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The UNIVERSITY of ML OMU 



KDMONI) I, GOOLD 







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f^4r 



VV - W>- 




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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 x aL P 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 f eet j i n 
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 f eet - ^ 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 



8 4 



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, sol a , doh a , re v soly 

Kircher thinks this contrary to the laws of harmony, and 

Substitutes 

sol, si, re, sol a , si,, re a , 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- 3 8 - 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. IO 9 

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- 
Fi g . 49.-Th e Pendulum. ijb r j um 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. 5 8.-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 

ta 9 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^/ < //V l 



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 



I 4 8 



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 t y 
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 doh 10 ; then he went to re 10 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 doh 7 , 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 re 7 , which corresponds to 9,400 
vibrations. 

We may take as the extreme limits of the human voice 
the fa-, of 87, and the doh 6 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 : doh 2 means 
the upper octave of doh (we never write doh,) ; doh 3 is the 
upper octave of doh 2 , 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 doh a 
Doll re 2 . 
Doh mi a 
Doh fa a . 
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 Ia 3 810. 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 Ia 3 (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 



! 7 6 



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 



I8 4 



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. 

doh a for the fundamental sound, we have the following 

series : 




doh, doh, so! 3 doh. im\ sol, latf, doh s 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 mi 6 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 



i 9 6 



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 doh 2 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 doh 3 . 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 doh 3 , 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^--?^ 

^^"^^^5 a ^^ 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 fa 4 ; a was obtained by giving sit> 2 , sii? 3 , and 
fa, moderately, and sifr 4 and re s with full force. The tuning- 
fork having siir 2 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 o f 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 si s and doh 6 ) 
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 doh 2 and 
so! 2 we can obtain doh t and mi 3 , 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 doh 9 of 32,000 vibrations, and a re 9 of 
36,000, by their differential sound the doh 6 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 doh 6 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 doh 6 to doh, (64,000). 
This last octave is almost beyond the limit of perceptible 
sound ; few people can hear the sol 9 (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, doh 4 , 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. 
(r r 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 fa 5 . 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. 22 9 

several passages that she sang before him. We only quote 
the last, which ends in doh fl . 







Trills were given on the re c , 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 
la s . 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 doh 6 . 

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 

mi 2 , fa 2 , and fa. The e prefers re 3 , 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 doh 3 turns involun- 
tarily to the o or on. Above mi 4 , the most easy note to 
sound is a. Passing si 4 , 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 m embrane, 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 
re 4 and re$ 4 . Another hair vibrated under the influence of 
the notes la& 3 , rett 2 , and lafl, which indicated the fundamental 
tone lajf v 

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, si 3 doh 4 , 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 re 2 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, mi 3 , 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 ... 

Doh s ... 2 4 6 8 ip . . . 

doh doh, sol, doh, mi, sol# 3 la s doh re mi 4 ... 

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 
doh a will beat with the untrue doh 2 , the doh 3 with the untrue 
doh v 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, sol a doh, mi s sol, . . . doh 4 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, tni s 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 re 3 of the series of SOL can beat with the doh 3 and the 
mi 3 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 doh 3 , rises by insensible degrees to 
the double octave doh s , 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 doh 2 , 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 doh a ; 

or 

Doh mifr fa sol la doh 2 ; 

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, doh 2 . 
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 doh a 

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 i ts 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 




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