produced by a change in the height of notes, and which we
can conceive imitated by mechanical movements. But the
mind would not have been able to appreciate, or even to
feel, these shades of expression if the progression of the
notes had not been arranged according to a definite value
— that is, by intervals of tones or half-tones, and in a fixed
rhythm.
The bar helps us to divide time; the progression of
notes by tones or semitones allows us to separate the
height of notes into fractional parts ; and thus we understand
movement by rhythm and melody. The sensations that we
experience at the sight of a rough sea, when the waves follow
each other at regular intervals, are of the same nature. In
the voice of the wind the notes blend without intermission,
therefore they produce upon us a painful and confused
impression, through the absence of all proportion and
distinctness. Music, on the contrary, has a standard for
measuring the ascending and descending movement of tones,
and this standard is the scale.
But why were the notes of which the scale is composed
adopted? Was there a reason for it? Why do we find
there the octave, with its fifths, fourths, and thirds? The
answer is easy, after what we have already remarked concern-
ing partial tones or harmonics. The following table repre-
sents the harmonics with consonant intervals :—
MUSIC AND SCIENCE. 263
Tonic (i) 123456789
Octave (2) — 2 — 4 — 6 — 8 —
Twelfth (3) — — 3 _ _ 6 — — 9
Fifth (!)— —3— _6— —9
Fourth (|) __— 4 _ _ _ g —
Third (f) — -5-
Third (f) _____ 6 — — —
The octave with its attendant harmonics being com-
prised in the tone of the voice, it is clear that in ascending
the octave a fractional part of the tonic is constantly re-
peated. Therefore we may say, with Rameau, that the
sharpened octave simply answers to the tonic, the harmonics
of which, 2, 4, 6 ... .it reproduces. It is in this sense
that the successive octaves of a key-board are only repe-
titions of the same scale.
The twelfth, being the third partial tone of the tonic, is
equally expressed by the tonic, but less completely than the
octave, because it only produces the harmonics 3, 6 ...
of the tonic. Lowering it an octave, we have the fifth, of
which the second partial tone reproduces the harmonic
3 of the tonic, the fourth the harmonic 6 of the tonic,
and so forth. The fifth is then, again, a partial echo of the
tonic ; but at the same time it contains new notes which are
not comprised in it, and has therefore less affinity for
the tonic than the octave and the twelfth. The affinity of
the fourth is still less, for there it is only the third partial
sound, which corresponds with the fourth of the tonic.
Therefore it was that the polyphonous songs of the Middle
Ages were accompanied by fifths. The thirds and sixths
answer to the tonic still less perceptibly ; they were intro-
duced into music only at the time when tnie harmony began
to develop itself.
M. Helmholtz calls those tones which have at least
264 ACOUSTICS.
one harmonic in common, affinities of the first degree ;
and two sounds which have an harmonic in common with a
third sound, he calls affinities of the second degree. Build-
ing upon this foundation, he succeeded in constructing in a
very reasonable manner a diatonic scale of notes, which
have either the first or second degree of affinity for the
tonic.
The direct relatives of the tonic doh are composed of
the notes doh2, sol, fa, la, mi, and mi,, if we stop at the first
six harmonics, the others being too weak to determine the
affinity. We have then the scales —
Doh mi — fa — sol — la doha ;
or —
Doh mifr — fa — sol — la doh2 ;
for two notes so similar as mi and mi ? could not be intro-
duced into the same scale.
In order to divide the two excessive intervals which exist
in this series, it is necessary to have recourse to the rela-
tives of sol, which consist of the notes doh, re, mip, si, doh2.
The re and the si are united to doh by an affinity of the
second degree, and by inserting them into the scales given
above, the diatonic scale
Doh — re — mi — fa — sol — la — si — doha
is obtained, which becomes the minor ascending scale if we
put mifr in the place of mi. The re which would be taken
amongst the relatives of fa, would differ by a comma from
the re fixed by sol. These examples suffice to render the
method followed by M. Helmholtz comprehensible.
In studying the rules of harmony, it becomes evident
that chords, considered as complex sounds, have amongst
MUSIC AND SCIENCE. 265
them the same relations of affinity as the notes of the scale,
in consequence of the coincidence of some of their notes.
The importance of the tonic in modern music, or that which
M. Fetis calls the principle of tonality, is also explained by
the nature of the superior tones of the tonic. These clear and
simple principles have allowed of the fundamental rules of
composition being deduced from mathematical considera-
tions, which M. Helmholtz has done. Nevertheless, it
must be confessed that the theory of music is not yet com-
pleted ; all the deductions that M. Helmholtz has drawn
cannot be considered fully proved, and they are not univer-
sally admitted. For instance, M. Arthur von Oettingen
has criticised (and with reason) the explanation that M.
Helmholtz gives of the difference between major and minor,
for the phenomenon of harmonics is sometimes very little
apparent. M. d'Oettingen traces this difference to the re-
ciprocal principles of tonics and phonics.
The tonicity of an interval or of a chord consists in the
possibility of considering it as a group of harmonics having
the same fundamental tone. Thus, the major chord is formed
of the harmonics 4, 5, 6 of the tonic, or fundamental bass,
i. The phonicity of that interval would be th2 inverse
property of having an harmonic in common ; the minor chord
i> i> i nas tne tone I as its common harmonic or phonic.
The major chord has for its phonic 60 ; the minor chord has
for its tonic ^. The relations may be explained as follows:
A - i '. i ' 1 - * 4-5-6-6o
Tonic — Minor — Phonic Tonic — Major — Phonic
chord
fa — la-doh-mi —
mi
chord
doh — doh-mi-sol —
Musicians call doh the tonic, and sol the dominant, of
266 ACOUSTICS.
the scale of doh major, which may be written in this
way : —
Doh re mi fa sol la si doh
i 8 I ! i i ¥ 2
M. d'Oettingen calls mi the phonic, and la the leading
note, of la minor ; and writes this scale in the following
manner : —
Mi fa sol la si doh re mi
In developing this dualism he establishes the parallel con-
struction of the major and minor modes. But we must
draw to a close details which have, perhaps, already weaned
the reader.
If it be possible thus to establish a priori the most im-
portant laws of music, however grand may be the result
with regard to the philosophy of the art, it does not follow
that the knowledge of these laws is all that is required in a
musician. We must here repeat what D'Alembert has said
in the preface to his book on music : " Nature must do the
rest ; without her, no one will compose better music for
having read these elements, any more than he would write
good verses for possessing Richelet's Dictionary. In a
word, it is the elements of music that I pretend to give, and
not the elements of genius."
In the works of art that we admire, we instinctively
divine a secret law which the artist has obeyed, however
ignorantly, and it is in this sense that we must use the words
of Leibnitz so often quoted : Musica est exerdtium arith-
metier occultum nescientis se numerare animi
When the law is so manifest that it instantly strikes the
eye, we feel the intention and the calculation, and the work
MUSIC AND SCIENCE. 267
does not move us ; for one essential condition of admira-
tion is, not to understand completely. Admiration ceases
as soon as we feel ourselves on an equality with the
artist. This is the unconscious law which distinguishes a
work of art from a systematic and calculated production ; it
must not therefore be supposed that science can, or ought
to, discover and lay bare all the resources of the creative
intellect
THE END.
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