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The  UNIVERSITY  of  ML  OMU 


KDMONI)  I,  GOOLD 


j'- 

•f^4r 


VV  -  W>- 


•o 


WONDERS 


OF 


ACOUSTICS; 

OR,   THE 

PHENOMENA  OF  SOUND. 


FROM    THE  FRENCH  OF    RODOLPHE  QADAU. 

THE   ENGLISH   REVISED   tf* 

ROBERT    BALL,  <M. 


With 


NEW 

CHARLES    SCRIBNER    &    CO. 

1870, 


Hustraied  pbrary  of  Wonders. 


PUBLISH  Kl>     BY 


(paite  jlrrtbiw  & 


654  BROADWAY,  NEW  YORK. 
Bach  one  volume  12mo.  Price  per  volume,  $1.50 


Titles  of  Books.  Ao.  of  Itluxtraiin-n* 

THUNDER  AND  LIGHTNING,     ....                      .           .  ;:;> 

WONDERS  OP  OPTICS,         ...  .  .70 

WONDERS  OP  HEAT.                  .....                      .  t>0 

INTELLIGENCE  op  ANIMAL*,           ......  54 

GREAT  HUNTS,     .                      .......  '22 

EGYPT  3,3-0  YKARS  AGO,     .......  40 

WONDERS  OP  POMPEII,             .                     .           .           .           .  :•> 

THE  8 UN,  BY  A.  GUII/LEMIN,         ......  ,\s 

SUBLIME  IN  NATURE,     .......  f  o 

WONDERS  OP  GLASS  MAKING,       .          .           ....  e:', 

WONDERS  OP  ITALIAN  ART,      .......  '28 

WONDERS  OP  THE  HUMAN  BODY,              .....  45 

WONDERS  OP  ARCHITECTURE.            .  5.1 

LIGHTHOUSES  AND  LIGHTSHIPS,     ......  6') 

BOTTOM  OP  THE  OCEAN,                      .                      .           .           .           .  f.8 

WONDERS  OP  BODILY  STRENGTH  AND  S^KILL,  TO 

WONDERFUL  BALLOON  ASCENTS,       ....           .           .  30 

ACOUSTICS      .........  114 

WONDERS  OP  THE  HEAVENS,    .......  48 

THE  MOON,  BY  A.  GUILLEMIN.          .        .                     .           .           .  6  > 

WONDERS  OP  SCULPTURE.         .  .  .  .  .  .  .61 

WONDERS  OP  ENGRAVING,              ......  32 

WONDERS  or  VEGETATION,      .           .           .....  46 

WONDERS  OP  THE  INVISIBLE  WORLD,         .          .           .           .  ;»7 

CELEBRATED  ESCAPES              .......  26 

WATER            .........  77 

HYDRAULICS  .  .  .  ...  .  .  .40 

ELECTRICITY,            ........  71 

SUBTERRANEAN  WORLD,          .......  2T 

*  In  Press  for  early  Publication. 


The  above  works  sent  to  any  address, postpaid,   upon  receipt  of  the  price  by  the 
publishers. 


CONTENTS. 


CHAPTER  L  PACH 

SOUND  IN  NATURE i 

CHAPTER   II. 

EFFECTS  OF  SOUND  ON  LIVING  BEINGS         .  .    23 

CHAPTER  III. 
PROPAGATION  OF  SOUND  BY  DIFFERENT  MEDIA   .       .    42 

CHAPTER   IV. 

INTENSITY  OF  SOUND 48 

CHAPTER  V. 
VELOCITY  OF  SOUND 68 

CHAPTER  VL 
REFLECTION  OF  SOUND 78 

CHAPTER  VIL 
RESONANCE 99 

CHAPTER  VIII. 
SOUND  is  A  VIBRATION 113 

CHAPTER  IX. 
PITCH  OF  SOUNDS 143 


viii  CONTENTS. 

CHAPTER  X.  FAG* 

THE  NOTES 157 

CHAPTER   XI. 
TIMBRE  OR  QUALITY  OF  SOUND 180 

CHAPTER   XII. 
INTERFERENCE  OF  SOUND 212 

CHAPTER   XIII. 
THE  VOICE 226 

CHAPTER   XIV. 

THE  EAR 236 

CHAPTER    XV. 

Music  AND  SCIENCE 244 


ACOUSTICS; 

OR, 

THE    PHENOMENA    OF    SOUND. 
CHAPTER  I. 

SOUND     IN     NATURE. 

Noise  and  Musical  Sound — Voices  of  Animals — Language  of  Animals 

—  M.  L and   the   Monkeys — The  Sloth  or  Ha-ou — Singing 

Birds — Insects — Reptiles  and  Fish — Nocturnal  Life  in  the  Forests. 

SOUND  is  movement.  Repose  is  dumb.  All  sound,  all 
noise,  tells  of  motion;  it  is  the  invisible  telegraph  which 
Nature  uses. 

Sound  is  an  appeal  to  sense.  It  cannot  be  understood 
without  the  attentive  ear,  just  as  light  cannot  be  understood 
without  the  eyes  which  it  enlightens.  In  voice,  and  word, 
and  song  it  becomes  the  chief  and  dearest  tie  to  social  life. 
Every  one  knows  that  the  blind,  who  hear  and  speak,  are 
better  off  than  the  deaf  and  dumb,  who  have  only  their  eyes 
to  learn  by.  It  is  by  the  voice,  that  offspring  of  the  air,  that 
living  beings  tell  most  clearly  their  thoughts,  their  needs, 
and  their  desires.  The  voice  invites,  attracts,  or  repulses, 
excites  or  soothes,  implores  or  curses.  As  speech  in  man's 
mouth,  it  expresses  all  that  mind  can  conceive,  or  heart 
can  feel.  Marvellous  incarnation  !  which  lends  an  invisible 
form  to  thought — which  carries  from  soul  to  soul  passions 

B 


2  ACOUSTICS. 

of  emotion,  faith  or  doubt,  trouble  or  peace.     To  imagine  a 
dumb  humanity  is  impossible. 

We  propose  to  study  sound  from  different  points  of 
view,  without,  j,t  f.rst,  discussing  the  exact  nature  of  the 
phenomena  to  which  it  gives  rise.  It  will  be  seen  afterwards 
that  these  phenomena  may  be  explained  as  clearly  as  can  be 
desired  by  the  theory  of  vibrations,  and  that  even  the  rules 
of  music  arise  in  a  large  measure  from  a  certain  number  of 
physical  and  physiological  facts  which  belong  to  the  domain 
of  the  experimental  sciences.  Let  not  the  reader  feel 
alarmed  at  this,  however ;  we  will  touch  but  lightly  on  this 
side  of  our  subject,  and  we  will  confine- ourselves  for  the 
most  part  to  a  description  of  the  results  which  have  been 
obtained,  without  entering  into  a  detailed  proof  of  the  laws 
which  we  shall  have  occasion  to  lay  down.  This  book  may, 
therefore,  be  read  without  great  effort  by  all  who  wish  to 
understand  the  phenomena  in  the  midst  of  which  our  life  is 
spent. 

The  sensations  that  the  ear  experiences  are  generally 
distinguished  as  "musical  sounds"  and  noises.  The  dis- 
tinction is  vague ;  we  cannot  admit  any  essential  difference 
between  them.  All  noises  consist  of  sounds  of  short  dura- 
tion, almost  instantaneous,  and  more  or  less  discordant. 
So,  also,  musical  sounds — or,  to  speak  more  correctly,  the 
sounds  employed  by  musicians — are  often  exceedingly  short 
in  duration,  and  the  combination  in  which  they  are  placed 
may  be  perfectly  discordant.  Where,  then,  lies  the  limit 
which  separates  a  musical  sound  from  a  noise  ?  It  is  fixed 
by  the  degree  of  pleasure  or  of  pain  with  which  it  impresses 
an  organ,  whose  delicacy  varies  with  different  individuals. 

The  most  striking  characteristic  of  noise  is  the  irregu- 
larity and  abruptness  of  the  impressions  made.  The  rolling 


SOUND    IN   NATURE.  3 

of  a  carriage  on  the  pavement  is  formed  of  a  series  of  dis- 
cordant explosions ;  the  noise  of  falling  water  in  a  fountain  is 
also  a  rapid  succession  of  jerked  or  unfinished  sounds. 

In  the  soft  murmur  of  a  river,  in  the  rustling  of  the 
leaves,  the  transitions  are  less  abrupt;  while  in  other  noises, 
such  as  the  long  moans  of  the  wind  in  the  chimney,  the 
notes  rise  and  fall  by  insensible  degrees.  In  all  these  cases, 
however,  we  have  an  irregular  succession  of  heterogeneous 
sounds,  which  follow  too  rapidly  to  allow  time  for  musical 
feeling  to  grow,  whilst  the  impressions  which  constitute 
musical  sound  are  sufficiently  prolonged  to  be  distinctly 
recognised.  In  this  same  fact  lies  the  difference  between 
spoken  language  and  songs.  Usually  a  confused  medley  of 
sounds,  which  we  cannot  blend  in  a  single  homogeneous 
sensation,  is  also  called  noise.  Thus,  a  noise  is  produced 
by  pressing  the  palm  of  the  hand  on  the  keys  of  a  piano, 
and  striking  all  the  notes  of  the  scale  together.  It  is 
clear  from  these  examples  that  the  distinction  between 
noise  and  sound  is  only  a  matter  of  opinion,  and  that  we 
may  pass  by  a  thousand  gradations  from,  the  one  to  the 
other,  although  the  distance  between  the  two  extremes  is 
great. 

The  clatter  made  by  falling  blocks  of  wood  is  called 
"  noise "  by  everybody,  yet  here  is  an  experiment  which  is 
often  made : — We  take  seven  pieces  of  hard  wood  of  the 
same  length  and  breadth,  but  of  a  thickness  decreasing 
according  to  a  certain  law.  One  of  these  dropped  alone 
upon  a  plank  makes  a  noise  seemingly  without  a  particle  of 
music  in  it,  but  throw  them  down  one  after  another  regularly, 
in  the  order  of  their  diminishing  thickness,  and  the  seven 
notes  of  the  scale  are  perfectly  heard. 

The  Chinese  get  sounds  pleasant  enough  for  a  melody 

B  2 


4  ACOUSTICS. 

by  striking  upon  flint  stones,  properly  chosen  and  suspended 
by  threads.  Many  instruments  used  in  the  orchestra  really 
produce  nothing  but  harmonious  noises,  which  blend  with 
the  music  to  sustain  the  rhythm.  Such  are  the  cymbals, 
castanettes  and  triangles,  &c. 

Inorganic  nature  produces  only  noises.  The  voice  of 
the  thunder,  of  the  storm,  and  of  the  sea  are  but  confused 
noises.  Yet  from  the  wind  we  may  win  most  musical  notes, 
by  presenting  to  it  an  Eolian  harp,  whose  strings  can  only 
vibrate  in  a  certain  manner. 

In  the  animal  world  we  meet  with  an  infinite  variety  of 
noises,  and  of  musical  sounds ;  these  noises  and  songs  con- 
stitute the  language  of  brutes.  "  Birds,  dogs,  and  other 
animals,"  says  the  Pere  Mersenne,  "  have  quite  a  different 
cry  when  they  are  angry,  or  complaining,  or  ill,  to  when  they 
are  happy  and  well ;  the  voice  is  more  shrill  in  sorrow  or 
anger  than  at  other  times,  for  bile  makes  the  voice  sharp, 
while  melancholy  and  phlegmatic  humour  render  it  grave, 
and  a  sanguine  temperament  modulates  it  to  softness. 
But  the  voice  of  animals  is  involuntary,  while  that  of  man 
is  free — that  is  to  say,  men  speak  freely,  and  animals  cry, 
sing,  and  use  their  voices  according  to  a  settled  law.  Many 
say  ti.j.t  animals  are  not  thus  restricted,  urging  that  nothing 
could  be  more  free  than  the  song  of  birds  like  the  nightingale, 
the  goldfinch,  and  others ;  nevertheless,  it  must  be  admitted 
that  they  only  sing  from  necessity.  It  may  be  that  delight 
or  sorrow  forces  them  to  sing,  or  they  may  be  excited  by 
some  natural  instinct,  which  leaves  them  no  possibility  of 
keeping  silent  or  of  ceasing  their  song.  And  when  they 
listen  to  a  lute,  or  some  other  harmonious  sound,  and  sing 
in  imitation  one  to  another,  the  sounds  which  they  imitate 
so  strike  their  imagination  that  they  cannot  be  silent ;  for 


SOUND    IN   NATURE.  5 

their  sensitive  affection,  being  warmed  by  the  impression  on 
the  imagination,  compels  the  creative  faculty  to  move  the 
organ  of  the  voice." 

This  theory  of  an  involuntary  or  necessary  noise  is  some- 
what arbitrary,  for  it  cannot  be  denied  that  many  animals 
contrive  to  hold  real  conversations  amongst  themselves. 
We  must  here  quote  G.  E.  Wetzel's  interesting  book, 
called  "A  New  Discovery  of  the  Language  of  Animals, 
founded  upon  Reason  and  Experience."  (Vienna,  1800.) 
The  frontispiece  represents  a  group  of  superior  animals, 
with  this  motto,  "  They  never  lie :  truth  is  their  language." 
The  author  endeavours  to  prove  that  animals  make  them- 
selves understood  by  combinations  of  sounds,  which  con- 
stitute the  simplest  language — a  language  full  of  repetitions ; 
that  they  try  to  make  themselves  understood  by  man,  and 
in  their  turn  understand  his  language;  in  a  word,  that  it 
would  be  possible  to  study  the  idioms  of  different  animals, 
and  from  them  determine  the  forms  and  the  variations  of 
their  speech. 

We  actually  find  in  Wetzel's  book  the  rudiments  of  a 
dictionary  of  the  beasts'  language  filling  twenty  pages.  The 
author  has  even  tried  to  translate  into  German  several 
dialogues  of  dogs,  cats,  chickens,  and  other  birds  in  illustra- 
tion of  his  principles.  He  recounts  a  conversation  composed 
of  little  abrupt  cries  that  he  overheard  between  some  captive 
frogs,  the  purport  of  which  was  to  arrange  means  to  facilitate 
their  escape.  It  may  be  surmised  that  the  drift  of  the  con- 
versation was  not  altogether  clear  to  our  linguist,  for  the 
three  frogs  succeeded  in  escaping.  There  is  no  doubt  that 
by  the  careful  watching  of  animals  we  may  come  to  under- 
stand their  mysterious  language  to  a  certain  point,  and  even 
to  speak  it 


O  •         ACOUSTICS. 

Apropos  of  this  is  an  amusing  story  from  M.  Jules 
Richard.  "  Going  to  visit  an  invalid  friend  in  a  military 
hospital/'  he  says,  "I  had  made  the  acquaintance  twelve 

years  ago  of  an  old  Government  official  named  L .  He 

was  a  Southerner,  somewhat  of  a  boaster  but  brave  at 
bottom,  who  swore  like  a  heathen,  and  loved  animals.  He 
had  grown  familiar  with  all  the  cats  in  the  hospital ;  and  at 
the  hour  when  rations  are  distributed,  his  '  Mi-aou-ou'  would 
bring  them  running  from  the  most  distant  part  of  the  building, 
round  the  old  soldier's  porringer.  I  had  always  supposed 
that  the  cats,  deceived  by  the  perfect  imitation  of  their  mew, 
or  accustomed  as  the  soldiers  were  to  the  dinner  hour,  came 
mechanically  to  gather  round  their  friend.  '  They  under- 
stand me,'  insisted  the  old  man — 'they  understand  me 
perfectly.  I  know  cat's  speech  and  dog's  speech,  but 
monkey  speech  I  know  better  than  the  monkeys  themselves/ 

"  As  I  smiled  with  an  expression  of  incredulity,  '  Will 

you/  said  M.  L ,  *  come  with  me  to-morrow  to  the 

Jardin  des  Plantes,*  and  I  will  show  you  something  re- 
markable. That's  all  I  have  to  say.' 

"  I  took  good  care  not  to  miss  the  appointment,  and 

M.  L was  as  punctual.  He  led  the  way  to  the 

monkey-house,  and  no  sooner  had  he  leant  upon  the  outer 
balustrade,  than  I  heard  close  beside  me  his  guttural  cry — 
1  Kirrouu  !  kirrikiou  !  courouki !  courrikiou  ! ;  I  tried  to 
imitate  the  sounds  that  came  from  my  neighbour's  mouth  : 

"'Kirrouu!' 

"  Throe  monkeys  fell  into  place  before  L . 

"'Kirrikiou!-' 

"  Four  monkeys  followed  their  companions. 

*  Zoological  Gardens. 


SOUND   IN   NATURE.  7 

"'Courouki!' 

"Tli  ere  were  twelve. 

"'Courrikiou!' 

"  All  of  them  were  there.  L  *s  discourse  lasted  for 
ten  minutes,  during  which  the  monkeys — ranged  in  several 
rows,  seated  on  the  ground,  their  front  paws  crossed  on 
their  knees — laughed,  nodded,  listened,  and  replied.  Yes 

indeed,  they  answered,  and  L went  on  in  fine  style 

with  his  '  Kirrouu  !  kirrikiou  !  courouki !  courrikiou  !'  We 
stayed  for  twenty  minutes,  and  I  assure  you  the  monkeys 

were  not  tired.  Suddenly  L made  a  move  to  go  :  his 

auditors  became  uneasy ;  then  as  L left  the  balustrade 

they  uttered  cries  of  distress.  We  went  off,  but  from  a 
distance  could  still  see  the  monkeys,  who  climbing  up  the 
wires  of  their  cage  made  signs  of  farewell.  It  seemed  to  me 
that  they  wanted  to  say,  *  If  you  do  not  come  again,  write  to 
us  at  least.' " 

We  sometimes  hear  of  a  cats'  concert.  There  was  a 
time  when  that  might  have  been  talked  of  without  metaphor. 
There  used  to  be  cats'  concerts  (I  do  not  mean  those  held 
upon  the  tiles  at  midnight),  pigs'  concerts,  bears',  monkeys', 
donkeys',  and  little  birds'  concerts,  that  sang  not  from 
gaiety  of  heart. 

This,  according  to  the  Chronicles,  is  what  happened  at 
Brussels  in  Ascension  week,  1549,  in  honour  of  a  miraculous 
image  of  the  Virgin : — A  bear  played  the  organ.  This  organ 
was  composed  of  twenty  cats,  shut  in  narrow  boxes ;  their  tails 
were  tied  to  cords  connected  with  the  notes  of  the  organ. 
Each  time  that  the  bear  struck  the  keys,  he  pulled  the 
tails  of  the  poor  cats,  and  forced  them  to  mew  in  tune. 
Musical  historians  also  speak  of  organs  with  pigs  and 
cats  together.  Conrad  von  der  Rosen,  jester  to  the 


8 


ACOUSTICS. 


Emperor  Sigismond,  succeeded,  they  say,  in  curing  his 
master  of  a  deep  melancholy,  by  playing  an  organ  of 
cats,  arranged  in  scales,  whose  tails  he  pinched  by  striking 
the  keys. 

Father  Kircher  devotes  one  of  the  most  curious  chapters 
of  his  "  Musurgie  "  to  the  voices  of  animals.     First  of  all  he 


*&$<':£, 


Fig.  i.— The  Ha-ou,  or  Sloth. 

places  the  "  Sloth"  (in  Latin  called  Pigritia,  or  the  Ha-ou 
animal).  He  gives  a  description  of  it,  together  with  an 
illustration,  which  he  professes  to  have  received  from  a  pro- 
vincial of  his  order,  returned  from  Brazil.  We  give  it  for 
the  sake  of  its  curiosity. 

According  to  this  account,  the  sloth  only  makes  him- 
self heard  at  night:  his  cry  is  a  ha-ha-ha-ha-ha,  running 
six  notes  up  and  down  the  scale — doh,  re',  mi,  fa,  sol,  la, 
sol,  fa,  md,  ri,  doh.  These  notes  are  "tittered  at  regular 


SOUND    IN    NATURE.  9 

intervals,  each  one  being  separated  from  the  following  by  a 
short  pause.  When  the  Spaniards  settled  in  the  country, 
they  took  these  nocturnal  cries  for  the  singing  of  men  in  the 
forests.  Kircher  does  not  stint  his  admiration  for  the  voice 
of  the  sloth.  "  If  music  had  been  invented  in  America," 
he  says,  "  I  should  not  hesitate  to  say  that  it  was  derived 
from  the  song  of  this  creature." 

But  Father  Kircher  has  other  wonders  in  store  for  us. 
He  interprets  the  voices  of  men  in  a  most  singular  fashion. 
Those  who  speak  with  a  strong,  deep  voice,  he  classes  with 
donkeys,  after  Aristotle's  example.  The  ass  truly  possesses  a 
voice  strong  and  deep  enough,  and  he  is  rash,  obstinate,  and 
rude;  so  those  who  have  the  same  voice  are  rash,  obstinate, 
and  rude.  Father  Kircher  finds  no  difficulty  in  explaining  the 
reason  of  this  phenomenon,  and  he  finishes  by  saying  that 
the  owners  of  bass  voices  are  cowardly,  avaricious,  unbearably 
arrogant  in  prosperity,  but  more  timid  than  hares  in  time  of 
danger.  "Such,"  he  says,  "was  Caligula."  Those  whose 
voices  begin  their  utterance  in  a  low  key,  but  grow  shrill 
before  they  finish,  are  sad,  morose,  and  passionate  like  oxen. 
A  weak,  shrill  voice  betrays  an  effeminate  character.  With 
those  who  speak  fast,  a  low-pitched  voice  bespeaks  strength 
and  courage.  A  shrill  and  piercing  voice  is  peculiar  to  the 
goat :  it  indicates  a  petulant  and  wantonly  nature.  Never- 
theless, these  bad  natural  dispositions  may  be  overcome  by 
education  and  by  the  will  ! 

Of  all  animals,  birds  are  the  most  highly  gifted  as  to 
voice.  To  the  parrot  nothing  is  wanting  for  the  mimicry 
of  human  speech ;  but  this  is  quite  mechanical,  and  the 
wonderful  faculty  that  we  admire  in  the  parrot  indicates  no 
advantage  or  superiority  over  other  animals ;  in  repeating 
the  words  he  hears,  he  simply  proves  his  utter  stupidity. 


10  ACOUSTICS. 

The  starling,  the  blackbird,  the  jay  and  jackdaw,  who  all 
have  the  thick  round  tongue  of  the  parrot,  are  more  or  less 
clever  in  mimicking  speech.  Then  why  do  these  birds 
remain  for  ever  without  the  expression  of  intelligence  which 
speech  would  give  them  ?  BufTon  accounts  for  the  fact  by 
their  rapid  growth  in  infancy,  and  by  their  early  separation 
from  their  parents,  who  do  not  continue  the  education  of 
their  children  long  enough  to  form  durable  and  reciprocal 
impressions,  which  are  the  sources  of  intelligence. 

Those  birds  who  have  the  tongue  forked  whistle  more 
easily  than  they  talk.  When  this  natural  aptitude  is  joined 
with  a  musical  memory,  they  learn  to  repeat  airs.  The  canary, 
linnet,  siskin,  and  bullfinch  are  noted  for  their  readiness  to 
learn.  The  parrot,  on  the  contrary,  does  not  learn  to  sing, 
but  imitates  the  cries  of  any  animals  that  he  hears  :  he  mews 
and  barks  as  easily  as  he  talks. 

The  nightingale  is  the  true  songster  of  our  forests.  By 
the  wonderful  variety  of  its  intonations,  by  the  deep  passion 
of  its  voice,  it  bears  the  palm  from  all  its  comrades.  The 
nightingale's  song  usually  begins  with  an  uncertain,  timid 
prelude ;  by  degrees  it  becomes  animated,  eager,  and  soon 
we  hear  the  brilliant,  thrilling  notes  pour  forth  heavenward. 
The  full,  clear  warbling  alternates  with  low  murmurs,  scarcely 
audible ;  the  trills  and  rapid  runs  so  clearly  articulated,  the 
plaintive  cadences,  the  long-drawn  notes,  the  passionate 
sighs,  give  place  from  time  to  time  to  a  short  silence ;  then 
the  warbling  begins  once  more,  and  the  woods  resound  with 
the  soft  and  stirring  accents  which  fill  the  soul  with  sweet- 
ness. The  voice  of  the  nightingale  reaches  as  far  as  the 
human  voice  :  it  can  be  heard  at  a  distance  of  upwards  of  a 
mile  when  the  air  is  calm,  and  so  much  the  more  clearly 
because  the  nightingale  only  sings  at  night,  when  all 


SOUND   IN   NATURE. 


IT 


is  silent  around.  In  general,  it  is  only  the  male  who  sings, 
but  females  have  been  known  to  sing  as  well.  In  captivity 
the  nightingales  sing  during  nine  or  ten  months  of  the  year; 
when  at  liberty  they  only  begin  in  April,  and  end  in  June ; 
after  this  month  they  have  a  hoarse  cry.  To  make  them 


Fig.  2.— The  Nightingale. 


sing  in  a  cage,  it  is  necessary  to  treat  them  well,  and  cheer 
their  captivity  by  surrounding  them  with  foliage.  Then  they 
will  sing  even  better  than  the  wild  nightingales.  The  im- 
prisoned nightingale  will  vary  its  natural  song  with  such 
passages  as  please  it  from  the  songs  of  other  birds  which 
it  has  heard.  Musical  instruments,  or  a  melodious  voice, 
excite  and  stimulate  its  talent ;  it  tries  to  sing  in  unison,  or 


1 2  ACOUSTICS. 

to  eclipse  its  rivals,  or  to  drown,  all  the  noises  round. 
Nightingales  have  even  been  seen  to  drop  down  dead  in  the 
struggle  against  a  rival  singer. 

Father  Kircher,  in  his  "  Musurgie,"  analyses  the  song  of 
the  nightingale  at  some  length.  "  This  bird,"  he  says,  "  is 
ambitious  and  eager  for  praise ;  he  makes  as  much  parade 
of  his  song  as  a  peacock  of  his  tail.  When  alone,  he  sings 
simply;  but  no  sooner  is  he  sure  of  an  audience  than  he 
displays  with  delight  the  treasures  of  his  voice,  and  invents 
the  most  varied  modulations." 

Barrington  has  also  tried  to  note  the  song  of  the  night- 
ingale, but,  as  he  himself  confesses,  without  success.  The 
written  notes  executed  by  the  most  skilful  flute-player  do 
not  recall  the  natural  song. 

Barrington  says  that  the  difficulty  lies  in  the  impossibility 
of  exactly  estimating  the  value  of  each  note.  But,  though 
we  have  not  succeeded  yet  in  transcribing  this  wonderful 
song,  it  has  sometimes  been  well  imitated  in  whistling. 

Buffon  tells  of  a  man  who  could,  by  his  song,  so  charm 
the  nightingales,  that  they  would  come  to  perch  upon  him, 
and  suffer  him  to  take  them  in  his  hand. 

As  to  the  compass  of  the  nightingale's  voice,  it  seems 
not  to  be  beyond  an  octave.  Very  occasionally  some  shrill 
sounds  can  be  heard  which  mount  to  a  higher  octave,  but 
they  pass  like  lightning,  and  it  is  by  an  exceptional  effort 
that  the  bird  reaches  such  a  height. 

It  is  by  no  means  proved  that  the  nightingale  can  learn 
to  speak,  though  Pliny  tells  of  one  belonging  to  the 
Emperor  Claudius,  who  spoke  Greek  and  Latin.  Father 
Kircher  inclines  to  believe  that  this  bird  could  be  taught 
to  imitate  human  speech,  "  but,"  says  he,  "  the  story  that 
Aldrovande  relates  of  three  nightingales  who  told  one  to 


SOUND    IN   NATURE. 


another  during  the  night  all  that  had  happened  in  the  day, 
at  a  certain  hotel  in  Ratisbonne,  has  appeared  fabulous  to 


many  people,  or  at  least  inexplicable  without  some  signal 
imposture,  or  help  of  the  devil." 


Fig.  4. —The  Coc::. 

He  has  also  arranged  in  notes  the  songs  of  the  cuckoo, 
the  quail,  the  cock,  and  of  the  hen  when  she  is  about  to  lay, 
and  when  she  calls  her  little  ones.  We  reproduce  the 


ACOUSTICS. 


curious  plates  where  he  gives  the  result  of  these  observations, 
only  omitting  the  parrot,  whose  natural  cry  is  expressed 
by  the  Greek  word  xaLP€i  which  signifies  "Good  morning!" 
It  may  be  said  of  most  birds  that  their  song  is  a  love- 
call.  The  lark  is  almost  the  only  one  that  can  be  heard 
from  spring  time  to  winter,  and  that  is  because  it  alone 
is  faithful  to  its  love  throughout  the  summer.  The  lark 


Fig.  5.— The  Cuckoo. 


Fig.  6.— The  Quail. 


sings  while  flying;  the  higher  it  rises  the  louder  it  sings.  We 
can  hear  it  even  when  it  has  disappeared  in  the  blue  of  the 
sky.  Nothing  is  so  joyous  as  the  exquisite  notes  of  this 
song. 

There  is  a  species  twice  the  size  of  the  ordinary  lark 
common  in  Italy  and  the  south  of  France.  Gifted  with 
a  strong  and  pleasant  voice,  it  varies  its  song  by  counter- 
feiting the  warble  of  the  goldfinch,  the  canary,  and  the 
linnet,  and  even  the  chirp  of  young  chickens,  or  the  cry  of 
a  cat. 

The  little  birds  whose  gay  song  fills  the  woods,  orchards, 


SOUND   IN   NATURE.  15 

gardens,  and  thickets  during  the  summer,  belong  for  the 
most  part  to  the  tribe  of  wrens.  One  of  the  most  remarkable 
families  is  that  of  the  "  pewets,"  who  imitate  the  song  of  all 
the  other  birds  so  as  to  be  mistaken  for  them.  They  might 
be  called  the  mocking-birds  of  France. 

The  campanero  has  a  clear  bell-like  voice,  which  can,  it  is 
said,  be  heard  at  a  distance  of  more  than  eight  miles  in  the 


Fig.  7.— The  Common  Lark. 

region  it  inhabits.  Each  morning  it  raises  its  song,  and 
again  at  noon,  when  the  heat  has  silenced  all  its  feathered 
colleagues,  it  enlivens  the  solitude.  There  comes  first 
a  piercing  cry,  followed  by  a  pause,  and  once  more  a  cry 
that  ends  in  a  silence  of  six  or  eight  minutes,  which  is 
again  broken  by  a  fresh  series  of  cries. 

Among  the  ancients,  the  swan  was  also  reckoned  with 
the  birds  gifted  with  the  power  of  song,  but  he  only  sang 
at  the  hour  of  death.  This  fable  was  long  believed,  and 
to  the  present  day  it  serves  as  a  comparison  for  the  last 
effort  of  a  dying  genius.  But  the  voice  of  the  swan  is  only 


i6 


ACOUSTICS. 


a  kind  of  croak.  It  is  however  true,  according  to  Buffon, 
that  we  can  distinguish  in  the  cries  of  the  wild  swan 
a  kind  of  modulated  song,  composed  of  clarion-like 
notes. 

The  ancients  had  very  different  ideas  in  the  matter  of 
harmony  from  our  own.  They  adored  the  song  of  the  grass- 
hopper. Anacreon  dedicated  an  ode 
to  it.  "  Happy  grasshopper !"  says  he, 
"  who,  on  the  highest  branches  of  trees 
moist  with  dew,  singest  like  a  queen, 
cherished  by  the  Muses  and  Phoebus, 
who  has  given  thee  thy  sweet  song." 
Homer  compares  the  eloquence  of  the 
old  men  of  Troy  to  the  song  of  cicadas, 
and  a  legend  relates  that  a  trial  of  skill 
between  Eunomus  and  Ariston,  two 
players  on  the  cithara,  was  decided  by 
a  grasshopper;  for  one  of  the  former's 
strings  snapping,  the  gods  sent  a  grass- 
hopper, which,  perching  on  the  instru- 
ment, filled  so  well  the  place  of  the 
broken  string,  that  Eunomus  was  pro- 
claimed the  victor.  In  modern  times 
we  cannot  recognise  music  in  this  insect's  monotonous  and 
piercing  notes. 

Its  musical  apparatus  consists  in  two  scaly  valves  placed 
below  the  abdomen,  and  found  only  in  the  male ;  these 
valves  cover  two  cavities  containing  two  membranes  like  dry 
parchment,  the  rapid  motion  of  which  produces  a  sharp, 
resonant,  screeching  noise.  The  other  parts  of  the  appa- 
ratus intensify  and  prolong  the  sound. 

The  common  grasshopper  is  very  common  in  Provence, 


Fig.  8.—  The  Locust. 


SOUND    IN    NATURE.  I/ 

and  is  found  also  pretty  far  to  the  north  ;  it  is  met  with  at 
Fontainebleau.  "  In  singing,"  says  M.  Maurice  Gerard,  "  it 
moves  its  abdomen  rapidly,  so  as  to  cover  and  uncover  the 
openings  of  the  sonorous  cavities.  Its  sound  is  strong  and 
sharp,  and  consists  of  one  note  frequently  repeated,  and 
dying  away  into  a  hiss  like  "  st,"  or  like  air  coming  from  a 
narrow  aperture  nearly  closed.  If  caught  it  emits  strong 


Fig.  9.— The  Hearth  Cricket 


cries,  which  differ  perceptibly  enough  from  its  song  when  at 
liberty.  By  whistling  to  a  grasshopper  to  imitate  its  song, 
you  can  please,  attract,  and  easily  catch  it. 

In  northern  countries  the  green  grasshopper  is  often 
taken  for  the  cicada,  its  cry  being  much  the  same.  In  the 
old  editions  of  La  Fontaine,  the  fable  of  the  cicada  and 
the  ant  has  a  grasshopper  as  illustration.  But  the  two 
animals  belong  to  distinct  orders.  Among  the  tribe  of 
crickets  and  grasshoppers,  the  male  calls  the  female  by  a 
cry  produced  by  rubbing  the  elytra  (wing-cases);  but  the 

c 


iS 


ACOUSTICS. 


mechanism  that  produces  this  monotonous  noise  differs  a 
little  in  different  species.  The  field-cricket  rubs  the  whole 
elytra,  furnished  with  strong,  hard  nerves,  projecting  like 
cords,  one  against  the  other.  Travellers  say  that  in  some 
parts  of  Africa  they  are  kept  in  little  transparent  cages  :  their 
monotonous  song  charms  the  natives  to  sleep 

The  note  of  the  hearth-cricket  is  slower,  more  mono- 
tonous, less  shrill,  resembling  the  cry  of  the  screech-owl. 


Fig.  10. —  The  Grasshopper. 

The  grasshoppers  produce  a  cry  by  striking  two  trans- 
parent membranes,  furnished  with  nerves  placed  at  the  base 
of  the  wing-cases,  like  cymbals.  Their  monotonous  singing 
is  heard  in  the  evening,  and  all  night  in  damp  meadows. 
The  "  dectique  "  sings  by  day  in  the  ripe  wheat. 

Finally,  the  small  cricket  produces  sounds  less  musical, 
but  more  varied,  than  the  preceding  species.  Their  thighs 
and  wing-cases  (elytra)  have  hard  projecting  nerves,  and 
they  strike  the  thighs  on  the  wing-cases,  as  the  bow  touches 
the  chords  of  a  violin,  generally  both  at  once,  but  sometimes. 


SOUND    IN    NATURE.  19 

left  and  right  alternately.  A  kind  of  drum,  covered  with  a 
very  fine  skin,  placed  near  the  base  of  the  abdomen  on  each 
side  of  the  body,  seems  intended  to  increase  the  sound. 
The  cricket's  cry  is  something  like  a  rattle,  but  of 
different  quality  in  different  species.  One  can  distinguish 
many  notes,  and  the  sound  changes  when  calling  a  female, 
or  provoking  a  rival. 

Yersin  tried  to  note  down  the  song  of  these  insects. 
Charles  Butler,  the  author  of  the  "  Feminine  Monarchy," 
tried  in  the  same  way  to  note  the  murmur  of  the  wings  that 
is  heard  in  a  hive  of  bees  about  to  swarm.  "He  has 
fixed,"  says  Reaumur,  "all  the  accents  of  the  song  of  the 
bee  who  aspires  to  lead  a  swarm,  the  different  keys  in  which 
it  is  composed,  and  even  the  song  of  the  queen-mother 
herself."  The  drones  produce  with  their  wings  a  humming 
noise,  of  which  their  name  is  an  imitation. 

The  Death-watches,  moving  backwards  and  forwards  on 
their  six  feet,  strike  the  wood  of  old  furniture  with  their 
closed  jaws,  and  so  cause  the  noise  heard  at  night. 

Reptiles  are  not  silent.  The  voice  of  crocodiles  and 
alligators  may  be  compared,  in  infancy,  to  the  mewing 
of  a  cat,  and  at  a  riper  age  to  broken  sobs,  or  bellowing, 
which  travellers  have  sometimes  mistaken  for  the  cries  of  a 
child.  The  lizard  of  Birmania,  M.  Thomas  Anquetil  tells 
us,  foretells  an  earthquake  by  its  frequent  and  piercing  cries. 

Serpents  have  only  a  shrill  whistle  to  serve  as  voice, 
excepting  the  rattle-snake,  who  carries  at  the  end  of  his  tail 
a  curious  instrument  formed  of  scaly  horns,  fitting  one  into 
another,  which  become  more  numerous  as  he  grows  older. 

The  croaking  frogs  are  renowned  for  their  talkativeness, 
which,  according  to  La  Fontaine,  once  brought  them  into 
trouble ;  for,  in  consequence  of  their  clamour,  they  were 

C    2 


20  ACOUSTICS. 

deprived  of  their  free  democracy  and  put  under  a  monarchy. 
The  fish,  who  pass  for  dumb  creatures,  are  not  so  by  any 
means.  Several  of  them  give  very  peculiar  sounds.  This 
power,  which  belongs  to  both  male  and  female,  is  great  at 
the  time  for  spawning.  When  the  "  maigres  "  assemble  in 
shoals,  such  a  noise  is  heard  to  come  from  the  water  that 
they  have  gained  the  name  of  "  living  organs."  M.  Dufosse, 
who  is  specially  interested  in  the  subject,  discovered  that  the 
noise  is  caused  by  the  quivering  of  certain  muscles;  in  some 
species  it  is  sustained  and  strengthened  by  air-bladders. 

Thus,  by  day  and  by  night,  a  thousand  voices  join  to  swell 
the  grand  concert  of  nature.  Even  when  we  imagine  our- 
selves in  complete  silence,  we  are  still  surrounded  by  noises. 
Try  at  such  a  time  to  listen  to  some  very  faint  sound,  and 
you  will  find  that  these  noises  prevent  your  hearing  it  dis- 
tinctly. To  feel  what  real  silence  is,  one  should  climb  the 
lonely  summit  of  a  high  mountain.  Every  region  has,  so  to 
say,  an  acoustic  physiognomy.  In  the  neighbourhood  of 
great  towns  a  thousand  confused  noises  are  heard,  which 
betray  human  activity,  as  the  humming  of  bees  in  a  hive 
tells  us  it  is  inhabited. 

At  Paris  this  hoarse  murmur  rolls  on  through  the  night. 
There  are  streets  where,  in  the  day,  a  passenger  cannot  hear 
his  own  voice  for  the  noise  of  the  wheels.  The  rumbling  is 
increased  by  the  firm  and  elastic  nature  of  the  soil,  which 
covers  the  catacombs  like  the  sounding-board  of  a  violin. 

In  Europe  there  are  small  singing  birds  who  lead  the 
orchestra  of  the  forest.  In  America  there  are  stronger 
voices  to  take  the  lead.  Listen  to  the  account  Alexander 
von  Humboldt  gives  of  the  nocturnal  life,  or  rather  the 
voices  of  the  animals,  in  a  tropical  forest  at  night : — 

He  was  passing  the  night  under  the  spreading  heavens, 


SOUND    IN    NATURE.  21 

having  chosen  a  sandy  plain  on  the  banks  of  the  Apure, 
bordering  on  a  thick  virgin  forest.  The  night  was  cool  and 
moonlight.  A  deep  silence  reigned  on  plain  and  river,  only 
broken  from  time  to  time  by  the  gentle  play  of  the  dolphins  in 
the  water.  "Soon  after  eleven  there  began  in  the  neighbour- 
ing forest  such  a  hubbub,  that  any  thought  of  sleep  for  the 
remainder  of  the  night  was  out  of  the  question.  All  the 
thicket  resounded  with  wild  cries.  Amongst  the  many  voices 
which  mingled  in  this  concert,  the  Indians  could  only  recog- 
nise those  which  paused  for  a  moment,  to  gather  fresh 
vigour,  and  began  again  in  a  lull  of  the  general  chorus. 
There  were  the  guttural  and  monotonous  growls  of  the 
alouates,  the  sweet  and  plaintive  voice  of  the  little  mar- 
moset, the  snore  of  the  monkey,  the  abrupt  cries  of  the 
American  jaguar,  of  the  puma,  or  maneless  lion,  of  the 
peccary,  the  sloth,  and  a  swarm  of  parrots.  When  the 
jaguars  approached  the  edge  of  the  forest  our  dog,  who  had 
hitherto  barked  incessantly,  crept  whimpering  to  find  an 
asylum  under  our  hammocks.  Sometimes  the  roar  of  the 
jaguar  was  heard  from  the  top  of  the  trees,  and  then  it  was 
always  accompanied  by  sharp  cries  of  distress  from  the  mon- 
keys, who  tried  to  escape  this  new  danger." 

If  you  ask  the  Indians  the  cause  of  this  continued 
tumult,  they  answer,  laughing,  that  the  animals  love  to  see 
the  moon  shine  in  the  forest,  and  hold  a  festival  at  full  moon. 
But  it  is  not  the  moon  which  excites  them  most;  it  is  during 
a  violent  storm  that  their  cries  are  loudest,  or  when,  in  the 
midst  of  a  peal  of  thunder,  the  lightning  flashes  in  the 
forest. 

These  kind  of  scenes  afford  a  strange  contrast  to  the 
calm  which  reigns  in  the  tropics  towards  noon  in  the  time  of 
the  great  heat,  when  the  thermometer  stands  at  104°  (Fahr.) 


22  ACOUSTICS. 

in  the  shade.  At  this  time  the  larger  animals  are  buried  in 
the  depths  of  the  forest,  and  the  birds  hide  themselves  under 
the  foliage  of  the  trees,  or  in  the  crevices  of  the  rocks,  and 
so  escape  the  burning  rays  of  the  sun,  which  pour  from  the 
zenith.  To  make  up  for  this,  however,  the  smooth  rocks 
and  stones  are  covered  with  iguanas,  geckos,  salamanders, 
who  rest  motionless,  and  with  lifted  head  and  gaping  mouth 
seem  to  breathe  the  fiery  air  with  delight.  "  But,"  says  Hum- 
boldt,  "during  this  apparent  calm  of  nature,  an  attentive 
listener  for  almost  imperceptible  sounds  could  distinguish 
along  the  surface  of  the  ground,  in  the  air,  a  confused 
rustling,  caused  by  the  buzzing  and  humming  of  insects. 
Everything  betokens  a  world  of  organic  forces  in  motion.  In 
each  bush,  in  the  bark  torn  from  the  trees,  in  the  earth 
furrowed  by  the  insects,  life  works  and  manifests  itself.  It 
is  as  one  of  the  thousand  voices  of  nature  speaking  to  the 
thoughtful  and  pious  soul  of  man." 


CHAPTER  II. 

EFFECTS   OF   SOUND   ON   LIVING   BEINGS. 

rower  of  Music — Legends  and  Anecdotes — The  Remedial   Effects  of 
Music — Influence  of  Music  on  Animals. 

As  the  painter  uses  light  for  a  messenger  of  his  thought,  the 
musician  bids  sound  convey  his  feelings.  Music  is  a  lan- 
guage, and  the  sweetest  of  languages,  inasmuch  as  it  is  less 
formed  than  any  other :  it  is  the  ideal  of  speech. 

Music  is  generally  defined  as  an  agreeable  combination 
of  sounds ;  but  the  ancients  gave  it  a  far  wider  meaning. 
With  them  music  included  the  dance,  gymnastics,  poetry,  and 
almost  all  the  sciences.  Hermes  declares  that  music  is  the 
knowledge  of  the  order  of  all  things,  while  Pythagoras  and 
Plato  teach  that  everything  in  the  universe  is  music.  Hence 
the  phrases  "celestial  music,"  "harmony  of  worlds,"  &c., 
which  were  used  by  ancient  writers. 

In  all  probability  music  was  the  first  of  the  arts,  for 
man  had  a  singing  master  in  the  bird.  Wind  instruments 
must  have  come  after.  Diodorus  attributes  the  invention  of 
them  to  some  shepherd,  who  had  studied  the  whistling  of 
the  wind  among  the  reeds.  Lucretius  holds  the  same 

opinion  : 

"  Et  Zepnyri  cava  per  calamorum  sibila  primura 
Agresteis  docuere  cavas  inflare  cicutas." 

Stringed   instruments,  and  those  from  which  sound   is 


ACOUSTICS. 


produced  by  percussion,  are  also  very  old.  The  ancients 
attribute  the  invention  of  music  to  either  Mercury  or  Apollo. 
Cadmus,  who  brought  Hermione  the  musician  to  Greece, 


Fig.  15. 
Cithare. 


Fig.  16. 
Cithare. 


Dou 


able  Flute. 


Fig.  18. 
Flute  of  Pan. 


Amphion,  Orpheus,  and  others,  are  spoken  of  as  the  fathers 
of  instrumental  music.  According  to  the  book  of  Genesis, 
the  players  on  the  harp  and  organ  are  descended  from 
Jubal,  the  son  of  Lamech  and  Adah,  of  the  race  of  Cain. 


EFFECTS   OF   SOUND   ON    LIVING    BEINGS.  25 

The  influence  of  music  on  the  manners  of  a  people,  and 
its  power  over  the  mind,  are  recognised  by  the  philosophers 
of  antiquity.  Plato  supposes  that  we  can  distinguish  the 
sounds  which  incite  sordid  or  mean  feelings,  as  well  as  these 
which  call  into  action  the  opposite  virtuous  feelings.  With 


Fig.  19.  -  Pastoral  Pipes,  or  Flutes  of  Pan. 

him  it  seems  that  a  change  in  the  popular  music  would  be 
simultaneous  with  a  change  in  the  constitution  of  the  state. 
Polybius  tells  us  that  in  Arcadia,  a  dull  and  cold  country, 
music  was  necessary  to  soften  the  manners  of  the  people,  and 
that  in  no  place  were  so  many  crimes  committed  as  in 
Cynetus,  where  it  was  neglected. 


26  ACOUSTICS. 

Formerly  Divine  and  human  laws,  precepts  and  morals, 
legends  and  history,  were  set  to  music,  and  sung  in  chorus 
publicly.  The  Israelites  had  similar  customs.  Music  lent  a 
peculiar  charm  to  abstract  things,  and  fixed  them  on  the  mind 
of  the  hearer.  Is  it  some  memory  of  this  sort  which  has 
recently  inspired  a  Yankee  Meyerbeer  with  the  absurd  notion 
of  putting  the  American  constitution  into  a  symphony? 

The  Pythagoreans  said  that  the  human  soul  is  in  some 
way  formed  of  harmony.  They  believed  it  possible  to  re- 
establish, by  means  of  music,  that  pre-existing  and  primitive 
harmony  of  our  intellectual  faculties,  too  often  troubled  by 
contact  with  this  lower  world.  The  old  writers  are  full  of 
stories  bearing  on  the  miraculous  power  of  sounds.  The 
song  of  Orpheus  subdued  wild  beasts,  arrested  the  course 
of  the  waves,  and  made  the  trees  and  the  rocks  dance. 
When  death  had  bereaved  him  of  his  Eurydice,  he  de- 
scended to  Hades.  The  infernal  gods,  charmed  by  the 
sweetness  of  his  music,  granted  him  the  return  of  his  wife, 
whom  he  would  have  brought  to  earth  again,  if  he  could 
have  abstained  from  looking  behind  during  their  journey. 
Amphion  "  the  divine  "  built  the  walls  of  Thebes.  At  the 
sound  of  his  lyre  the  stones  came  and  ranged  themselves 
one  upon  another : 


" agitataque  saxa  per  ortem 

Sponte  sua  in  mud  membra  coisse  ferunt." 

In  the  Old  Testament  we  find  music  connected  in  a  certain 
sense,  with  the  destruction  of  a  city.  At  the  trumpet-blasts 
of  the  priests  cf  Israel  the  walls  of  Jericho  fell  down. 

In  the  songs  of  Finland  we  see  the  river  sands  change  to 
diamonds,  the  haycocks  run  to  stow  themselves  in  barns,  the 
sea  calmed,  the  bears  tamed  by  the  lyre  of  Wainamoinen ; 


EFFECTS   OF   SOUND    ON    LIVING   BEINGS.  2J 

and  he  himself,  falling  at  last  under  the  spell,  sheds  in  his 
ecstacy  a  torrent  of  pearls  instead  of  tears. 

The  holy  books  of  the  Hindoos  are  not  behind-hand  in 
celebrating  the  power  of  music.  Men  and  animals  move  in 
harmony  with  the  musician's  wand,  while  inanimate  Nature 
obeys  the  influence  of  music  composed  by  the  god  Mahedo 
and  his  wife  Parbute'a.  In  the  reign  of  Akbar,  the  cele- 
brated singer  Mia  Tousine  once  sang  a  "  raga  "  consecrated 
to  the  night,  in  open  day.  Immediately  the  sun  was  eclipsed, 
and  darkness  spread  as  far  as  the  voice  was  heard.*  There 
was  another  "  raga "  which  burned  him  who  dared  to  sing 
it.  Akbar,  desiring  to  make  a  trial  of  it,  ordered  a  musician 
to  sing  this  song  while  plunged  up  to  the  chin  in  the  river 
Jumna.  It  was  of  no  use  :  the  unfortunate  singer  became  a 
prey  to  the  flames. 

Every  one  knows  how  David  played  before  Saul,  when 
the  evil  spirit  troubled  the  king.  When  Farinelli  came  to 
Spain  in  1736,  the  accents  of  his  voice  aroused  Philip  V. 
from  a  deep  melancholy.  The  king  kept  the  musician 
henceforth  near  him,  forbade  him  to  sing  in  public,  and 
loaded  him  with  honours.  He  retained  the  same  position 
with  Ferdinand  VI.  This  power  of  music  on  the  passions 
has  furnished  material  for  numberless  legends.  They  say 
that  Alexander  the  Great  was  roused  to  fury  by  the  Phrygian, 
and  calmed  by  the  Lydian  melodies  of  Timotheus.  There 
is  q,  story  too  of  a  young  man  whom  Pythagoras  found  so 
maddened  by  jealousy,  wine,  and  a  Phrygian  air  which  had 
turned  his  head,  that  he  was  about  to  set  fire  to  the  house 
of  his  mistress.  The  philosopher  of  Samos  simply  caused 

*  It  seems  that  these  marvels  are  renewed  no\v-a-days,  for  a  Paris 
newspaper  announced  lately  that  Dreyschock  had  played  the  piano  so 
divinely,  that  the  wax  lights  shone  with  unwonted  brilliancy. 


28  ACOUSTICS. 

a  calmer  melody  to  be  played  upon  the  flute,  and  the  young 
maniac  was  brought  to  his  senses.  On  another  occasion,  a 
terrible  insurrection  which  had  broken  out  in  Lacedeemon 
was  quelled  by  Terpander,  who  sang  to  the  accompaniment 
of  his  harp.  It  might  have  succeeded  in  that  age,  but  I 
doubt  whether  in  the  present  day  the  same  end  could  be 
gained  by  arming  the  police  with  flutes  and  guitars. 

The  Celtic  priests  used  music  for  softening  the  manners 
of  the  people.  Among  the  Gauls,  their  bards  could  abate 
the  fury  of  combatants.  St.  Augustine  tells  how  a  simple 
flute-player  excited  such  enthusiasm  in  a  certain  tribe  that 
he  was  elected  king. 

There  is  another  legend  which  recalls  the  story  of 
Alexander  the  Great  and  Timotheus.  Eric  the  Good, 
King  of  Denmark,  heard  a  musician  boast  that  he  could 
at  pleasure  excite  in  his  hearers  emotions  of  joy,  sorrow, 
or  anger.  Eric  wished  to  put  him  to  the  proof.  The 
musician  was  unwilling,  and  represented  to  the  king  the 
danger  of  such  a  trial.  But  the  more  he  drew  back, 
the  more  the  king  insisted.  Seeing  that  it  must  be, 
the  musician  had  all  weapons  removed,  and  arranged 
that  some  spectators  should  be  placed  outside  the  door, 
beyond  the  sound  of  his  harp.  They  were  to  wait  at 
a  distance,  and  at  a  given  signal  to  run  and  seize  the 
instrument,  and  strike  him  with  it.  Then  he  shut  him- 
self up  with  the  king  and  a  few  trusty  servants,  and 
began  to  play  on  his  harp — first  of  all  a  melancholy  air, 
which  plunged  the  listeners  in  deep  sadness;  then  changing 
to  a  joyous  tone,  he  set  them  leaping  and  dancing.  But 
suddenly  the  music  became  wild  and  fierce — they  were 
excited  beyond  measure,  and  the  king  appeared  in  a 
fury.  Immediately  his  attendants  who  waited  outside  ran, 


EFFECTS    OF    SOUND   ON    LIVING    BEINGS.  29 

snatched  the  harp  from  the  hands  of  the  player,  and  struck 
him  with  it ;  but  the  king  was  difficult  to  subdue,  and  dealt 
many  heavy  blows  before  they  managed  to  quell  him  under 
heaps  of  pillows.  Another  version  tells  how  Eric  broke 
open  the  door,  seized  a  sword,  and  killed  four  people;  of 
which  crime  he  repented  so  bitterly  that  he  abdicated,  and 
afterwards  set  out  for  Jerusalem  as  an  expiation,  but  died  at 
Cyprus. 

Under  Henry  III.  the  musician  Claudin.  playing  at 
the  wedding  of  the  Duke  de  Joyeuse,  excited  a  courtier 
to  such  a  degree,  that  he  forgot  himself  so  far  as  to  seize 
his  weapons  in  the  presence  of  the  king ;  but  Claudin  quickly 
calmed  him  by  changing  the  measure. 

The  troubadour  Pierre  de  Chateauneuf,  who  lived  in 
the  thirteenth  century,  had  a  marvellous  power  over  the 
feelings  of  his  audience.  Here  is  a  story  told  of  him 
by  Nostradamus,  in  his  "Lives  of  the  Troubadours." 
This  poet,  passing  through  the  wood  of  Vallongue,  on 
his  way  from  Roquemartine  to  visit  the  lord  of  the  place, 
fell  into  the  hands  of  robbers,  who,  after  taking  his  money 
and  stripping  him,  were  about  to  kill  him.  The  poet 
prayed  them  to  hear  a  song  he  wished  to  sing  before  he 
died,  and  they  consented.  He  improvised  a  song  in  praise 
of  the  brigands,  and  when  he  had  finished  they  gave  him 
back  his  horse,  his  money,  and  accoutrements,  in  their 
delight  at  the  sweetness  of  his  voice  and  verse. 

A  celebrated  German  legend  tells  of  a  wonderful  magi- 
cian with  an  enchanted  flute.  In  the  year  460  there  came 
to  Hameln,  in  Saxony,  a  man  who  offered  to  rid  the  town  of 
the  rats  which  infested  it.  The  corporation  promised  him  a 
large  reward.  He  set  himself  to  play  upon  his  flute  an  air, 
which  brought  the  rats  streaming  out  of  the  houses  by  thou- 


30  ACOUSTICS. 

sands.  He  drew  them  by  his  enchantment  to  the  river 
Weser,  where  all  were  drowned,  and  he  returned  to  claim 
his  promised  payment.  But,  the  rats  being  gone,  the  towns- 
folk thought  to  escape  their  bargain,  and  offered  him  a  petty 
sum,  which  he  refused.  He  said  no  more,  but  the  next 
day  appeared  with  another  flute,  which  when  he  played,  all 
the  children  followed  him.  He  led  them  to  a  cavern  in  the 
mountains,  and  they  were  never  seen  again.  Then  the 
people  repented  their  broken  faith ;  and  since  that  time 
they  date  their  years  from  "  the  emigration  of  the  children," 
as  the  Turks  do  from  the  flight  of  the  Prophet.  There  is  a 
picture  of  the  tragedy  in  the  church  at  Hameln. 

Without  going  to  legends,  we  may  find  in  modern  history 
abundant  notice  of  the  power  of  music.  Who  has  not 
heard  of  the  "Ranz  des  Vaches,"  that  air  which  brings 
home-sickness  to  the  Swiss  engaged  in  foreign  service  ?  At 
last  it  was  forbidden,  under  pain  of  death,  to  play  it  in  the 
army ;  for  when  they  heard  it  the  soldiers  would  burst  into 
tears,  or  desert,  or  even  die.  "  One  seeks  in  vain,"  says 
J.  J.  Rousseau,  "  anything  in  this  air  to  account  for  such  an 
effect.  It  has  no  power  over  foreigners,  and  only  acts  on 
the  Swiss  by  memory  and  custom — a  thousand  circumstances 
which,  recalled  by  this  music,  bring  to  mind  their  native 
land,  their  old  pleasures,  their  youth,  and  former  ways  of 
life,  exciting  sad  thoughts  of  times  gone  by.  The  music 
then  does  not  act  as  music,  but  as  an  aid  to  the  memory. 
Although  unchanged,  this  air  has  not  the  same  power  as  for- 
merly upon  the  Swiss,  for  having  lost  the  taste  for  their  early 
simplicity,  they  do  not  regret  it  when  it  is  recalled.  So  true 
it  is  that  we  must  not  seek  for  the  effect  of  music  on  the 
human  heart  simply  in  its  physical  action." 

Military  music  plays  an  important  part  in  the  history  of 


EFFECTS   OF   SOUND    ON   LIVING   BEINGS.  31 

battles.  A  quick,  brilliant  measure,  composed  of  short 
notes,  stirs  the  blood  and  incites  to  action.  Shakespeare 
speaks  of  the  "spirit-stirring"  drum.  How  the  Marsellaise 
has  set  the  pulses  beating  ! 

Men  are  not  equally  sensitive  to  the  effect  of  music. 
Some  are  indifferent,  and  some  even  averse  to  it.  St.  Augus- 
tine anathematises  such.  In  his  eyes  a  dislike  for  music  is 
a  sign  of  reprobation.  This  is  going  too  far,  for  such  an 
exception  can  only  be  explained  by  some  defect  in  physical 
organisation,  and  one  could  mention  many  great  men  who 
suffered  from  this  infirmity.  Boyle  speaks  of  women  who 
were  moved  to  tears  by  a  tone  which  did  not  a.Tect  the  rest 
of  the  audience.  Rousseau  mentions  a  lady,  known  to  him, 
who  could  not  listen  to  any  piece  of  music  without  being 
seized  with  convulsive  laughter.  In  the  History  of  the 
Academy  of  Sciences  we  read  of  a  musician  being  cured  of 
a  violent  fever  by  a  concert  given  in  his  bedroom. 

It  is  certain  that  music  will  serve  in  many  cases  as  a 
means  of  cure.  Doctors  of  the  insane  often  use  it  to  calm 
their  patients.  In  the  Middle  Ages  it  was  believed  that 
epilepsy,  hysterics,  nervous  fevers,  and  idiotcy  could  be 
cured  by  music.  According  to  Batiste  Porta,  a  flute  of 
hellebore  cured  dropsy;  a  flute  of  poplar  wood,  sciatica ;  and 
a  pipe  of  cinnamon  weed  was  a  sovereign  remedy  for  faint- 
ing fits. 

Father  Kircher  tells  us  that  music  is  the  usual  cure  for 
St.  Guy's  dance.  The  sufferers  in  this  malady  dance  and 
leap  till  they  fall  exhausted.  They  are  cured  by  a  strongly 
marked  music,  which  excites  them  more  and  more,  till  it 
brings  them  to  a  crisis.  When  the  disease  wa.s  raging  in 
Italy,  musicians  roamed  the  country  to  offer  their  assistance. 
Tha  rapid  dance  they  played  was  known  by  the  name  of 


32  ACOUSTICS 

"  Tarantella,"  a  name  which  reminds  us  that  the  malady  was 
supposed  to  be  produced  by  the  bite  of  the  "  tarantula,"  a 
large  and  venomous  spider. 

Father  Kircher  affirms  that  the  spider  himself  has  a  great 
desire  to  dance  when  he  hears  that  air.  The  experiment 
was  tried  in  Andria,  before  the  duchess  and  her  court.  They 
placed  a  tarantula  on  a  straw,  and  saw  him  jump  in  time  to 
the  music. 

Under  the  title  "Phonurgia  latrica,"  Father  Kircher 
devotes  a  long  chapter  to  the  employment  of  music  as  a 
therapeutic  agent.  This  idea  should  be  developed,  and 
might  receive  a  wider  application  than  hitherto.  It  is 
undeniable  that  music  maybe  used  as  an  exciting  or  calming 
agent,  according  to  the  rhythm  of  the  air  employed. 

It  is  known  that  with  children  the  nervous  system  is 
always  excitable.  The  most  trifling  thing  frightens  them,  or 
excites  their  imagination  to  great  joy  or  sudden  terror, 
laughter  or  astonishment.  Their  nurses  quiet  them  by  a 
soft  lullaby.  Cradled  in  melody,  the  children  sleep.  A 
joyous  tune  puts  them  in  a  merry  mood.  For  this  reason 
Montaigne  always  had  his  son  awakened  by  music,  that  he 
might  be  kept  in  a  quiet  and  happy  temper. 

Music  rests  or  excites  the  mind,  calms  or  inflames  the 
senses,  saddens  or  rejoices  the  heart.  It  acts  even  as  medi- 
cine. Every  one  knows  how  a  strongly-accented  air  helps 
one  to  walk  without  fatigue.  The  workman  at  the  crane, 
and  sailors  at  the  capstan,  help  themselves  by  singing  in 
time  to  their  movements  ;  and  a  merry,  spirited  waltz  will  set 
the  feet  tingling  for  a  dance. 

Many  animals  are  sensitive  to  music,  and  if  all  the  stories 
told  may  not  be  depended  on,  there  are  plenty  well  authen- 
ticated. At  the  head  of  these  stand  the  singing  birds,  who 


t 

1 

4 


EFFECTS   OF   SOUND    ON   LIVING   BEINGS.  35 

form  an  orchestra  of  professionals.  Besides  these  are  some 
simple  amateurs.  The  horse  easily  learns  to  regulate  his 
motions  to  music.  It  is  told  how  the  Sybarites  employed 
special  musicians  to  train  their  horses  to  dance  to  the  sound 
of  flutes.  One  of  these  musicians,  having  a  quarrel  against 
the  Sybarites,  went  over  to  the  Crotonites,  and  excited 
them  to  war.  He  marched  before  the  army  with  a  band  of 
musicians,  and  on  seeing  the  cavalry  in  the  distance  he 
played  familiar  airs,  which  threw  them  into  a  confusion  that 
ended  in  defeat. 

It  has  been  fancied  that  cattle  graze  more  heartily  to  the 
sound  of  the  flageolet  or  some  other  instrument,  and  the 
Arabs  say  that  music  fattens  them.  In  the  desert,  when  the 
camels  are  ready  to  drop  from  fatigue,  the  drivers  encourage 
them  with  cheerful  songs.  Vigneul  Marville,  of  Argonne, 
tells  an  interesting  anecdote  of  the  effects  of  music  on  dif- 
ferent animals.  While  some  one  was  playing  on  a  marine 
trumpet  (a  kind  of  stringed  instrument  invented  by  Marino), 
he  watched  a  cat,  a  dog,  a  horse,  an  ass,  a  doe,  some  cows, 
some  birds,  a  cock,  and  some  chickens  which  were  in  the 
court  below.  "  The  cat,"  he  says,  "  seemed  perfectly  indif- 
ferent to  the  sound  of  the  trumpet,  and  I  judged,  from  her 
appearance,  that  she  would  have  willingly  exchanged  all 
the  music  in  the  world  for  a  mouse;  she  gave  no  sign  of 
pleasure,  but  slept  on  in  the  sun.  The  horse  stopped  short 
under  the  window,  and  raised  his  head  from  time  to  time  as 
he  fed.  The  dog  sat  up  on  his  hind  legs  like  a  monkey, 
with  his  eyes  fixed  on  the  performer;  he  stayed  so  above 
an  hour,  and  seemed  to  delight  in  it.  The  ass  gave  no  sign 
of  emotion,  but  ate  his  thistles  in  peace.  The  doe  pricked 
up  her  beautiful  ears,  and  seemed  very  attentive.  The  cows 
stopped  a  little,  and  after  having  looked  at  us  as  if  we  were 

D    2 


36  ACOUSTICS. 

acquaintances,  passed  on  their  way.  Some  birds  in  a  ca^e, 
as  well  as  those  on  the  trees,  sang  as  if  they  would  split  their 
throats.  But  the  cock,  thinking  only  of  his  hens,  and  the 
hens,  caring  only  for  scratching  and  grubbing,  gave  me  to 
understand  that  they  cared  nothing  at  all  for  a  marine 
trumpet." 

Buffon  says  that  dogs  are  easily  touched  by  musical 
sounds.  "  I  have  seen  some  dogs  with  a  decided  taste  for 
music,  who  would  come  to  the  court-yard  while  a  concert 
was  going  on  within,  and  wait  till  the  end,  then  return 
quietly  home.  I  have  seen  others  take  the  exact  unison 
of  a  tone  that  was  sounded  into  their  ears."  But  there  is 
a  wide  difference  among  dogs  in  this  respect.  Many  will 
howl  at  the  sound  of  some  particular  instrument,  while  per- 
fectly indifferent  to  all  others.  We  often  see  poodles  show 
their  repugnance  to  certain  noises  by  twisting  themselves 
about  in  the  most  ridiculous  fashion,  and  howling  piteously. 
I  knew  a  white  greyhound  who  always  trembled  when 
her  mistress  played  her  scales.  One  day,  after  listening 
silently  for  some  time  to  -an  air  that  was  being  played, 
she  broke  out  in  little  sharp  cries,  and  then  accompanied 
the  piano  in  harmony.  Surprised  and  pleased  at  this  new 
accomplishment,  her  mistress  fondled  her,  and  gave  her 
some  sweetmeats.  Lolette  remembered  the  circumstance, 
and  afterwards,  whenever  she  had  danced  before  the  sugar 
cupboard  in  vain,  she  had  recourse  to  her  grand  expedient 
and  sang  her  song :  she  knew  that  would  bring  her  sugar- 
plums. Scheitlin,  in  his  "Psychologic  Animale,"  asserts 
that  dogs  may  be  taught  to  pronounce  certain  words.  I 
cannot  tell  how  far  this  is  worthy  of  belief. 

According  to  Buffon,  the  elephant  loves  music,  and  easily 
learns  to  move  in  time  to  it,  and  even  to  join  his  own  voice 


EFFECTS   OF   SOUND   ON   LIVING  BEINGS.  37 

to  the  accompaniment  of  drum  and  trumpet  To  test  this 
theory,  a  concert  was  once  given  to  a  pair  of  elephants  in 
the  Jardin  des  Plantes.  An  air  on  the  violin  seemed  to  give 
much  pleasure  to  one  of  them,  but  to  the  variations  of  the 
same  air  he  was  utterly  indifferent.  A  martial  air  of 
Monsigny's  had  no  effect  on  him.  The  thing  which  seemed 
to  please  him  most  was  "  Charmante  Gabrielle,"  played 
upon  the  cornet ;  he  listened,  swinging  himself  on  his  huge 
legs,  and  grunting  from  time  to  time  in  unison;  and  oc- 
casionally he  stretched  out  his  trunk  and  blew,  so  as 
to  nullify  the  sound  of  the  cornet.  When  the  piece  was 
finished  he  fondled  the  musician  with  his  trunk  as  if  to 
thank  him.  From  this  account  we  may  conclude  that  the 
elephant  prefers  the  low  notes  to  the  high,  melody  to 
harmony,  simple  airs  to  complex,  and  adagio  to  allegro. 
His  tastes  are  essentially  simple. 

Plutarch  and  Pliny  add  to  the  stock  of  anecdotes 
bearing  on  the  same  subject.  We  know  the  story  of  the 
dolphin  charmed  by  the  music  of  Arion — Schiller  has  a 
ballad  on  it.  The  authors  of  the  Middle  Ages  believed  that 
each  animal  has  its  favourite  instrument.  To  the  bear 
they  allot  the  fife,  to  the  stag  the  flute,  the  harp  to  the  swan, 
the  flageolet  to  the  singing  birds,  the  cymbal  to  the  bees,  and 
so  on.  Imagination  evidently  plays  a  great  part  in  these 
theories.  There  is  a  more  probable  story  of  a  village 
musician,  who,  returning  from  a  wedding  where  he  had  been 
performing  at  the  dance,  fell  into  a  pit  in  which  lay  a  wolf. 
He  began  instinctively  to  scrape  his  violin.  The  wolf 
crouched  in  the  opposite  corner  howling.  He  played 
on  till  the  morning,  frantically,  madly.  The  strings 
snapped  one  after  the  other.  He  was  at  the  last  string, 
when  by  good  fortune  some  villagers  passed  by.  Their 


38  ACOUSTICS. 

curiosity  was  aroused  by  the  strange  music  that  came  from 
the  ground.  They  proceeded  to  search  out  the  mystery, 
and  discovered  Daniel  in  the  ditch.  He  was  saved,  and 
the  wolf  killed. 

The  serpent  is  particularly  amenable  to  the  influence 
of  sounds.  Amongst  the  accounts  we  have  of  snake- 
charmers,  who  taught  the  serpents  to  dance  to  soft  music, 
Chateaubriand  gives  us  his  Canadian  experience  in  the 
following  story  : — 

"In  the  month  of  June,  1796,  we  were  travelling  in 
Upper  Canada,  with  some  families  of  the  tribe  of  Onon- 
tague's.  One  day,  when  encamped  in  a  plain  on  the  banks 
of  the  river  Jenesie,  a  rattle-snake  made  its  appearance. 
There  was  a  Canadian  with  us  who  played  the  flute;  he 
wished  to  exhibit  his  power,  and  advanced  towards  the 
animal  with  the  novel  weapon.  At  his  approach  the  reptile 
raised  itself  in  a  spiral,  flattened  its  head,  inflated  its  cheeks, 
and  drawing  back  its  lips,  displayed  its  poisonous  fangs  and 
cruel  jaws ;  its  forked  tongue  glanced  like  a  flame,  its  eyes 
shone  like  coals,  its  body  swollen  with  rage  rose  and  fell 
like  the  billows  of  a  furnace,  its  skin  became  stiff  and 
homy,  and  its  tail  moved  with  such  rapidity  as  to  look  like 
a  vapour,  making  the  while  a  horrid  sound.  Then  the 
Canadian  begins  to  play  on  his  flute.  The  serpent  draws 
back  his  head  with  a  motion  of  surprise.  As  it  falls  under 
the  magical  influence,  its  eyes  lose  their  awful  glitter,  the 
vibration  of  its  tail  lessens,  and  the  noise  dies  away. 
The  coils  of  the  snake  relax  by  degrees,  taking  a  wider 
circuit,  and  at  last  they  lie  one  by  one  upon  the  ground  in 
concentric  circles.  The  shades  of  blue  and  green,  of  white 
and  gold  re-appear  in  all  their  brilliancy  on  its  sensitive  skin, 
and  lightly  turning  its  head  it  rests  motionless,  in  an  attitude 


EFFECTS    OF    SOUND   ON    LIVING   BEINGS.  3Q 

of  attention  and  pleasure.  At  this  moment  the  Canadian 
walks  a  few  steps,  still  playing  on  his  flute  a  sweet,  mono- 
tonous air;  the  reptile  lowers  his  neck,  and  dividing  the 
fine  grass  with  his  head,  crawls  on  in  the  footsteps  of  the 
musician  who  leads  him,  stopping  when  he  stops,  and  fol- 
lowing when  he  goes.  He  was  thus  led  outside  the  camp, 
in  the  midst  of  a  crowd  of  spectators,  native  and  Europe 
who  could  scarcely  believe  their  eyes,  and  with  unanimous 
voice  it  was  agreed  that  the  wonderful  creature  should  be 
allowed  to  escape." 

Lizards  are  also  said  to  be  remarkably  alive  to  the 
influence  of  music.  Pere  Labat  went  to  a  lizard-hunt  with  a 
negro  armed  with  a  noose  at  the  end  of  a  pole.  They  soon 
found  one  stretched  in  the  sun  upon  the  branch  of  a  tree. 
The  negro  began  to  whistle  to  the  animal,  who  stretched  his 
neck  to  see  where  the  sound  came  from.  Then  the  negro 
quietly  approached,  still  whistling,  and  tickled  the  creature's 
sides  and  throat  with  the  end  of  the  rod.  The  lizard, 
in  delight,  rolled  over  on  his  back,  stretching  his  neck  for 
the  caress,  and  when  within  reach  the  noose  was  slipped 
over  him. 

The  love  of  the  spider  for  music  is  also  well  known.  M. 
Michelet  tells  the  following  anecdote : — "  Berthome,  the 
celebrated  violinist,  owed  his  early  success  to  the  seclusion 
in  which  he  was  made  to  work  while  very  young.  But  in 
his  solitude  he  had  one  companion  unsuspected — viz.,  a 
spider.  First  of  all  it  lived  in  the  corner  of  the  wall,  but 
gradually  it  ventured  to  the  corner  of  the  desk,  then  on  to 
the  child,  and  at  last  it  would  take  up  its  place  on  the  arm 
that  held  the  violin,  where  it  listened,  breathless  with  delight 
and  emotion.  It  served  as  an  audience;  the  child-artist 
needed  no  other  encouragement — no  other  sympathy  But 


40  ACOUSTICS. 

the  child  had  a  stepmother,  and  she  one  day,  bringing  a 
stranger  to  hear  the  boy's  practice,  saw  the  creature  at  its 
accustomed  post,  and  with  a  single  blow  from  her  slipper 
annihilated  the  audience.  The  child  took  it  so  to  heart  that 
he  was  ill  for  three  months,  and  almost  died.'* 

Whence  comes  the  power  that  music  exercises  over  the 
soul?  What  is  the  secret  affinity  by  which  sounds  excite 
passions  ? 

Music  is  the  image  of  motion.  It  employs  sounds 
arranged  in  regular  intervals,  between  which  the  voice 
mounts  and  falls,  according  to  the  fancy  of  the  musician. 
In  varying  the  duration  and  the  intensity  of  the  different 
notes  that  succeed  one  another,  every  shade  of  expression, 
every  possible  difference  of  time  is  given,  from  the  drowsy 
meandering  of  a  stream,  which  loses  itself  in  the  sands,  to 
the  stormy  impetuosity  of  a  mountain  torrent.  Now  sounds 
act  directly  on  the  nervous  system  by  the  vibration  they 
impart  to  the  sensitive  nerves,  and  thus  they  provoke  the 
disposition  of  mind  agreeing  to  the  kind  of  movement 
expressed  by  the  music.  Gaiety  is  characterised  by  a 
measure  quick  and  light,  gravity  by  a  slow  and  solemn 
movement,  anger  by  an  abrupt  and  hasty  staccato.  These 
different  characteristics  apply  equally  well  to  the  motions  of 
the  body,  and  it  is  in  this  unanimity  of  impression  and  action 
in  soul  and  body  that  we  must  seek  the  explanation  of  the 
effects  of  music.  Sorrow  paralyses  our  limbs,  while  it  makes 
our  speech  slower,  and  stops  the  flow  of  ideas.  Music  com- 
posed of  notes  which  painfully  climb  a  slow  ascent  of  semi- 
tones disposes  to  melancholy  reverie,  while,  on  the  contrary, 
notes  which  leap  by  fifths  and  octaves  fill  us  with  a  flutter  of 
excitement,  which  has  its  symbolic  expression  in  laughter 
and  the  dance.  This  explanation  of  the  psychological 


EFFECTS    OF   SOUND   ON    LIVING   BEINGS.  4! 

effects  of  music  has  not  escaped  Aristotle.  "  Why,"  says  he, 
"  do  rhythms  and  melodies  adapt  themselves  to  moods  of 
the  mind,  and  not  flavours,  or  colours,  or  odours  ?  Is  it 
because  they  are  movements  corresponding  to  actions? 
Their  intrinsic  power  rests  on  a  certain  tone,  and  also  gives 
this  tone.  Flavours  and  colours  do  not  act  so." 

There  are  other  movements  which  produce  just  the  same 
effects  upon  us.  The  cascade  which  falls  from  the  height  of 
a  rock,  the  limpid  stream  which  ripples  softly  in  its  sandy 
bed,  the  waves  that  beat  unceasingly  on  the  shore,  affect  us 
like  visible  music.  One  could  watch  the  waves  for  hours 
together  break  upon  the  level  strand.  "  The  rhythm  of  this 
movement,"  says  Helmholtz,  "which  is  not  without  a  con- 
tinual change  in  detail,  awakens  a  feeling  of  repose  without 
tedium,  and  generates  an  idea  of  life  wide  and  grand,  but  in 
perfect  and  harmonious  order.  When  the  sea  is  calm  we 
can  be  pleased  for  a  time  by  watching  its  beautiful  colours, 
but  this  pleasure  does  not  last  as  when  the  water  is  agitated. 
The  ripples  which  are  found  on  small  sheets  of  water  are  too 
hurried  in  their  motions,  and  rather  worry  than  soothe  the 
spirit" 


CHAPTER  IIL 


PROPAGATION   OF   SOUND    BY   DIFFERENT  MEDIA. 

Effect  of  Vacuum — Propagation  of  Sound  in  Gas— In  Water— In  the 
Earth — Experiments  by  Mr.  Wheatstone — Hearing  by  the  Teeth. 

How  is  sound  carried  to  the  ear  which  hears  it  ?  What  is 
the  invisible  bridge  by  which  it  travels?  The  answer  is 
easy.  A  light  and  elastic  fluid  surrounds  us  on  every  hand. 
The  winds  show  us  that  it  can  produce  the  most  powerful 
mechanical  effects.  Every  commotion  at  once  disturbs  this 
fluid,  and  is  felt  at  a  considerable  distance  from  its  starting- 
point.  Is  it  not,  therefore,  natural  to  admit  that  the  aerial 
fluid  in  like  manner  propagates  the  movements  which  produce 
sound  ?  We  see,  besides,  that  any  violent  explosion  is  always 
accompanied  by  a  sudden  displacement 
of  the  air.  Hence  scientific  men  have 
not  hesitated  to  say  that  the  air  is  the 
material  vehicle  of  sound.  There  is 
no  sound  without  air.  Here  is  the 
simple  experiment  by  the  aid  of  which 
we  may  prove  the  fact : — Hang  a  small 
bell  by  a  silk  thread  in  a  glass  globe, 
from  which  the  air  has  been  exhausted 
by  means  of  an  air-pump.  Ring  the 
bell  by  shaking  the  thread.  Nothing 
is  heard.  The  tongue  strikes  the  metal,  but  the  blow  is  in 
a  vacuum.  But  if  the  stop-cock  be  opened,  and  the  air 


Fig.  at. 


PROPAGATION  OF  SOUND  BY  DIFFERENT  MEDIA.  43 

allowed  to  enter,  the  charm  is  broken  and  the  bell  no 
longer  dumb  (Fig.  21).  This  experiment  maybe  made  with 
an  alarum  introduced  into  the  receiver  of  an  air-pump.  At 
first  it  is  heard  distinctly,  but  as  the  air  becomes  rarified  the 
sound  grows  fainter,  and  at  last  dies  away.  You  may  even 
fire  a  small  pistol  under  the  receiver.  You  see  the  flash  but 
hear  no  report.  These  experiments  will  only  succeed  when 
the  pistol  or  alarum  is  placed  upon  a  wadded  cushion,  which 
deadens  the  sound.  If  not,  the  vibration  is  transmitted  to 
the  stand  of  the  air-pump,  and  from  that  to  the  surrounding 
air,  which  carries  it  to  the  ear.  For  this  reason  it  is 
difficult  completely  to  insulate  the  sound  which  is  pro- 
duced in  the  interior  of  the  receiver.  It  is  through 
having  forgotten  this  means  of  communication  between 
the  sounding  body  and  the  external  air,  that  Kircher  thought 
he  had  found  in  the  same  experiment  a  conclusive  argument 
against  the  existence  of  a  vacuum.  He  had  exhausted  the 
air  from  a  hundred  feet  length  of  leaden  tubing,  which 
terminated  above  in  a  glass  chamber,  in  which  were  fixed  a 
bell  and  a  small  hammer  that  could  be  raised  from  outside. 
When  the  hammer  fell  upon  the  bell,  it  gave  out  a  clear 
ringing  sound,  and  from  this  Kircher  concluded  that  this 
supposed  "  vacuum  "  was  but  a  fiction  of  the  philosopher. 

According  to  Kircher,  thick  and  massive  bodies  such 
as  walls  or  rocks  do  not  transmit  sound  directly.  How 
is  it,  he  asks,  that  if  one  person  strikes  a  wall,  another 
can  hear  the  noise  by  placing  his  ear  on  the  opposite  side  ? 
This  transmission  he  explains  by  the  presence  of  air  in  the 
pores  of  all  bodies.  It  is  this  confined  air  which  conducts 
the  sound.  If  a  body  be  very  dense  it  only  allows  a  small 
portion  of  sound  to  pass,  because  it  contains  but  a  small 
portion  of  air.  He  states  that  glass  is  the  least  porous  of  all 


44  ACOUSTICS. 

substances,  and  that  a  mouse  shut  up  in  a  glass  chamber 
heimetically  sealed  would  hear  nothing  in  his  prison,  what- 
ever noise  was  made  outside.  Kirch er  adds  that  there  is  in 
Scotland  a  rock  called  "  The  Deaf  Rock,"  hiding  behind 
which  one  cannot  hear  even  the  firing  of  a  cannon.  The 
reason  of  this  phenomenon  must  be  sought  in  the  excessive 
density  of  the  rock.  It  is,  he  says,  opaque  as  to  sound, 
just  as  other  bodies  are  opaque  to  the  light. 

Although  it  is  true  that  it  is  usually  by  the  intervention 
of  air  that  sounds  reach  the  ear,  it  is  now  known  that  the 
presence  of  a  gaseous  fluid  is  not  necessary  to  their  trans- 
mission. All  elastic  bodies — gaseous,  liquid,  or  solid — con- 
duct sound.  A  repeater  plunged  in  water  under  a  glass  bell 
may  be  heard  distinctly  above.  The  divers  can  hear  under 
water  what  is  going  on  at  the  surface.  It  is  true  the  sound 
reaches  them  but  faintly ;  that  is  because  it  loses  intensity 
by  entering  into  a  medium  more  dense  than  the  air.  The 
motion  which  has  once  passed  into  the  water  is  carried  on 
there  without  hindrance.  This  is  proved  by  the  fact  that 
sound  is  as  distinct  at  the  depth  of  several  feet  as  close 
to  the  surface.  Were  it  otherwise  the  organs  of  hearing 
in  fish  would  be  utterly  useless.  It  is  certain  they  can 
hear :  tame  fish  have  been  known  to  respond  to  a  whistle. 

Solid  bodies  are  good  conductors  of  sound.  The  tick  of 
a  watch  held  at  one  end  of  a  hewn  trunk  is  heard  perfectly 
at  the  other,  not  because  of  the  air  in  the  pores  of  the  wood, 
but  because  the  wood  resounds  under  the  beating  of  the 
escapement  wheel.  By  listening  with  the  ear  on  the  ground, 
the  report  of  a  cannon  can  be  heard  at  a  distance  of  twenty- 
five  miles,  and  in  the  same  manner  the  trampling  of  horses' 
feet  is  audible  from  a  great  distance. 

"  Scuta  sonant,  pulsuque  pedum  trerait  excita  tellus." — VIRGIL. 


PROPAGATION  OF  SOUND  BY  DIFFERENT  MEDIA,  45 

This  transmission  of  sound  may  be  rendered  visible  by 
placing  a  drum,  covered  with  small  pebbles,  on  the  ground. 
When  horsemen  pass,  even  at  some  distance,  these  pebbles 
are  seen  to  move  about.  In  the  Cornish  mines  they  exca- 
vate far  out  under  the  sea,  and  there,  at  this  great  depth,  the 
noise  of  the  waves  and  even  the  rushing  murmur  of  the 
shingle  can  be  heard.  In  the  opposite  workings  of  mines, 
too,  the  miners  can  hear  through  the  intervening  soil, 
and  are  able  to  direct  one  another.  Such  subterranean  noises 
have  given  rise,  doubtless,  to  many  of  the  most  thrilling 
ghost  stories. 

It  appears  that  wood  conducts  sound  better  than  any 
other  solid  body.  Deal  is  a  better  conductor  than  box,  and 
box  than  oak.  With  four  deal  rods  Wheatstone  contrived 
to  carry  the  sounds  of  a  concert  held  in  the  cellar  through 
several  storeys  to  the  upper  room  of  a  house.  It  was  done 
in  this  way : — The  rods  rested,  one  upon  the  sounding-board 
of  the  piano,  another  upon  the  bridge  of  the  violin,  the  third 
upon  the  violoncello,  and  the  fourth  touched  a  clarionet. 
They  passed  through  the  roof  of  the  cellar,  and  on  to  the 
upper  storey  where  the  audience  sat.  Each  rod  ended  in  a 
sounding-board  of  thin  and  elastic  wood.  The  whole 
structure  vibrated  considerably  when  a  piece  of  music  was 
played  below,  and  the  room  above  was  filled  with  sounds, 
which  seemed  to  proceed  from  witchcraft.  Indeed  this 
experiment  has  a  magical  effect.  The  wood  suddenly  sings 
as  if  it  were  alive,  and  a  listener,  trusting  to  his  ears  alone, 
would  fancy  himself  in  the  presence  of  a  real  orchestra. 
Mons.  Kcenig  tried  the  same  experiment  with  a  musical 
box  shut  in  a  large  padded  chest.  A  lath  of  wood  passed 
out  from  the  interior,  and  was  surmounted  by  a  sounding- 
board.  When  this  shelf  was  lifted  nothing  could  be  heard, 


46  ACOUSTICS. 

but  no  sooner  was  it  placed  on  the  free  end  of  the  lath 
than  the  tune  which  was  being  played  inside  the  chest 
became  perfectly  audible. 

The  bony  parts  of  the  head  act  as  sound-conductors  to 
the  ear.  Thus  sound  can  be  communicated  by  the  forehead 
or  by  the  teeth.  Two  people  holding  a  thin  slit  of  wood 
between  their  teeth,  and  talking  in  an  undertone,  can  hear 
one  another  at  a  considerable  distance.  The  stethoscope, 
invented  by  Laennec  in  1819,  is  based  on  the  same  principle. 
It  consists  of  a  wooden  cylinder,  which  the  doctor  places  on 
the  chest  of  the  patient,  so  as  to  hear  more  plainly  the  noise 
from  the  heart.  Wheatstone  has  proposed  an  instrument, 
to  which  he  gives  the  name  of  microphone,  also  intended 
to  facilitate  the  hearing  of  very  faint  sounds.  It  is  a  small 
copper  basin,  which  is  placed  over  the  ear,  and  to  the  centre 
is  fixed  a  long  metal  stem,  a  kind  of  tentaculum,  which  carries 
the  sound.  Such  an  apparatus  might  be  fitted  to  each  ear, 
the  stems  uniting  into  a  single  tube. 

If  you  strike  on  a  silver  spoon,  a  glass  bell,  or  any  other 
sonorous  body  suspended  by  a  thread,  the  free  end  of  which 
is  introduced  into  an  ear-trumpet,  or  held  between  the  teeth, 
the  ears  being  stopped,  you  will  hear  a  deep,  full  sound,  like 
a  distant  bell.  A  Danish  physician,  Herhold,  tried  this 
with  a  spoon  fastened  to  a  thread  nearly  700  feet  in  length, 
of  which  one  end  was  fastened  to  a  pole,  and  the  other  held 
between  his  teeth. 

The  deaf  and  dumb  can  hear  well  by  their  teeth,  when 
the  deafness  does  not  proceed  from  paralysis  of  the  nerves. 
If  you  make  them  hold  the  edge  of  a  musical  box,  or  a  rod 
of  wood  resting  on  the  sounding-board  of  a  piano,  between 
their  teeth,  they  will  hear  the  sound  of  the  instrument. 


PROPAGATION    OF   SOUND    BY    DIFFERENT   MEDIA.          47 

One  who  is  partially  deaf  can  understand  easily  what  is 
said  to  him,  if  the  words  be  spoken  into  a  copper  or  glass 
basin  which  is  applied  to  his  ear  or  teeth. 

Dull  bodies,  such  as  hemp,  wadding,  stuffs  of  all  kinds, 
flour,  and  sawdust,  do  not  sensibly  transmit  sounds.  A 
Turkey  carpet  stifles  the  sound  of  footsteps,  while  a  thick 
door-curtain  prevents  the  sound  of  voices  passing  from  room 
to  room. 


CHAPTER  IV. 

INTENSITY   OF   SOUND. 

Circumstances  that  Vary  the  Intensity  of  Sound— Intensity  at  Night — 
Extent  or  Reach  of  Sound — The  Inverse  Square  of  Distance — 
Speaking  Trumpets — Acoustic  Tubes — Acoustic  Cornets. 

THE  strength  or  intensity  of  sound  is  determined  first  of 
all  by  the  energy  of  the  movement  which  produces  it,  but  the 
effect  on  the  ear  depends  on  the  nature  of  the  medium 
by  which  it  is  conducted.  We  have  already  seen  that 
under  the  bell  of  an  air-pump  any  sound  will  die  away 
gradually,  as  the  air  becomes  rarified.  On  high  mountains, 
where  the  air  has  not  much  density,  all  noises  lose  their 
force,  and  seem  more  distant  than  they  really  are.  At  the 
summit  of  Mont  Blanc,  15,000  feet  above  the  sea-level, 
Saussure  found  that  a  pistol  report  sounded  no  louder  than 
a  cracker  in  the  plains.  In  some  experiments  tried  at 
Quito  between  two  stations,  the  one  at  an  altitude  of 
10,000  and  the  other  13,000  feet,  the  report  of  a  nine- 
pounder  cannon,  fired  at  twelve  miles  distance,  did  not 
equal  that  of  an  eight-pounder  heard  in  the  plains  of  Paris 
at  a  distance  of  twenty  miles.  Aeronauts  have  often  told 
how  feeble  their  voices  become  in  the  high  regions  of  the 
air.  A  railway  whistle  was  heard  at  a  height  of  three  miles 
and  a  half  or  four  miles.  That  is  the  greatest  distance  at 
which  the  human  ear  has  been  able  to  catch  sounds  from 
the  earth.  At  this  time  the  air  was  unusually  damp. 


INTENSITY   OF   SOUND.  49 

In  thinking  of  the  diminution  that  all  sound  is  subject 
to  in  the  upper  air,  one  is  surprised  at  the  intensity  of  the 
noise  sometimes  produced  by  an  explosion  of  a  thunder- 
bolt. A  meteor  which  was  observed  in  1719,  and  ac- 
cording to  Halley's  calculation  travelled  through  the  air 
at  a  height  of  more  than  sixty  miles,  burst  with  an  explosion 
equal  to  that  of  a  great  cannon. 

Thunderbolts  generally  burst  with  a  great  noise,  and 
since  we  know  the  explosion  is  very  high  above  the  surface 
of  the  earth,  it  must  be  of  almost  inconceivable  violence. 

In  a  confined  space  sound  is  exaggerated.  In  the  tunnels 
where  the  workmen  laboured  at  the  foundations  of  the 
Pridge  of  Arcueil,  every  sound  took  a  metallic  ring — even 
the  voice  produced  an  unpleasing  ringing  effect  in  the  head. 

Priestley  made  very  many  experiments,  using  different 
gases  in  place  of  air.  Having  filled  a  receiver  with 
hydrogen,  and  put  a  bell  within  it,  he  found  that  the  sound 
ceased  almost  instantly.  The  density  of  hydrogen  is  only 
one-fourteenth  that  of  the  air.  Pilatre  de  Rosier,  having 
breathed  great  quantities  of  this  gas,  found  his  voice  had 
become  feeble  and  nasal.  Mannoir  and  Paul  did  the  same 
thing  at  Geneva,  and  their  voices  were  singularly  shrill 
and  thin. 

Sound  has  much  greater  force  in  water.  By  experiments 
tried  on  the  Lake  of  Geneva,  Collaclon  estimated  that  a  bell 
submerged  in  the  sea  might  be  heard  at  a  distance  of  more 
than  sixty  miles.  Franklin  asserts  that  he  has  heard  the 
striking  together  of  two  stones  in  the  water  half  a  mile 
away. 

When  sound  passes  from  one  medium  to  another  of  a 
different  density,  it  loses  more  or  less  in  intensity.  As  before 
stated,  divers  hear  noises  from  the  surface  but  faintly,  while 

£ 


$0  ACOUSTICS. 

those  outside  can  hear  well  what  passes  under  water.  For 
instance,  the  stroke  of  a  bell  can  be  heard  at  a  depth  of 
forty  feet.  From  this  we  conclude  that  water  gives  vibrations 
to  the  air  more  easily  than  air  to  water.  If  the  vibrations 
of  a  solid  body,  instead  of  passing  directly  through  the  air, 
are  conveyed  through  an  intermediate  liquid,  the  result  is 
increased  power.  Perolle  has  experimented  on  this.  He 
took  a  watch,  carefully  sealed  with  wax,  and  suspended  it 
by  a  thread  in  a  vase,  which  he  filled  successively  with 
different  liquids.  In  the  air  the  tick  of  the  watch  became 
imperceptible  at  ten  feet  distant.  Liquids  strengthened 
the  sound.  In  spirits  of  wine  the  watch  was  heard  at 
thirteen  feet ;  in  oil,  at  sixteen ;  in  water,  at  nineteen  feet : 
by  all  which  we  see  that  the  force  of  sound  augments  with 
the  density  of  the  fluid  through  which  it  passes  to  the  air. 

The  vibrations  of  a  solid  body  travel  with  difficulty 
through  a  gaseous  medium ;  a  large  surface  is  necessary 
to  increase  the  sound,  and  for  this  reason  a  sounding-board 
heightens  the  effect  of  any  musical  instrument  connected 
with  it,  by  conveying  the  vibration  to  a  large  mass  of  air,  as 
already  described  in  Wheatstone's  experiments, 

In  passing  through  the  air  itself,  ascending  or  de- 
scending, sound  must  cross  layers,  so  to  say,  of  varying 
density.  Saussure  and  Schultes  have  stated  that  sound 
travels  better  up  than  down  a  mountain  height,  and  aero- 
nauts notice  the  same  thing.  This  may  be  explained  by 
the  fact  that  the  voice,  and  all  other  sounds,  have,  even  at 
the  moment  of  their  production,  less  power  in  the  rarified 
air  of  the  higher  regions  than  in  the  denser  air  of  the 
plains. 

When  the  air  is  unequally  heated  by  the  rays  of  the 
sun  and  other  means,  sound  loses  in  power,  and  does  not 


INTENSITY  OF   SOUND.  51 

travel  far.*  By  this  circumstance  Humboldt  explains  the 
difference  in  intensity  of  sound  by  night  and  by  day. 
Nicholson  seeks  to  account  for  it  by  the  absence  of  those 
thousand  confused  noises  which  during  the  day  disturb  the 
atmosphere  around  us.  The  silence  of  night,  he  says, 
rests  our  organs,  and  renders  them  more  alive  to  slight 
impressions.  Silence  makes  our  hearing  more  acute,  as 
obscurity  tends  to  sharpen  our  sight.  But  Humboldt  brings 
his  observations  in  America  to  bear  against  this  opinion. 
In  tropical  countries  the  animals  make  more  uproar  at 
night  than  in  the  day,  and  the  wind  only  rises  after  sunset. 
Yet  the  noise  of  the  cataracts  of  Orinoco  is  heard  at 
Ature's  (more  than  a  league  distant)  three  times  more  plainly 
at  night.  Humboldt  has  also  remarked  that  this  nocturnal 
increase  in  the  intensity  of  sound  is  more  noticeable  in  the 
lower  plains  than  on  the  table-lands  or  at  sea. 

It  would,  perhaps,  be  more  correct  to  attribute  these 
facts  to  the  united  influence  of  the  different  causes  men- 
tioned, to  which  might  be  added  the  coldness  of  night.  It 
is  as  true  indoors  as  in  the  open  country,  that  night  inten- 
sifies sound.  A  mouse  nibbling  at  the  wainscot  sounds 
altogether  different  by  night  and  by  day.  This  cannot  be 
from  any  inequality  in  the  density  of  the  air,  and  we  must 
account  for  it  by  the  contrast  of  silence.  Darkness  may 
also  count  for  something.  Many  people  shut  their  eyes  in 
order  to  hear  the  better,  and  the  sense  of  hearing  is  generally 
very  acute  with  the  blind. 

We  have  just  said  that  cold  is  favourable  to  the  propaga- 

*  At  the  time  when  the  ventilation  of  the  Houses  of  Parliament 
was  under  discussion,  it  was  stated  that  the  current  of  heated  air,  which 
rose  from  the  hall,  prevented  the  voice  of  the  speaker  being  heard  at 
the  opposite  side. 

E    2 


52  ACOUSTICS. 

tion  of  sound.  This  is  a  fact  acknowledged  by  many.  In 
Polar  regions  Captain  Parry  often  heard  a  conversation, 
carried  on  in  an  ordinary  voice,  at  a  mile  distance.  One  of 
his  comrades  at  Port  Bowen  was  able  to  converse  with  some 
of  the  crew  6,700  feet  off,  the  thermometer  standing  at  the 
time  28°  below  zero.  It  might  be  supposed  that  this 
phenomenon  is  due  to  the  condensation  of  the  air,  but  the 
experiments  of  Bravais  and  Martin  do  not  confirm  such  an 
opinion.  They  ascertained  that  at  St.  Cheron  a  diapason 
mounted  on  a  sounding-board  was  heard  at  833  feet  distance 
soon  after  midday,  and  at  midnight  the  sound  reached  nearly 
1,243  feet.  On  the  Faulhorn  the  sound  was  heard  at  above 
1,804  feet  by  night,  and  even  on  Mont  Blanc  at  1,105  feet, 
although  the  air  is  much  less  dense  on  these  heights  than  in 
the  plains.  This  unexpected  result  proves  that  it  is  not  the 
condensation  due  to  the  cold  which  produces  an  increase  in 
the  intensity  of  sound ;  the  phenomenon  is  evidently  more 
complex,  and  it  may  probably  be  accounted  for  in  some 
degree  by  the  wonderful  calm  of  mountain  and  Polar 
regions. 

The  wind  has  much  to  do  with  carrying  sound.  In  the 
direction  of  the  wind,  of  course,  it  travels  far.  De  Haldat 
made  some  experiments  near  Nancy  with  a  small  drum, 
from  which  he  concluded  that  with  the  wind  it  travels  two 
or  three  times  farther  than  against  it.  Since  then  Dela- 
roche  and  Dunal  have  taken  more  exact  measurements 
in  the  plain  of  Arcueil.  They  placed  themselves  between 
two  drums  of  equal  size,  which  were  beaten  with  equal  force, 
and  ascertained  the  distance  at  which  the  two  sounds  seemed 
of  the  same  intensity,  when  a  straight  line  drawn  from  one 
drum  to  the  other  made  a  given  angle  with  the  direction  of 
the  wind.  The  faintest  sound  was  that  which  came  from 


INTENSITY   OF   SOUND.  53 

the  nearest  drum.  In  this  way  they  found  that  for  distances 
of  eighteen  or  nineteen  feet  the  influence  of  wind  was  im- 
perceptible ;  above  that  it  became  appreciable,  and  increased 
with  the  distance.  It  was  most  marked  in  faint  sounds.  A 
contrary  wind  deadened  the  sound,  but  (and  this  was  the 
most  important  result)  all  other  winds  deadened  it  too, 
though  to  a  smaller  degree.  In  still  weather,  or  in  a  line 
perpendicular  to  the  direction  of  the  wind,  the  sound 
extended  to  its  greatest  distance.  A  commotion  in  the  air 
is  always  injurious  to  the  progress  of  sound,  and  this  is 
intelligible  if  the  gusts  produce  undulations  in  the  air,  which 
act  on  those  of  sound  by  the  principle  of  interference. 
Derham  made  the  same  observation  at  Port  Ferajo  in  Elba, 
apropos  of  the  cannon  of  Leghorn,  which  was  heard  better 
in  calm  than  in  windy  weather,  even  though  the  wind  blew 
from  Leghorn. 

We  may  quote  a  remark  of  the  Baron  de  Zach  on  this 
subject.  This  astronomer  says  that  at  the  Seeberg  Observa- 
tory, which  is  in  a  high  and  lonely  situation,  the  sound  of 
the  neighbouring  church  bells,  the  noise  of  the  mills,  the 
barking  of  dogs,  and  the  voices  of  men  reached  him  clearly 
during  the  nights  when  the  stars  shone  still  and  bright, 
while  he  could  hear  next  to  nothing  when  the  stars  trembled 
in  the  field  of  his  telescope.  Therefore  the  force  of  sound 
will  indicate  to  a  certain  extent  the  state  of  the  atmosphere. 

The  great  difficulty  in  all  these  experiments  is  the  want 
of  an  instrument  to  measure  the  intensity  of  sound  ;  one  is 
obliged  to  trust  entirely  to  the  ear.  Now  the  delicacy  of 
hearing  may  vary  day  by  day,  and  it  is  never  the  same  in 
two  different  persons,  and  even  the  same  person  often  hears 
better  with  one  ear  than  the  other,  and,  which  is  worse  than 
all,  the  ear  is  more  impressed  by  shrill  tones  than  by  deep. 


54  ACOUSTICS. 

One  would  have  thought  that  the  apparent  intensity  of  a 
sound  must  be  proportioned  to  the  mechanical  power  em- 
ployed to  produce  it,  but  it  is  not  so.  When  a  siren  is 
turned  by  pressure  of  air  from  the  bellows,  the  deep  musical 
notes  that  it  emits  at  first  are  far  less  piercing  than  the  shrill 
notes  produced  as  the  velocity  of  rotation  increases.  The 
ear  becomes  more  sensitive  as  the  pitch  of  the  note  is  raised, 
and  it  has  been  demonstrated  that  the  high  treble  notes 
resound  in  the  ear  with  a  force  beyond  all  others.  There- 
fore it  is  certain  that  by  the  ear  we  can  only  compare 
sounds  of  the  same  quality.  Should  an  exact  measure 
for  the  intensity  of  sound  be  attempted,  this  is  how  it 
must  be  done: — The  phonometer  should  be  an  instrument 
giving  always  an  equal  force  to  the  sounds  produced,  by 
means  of  a  constant  pressure  from  a  bellows.  The  distance 
must  then  be  ascertained  at  which  a  sound  from  the  phono- 
meter would  appear  as  powerful  as  that  of  which  the  intensity 
is  to  be  tested.  This  intensity  would  be  to  that  of  the 
standard  in  the  inverse  proportion  of  the  square  of  the 
distances  of  the  phonometer  and  the  sonorous  source. 

All  movement  which  radiates  freely — such  as  light, 
electricity,  heat,  and  sound — spreads  from  its  starting-point 
in  concentric  spheres.  Thus,  the  surface  of  these  spheres 
increasing  always  in  proportion  to  the  square  of  the  radius, 
it  follows  that  the  intensity  of  force  emanating  from  the  centre 
must  diminish  in  the  same  proportion  as  it  is  distributed 
over  successive  spheres.  Hence  the  intensity  of  radiation 
decreases  with  the  distance  from  the  centre,  in  inverse  ratio 
to  the  square  of  the  distance.  This  law  also  governs 
gravitation ;  all  the  forces  of  attraction  or  repulsion  submit 
to  it  Theorv  would  suggest  that  it  should  equally  apply 
to  sound  Delaroche  and  Dunal  verified  it  in  the  following 


INTENSITY   OF   SOUND.  55 

manner : — Having  procured  five  bells,  perfectly  identical  in 
tone,  they  placed  one  bell  at  one  end  of  a  straight  line 
measured  along  the  ground ;  the  other  four  they  hung  at  the 
opposite  end.  Standing  midway  between  the  bells,  the 
sound  emitted  by  the  four  ought  to  be  four  times  as  strong 
as  the  sound  emitted  by  the  one.  Standing  at  one-third 
of  the  distance  which  separated  the  bells — that  is  to  say, 
twice  as  far  from  the  group  as  from  the  single  bell — the 
observer  found  the  sounds  were  equal.  The  law  then  was 
exact.  The  square  of  2  being  4,  and  its  inverse  square  j, 
the  law  requires  that  at  a  distance  of  2  feet  a  sound  should 
have  only  a  fourth  of  the  intensity  which  it  possesses  at  the 
distance  of  i  foot.  Thus  the  sound  of  the  four  bells  to- 
gether being  equal  to  4,  at  the  distance  of  i  foot,  ought  to 
be  no  more  than  J  of  4,  that  is  to  say  i,  at  the  distance  of 
2  feet.  This  the  experiment  proved,  since  at  such  a  distance 
the  four  bells  gave  a  sound  equal  to  that  of  the  single  bell, 
at  half  the  distance. 

The  distance  at  which  the  ear  can  distinguish  sounds 
represents  in  some  degree  the  measure  of  their  intensity. 
The  human  voice  is  sometimes  heard  at  a  great  distance. 
We  have  already  told  how  in  the  Polar  regions  Foster  was 
able  to  converse  at  a  distance  of  6,700  feet  from  his 
companion.  Nicholson  relates  how,  standing  one  night  on 
Westminster  Bridge,  he  heard  the  voices  of  workmen  at  Bat- 
tersea,  more  than  three  miles  off.  The  voices  of  the  sentinels 
at  Portsmouth  may  be  heard  at  night  in  the  Isle  of  Wight, 
five  miles  distant.  The  laughter  of  the  sailors  of  an  English 
man-of-war,  stationed  at  Spithead,  reached  Portsmouth.  It 
is  hardly  possible  to  credit  Derham's  affirmation  that  at 
Gibraltar  the  human  voice  has  been  heard  above  ten 
miles  distant.  Hinrichs  assures  us  that  a  brass  band  may 


5  6  ACOUSTICS. 

be  distinguished  at  four  miles,  and  the  drum  beating 
a  retreat  at  Edinburgh  Castle  has  been  heard  at  nineteen 
miles.  The  report  of  a  cannon  travels  very  far,  because  it 
communicates  a  vibration  to  the  soil.  The  cannonade 
of  Florence  was  heard  beyond  Leghorn — that  is  to  say,  to 
a  distance  of  about  56  miles — and  that  of  Genoa  to  about 
100.  In  1/62  the  cannon  of  Mayence  was  heard  at 
Timbeck,  a  small  village  about  148  miles  off.  In  1809 
the  booming  of  the  cannon  in  Heligoland  reached  Hanover 
— 157  miles;  and  on  December  4th,  1832,  the  cannon  of 
Antwerp  was  heard  on  the  Erzgebirge  mountains,  370  miles 


Fig.  28.— Speaking-Trumpet. 

distant  The  eruption  of  St.  Vincent  in  1815  was  heard 
at  Demerara,  341  miles  distant. 

To  increase  the  natural  range  of  voice  an  instrument  is 
often  used,  called  in  English  a  speaking-trumpet,  in  Latin 
tuba  stentorea.  ft  is  formed  of  a  conical  tube,  furnished 
with  a  mouthpiece,  and  terminating  in  a  wide-spreading 
cup  ;  and  is  much  used  at  sea  to  surmount  the  noise  of 
wind  and  wave;  and  formerly  the  watchman  used  it  to  give 
warning  of  fires,  or  to  call  the  labourers  to  their  work  in 
the  fields. 

It  appears  that  the  speaking-trumpet  was  invented  by 
Samuel  Morland  in  1670.  He  had  several  models  made  in 
glass  and  copper,  which  were  exhibited  before  King 


INTENSITY    OF    SOUND. 


57 


Charles  II.  and  Prince  Rupert.  In  one  experiment  made 
at  Deal,  with  an  instrument  about  5  feet  in  length  and  a 
diameter  of  2  and  20  inches  at  its  respective  openings,  the 
voice  was  carried  over  three  miles. 

When    Morland's   invention    was   made  public,   Fathei 
Athanasius  Kirch cr  claimed  it  on  the  pretext  that  he  had 


Fig.  23.— The  Horn  of  Alexander. 


already  employed  tubes  of  a  conical  form  ;  but  it  is  easy  to 
see,  from  his  earlier  writings,  that  the  learned  Jesuit  was 
speaking  only  of  ear-trumpets.  He  gives  in  this  connection 
a  description  of  "The  Horn  of  Alexander,"  from  an  old 
MS.  entitled  "  Secreta  Aristotelis  ad  Alexandrum  Magnum," 
to  be  found  in  the  Library  of  the  Vatican.  According  to 
this  unknown  author,  the  horn  enabled  Alexander  to  call 
his  soldiers  from  a  distance  of  ten  or  twelve  miles.  The 


t. 


58  ACOUSTICS. 

diameter  of  the  ring  must  have  been  about  eight  feet. 
Father  Kircher  conjectures  that  it  was  mounted  on  three 
poles.  Towards  the  end  of  the  last  century,  a  German,  Pro- 
fessor Huth,  wished  to  try  the  effect  of  such  an  instrument. 
He  had  a  model  constructed  of  thin  iron  plates,  but  on 
a  somewhat  smaller  scale  than  that  indicated  by  Kircher ; 
and  he  found  that  a  horn  of  this  kind  served  as  a  powerful 
speaking-trumpet,  especially  when  furnished  with  a  widely 
spreading  cup.  In  1654,  an  Augustine  monk  named  Salar 
made  a  similar  trial,  but  no  record  was  kept  of  the 
result. 

Shortly  after  the  invention  of  Morland,  Cassegrain  pro- 
posed that  a  hyperbolic  form  should  be  given  to  the 
speaking-trumpet.  Conyers  changed  it  to  a  paraboloid,  and 
Jean  Matthieu  Hase  made  an  elliptic  mouth-piece,  and  a 
parabolic  cup.  All  these  plans  (which  have  not  stood  the 
test  of  experience)  suppose  the  increase  of  sound  in 
the  speaking  trumpet  is  due  to  the  interior  reflection  of  the 
sonorous  waves.  This  idea  was  enlarged  on  by  Lambert 
in  his  theory  of  the  speaking-trumpet,  published  in  1763, 
and  quoted  in  almost  all  treatises  on  physics.  It  is  laid 
down  as  a  principle  that  the  object  of  the  instrument  is  to 
render  the  sonorous  radiation  parallel  to  the  axis  of  the 
tube,  wherefore  the  most  suitable  form  must  be  chosen  for 
realising  this  parallelism.  Nothing  could  be  more  at 
variance  with  ascertained  facts.  According  to  the  theory 
of  reflections  a  cylindrical  tube  would  be  useless.  Now, 
Hassenfratz  has  proved  the  contrary.  The  tick  of  a 
watch  that  in  ordinary  circumstances  would  be  indis- 
tinguishable at  a  distance  of  about  three  feet,  when  placed  at 
the  end  of  a  cylindrical  tube  twenty  inches  long,  may  be 
heard  at  a  distance  of  six  or  seven  feet  A  cylindrical  tube, 


INTENSITY   OF   SOUND.  59 

furnished  with  an  open  cup  or  bell,  would  make  a  very 
good  speaking-trumpet.  Lambert  thought  the  cup  unneces- 
sary. Experience  proves  the  contrary :  it  contributes  very 
sensibly  to  the  increase  of  sound.  Finally,  Hassenfratz 
found  that  lining  the  interior  of  the  trumpet  with  woollen 
stuff  scarcely  deadened  the  sound.  Now,  this  lining  must 
have  prevented  any  reflection  from  the  inner  walls  of  the 
tube. 

It  results  from  these  facts,  that  the  augmentation  of 
sound  depends  entirely  on  the  geometrical  form  given  to 
the  column  of  air  by  the  first  impulsion.  How  is  this 
influence  exerted?  No  theory  has  yet  explained  the 
mystery.  All  that  can  be  said  is  that  the  speaking-trumpet 
confines  the  sonorous  waves,  and  keeps  them  from  too  soon 
dispersing,  and  as  it  were  concentrates  them.  This  notion 
makes  us  instinctively  use  our  hands  as"  a  speaking-trumpet. 
The  ancients  used  to  fit  a  kind  of  cup  or  mouth-piece 
to  the  masks  worn  by  their  actors,  to  serve  the  same 
purpose. 

Notice,  still  further,  that  sound  is  not  augmented  by  a 
speaking-trumpet  in  the  direction  of  its  axis  only.  It  is 
equally  observable  in  every  direction.  Thus,  if  you  speak 
through  a  trumpet  at  a  certain  distance  from  a  high  wall, 
the  echo  is  almost  equally  powerful  whether  the  mouth  be 
turned  towards  the  wall  or  in  the  opposite  direction. 

The  tubes  used  on  board  ship  are  seldom  more  than  six 
feet  in  length,  and  eleven  inches  in  diameter.  One  was  made 
in  England  of  twenty  feet  or  more,  which  carried  words 
two  miles.  When  used  only  for  an  inarticulate  cry,  a  good 
speaking-trumpet  will  carry  the  sound  three  or  four  miles. 
Further  experiments  on  this  subject  would  be  interesting. 

In  England  and  America  they  are  trying  many  different 


60  ACOUSTICS. 

means  for  warning  vessels  at  sea,  when  the  lighthouses  are 
invisible  through  fog.  The  common  method  is  a  bell. 
There  is  one  on  the  Isle  of  Copeland,  in  the  Irish  Sea,  rung 
by  machinery,  which  may  be  heard  at  a  distance  of  fourteen 
or  fifteen  miles.  At  Boulogne,  a  bell  is  fixed  in  the  focus  of 
a  parabolic  reflector,  and  struck  alternately  by  three  ham- 
mers, which  are  set  in  motion  by  a  falling  weight.  On 
board  some  of  the  floating  lighthouses  they  use  drums  or 
cannons.  At  New  Brunswick  they  have  a  steam  whistle. 
In  a  small  island  off  Holyhead  they  protect  the  sea-gulls, 
that  their  cry  may  warn  vessels;  but,  unfortunately,  in  1856 
the  Regulus  was  wrecked  in  this  part  of  St.  George's 
Channel,  and  some  rats  escaping  from  the  sinking  vessel 
found  their  way  to  the  island,  and  have  multiplied  to  such  a 
degree  as  seriously  to  affect  the  bird  population.  A  cat  was 
introduced  to  work  havoc  among  the  rats,  but  she  made 
common  cause  with  them,  showing  quite  as  great  a  partiality 
for  the  birds  as  they  did. 

The  principal  difficulty  in  this  kind  of  signal  is  that  the 
fog  interferes  with  the  propagation  of  sound — at  least,  it 
would  seem  so  from  Cunningham's  experiments,  but  positive 
proof  is  wanting.  To  distinguish  the  signals  of  different 
stations  they  can  employ  intermittent  sounds,  or  a  succession 
of  different  notes.  Cowper  and  Holmes  have  proposed 
steam  trumpets  for  this  purpose.  Captain  Ryder  would 
unite  a  cannon  with  a  whistle.  It  might  be  possible  to 
propagate  a  very  powerful  sound  through  the  water  itself,  in 
which  case  the  sailors  must  use  a  long  ear-trumpet,  like  that 
which  Colladon  had  for  his  experiments  on  the  lake  of 
Geneva.  They  must  fish  for  the  sound.  Prsetorius  invented 
an  instrument  of  the  same  kind  for  the  solid  earth.  It  was 
a  sort  of  shovel,  driven  into  the  ground ;  the  ear,  being 


INTENSITY   OF   SOUND.  6 1 

applied  to  the  handle,  became  conscious  of  a  vibration  at 
the  approach  of  the  enemy.  The  inconvenience  of  these 
contrivances  is  that  they  never  tell  the  direction  whence  the 
noise  proceeds. 

When  sound  is  propagated  in  a  limited  space  of  air,  it 
loses  but  little  in  intensity.  Of  this,  hearing-tubes  afford  a 
striking  example.  These  are  long  tubes  of  metal  or  gutta- 
percha,  by  means  of  which  conversation  may  be  held  be- 
tween persons  at  some  distance.  They  are  much  used  in 
houses  for  communicating  from  the  upper  to  the  lower 
storeys,  and  on  board  ship  for  speaking  to  the  man  aloft,  &c. 

In  the  experiments  made  by  Biot  in  the  empty  water- 
pipes  of  Paris,  he  found  that  the  lowest  sounds  were  per- 
fectly transmitted  through  a  column  of  air  3,120  feet  in 
length.  "Indeed,"  says  he,  "there  was  but  one  way  to 
avoid  hearing,  and  that  was  not  to  speak,  even  in  the  faintest 
whisper."  The  firing  of  a  pistol  at  one  end  of  the  tube  ex- 
tinguished a  lighted  candle  at  the  other,  and  blew  some 
light  bodies  to  a  distance  of  twenty  inches.  3  ^  ^^ 

Once  upon  a  time,  in  almost  every  fair  might  be  found  a 
"  Delphic  oracle,"  a  Turk's  head  which  answered  all  ques- 
tions whispered  into  its  ear.  This  was  managed  by  a  hear- 
ing-tube hidden  in  the  pedestal  of  the  apparatus,  and  com- 
municating with  a  confederate.  The  most  ingenious  thing 
of  the  kind  was  M.  de  Kempelen's  "  speaking  woman."  This 
piece  of  wax- work  was  seated  on  a  chair  placed  alternately 
in  two  different  spots  of  the  hall,  where  spectators  were  re- 
ceived. They  spoke  in  her  ear,  and  the  answer  seemed  to 
come  from  her  mouth.  The  plan  of  the  thing  was  this  :  A 
tube  passed  from  the  hollow  of  the  wax  head  through  one 
of  the  feet  of  the  chair.  Two  other  tubes,  connected  with 
an  adjoining  chamber,  passed  under  the  flooring  of  the  hall 


02  ACOUSTICS. 

to  two  points,  each  marked  by  a  small  hole.  Round  these 
points  the  boards  had  been  planed  underneath  to  a  very 
thin  partition,  and  pierced  with  a  small  hole.  They  took 
care  to  place  the  chair  so  that  the  hollow  foot  covered  one 
of  these  holes. 

The  "  invisible  woman,"  who  created  such  a  sensation  at 


Fig.   24. — The  Invisible  Woman. 

the  beginning  of  this  century  in  all  the  principal  towns  of 
the  Continent,  may  be  explained  as  simply.  The  most  striking 
part  of  this  machine  was  a  hollow  globe  (Fig.  24),  furnished 
with  four  horns  in  the  shape  of  trumpets,  and  suspended  by 
an  iron  bar,  or  more  likely  by  four  silk  ribands,  from  the  ceiling 
of  the  hall.  This  globe  was  enclosed  in  a  cage  of  open  trellis- 
work,  sustained  by  four  pillars,  one  of  which  was  hollow. 
Through  this  passed  a  tube,  which  was  carried  also  half- 
way through  one  of  the  upper  horizontal  cross-bars,  whence 


INTENSITY   OF   SOUND.  63 

the  narrowest  possible  chink  faced  the  opening  of  one  of  the 
trumpets.  The  voice  seemed  then  to  proceed  from  the 
globe.  Probably  the  persons  who  gave  the  answers  from  a 
neighbouring  room  had  a  peep-hole  by  which  they  could 
watch  what  was  passing  in  the  hall.  The  questions  were 
always  put  at  one  of  the  trumpets'  mouths. 

Sound  is  wonderfully  propagated  by  means  of  chimneys, 
gas-pipes,  heating  apparatus,  &c.  Some  chimneys  will 
convey  all  kinds  of  noises  from  out-doors  into  the  house ; 
therefore  in  prisons  and  .mad-houses  they  are  specially 
careful,  in  the  arrangement  of  such  parts  of  the  building,  to 
avoid  any  possibility  of  communication  between  the  prisoners 
or  patients  by  such  means. 

At  Carisbrook  Castle,  in  the  Isle  of  Wight,  there  is  a 
well  celebrated  for  its  acoustic  properties.  When  a  pin  is 
dropped  down  its  contact  with  the  water  is  distinctly  heard, 
and  shouting  or  couching  into  the  well  produces  a  long- 
drawn  echo.  The  depth  of  this  well  is  210  feet,  and  its 
diameter  j  2  feet. 

In  facts  of  this  kind  it  is  sometimes  difficult  to  determine 
how  much  of  the  effect  is  due  to  the  material  of  which  the 
walls  of  the  enclosed  channel  are  formed.  The  same  remark 
may  apply  to  the  transmission  of  sounds  along  a  smooth 
surface.  Hutton  believed  that  a  person  reading  aloud  upon 
the  Thames  might  be  heard  118  feet  off,  while  upon  solid 
ground  the  distance  must  be  limited  to  75  feet.  In  the 
Argentine  Theatre  at  Rome  it  has  been  noticed  that  the 
voices  of  the  actors  are  much  better  heard  since  a  water-pipe 
was  carried  under  the  flooring  of  the  hall,  and  it  is  natural  to 
suppose  that  the  water  has  something  to  do  with  this  im- 
provement. 

Most   extraordinary  acoustic   effects    may  be    noticed 


64  ACOUSTICS. 

under  the  domes  of  different  churches,  that  can  no  more 
be  explained  by  theories  of  the  reflection  of  sound  than  the 
speaking-trumpets.  The  vaulted  dome  seems  to  guide  the 
sound.  It  has  been  noticed  that  two  persons  talking  in  a 
whisper  at  opposite  sides  of  a  gallery  under  the  cupola  of  St. 
Peter's  at  Rome  can  hear  one  another  distinctly,  without 
being  audible  to  others.  In  the  Whispering  Gallery  under 
the  dome  of  St.  Paul's,  the  same  phenomenon  occurs ;  the 
ticking  of  a  watch  even  may  be  heard.  In  Gloucester  Cathe- 
dral, a  person  speaking  in  low  tones  in  the  gallery  east  of  the 
choir  can  be  heard  at  the  other  end,  i6ofeet  away.  Brydone 
says  the  same  thing  happens  in  Girgenti  Cathedral.  When, 
the  great  door  is  shut  every  syllable  spoken  near  it  reaches 
the  other  end  of  the  nave,  but  cannot  be  heard  midway. 

These  effects  are  but  imperfectly  explained  by  the  re- 
verberation of  sonorous  reflections,  which  accounts  for  the 
phenomena  of  elliptical  vaults,  as  will  be  seen  in  the  fol- 
lowing chapter.  It  seems  as  though  the  surface  guided  the 
sound.  Hutton  tells  how  in  a  garden  at  Kingston  a  whisper 
along  the  wall  was  heard  at  a  distance  of  197  feet.  It  is 
still  more  striking  to  notice  how  a  semi-cylindrical  channel 
will  guide  sound.  Hassenfratz  put  a  watch  at  one  end  of  a 
passage  formed  by  two  planks  of  wood  resting  edge  to  edge. 
He  could  then  hear  the  beats  at  a  distance  of  seventy-five 
feet,  while  in  the  open  air  they  became  inaudible  at  six  feet 
Some  buildings  have  an  accidental  channel  of  this  kind. 
There  is  one  in  an  hexagonal  hall  of  the  Paris  Observatory, 
where  the  opposite  corners  are  furnished  with  a  means  of 
communication  by  a  sort  of  gutter  passing  round  the  roof. 
A  conversation  may  be  carried  on  there  in  utter  privacy, 
though  the  hall  be  filled  with  listeners.  At  the  foot  of  the 
grand  staircase  in  the  Conservatory  of  Arts  and  Manufac- 


INTENSITY   OF   SOUND.  Oj 

tures  in  Paris  is  a  vaulted  lobby,  where  the  sound,  following 
the  arches,  descends  in  the  corners  of  the  walls. 

The  same  principle  explains  the  mystery  of  "  speaking 
chambers."  Very  often  they  are  but  the  consequence  of  an 
accidental  arrangement  of  the  walls.  We  have  the  most 
curious  of  these  phenomena  in  "  The  Ear  of  Dionysius,"  a 
cavern  in  the  quarries  of  Syracuse,  in  Sicily.  In  the  depths  of 
this  cave  the  tyrant  of  Syracuse  had  a  cell  formed  for  his  pri- 
soners, whence  the  least  sound  was  carried  to  the  ear  of  the 
sentinel  watching  at  the  entrance  of  the  subterranean  passage. 

Here  is  Kircher's  plan  of  the  cave ;  c  is  the  entrance,  d 


Fig.  25  — Plan  of  the  Ear  of  Dionysius. 

the  cell ;  //is  the  projection  of  a  large  groove,  thirty  inches 
in  diameter,  hollowed  in  the  middle  of  the  roof,  nearly  100 
feet  above  the  pavement,  and  ending  at  e,  where  the  sentinel 
was  stationed  ;  b  is  a  recess  contrived  in  the  side  wall.  The 
groove //acts  as  a  sound-conductor.  The  opening  e  has 
long  been  walled  up,  and  consequently  at  the  present  day 
the  cave  exhibits  most  curious  effects  of  echo.  Kircher 
visited  it,  and  he  tells  how  the  faintest  sound  is  exag- 
gerated, so  that  a  word  pronounced  in  an  undertone  becomes 
a  clamour,  and  a  clap  of  the  hands  is  like  the  report  of  a 
cannon.  A  duet  sung  by  two  voices  is  repeated  as  a 
quartet  The  length  of  the  cavern  is  about  fifty-two  feet. 


66  ACOUSTICS. 

Kircher  has  planned  numberless  imitations  of  "  The  Ear 
of  Dionysius."  Some  consist  of  a  large  twisted  tube,  with  a 
wide  mouth  opening  towards  the  place  where  the  sounds  are 
produced,  and  passing  into  the  interior  of  the  room  where 
the  sounds  are  to  be  heard.  This  leads  us  to  speak  of  the 
ear-trumpet,  an  instrument  for  gathering  sound  and  con- 
densing it  in  the  ear.  They  are  made  in  various  forms,  the 
simplest  and  the  worst  of  which  is  the  cone.  It  is  requisite 
that  the  outer  opening  should  be  larger  than  the  one 
introduced  into  the  ear ;  then  it  is  easy  to  understand  how 
the  movement  in  that  portion  of  air  which  filled  the  wider 
mouth  of  the  tube  is  concentrated  in  the  narrower  passage, 
and  so  reaches  the  ear  intensified  in  power. 

Towards  the  end  of  the  seventeenth  century,  they  tried 
ear-trumpets  in  the  form  of  hunting-horns.  One  of  the 
commonest  forms  is  that  given  as  i  in  the  accompanying 
plate.  No.  2  is  another  of  the  most  usual.  Curtis  had 
some  made  to  lengthen  out  like  a  telescope  (No.  3).  Ittard 
has  devised  numerous  shapes.  For  instance,  No.  4  is  a 
kind  of  ellipsoid,  furnished  with  a  wide  mouth,  and  a  bent 
tube  to  fix  in  the  ear.  The  dotted  line  shows  a  membrane 
of  gold-beaters'  skin,  which  renders  the  sound  less  confused, 
though  it  does  not  strengthen  it.  In  No.  5  we  have  a  shell, 
with  a  mouth  and  a  tube  added,  and  two  membranes  of 
gold-beaters'  skin. 

Quite  recently  Kcenig  has  constructed  an  ear-trumpet, 
which  serves  also  as  a  stethoscope  (No.  6).  A  capula, 
closed  by  a  membrane,  communicates  with  the  ear  through 
an  india-rubber  tube  terminating  in  an  ivory  top.  When  any 
one  speaks  before  this  membrane  it  takes  the  impression 
from  the  motion  of  the  air,  and,  carrying  it  to  the  air  con- 
tained in  the  tube,  forces  it  against  the  tympanum  of  the 


INTENSITY   OF    SOUND.  67 

ear.  When  employed  as  a  stethoscope,  this  simple  mem- 
brane is  replaced  by  a  lens  formed  of  a  double  membrane, 
that  can  be  inflated  by  means  of  a  cock  at  the  side.  The 
upper  membrane  is  placed  upon  the  chest  of  the  invalid, 
where  it  moulds  itself  to  the  skin,  and  faithfully  transmits 
the  motion  of  the  air  imprisoned  in  the  lens  to  the  ear  of  the 


Fig.  26.— Ear-Trumpets. 

doctor.  With  this  apparatus  the  patient  might  sound  his 
own  lungs,  by  pressing  the  capula  against  his  chest  and 
introducing  the  tube  into  his  ear;  or  a  whole  class  of 
medical  students  might  auscultate  the  same  patient  simul- 
taneously, since  several  tubes  can  be  introduced  into  the 
capula.  The  tubes  may  be  lengthened  to  twelve  rr  fifteen 
feet,  without  materially  weakening  the  sound;  so  that  a 
doctor  could  sit  in  his  library,  and  listen  to  the  beating  of 
his  patient's  heart  in  an  upper  room. 


F  2 


CHAPTER  V. 

VELOCITY    OF    SOUND. 

Mersenne — Bureau  des  Longitudes — Captain  Parry— R -gnault — Beu- 
dant — Colladon  and  Sturm  —  Biot — Wertheim  —  Distances  by 
Sound — Depth  of  a  Lake  by  the  Echo  from  the  Bottom. 

THAT  sound  is  not  propagated  instantaneously  was  noticed 
by  the  first  inquirers  into  its  phenomena.  Every  one  knows 
that  thunder  is  generally  not  heard  till  long  after  the  lightning 
flash  has  passed,  and  the  interval  increases  according  to  the 
distance  of  the  storm.  But  what  is  the  exact  time  that 
sound  must  take  to  travel  a  certain  distance  ?  in  other  words, 
what  is  its  velocity  ?  This  was  the  question  that  Mersenne 
and  Kircher  set  themselves  to  solve.  "Light,"  says  Mer- 
senne, "  spreads  through  the  sphere  of  its  activity  in  a 
moment ;  or,  if  it  takes  time,  it  is  so  short  a  time  as  to  be 
imperceptible.  But  sound  occupies  time  in  travelling,  which 
increases  with  the  distance  between  the  place  of  its  produc- 
tion and  the  listener.  This  has  been  verified  by  many 
experiments.  The  axe  of  the  wood-cutter  will  have  struck 
a  second  blow  before  the  sound  of  the  first  is  heard  at  a 
distance  of  600  paces.  Repeated  experiments  are  necessary 
to  ascertain  if  this  delay  in  sound  is  proportional  to  the 
distance."  He  then  proceeds  to  describe  the  different  ex- 
periments by  which  its  velocity  has  been  tested,  such  as 
counting  the  beats  of  the  pulse  from  the  moment  when  the 
flash  of  a  musket  or  a  piece  of  artillery  is  seen  to  the  time 


VELOCITY   OF   SOUND.  69 

when  the  report  is  heard.  He  records  observations  of  this 
kind  made  at  the  siege  of  Rochelle  by  one  of  the  officers ; 
but  the  results  are  very  inconsistent,  and  Mersenne  there- 
fore concludes  that  the  velocity  of  sound  varies  according  to 
local  and  atmospheric  circumstances.  Yet  in  any  case  he 
holds  it  certain  that  sound  does  not  travel  so  fast  as  the  ball 
from  an  arquebus ;  indeed  he  says,  "  The  birds  are  often 
seen  to  fall  from  the  branches  of  the  trees  before  the  report 
is  heard,  although  one  may  be  quite  close  to  the  arquebus." 
In  1673  Kircher  declared  that  nothing  was  yet  known 
certainly  as  to  the  velocity  of  sound,  but  the  Florentine  Aca- 
demy was  instituting  experiments  for  the  purpose  of  throw- 
ing light  on  this  interesting  subject.  These  experiments 
seem  to  have  taken  place  in  1660.  They  reckoned,  from  the 
time  elapsing  between  the  flash  and  the  report  of  a  cannon, 
that  the  velocity  must  be  1,175  ^eet  a  second.  A  simple 
means  of  gaining  an  approximate  idea  of  the  velocity  of 
sound  is  found  in  an  echo.  Mersenne  reckoned,  with  the 
help  of  a  pendulum,  that  seven  syllables  could  be  pro- 
nounced in  a  second.  Now,  an  echo  at  519  feet  distance 
will  give  back  seven  syllables.  It  takes  one  second  to  pro- 
nounce them,  and  they  are  heard  again  the  following  second. 
Therefore  the  sound  travels  519  feet  going,  and  the  same 
returning — 1,038  feet  in  all — in  one  second ;  "  so  that,"  says 
Mersenne,  "  we  may  take  this  as  the  velocity  of  reflected 
sounds,  which  I  have  found  always  the  same,  whether  pro- 
ceeding from  trumpets,  firearms,  stones,  or  voices."  These 
experiments,  according  to  which  the  velocity  of  sound  would 
be  about  1,038  feet  per  second  (we  shall  see  presently 
that  this  number  was  pretty  near  the  truth),  were  disputed 
by  Kircher,  who  raised  a  host  of  objections  against  the  sup- 
posed equality  in  time  for  the  transmission  of  sounds  of 


70  ACOUSTICS. 

different  kinds.  He  supposed  that  a  very  strong  sound 
must  of  necessity  be  returned  more  quickly,  just  as  a  ball 
would  rebound  from  a  wall  the  faster  according  as  the  pro- 
pelling force  was  stronger ;  but  this  comparison  is  altogether 
false,  for  sound  does  not  rebound  like  the  ball,  since  the 
mass  of  air  in  which  the  sound  is  propagated  does  not 
change  its  place.  The  air  is  not  thrown  against  the  obstacle, 
neither  does  it  return  to  the  ear ;  there  is  no  analogy  be- 
tween the  sonorous  motion  and  that  of  the  ball.  Kircher 
also  fancies  that  the  echo  is  quicker  in  the  silence  of  night 
than  in  the  noisy  day,  and  that  the  winds  have  something  to 
do  with  the  matter. 

The  first  exact  experiments  on  the  velocity  of  sound  in 
air  were  instituted  in  lyJS  by  a  commission  of  the  Academy 
of  Science,  composed  of  La  Caille,  Maraldi,  and  Cassini  de 
Thury,  who  associated  several  others  with  them.  They 
chose  for  their  stations  the  Paris  Observatory,  the  Pyramid 
of  Montmartre,  the  Mill  of  Fontenay-aux- Roses,  and  the 
Chateau  de  Lay,  at  Montlhery.  Cannons  placed  on  the 
heights  of  Montlhe'ry  and  Montmartre  were  fired  alternately, 
and  the  observers  at  the  four  stations  measured,  by  help  of 
pendulums,  the  time  which  elapsed  between  the  arrival  of 
the  flash  and  of  the  report.  They  found  that  on  an  average 
the  sound  took  one  minute  twenty-four  seconds  to  travel 
93,140  feet — that  is,  about  1,106  feet  per  second,  at  a  tem- 
perature of  6°  (Cent).  Afterwards,  when  the  influence  of 
temperature  came  to  be  better  known  (augmenting  the 
velocity  about  two  feet  for  every  degree  Centigrade),  they 
deduced  from  this  reckoning  a  velocity  of  1,093  feet  for  o°. 
The  observations  made  at  the  intermediate  stations  showed 
that  the  velocity  of  sound  is  uniform — that  is  to  say,  it  does 
not  slacken  towards  the  end  of  its  journey,  however  great 


VELOCITY   OF   SOUND.  fl 

the  distance.  They  proved,  moreover,  that  it  is  the  same 
by  day  and  by  night,  in  fair  weather  and  foul,  and  whatever 
may  be  the  direction  of  the  cannon-mouth;  but  that  it  is 
influenced  by  the  wind,  according  to  its  force,  and  the  angle 
that  it  makes  with  the  direction  of  the  sound.  A  contrary 
wind  retards,  while  a  favourable  one  accelerates  its  trans- 
mission. These  experiments  were  repeated  with  some  modi- 
fications by  Kaestner,  Benzenberg,  Goldingham,  and  others, 
but  their  conclusions  were  not  altogether  satisfactory.  A 
new  measurement  was  taken  in  1822,  at  the  request  of 
Laplace,  by  the  members  of  the  Bureau  des  Longitudes. 
Two  pieces  of  cannon  were  placed,  one  on  the  elevation  of 
Montlhery,  the  other  at  Villejuif:  the  distance  is  about 
61,067  feet.  Prony,  Arago,  and  Mathieu  were  stationed  at 
Villejuif;  Alexander  Humboldt,  Gay-Lussac,  and  Bouvard  at 
Montlhery.  Each  was  provided  with  a  good  stop  chro- 
nometer, recording  at  least  the  tenth  of  a  second.  The 
cannons  fired  at  Villejuif  were  all  heard  at  Montlhery,  but 
the  return  shots  were  so  faint  that  few  of  them  were  heard 
at  Villejuif.  This  singular  circumstance  prevented  their 
noting  the  influence  of  the  wind  as  accurately  as  they  would 
have  done.  According  to  their  calculation,  the  velocity  of 
sound  at  a  temperature  of  zero  is  1,086  feet.  For  every 
degree  of  heat  two  feet  must  be  added,  so  that  at  15°  the 
velocity  would  be  1,116  feet. 

Since  these  memorable  experiments,  others  have  been 
made  in  Germany,  Holland,  America,  and  other  places. 
During  Franklin's  voyage  to  the  Arctic  Seas  in  1825, 
Lieut.  Kendall  discharged  forty  rounds  of  cannon,  the 
temperature  varying  from  2°  to  40°  below  zero.  Captain 
Parry  also  made  some  observations  on  the  propagation  of 
sound  in  equally  low  temperatures.  The  united  results  of 


72  ACOUSTICS. 

these  inquiries  tend  to  the  conclusion  that  in  calm  air  the 
velocity  of  sound  is  somewhere  about  1,088  feet  per  second. 

Biot  contrived  an  ingenious  plan  for  ascertaining  whether 
sounds  varying  in  pitch  are  equal  in  velocity.  If  not,  it  is 
clear  that  the  notes  of  a  musical  air  heard  afar  off  would 
be  altogether  changed,  since  certain  notes  must  be  heard 
either  too  soon  or  too  late.  In  ordinary  circumstances  this 
slight  inequality  would  not  be  noticed,  the  distance  of  the 
instruments  being  insufficient  to  render  such  delay  appre- 
ciable. Biot,  therefore,  arranged  that  a  flute  should  be 
played  at  one  end  of  the  aqueduct  of  Arcueil  (which  was 
then  empty)  while  he  listened  at  the  other.  The  melody 
reached  him  in  perfect  time  and  tune,  having  lost  nothing  in 
its  transit  through  3, 1 20  feet  of  tubing. 

About  four  years  ago,  M.  Victor  Regnault  resumed  these 
inquiries  with  all  the  appliances  of  modern  science.  Nearly 
400  discharges  of  cannon  were  fired  in  the  plain  of  Vincennes. 
The  arrival  of  the  sound  was  ascertained  by  means  of  a 
membrane,  which,  swinging  a  little  pendulum  at  the  arrival 
of  the  shock,  thereby  interrupted  an  electric  current.  The 
instant  both  of  the  flash  and  the  report  were  registered  on 
prepared  paper  by  a  Morse  telegraph.  On  the  same  paper 
an  electric  pendulum  marked  the  second,  close  by  the  spot 
where  a  vibrating  tuning-fork  registered  the  hundredth  part 
of  a  second. 

These  experiments  were  terminated  last  year  in  the  new 
sewers  of  St.  Michel,  a  series  of  large  tubes  extending  for  a 
mile  or  more.  The  opening  being  closed  the  moment  that  the 
sound  was  thrown  into  the  tube,  it  was  observed  that  the  noise 
of  a  pistol  or  trumpet  rebounded,  so  to  say,  going  backwards 
and  forwards  as  many  as  ten  times,  swinging  each  time  the 
pendulums  placed  along  its  route.  M.  Regnault  also  tried 


VELOCITY   OF   SOUND.  73 

the  effect  of  a  simple  shock  or  impetus  given  to  a  column  of 
air  without  sound.  I  was  present  at  some  of  these  experi- 
ments, of  which  the  results  were  curious  enough  ;  but  as 
nothing  has  been  yet  published,  it  will  be  understood  that  I 
can  say  no  more. 

The  velocity  of  sound  in  different  -gases  has  only  been 
tested  partially.  It  is  believed  that  in  oxygen,  carbonic  oxide, 
olefiant  gas,  nitrogen,  and  sulphuretted  hydrogen  it  is  about 
the  same  as  in  air ;  but  in  hydrogen,  four  times  greater — 
that  is  to  say,  about  4,167  feet  per  second. 

The  velocity  of  sound  in  liquids  was  first  experimented 
upon  by  Beudant  He  had  two  vessels  moored  in  the 
harbour  of  Marseilles,  a  certain  distance  apart.  An  assistant 
on  board  one  of  these  vessels  struck  a  bell  sunk  at  its  side, 
at  the  same  time  giving  a  signal  which  could  be  seen  from 
the  other  boat,  where  the  moment  of  arrival  of  the  sound 
in  the  water  was  recorded.  The  velocity  as  determined  on 
this  occasion  was  4,921  feet;  but  Beudant  thought  the  result 
not  worth  publishing,  on  account  of  the  imperfection  of 
the  means  employed.  It  is  only  to  be  found  in  the  Memoir 
of  Colladon  and  Sturm.  These  two  measured  the  velocity  of 
sound  in  the  water  of  the  Lake  of  Geneva.  The  depth  of  the 
lake  (45  9  feet),  and  the  clearness  of  its  waters,  recommended 
it  in  a  special  manner  for  experiments  of  this  kind.  The 
greatest  extent  of  deep  water  was  found  between  Rolle  and 
Thonon,  a  distance  of  about  eight  miles.  A  vessel  was  moored 
off  Rolle,  carrying  a  bell  of  nearly  140  pounds  weight,  which 
was  submerged.  It  was  so  arranged  that  when  the  hammer 
struck  the  bell,  a  lighted  match  fell  upon  a  heap  of  powder 
lying  on  the  deck.  Another  vessel  was  moored  off  Thonon, 
from  which  they  observed  the  flash,  and  noted  the  arrival  of 
the  sound  by  means  of  a  curiously  shaped  hearing-trumpet 


74  ACOUSTICS. 

(Fig.  27).  It  was  formed  of  a  long  tube,  opened  and  bent,  and 
had  a  membrane  stretched  across  the  mouth.  The  observer 
turned  the  surface  of  this  membrane 
towards  the  bell,  and  placing  his  ear 
to  the  upper  extremity  of  the  cone, 
watched  for  the  signal.  The  moment 
the  flash  was  apparent  he  touched  the 
spring  of  a  "  stop  watch"  (a  kind  of 
watch  whose  hands  can  be  either 
stopped  or  set  at  liberty,  by  a  simple 
pressure  on  the  spring),  stopping  it 
Fi  2  immediately  the  sound  reached  him. 

This  was  invariably  nine  seconds  after 
the  flash.  Dividing  the  distance  between  the  two  vessels 
by  the  interval  of  time,  the  velocity  is  determined  to  be  4,708 
feet  per  second — more  than  four  times  greater  than  in  the  air. 
These  experiments  gave  rise  to  many  interesting  remarks 
upon  the  propagation  of  sound  in  water.  Instead  of  the 
prolonged  resonance  that  is  produced  in  air,  the  sound  of 
the  bell  was  short  and  flat,  like  the  clashing  of  two  steel 
blades.  The  water,  which  is  but  slightly  compressible,  had 
robbed  it  completely  of  its  ringing  tone.  At  one  time  the 
lake  was  rough  and  stormy,  and  they  had  great  trouble  in 
keeping  the  boats  to  their  moorings,  but  this  had  not  the 
slightest  influence  on  their  experiment.  Wertheim  afterwards 
determined  the  velocity  of  sounds  in  different  liquids,  and 
of  his  results,  these  are  the  two  extremes:  in  absolute 
alcohol,  at  a  temperature  of  23°  C,  the  velocity  is  3,808 
feet  per  second ;  and  in  a  solution  of  chloride  of  calcium, 
6,496  feet. 

Through  solids  the  transmission  of  sound  is  much  more 
rapid  than  in  gases  or  liquids.    The  early  experimenters  who 


VELOCITY   OF   SOUND.  75 

tried  to  measure  its  velocity  by  laths  of  wood,  cords,  &c., 
found  it  too  great  to  be  appreciable.  The  efforts  of  Hassen- 
fratz  were  fruitless.  Biot  and  Martin  tried  by  means  of 
the  iron  pipes  made  to  carry  the  waters  of  the  Seine  from 
Marly  to  the  aqueduct  of  Luciennes,  and  found  that  from 
a  small  bell  hung  at  one  extremity,  two  sounds  reached  the 
ear  in  succession.  The  first  was  transmitted  through  the 
iron,  and  after  an  interval  of  between  two  and  three  seconds 
was  followed  by  another  through  the  air.  From  this  ex- 
periment they  calculated  a  velocity  of  8,859  feet.  This 
deduction  is  not  correct :  the  result  is  too  small.  This  may 
be  explained  by  the  lead  used  at  the  joining  of  the  pipes 
interrupting  slightly  the  transmission  of  the  sound.  When 
Breguet  and  Wertheim  afterwards  experimented  on  the  tele- 
graph wires  of  the  Versailles  Railway,  they  gave  as  the  result 
of  their  calculation  11,434  feet  per  second  for  the  velocity  of 
sound  in  iron  wire.  By  the  method  of  vibrations  (an  in- 
direct mode)  Wertheim  determined  the  velocity  of  sound  in 
some  metals.  In  lead  it  is  equal  to  four  times  what  it  is  in 
air,  about  4,265  feet;  in  silver  and  platinum,  8,859  feet  j  in 
zinc  and  copper,  12,140  feet ;  in  iron  and  steel,  16,404  feet. 
The  highest  known  velocity  of  sound  is  that  which  Chladni 
found  in  the  wood  of  the  fir-tree,  about  19,685  feet — eighteen 
times  that  of  transmission  through  the  air. 

To  form  a  comparison  of  these  different  results,  let 
us  imagine  for  a  moment  that  the  stone  tunnel  pro- 
jected by  M.  T.  Gamond  is  constructed  under  the 
English  Channel.  The  distance  from  Cape  Grisnez  to  East- 
ware  Point  (the  proposed  stations)  is  about  twenty-one  miles. 
A  cannon  fired  at  Grisnez  would  be  heard  at  the  English 
station  in  ninety-seven  seconds,  through  the  air ;  the  sea-water 
would  transmit  the  sound  in  twenty-three  seconds ;  by  the  iron 


76  ACOUSTICS. 

rails  it  would  come  in  a  little  over  six  seconds,  and  by  the 
telegraphic  wires  probably  a  little  faster.  Finally,  if  there 
were  a  lath  of  fir-wood  long  enough  to  join  the  opposite 
shores  it  would  transmit  the  sound  in  five  seconds. 

The  velocity  of  sound  in  air  being  known,  we  can  em- 
ploy it  as  a  means  of  approximately  measuring  distances. 
Every  second  that  elapses  between  the  flash  and  the  report 
of  a  firearm  represents  a  distance  of  1,116  feet  between  the 
station  where  it  is  fired  and  the  position  of  the  observer. 
We  have  already  seen  how  Mersenne  made  use  of  this  fact. 
M.  d'Abbadie  measured  different  sites  in  Ethiopia  by  the 
same  means.  In  the  island  of  Mocawa,  during  the  Rama- 
dam  (a  religious  fast  of  the  Mussulmans),  a  cannon  was 
always  fired  at  sunset  announcing  the  end  of  the  day's  fast. 
M.  Antoine  d'Abbadie  took  the  opportunity  of  noting  the 
time  which  passed  between  the  flash  and  the  arrival  of  the 
sound  on  the  opposite  bank.  He  took  his  station  on  a  hill 
near  the  village  of  Omkullu,  and  there  awaited  the  report  of 
the  cannon.  The  sound  reached  him  eighteen  seconds  after 
he  saw  the  flash:  the  distance  he  reckoned  to  be  21,129 
feet.  Another  time  he  measured  in  the  same  way  the 
distance  from  the  town  of  Aoua  to  Mount  Saloda.  His 
brother  Arnauld  took  his  stand  on  the  mountain,  while 
he  himself  was  upon  the  roof  of  a  house  in  the  town,  armed 
with  a  blunderbuss.  They  fired  alternately,  and  each  one 
marked  the  seconds  by  his  watch :  the  distance  was  found 
to  be  nearly  two  miles.  But  it  seems  the  brothers  made  too 
much  noise,  for  they  were  both  banished  from  the  Tigris. 

Newton  gives  a  formula  by  which  to  calculate  the  depth 
of  a  well  from  the  time  that  passes  between  the  moment 
when  a  stone  leaves  the  margin  and  that  at  which  it  is  heard 
to  strike  the  water.  Ten  seconds  would  give  a  depth  of  about 


VELOCITY   OF   SOUND.  77 

1,247  feet-  ^e  might  get  the  depth  of  a  lake,  or  even  of 
the  sea,  if  we  could  note  the  reflection  of  a  sound  strong 
enough  to  be  returned  from  the  bottom.  Arago  proposed 
this  to  Colladon  in  1826,  but  it  was  never  tried  till  1838, 
when  at  the  request  of  the  Admiralty  of  the  United  States 
Mr.  Bonnycastle  made  the  experiment.  The  American 
professor  found  that  sound  was  better  perceived  in  the  water 
than  in  the  air,  and  that  the  greatest  distance  at  which  a  bell 
could  be  heard  under  the  water  was  two  miles.  These  conclu- 
sions were  disputed  by  Colladon,  who  urged  his  experiments 
made  on  the  Lake  of  Geneva.  In  1826  he  had  heard  a  bell  of 
nearly  1 40  pounds  weight  at  a  distance  of  eight  miles.  In  1 84 1 
a  bell  of  about  180  pounds,  lent  by  one  of  the  churches  of 
the  canton  of  Geneva,  was  heard  at  a  distance  of  twenty-one 
miles.  It  was  suspended  forty-nine  feet  under  water,  and 
the  hammer  which  struck  it  weighed  over  twenty  pounds; 
from  which  Colladon  concluded  that,  under  favourable  con- 
ditions, sound  would  be  propagated  under  water  to  a  vast 
distance.  The  noise  of  the  paddle-wheels  of  a  steamboat 
is  not  heard  beyond  3,000  to  4,000  feet  under  water ;  but 
the  noise  of  a  chain  shaken  at  a  certain  depth  is  so  distinct, 
that  a  ship  at  two  miles  distance  may  be  heard  to  weigh 
anchor. 

It  is  understood  that  in  these  experiments  it  is  always 
necessary  to  use  a  hydro-acoustic  trumpet.  During  the  trial 
of  the  great  bell,  each  blow  could  be  heard  in  a  house  built 
upon  an  embankment  at  a  distance  of  two  miles,  although 
the  house  was  separated  from  the  bell  by  a  promontory  :  the 
sound  seemed  to  come  from  the  foundations  and  the  walls. 
Colladon  says  nothing  of  the  possibility  of  measuring  the 
depth  of  water  by  an  echo  from  the  bottom. 


CHAPTER  VI. 

REFLECTION     OF    SOUND. 

Laws  of  Reflection — Echo— Polysyllabic  Echo— Polyphonic  Echo — 
Heterophonic  Echo  —  Reflection  and  Resonance  —  Celebrated 
Echoes— Legends — Refraction  of  Sound. 

THE  laws  of  reflection  show  a  perfect  analogy  between  light 
and  sound.  Sounds  are  reflected,  like  luminous  rays,  from 
any  obstacle  they  may  encounter ;  and  just  as  we  find  the 
polished  surface  of  a  mirror  giving  back  more  light  than  a 
rough  surface,  so  different  substances  return  the  sonorous 
waves  with  more  or  less  force.  Hard  and  solid  bodies  re- 
flect much  better  than  soft  and  flexible  ones,  that  cannot 
easily  right  themselves  after  pressure. 

The  laws  of  the  reflection  of  sound  do  not  appear  quite 
so  simple  as  those  which  govern  the  movement  of  luminous 
rays,  for  the  sound-waves  travel  in  curved  lines,  bending 
round  obstacles.  Nevertheless,  for  the  sake  of  simplifying 
our  explanation,  we  may  be  permitted  to  speak  of  sonorous 
"  rays"  just  as  we  speak  of  luminous  rays,  meaning  thereby 
the  direction  in  which  a  sound  arrives  in  greatest  power, 
when  propagated  through  the  air.  Therefore  we  may  say 
for  sound  as  for  light,  that  the  incidental  and  the  reflected 
ray  make  equal  angles  with  the  reflecting  surface,  and  that 
they  are  comprised  in  a  plane  perpendicular  to  this  surface. 
The  same  law  obtains  in  the  shock  of  elastic  bodies.  Bil- 


REFLECTION   OF   SOUND. 


79 


liard-players  know  that  the  ball  rebounds  from  the  cushion 
in  a  direction  symmetrical  with  that  in  which 'the  propelling 
force  was  given.  It  is  thus  that  a  voice  striking  the  wall 
M,  in  the  direction  A,  M,  is  thrown  back  in  the  direction 
M,  B,  symmetrical  with  the  first  as  regards  its  relation  to  the 
wall,  or  (which  comes  to  the  same  thing)  to  the  perpen- 
dicular M,  N.  The  angle  which  this  perpendicular  makes 


N 
Fig.  28.— Reflection  of  Sound. 


with  A,  M,  is  called  the  angle  of  incidence ;  that  which  it 
makes  with  M,  B,  is  the  angle  of  reflection.  These  two 
angles  are  always  equal,  and  the  reflected  ray  M,  B,  is 
always  in  the  same  plane  as  A,  M,  and  the  perpendicular 
M,  N. 

When  the  point  A,  whence  the  sound  emanates,  ap- 
proaches the  line  M,  N,  the  point  B,  towards  which  the 
sound  is  reflected,  approaches  it  also,  and  these  two  points 
coincide  when  the  sound  travels  in  the  direction  of  the 
perpendicular.  That  is  to  say,  a  voice  thrown  out  at  N, 


8o  ACOUSTICS. 

and  striking  the  wall  in  the  direction  of  the  perpendicular 
N,  M,  would  return  by  the  same  path  from  M  to  N. 

These  principles  will  help  us  to  understand  the  pheno- 
mena of  echoes,  as  we  call  the  repetition  of  a  sound  when 
reflected  by  some  distant  object  Let  us  suppose,  to  begin 
with,  that  we  have  but  one  reflecting  surface.  If  the  ob- 
server wishes  to  hear  the  echo  of  his  own  voice,  he  must 
place  himself  on  the  line  M,  N,  which  is  perpendicular  to 
the  reflecting  surface.  If  he  wishes  to  hear  the  echo  of  a 
noise  produced  at  a  point  A,  he  must  place  himself  at  a 
point  B,  symmetrical  with  reference  to  the  perpendicular 
M,  N.  Before  hearing  the  reflected  sound,  which  travels  by 
the  broken  line  A,  M,  B,  he  will  of  necessity  hear  the  sound 
which  passes  direct  from  A  to  B,  since  this  has  a  shorter 
road  to  travel.  We  assume,  of  course,  that  no  obstacle 
stands  between  these  two  points  which  could  impede  its 
passages  The  observer  will  then,  in  general,  hear  two 
sounds  in  succession,  if  the  first  has  ceased  before  the 
arrival  of  the  second.  This  is  a  necessary  condition  for  a 
distant  echo,  and  it  evidently  depends  on  the  distance  of 
the  reflecting  surface. 

We  will  first  consider  a  case  where  the  sound  returns  to 
the  place  of  its  departure.  The  observer  is  then  at  N  ;  he 
hears  his  own  voice  first  at  the  moment  of  utterance,  then 
again  after  the  sound  has  travelled  twice  the  distance  M,  N. 
Now,  it  takes  at  least  one-tenth  of  a  second  to  pronounce 
one  syllable,  and  that  is  pretty  .quick  speaking;  on  an 
average  we  do  not  pronounce  more  than  five  syllables  in 
a  second.  If,  then,  the  reflecting  obstacle  be  too  near  the 
observer,  the  first  syllable  will  return  before  he  has  uttered 
the  last,  and  there  will  be  confusion,  the  last  syllables  only, 
or  perhaps  none  at  all,  being  given  distinctly. 


REFLECTION    OF   SOUND.  8 1 

V7e  have  seen  that  sound  travels  on  an  average  about 
1,1 16  feet  per  second;  in  the  tenth  of  a  second,  then,  it 
would  be  112  feet  nearly,  and  224  feet  in  the  fifth  of  a 
second.  An  obstacle  distant  112  feet  in  a  straight  line 
would,  therefore,  send  back  the  sound  after  one-nfdi  of  a 
second,  allowing  one-tenth  for  its  journey  there  and  one- 
tenth  for  its  return.  This  distance  would  suffice  for  a  mono- 
syllabic echo — that  is  to  say,  for  the  repetition  of  a  single 
syllable.  One-fifth  of  a  second  it  would  take  to  pronounce 
it,  so  that  as  I  pronounce  the  end  of  my  syllable  the  begin- 
ning has  already  returned  to  me.  If  the  obstacle  is  nearer 
than  112  feet,  the  reflected  sound  breaks  in  upon  the  ar- 
ticulated sound  and  confuses  it.  If  the  obstacle  is  at  a 
greater  distance,  a  longer  or  a  shorter  time  will  elapse  be- 
tween the  spoken  syllable  and  the  echo  which  repeats  it. 

All  that  has  been  said  of  the  monosyllabic  echo  will 
apply  to  the  polysyllabic,  or  the  echoes  of  many  syllables. 
We  have  only  to  increase  the  distance  in  proportion  to  the 
number  of  syllables  to  be  repeated.  For  two  syllables  w 
must  allow  224  feet;  for  three,  336  feet,  and  so  on.  Of 
course,  if  more  than  five  syllables  are  uttered  in  a  second, 
the  distance  allowed  may  be  smaller ;  but  if  less  than  five, 
the  distance  must  be  greater.  The  principle  is  always  the 
same.  The  distance  must  allow  the  sound  to  go  and  re- 
turn during  the  time  taken  for  the  utterance  of  the  phrase. 
However,  it  is  true  that  several  syllables  spoken  in  suc- 
cession are  produced  more  rapidly  than  a  single  one  is  apt 
to  be,  which  explains  why  Kircher  found  the  distances  de- 
crease slightly  for  polysyllabic  echoes.  Whilst  he  gave  100 
feet  for  an  isolated  syllable,  he  reckoned  only  190  for  two, 
and  600  for  the  seven  syllables — 

"  Arma  virumque  caao." 

G 


S3  ACOUSTICS. 

He  states  elsewhere  that  the  distances  allow  of  a  great  lati- 
tude. The  echo  of  a  trumpet  is  distinct  from  90  to  no 
feet,  and  the  distance  for  an  echo  of  seven  syllables  may  be 
reduced  to  400  feet,  while  sometimes  600  feet  is  not 
sufficient  for  the  repetition  of  seven  syllables.  When  too 
many  syllables  are  given  for  the  echo  to  repeat  distinctly, 
the  first  which  return  are  drowned  by  the  last  uttered,  and 
only  a  mutilated  edition  of  the  phrase  is  obtained.  From 
this  circumstance  it  is  easy  to  hold  a  conversation  with  the 
echo,  by  question  and  answer,  remembering  only  that  the 
end  of  the  question  must  serve  as  reply. 

Cardan  tells  a  story  of  a  man  who,  wishing  to  cross  a 
river,  could  not  find  the  ford.  In  his  disappointment  he 
heaved  a  sigh.  "  Oh  !"  replied  the  echo.  He  thought  him- 
self no  longer  alone,  and  began  the  following  dialogue  : — 

"Onde  devo  passar?" 

«  Passa." 

«  Qui  ?" 

«  Qui." 

However,  seeing  he  had  a  dangerous  whirlpool  to  pass, 
he  asked  again — 

"  Devo  passar  qui  ?" 

"  Passa  qui." 

The  man  was  frightened,  thinking  himself  the  sport  of 
some  mocking  demon,  and  returned  home  without  daring 
to  cross  the  water.  He  told  his  adventure  to  Cardan,  who 
had  little  trouble  in  explaining  it. 

We  have  supposed  hitherto  that  the  observer  heard  the 
echo  of  a  sound  produced  by  himself,  returning  by  reflec- 
tion to  its  point  of  departure.  The  same  reasoning  applies 
in  cases  where  the  sound  rises  at  a  certain  distance  from  the 
observer,  as  in  Fig.  28,  where  the  listener  is  placed  at  B  and 


REFLECTION    OF    SOUND.  83 

the  sound  comes  from  A.  We  only  have  to  consider  the 
difference  of  the  direct  road  A,  B,  and  of  the  indirect  A,  M,  B. 
This  difference  represents  the  circuitous  route  by  which  the 
reflected  sound  has  travelled,  or  the  advance  gained  by  that 
sound  which  has  travelled  direct ;  and  it  must  be  equal  to 
twice  112  feet — that  is,  to  2 24  feet — fora  monosyllabic  echo  ; 
double  that  for  an  echo  of  two  syllables,  and  so  on. 

Lastly,  there  are  multiplied  or  polyphonic  echoes — those 


29  — The  Hcptaphonic  Echo. 


which  reproduce  several  times  consecutively  the  same  sound 
or  phrase.  They  are  caused  when  several  obstacles  placed  at 
different  distances,  acting  either  alone  or  together,  send  back 
the  sound  in  successive  echoes.  The  accompanying  figure 
represents  a  heptaphonic  echo,  that  is,  of  seven  voices.  The 
projecting  pieces  of  the  wall,  A,  B,  c,  D,  E,  F,  G,  which  throw 
back  the  .jimd,  are  at  nearly  equal  distances;  it  returns 
first  from  A,  then  from  the  others  in  succession.  If  the 
echo  have  to  repeat  a  single  syllable  seven  times,  the  succes- 
sive distances  must  differ  by  at  least  112  feet ;  for  two  syllables, 

G    2 


84 


ACOUSTICS. 


224  feet,  and  so  on.  The  farther  the  distance,  the  feebler  the 
echo,  as  the  sound  is  scattered  and  lost ;  thus  the  voice  dies 
gradually  until  it  completely  ceases.  When  the  obstacles 
which  produce  the  echo,  instead  of  being  placed  at  equal 
distances,  are  nearer  together  in  proportion  as  they  recede 
from  the  observer,  the  echoes  mingle,  the  second  arriving 
before  the  end  of  the  first,  the  third  before  the  second  is 


completed,  and  so  on.  Kircher  shows  how  this  law  may  be 
used  to  produce  a  sentence  from  a  word.  Suppose  a  five-voiced 
echo  so  disposed  (Fig.  30)  that  the  first  repeats  distinctly  the 
word  clamors  (voice) :  if  the  second  obstacle  be  at  double 
the  distance,  the  third  at  triple,  and  so  on,  a  trisyllable  in 
five  sounds  would  be  produced.  But  put  the  second  so  near 
that  the  sound  of  the  consonants  c  I  is  lost  in  the  first  echo, 
only  the  word  amore  would  be  heard ;  and  by  placing  the 
succeeding  obstacles  at  properly  arranged  intervals,  the 
third  would  repeat  more,  the  fourth  ore,  the  last  re.  So 


REFLECTION   OF   SOUND.  85 

that,  in  asking  in  a  loud  voice  the  question,  Tibi  vero  gratias 
agam,  quo  damore  ?  the  echo  replies,  Clamore — amore — more 
— ore — re.  The  word  constabis  would  divide  into  stabis — 
obis — bis — is,  but  without  giving  a  sentence  of  any  meaning. 


Fig   31. — The  Heterophonic  Echo. 


Ivircher  also  tried  to  construct  an  heterophonic  echo- 
one  that  should  reply  in  a  different  word — which  he  con- 
trived thus  :  At  the  salient  angle  of  a  wall  was  an  obstacle 
(Fig.  31)  which,  instead  of  throwing  the  voice  back  to  the  spot 
from  whence  it  had  come,  sent  it  round  to  the  other  side 
of  the  building,  where  an  accomplice  was  concealed ;  he 


86  ACOUSTICS. 

replying,  his  voice  followed  the  same  route  as  the  question, 
and  reached  the  mystified  hearer,  who,  having  heard  asked, 
Quod  tibi  no  mm  ?  (What  is  your  name  ?)  hears  the  answer, 
Constantinus.  Kircher  relates  that  he  had  been  much  amused 
at  his  friends'  expense  by  this  innocent  mystification,  in  the 
Campagna  at  Rome.  To  render  the  illusion  complete,  the 
voices  of  the  two  actors  should  be  alike. 

It  would  be  possible  to  utilise  the  echoes  of  a  church,  as 
ornaments  to  the  singing,  by  disposing  pauses  which  should 
be  filled  in  by  their  resoundings.  Kircher  gives  several  ex- 
amples of  musical  effects  thus  obtained,  and  adds  that  the 
churches  of  St.  Peter  and  St.  James  of  the  Incurables  at 
Rome  are  particularly  adapted  for  the  application  of  this 
artifice. 

The  Hebrew  name  for  echo  is  "  daughter  of  the  voice;"  to 
the  ancient  poets  Echo  was  a  nymph  who  loved  the  beautiful 
Narcissus,  whose  love  being  despised,  she  dissolved  in  tears, 
and  remained  only  a  voice  which  replied  to  the  passion  of 
another — 

"Nee  prior  ipsa  loqui  didicit  resonabilis  Echo." 

The  echoes  which  animate  a  landscape  seem  to  establish  a 
kind  of  sympathy  between  man  and  nature.  The  forest  par- 
takes in  our  joys,  and  repeats  the  cries  of  the  hunters  and  the 
notes  of  the  horn. 

"Non  canimus  surdis,  respondent  omnia  silvze." — ViRGIL. 

As  Mersenne  says,  God  has  given  a  voice  to  the  woods, 
rivers,  and  mountains. 

The  echoes  in  towns,  and  regions  of  peculiar  confor- 
mation, are  of  various  qualities :  sometimes  the  response  is 
muffled  and  hoarse,  sometimes  clear  and  distinctly  accented, 


REFLECTION    OF   SOUND.  87 

These  differences  in  quality,  depending  evidently  on  the 
character  of  the  reflecting  surfaces,  prove  that  an  echo  is 
something  more  than  mere  reflection.  It  is  beyond  doubt  that 
the  phenomena  of  resonance,  of  which  we  shall  speak  sub- 
sequently, play  a  certain  part  in  it.  All  the  facts  observed 
prove,  also,  that  the  reflection  of  sound  can  be  made  clear 
and  distinct  from  very  irregular  surfaces ;  an  old  rampart,  a 
ruined  tower,  a  tree,  a  hill,  a  wooded  gorge,  are  the  ob- 
stacles which  form  the  best  echoes.  The  luminous  image 
is  perfect  in  proportion  as  the  surface  which  reflects  it  is 
uniform  ;  the  sonorous  image  is  not  subject  to  these  con- 
ditions. We  must  conclude  that  in  most  cases  the  mode  of 
action  of  the  surfaces  which  form  an  echo  has  some  analogy 
with  the  effects  of  curved  mirrors.  Perhaps  the  resonance 
of  the  obstacles  themselves,  and  of  the  air  confined  in  them, 
contributes  largely  to  the  production  of  the  phenomenon. 

It  is  certain  that  the  concurring  conditions  which  should 
be  regarded  as  favourable  or  necessary  to  the  production  of 
an  echo,  are  far  from  being  known.  Theory  and  experiment 
are  equally  at  fault.  In  some  cases  the  local  conditions 
which  should,  according  to  the  theory  of  reflections,  produce 
an  echo,  do  really  produce  it ;  but  often  our  expectation 
is  deceived  where  no  reason  for  it  can  be  discovered. 

The  echoes  of  forests  depend  much,  probably,  on  the 
grouping  of  the  trees,  as  the  following  facts  may  show  : — 

Gay  Vernon,  in  his  youth,  had  often  amused  himself  by 
waking  an  echo  formed  by  the  buildings  of  a  mill.  After 
passing  several  years  in  Paris,  he  returned  to  his  native 
village :  to  his  surprise  the  echo  no  longer  existed ;  yet 
nothing  had  been  changed  about  the  mill — only  a  group  of 
trees,  which  formerly  shaded  it,  had  been  cut  down. 

In  the  plain  of  Montrougc,  near  Paris,  there  was  for- 


88  ACOUSTICS. 

merly  a  remarkable  echo  produced  by  a  wall,  before  which 
were  several  rows  of  trees.  Hassenfratz  tried  to  ascertain 
on  what  circumstances  the  phenomenon  depended.  He 
placed  an  assistant  at  a  certain  distance  to  call  out,  and 
approached  the  wall  slowly,  listening  carefully :  the  echo 
died  away  as  he  drew  near,  but  there  remained  a  faint 
sound,  proceeding  not  from  the  wall,  but  from  the  trees. 
Putting  his  ear  to  their  trunks  he  perceived  a  slight  tremor, 
while  in  the  wall  there  was  no  vibration.  He  also  observed 
that  the  walls  of  certain  houses  produced  an  echo  when  the 
windows  were  shut;  or  with  the  windows  open,  but  the 
doors  shut.  In  some  vaults  certain  notes  only  produce  the 
effect.  The  echo  of  the  ancient  college  of  Harcourt  has 
a  strange  peculiarity :  it  returns  the  voice  of  a  man  placed 
in  the  middle  of  the  court,  but  the  low  notes  were  heard  in 
the  direction  of  the  Rue  de  la  Harpe,  the  high  notes  in  a 
direction  fifty  degrees  more  to  the  north. 

All  these  facts  show  that  Echo  is  a  capricious  being, 
whose  caprices  are  not  easily  divined.  Here  is  a  story  in 
illustration:  —  An  Englishman,  travelling  in  Italy,  met 
with  an  echo  so  beautiful  that  he  determined  to  buy  it. 
It  was  produced  by  a  detached  house.  This  was  taken 
down,  carried  to  England,  and  reconstructed  on  one  of  his 
estates,  exactly  on  its  original  plan — a  place  having  been 
chosen  for  it  at  exactly  the  same  distance  from  his  dwelling 
as  it  stood,  in  Italy,  from  the  place  whence  the  echo  was 
most  distinctly  heard.  To  test  the  echo  he  sent  for  a  box  of 
pistols,  charged  both  the  weapons,  went  to  the  window,  and 
fired — no  sound  was  returned ;  drawing  the  trigger  of  the 
second,  he  shot  himself  through  the  brain  !  It  was  never 
known  what  defect  in  the  construction  was  the  cause  of  this 
lamentable  disappointment 


REFLECTION    OF   SOUND.  89 

Clouds  also  re-echo  terrestrial  noises.  The  members  of 
the  Bureau  des  longitudes,  in  the  course  of  their  experiments 
for  measuring  the  velocity  of  sound,  found  that  the  report 
of  cannon  was  always  followed  by  an  echo  if  clouds  were 
overhead.  The  rumbling  of  thunder  is  owing  partly  to  the 
multiplied  reflection  of  sound  between  the  earth  and  the 
storm  clouds.  Echoes  are  also  produced  by  excessively  high 
waves,  and  the  sails  of  ships,  and  it  is  said  that  words 
spoken  through  a  speaking-trumpet  come  back  if  they  strike 
on  the  convex  surface  of  the  sails. 

Echoes  are  especially  distinct  in  the  silence  of  night; 
the  noises  of  day  prevent  their  being  heard  distinctly. 
Mersenne  relates  that  the  echo  of  Ormesson,  in  the  valley  of 
Montmorency,  replies  fourteen  syllables  at  night,  and  only 
seven  in  the  day-time. 

In  deep  valleys,  and  the  hollowed  strands  of  rivers, 
remarkable  echoes  are  found.  In  one  well-known  echo, 
between  Coblenz  and  Bingen,  where  the  waters  of  the  Nahe 
flow  into  the  Rhine,  there  is  an  echo  which  gives  seventeen 
repeats,  the  voice  seeming  alternately  far  and  near.  One 
day,  the  steamer  not  having  the  usual  fire-arms  on  board  to 
rouse  the  echo  for  the  amusement  of  the  tourists,  there  were 
loud  cries  for  a  pistol.  A  Pole,  not  understanding  the  case, 
rushed  on  to  the  bridge,  exclaiming,  "  I  have  no  pistol,  but 
here  is  a  dagger."  Ebell  relates  that  an  echo  at  Derenberg, 
near  Holberstadt,  repeats  the  twenty-seven  syllables  of  this 
sentence  —  Conturbabantvr  Constantinopolitani  in/miner a- 
bilibus  solliritudinibus.  It  would  be  as  astonishing  to  find 
a  mouth  capable  of  pronouncing  them  quickly ;  but  as  he 
says  that  the  distance  was  only  254  paces,  which  is  not 
enough  for  such  an  echo,  there  must  be  some  mistake  in 
the  account 


90  ACOUSTICS. 

It  is  said  that  near  Brussels  there  is  an  echo  of  fifteen 
repeats ;  and  at  Rosneath,  near  Glasgow,  on  the  Clyde,  one 
which  repeats  an  air  of  music  three  times.  This  scarcely 
seems  credible. 

An  echo  at  Woodstock,  near  Oxford,  repeats  seven- 
teen times  by  day,  and  twenty  times  by  night ;  the  distance 
is  half  a  mile. 

At  Genetay,  two  leagues  from  Rouen,  in  a  semi-circular 
court,  there  is  a  remarkable  echo.  When  crossing  the  court 
singing,  the  singer  hears  only  his  own  voice,  while  those 
listening  hear  only  the  echo,  single  or  multiplied,  according 
to  their  position. 

At  three  leagues  from  Verdun  are  two  towers,  apart,  and 
isolated  from  the  building  to  which  they  belong ;  standing 
midway  between  them,  the  speaker's  voice  is  echoed  twelve 
or  thirteen  times  with  decreasing  force,  but  except  from 
this  spot  the  echo  is  lost ;  while  between  one  tower  and  the 
building  a  single  echo  is  heard.  Near  Heidelberg  is  an 
echo  which  imitates  thunder.  To  waken  it  a  pistol  is 
fired  from  the  base  of  the  hill  Heiligenberg ;  a  wooded 
gorge  in  front  so  reflects  the  sound,  that  instead  of  the 
report  of  the  pistol  a  noise  of  thunder  is  heard. 

In  Bohemia,  near  Aderbach,  there  is  a  circular  space  six 
leagues  in  diameter,  surrounded  by  bare  pointed  rocks.  At 
one  spot  in  the  centre  is  an  echo  which  repeats  three  times 
a  sentence  of  seven  syllables,  while  at  a  short  distance  off 
no  echo  is  perceived. 

In  the  walls  of  Avignon,  Kircher  found  the  voice  re- 
peated eight  times.  In  Rome  an  echo  is  repeated  from 
two  to  seven  times.  Boissard,  in  the  "  Roman  Topo- 
graphy," gives  this  description  of  the  tomb  of  Ccecilia 
Metella:  It  is  a  round  tower,  its  walls  twenty-four  feet 


1 


REFLECTION    OF   SOUND.  93 

thick,  and  ornamented  with  200  heads  of  bulls  in  marble, 
to  commemorate  the  two  hecatombs  sacrificed  at  the  funeral 
of  the  daughter  of  Metellus  Crs.ssus.  This  monument  is 
situated  near  St.  Sebastian,  and  called  "The  Bull's  Head." 
A  sentence  spoken  at  the  base  of  the  hill  on  which  it  stands 
produces  a  multiplied  echo.  Boissard  says  that  when  he 
sang  the  first  line  of  the  ^Eneid,  it  was  repeated  eight  times 
distinctly,  and  several  times  more  imperfectly.  Mersenne, 
speaking  of  this  echo,  says  the  place  can  still  be  seen 
in  which  the  hecatomb  was  immolated,  where  the  echo  would 
make  the  sacrifice  seem  larger  than  it  was.  Whether  the 
place  was  chosen  to  give  a  greater  solemnity  to  the  rite,  or 
whether  it  was  chosen  for  the  burial-place  of  the  house  of 
Crassus  to  immortalise  it  by  multiplying  their  names  to 
posterity,  he  could  not  tell. 

In  a  private  dwelling  an  echo  is  not  at  all  pleasant, 
as  it  causes  what  is  said  or  done  to  be  heard  at  a  dis- 
tance. It  is  only  in  large  halls  or  places  of  amusement 
that  it  would  be  desirable,  while  in  a  church,  if  it  makes  the 
preacher's  voice  better  heard,  it  also  frequently  interrupts 
him  by  the  re-echo. 

The  drawing  by  Kircher  (Fig.  32)  represents  the  Hall  at 
Simonetta,  near  Milan.  Measured  from  the  interior  of  the 
court,  the  fagade  is  121  feet,  and  the  wings  66  feet;  the 
height  of  the  upper  storey,  between  the  gallery  and  the  roof, 
32  feet,  the  gallery  16  feet.  When  a  pistol  is  fired  from 
the  window  in  the  left  wing,  it  is  repeated  forty  or  fifty 
times,  and  the  sound  of  the  voice  twenty-four  to  thirty 
times.  Addison  and  Monge  tried  it,  and  Bernouilli  believed 
he  counted  sixty  repetitions. 

In  vaulted  buildings  there  is  an  echo,  owing  its  peculiarity 
to  the  laws  of  geometric  curves.  The  ellipse  is  a  lengthened 


94 


ACOUSTICS. 


curve  like  a  flattened  circle,  and  two  points  in  its  interior, 
//(Fig.  33),  are  called  the  foci,  because  in  each  of  them 
are  collected  the  rays  of  light  or  sound,  which,  diverging 


Fig.  33- 

from  the  other,  are  reflected  from  the  interior  of  the  curve. 
A  person  placed  at  one  of  the  foci  of  an  elliptic  curve  hears  a 
whisper  from  the  other  focus,  so  that  two  persons  placed  at 


34- 


these  positions  could  converse  in  a  whisper  without  being 
overheard.  There  is  a  building  of  this  kind  at  Muiden,  near 
Amsterdam.  Parabolic  surfaces  have  one  focus,  to  which 
parallel  rays  converge  after  reflection,  while  those  diverging 
from  it  become  parallel  after  reflection;  so  that  if  two 


REFLECTION   OF   SOUND.  95 

parabolic  mirrors  are  placed  opposite  each  other,  the  slightest 
sound  made  at  the  focus  of  one  is  heard  at  the  focus  of  the 
other,  as  is  shown  in  Fig.  34.  This  makes  them  applicable 
in  lighthouses,  for  throwing  rays  of  light  or  the  sounds  of 
bells  to  a  distance.  With  less  reason  they  are  chosen  for 
acoustic  trumpets.  It  is  supposed  that  at  the  focus  where  the 
ear  is  placed  the  rays  coming  from  a  certain  distance  are  con- 
densed, as  a  parabolic  mirror  condenses  at  its  focus  the  sun's 


Fig   33- 

rays.  The  sails  of  a  ship  sometimes  produce  this  effect 
when  inflated  by  the  wind.  Arnott  says  that  in  a  coasting 
vessel  off  Brazil,  by  standing  before  the  mainsail  the  bells  of 
Sari  Salvador  could  be  heard  from  a  distance  of  no  miles. 

Church  vaults,  caves,  and  ramparts  very  often  furnish  some 
curious  illustrations  of  acoustic  effects.  In  an  elliptic  vault, 
sound  issuing  from  one  point  is  heard  at  another  fixed  point 
by  a  single  reflection  from  the  wall;  and  between  two 
opposite  parabolic  vaults  it  is  heard,  though  less  distinctly,  by 
means  of  a  double  reflection.  Other  systems  of  curves  might 
give  the  same  result  by  a  number  of  successive  reflections. 


96  ACOUSTICS. 

Thus  two  parabolas  combined  with  a  plare  surface,  as  in  Fig. 
35,  would  give  it  by  means  of  a  triple  reflection;  and  it  is 
possible  that  the  action  of  multiplied  reflections  would  go 
far  to  explain  many  curious  results. 

Sound  is  much  increased  by  the  echoes  in  a  closed  vault 
In  a  cave  of  the  Pantheon,  the  keeper  by  striking  the  flap  of 
his  greatcoat  makes  a  noise  like  the  report  of  a  cannon.  The 
same  phenomenon  is  found  in  the  caves  of  Kentucky.  In  the 
Cave  of  Smellin,  near  Viborg,  in  Finland,  by  throwing  in  a 
live  animal  you  hear  terrible  noises.  Olaus  Magnus  says 
that  when  an  enemy  approached  the  inhabitants  would 
conceal  themselves,  while  the  boldest  amongst  them  cast 
an  animal  into  the  cavern,  whose  terrible  roarings  "over- 
threw the  enemies  like  oxen  at  the  shambles,  when  the 
Finlanders  leaving  their  hiding-places  spoiled  the  slain." 
Pliny  tells  of  a  similar  cave  in  Dalmatia,  where  the  falling  of 
a  stone  raised  a  perfect  storm.  Fingal's  Cave,  in  the  island 
of  Staffa,  presents  another  remarkable  phenomenon.  The  end 
of  this  cavern  is  dark  and  gloomy,  and  may  be  compared 
to  the  chancel  of  a  church,  while  the  basaltic  columns  may  be 
likened  to  the  organ-pipes.  At  the  extremity  of  the  grotto, 
and  near  the  level  of  the  water,  is  a  small  opening,  whence 
come  harmonious  sounds,  which  are  produced  by  the  swell 
rising  and  falling. 

St.  Clement  of  Alexandria  relates  that  in  Persia  were 
three  mountains  in  an  open  country,  so  situated  that  ap- 
proaching the  first  you  heard  confused  voices  and  wrangling; 
on  nearing  the  second  the  hubbub  increased,  but  reaching 
the  third  you  heard  sounds  of  mirth  and  rejoicing. 

The  panic  terror  which  overcame  the  Gauls  near  the 
temple  of  Delphi,  defended  by  the  god  Pan,  is  attributed  to 
echoes.  In  the  same  way,  Mersenne  says,  "  The  Persians, 


REFLECTION   OF   SOUND.  97 

while  ravaging  Greece  and  Megara,  awaking  an  echo  in  the 
night,  imagined  they  heard  the  cries  of  numerous  enemies, 
and  attacked  the  resounding  rock,  on  which  they  spent  their 
courage  and  their  darts,  and  were  next  day  taken  captive." 

Another  remarkable  analogy  between  light  and  sound  is 
the  refraction  which  both  rays  undergo  in  passing  from  one 
medium  to  another.  A  spoon  put  into  a  glass  of  water 
seems  to  bend ;  this  is  the  effect  of  refraction.  The  rays  of 
light  which  meet  the  water  in  an  inclined  direction  are  bent 
when  they  emerge  into  the  air.  The  effect  of  prisms  and 
lenses  depends  on  the  successive  refractions  to  which  light 
is  subject  on  passing  from  the  air  into  the  glass,  and  back 
again ;  the  glass  being  so  prepared  as  to  give  the  requisite 
deviation.  M.  Hajech  thus  proves  that  the  rays  of  sound 
follow  the  same  laws  :  He  had  a  hole  made  in  the  partition 
wall  of  two  rooms,  and  placed  in  it  a  tube  closed  by  two  mem- 
branes. This  tube  was  successively  filled  with  water,  carbonic 
acid,  hydrogen,  ammoniacal  gas,  &c.  At  one  end  another 
tube  was  attached,  filled  with  air,  and  ending  in  a  wadded 
box  containing  an  alarum  watch.  The  sound  passed  through 
the  tube  containing  the  gas  or  liquid,  and  the  observer  in 
the  next  room  noticed  where  the  sound  had  most  force. 
When  the  two  membranes  were  perpendicular  to  the  axis  of 
the  tube,  the  direction  corresponded  with  the  axis,  without 
deviation ;  but  when  the  front  membrane  was  inclined  to 
the  axis,  a  sensible  deviation  was  perceived,  which  was 
measured  by  holding  a  plumb-line  to  the  ear,  which  traced 
the  arc  of  a  circle  on  the  floor.  These  experiments  showed 
that  the  rays  of  sound  are  refracted  by  the  same  laws  as  the 
rays  of  light :  they  depend  on  the  angle  at  which  the  rays 
strike  the  reflecting  body,  and  the  comparative  velocity 
with  which  they  are  transmitted*  through  the  two  media. 

H 


98  ACOUSTICS. 

This  was  the  same  for  water  and  hydrogen,  but  different  in 
the  case  of  carbonic  acid. 

M.  Sondhauss  observed  the  refraction  of  sound  by  means 
of  a  lens  of  collodion  filled  with  carbonic  acid.  When  a 
watch  was  placed  in  the  axis  of  this  lens,  the  sound  was 
concentrated  at  another  point  of  the  axis  on  the  opposite 
side.  This,  therefore,  was  the  focus,  and  the  sound  of  the 
watch  was  distinctly  heard  ;  but  when  the  lens  was  removed 
it  was  lost.  This  experiment  was  made  more  easily  by 
means  of  Helmholtz's  sonorous  globe;  this  was  moved 
slowly  before  the  lens,  and  the  india-rubber  tube  attached 
to  it  placed  in  the  ear.  . 

Mersenne  has  also  considered  the  question  "  whether 
sounds  are  bent  by  refraction,  as  light  is  when  it  passes 
from  one  medium  into  another."  But  he  only  explains 
how  light  is  affected  by  refraction,  and  hence  how  magni- 
fying lenses  should  be  cut ;  and  then  adds,  "  I  do  not  be- 
lieve that  these  effects  can  be  produced  in  sounds  by  human 
industry ;  as  to  the  angels,  if  they  like  to  dispose  the  vibra- 
tions of  the  air  as  they  please,  I  do  not  doubt  they  can  do 
the  same  thing  with  sound  as  with  light." 


CHAPTER    VIL 

RESONANCE. 

Resonance— Vitruvian  Vases— Harmonic  Tablets — Sonorous  Globes 
— Glasses  Broken  by  the  Voice — Acoustics  of  Churches  and 
Theatres. 

THE  assertion  that  sound  passes  round  an  obstacle  must  not 
be  taken  too  literally.  Very  massive  bodies  may  arrest  it, 
as  an  opaque  screen  does  light.  Two  persons  separated  by 
a  rising  ground  can  hear  each  other,  because  sound  passes 
over  the  obstacle  as  light  cannot ;  but  it  is  made  fainter,  and 
they  would  hear  much  better  if  it  were  removed.  It  is  only 
when  sound  is  conducted  through  a  closed  tube  or  passage 
that  its  direction  may  be  changed  without  diminishing  its 
force;  in  open  air  it  grows  fainter,  as  daily  experience  proves. 
To  hear  a  speaker  well  you  should  be  in  front  of  him,  and  to 
hear  an  indistinct  voice  you  instinctively  turn  the  ear  in  the 
direction  from  which  it  proceeds.  When  the  stream  of 
sound  meets  an  obstacle  it  can  turn  the  other  way,  as  a 
current  checked  by  an  island,  but  its  force  is  diminished. 

A  very  large  and  massive  object  will  entirely  arrest  sound. 
Under  the  arches  of  large  bridges  you  may  place  yourself  so 
that  no  sound  from  without  can  reach  you.  Behind  the 
vertical  fall  of  the  Rhine  at  Schaffhausen  there  is  complete 
silence.  The  sounds  of  bells  may  often  be  heard  in  streets 
from  an  opposite  direction  to  that  of  the  bells ;  the  houses 
arrest  their  sound,  and  only  the  reflected  sound  from  the 
opposite  walls  is  audible. 

H   2 


100  ACOUSTICS. 

Elastic  bodies  of  slight  density  offer  little  impediment  to 
the  passage  of  sound,  and  are  of  little  use  in  damping  it. 
It  would  be  as  wise  to  try  to  keep  out  light  with  a  glass 
screen  as  to  try  and  intercept  sound  by  a  boarded  par- 
tition. The  elastic  body  becomes  itself  sonorous  and 
vibrates  to  the  touch.  The  same  thing  is  observed  when 
sound  is  reflected  from  an  elastic  surface,  which  acts  as 
a  spring-board  to  return  the  sound  with  vigour.  By  this 
means  the  wonderful  intensity  of  some  echoes  is  to  be 
explained.  At  the  same  time  other  sounds,  arising  them- 
selves from  the  reflecting  surface,  mingle  faintly  with  the 
reflected  sound.  We  say  then  that  the  surface  resounds. 
It  is  analogous  to  the  reflection  of  the  solar  rays  by  a  body 
which,  besides  returning  the  direct  rays,  becomes  heated 
and  then  radiates  heat  in  all  directions. 

The  resonance  of  arches  is  a  complex  phenomenon  due 
both  to  resonance  and  reflection.  Sound  returns  too 
quickly  from  the  walls  of  a  high  arch  to  produce  a  distinct 
echo,  yet  not  quickly  enough  to  be  blended  with  the 
original  sound ;  the  vibrations  of  the  walls  bring  in  a  new 
element,  and  so  a  thousand  confused  noises  are  produced, 
which  give  rise  to  the  remarkable  effects  we  have  noticed  in 
speaking  of  echoes.  We  can  observe  these  phenomena 
when  passing  in  a  steamboat  under  a  bridge,  of  which  the 
sides  and  arches  intensify  the  sound  of  the  paddles.  When 
a  locomotive  rushes  with  great  velocity  underneath  a  bridge, 
the  reflection  of  the  noise  produces  a  sound  like  violent 
explosion,  and  in  a  tunnel  the  uproar  becomes  deafening. 
Sheets  of  water  are  very  favourable  to  these  effects,  by  the 
facility  with  which  they  reflect  sound.  Thus  Cagniard  de 
Latour,  having  compared  two  pits — one  dry,  the  other 
containing  a  little  water — found  the  latter  was  much  more 


RESONANCE.  IOI 

sonorous  than  the  former.  Undar  the  arches  of  bridges,  the 
resonance  is  sensibly  weaker  when  there  is  no  water  under- 
neath. 

Drapery,  tapestry,  and  all  fabrics  of  that  class  have  the 
effect  of  deadening  sound ;  they  destroy  sound  in  a  room 
which  contains  them  just  as  gloomy  colours  render  it  dark. 
It  is  for  this  reason  that  even  a  good  piano  is  often  not  well 
heard  in  a  room  carpeted,  hung  with  curtains,  and  filled 
with  cushioned  furniture.  Empty  rooms  are  always  re- 
markably sonorous.  In  churches,  or  in  rooms  where 
meetings  are  held,  too  great  resonance  is  very  injurious  to 
distinct  hearing.  It  is  apt  to  drown  the  voice  of  the 
speaker  and  render  him  unintelligible.  But  the  case  is  very 
different  in  a  concert-hall ;  there  we  endeavour  to  in- 
crease the  resonance  of  the  walls  by  a  casing  of  thin 
wood. 

In  the  time  of  Rousseau  the  best  constructed  orchestras 
were  to  be  found,  it  is  said,  in  the  Italian  theatres.  The 
platform  was  made  of  light  and  resonant  wood,  such  as  pine. 
It  was  supported  upon  arches  with  an  empty  space  beneath, 
and  it  was  separated  from  the  audience  by  a  railing  in  the 
pit  distant  a  foot  or  two  from  it  By  this  arrangement  even 
the  body  of  the  orchestra  was  supported  freely  and 
could  vibrate  without  obstacle,  thus  allowing  full  scope  to 
the  power  of  the  instruments.  At  the  Paris  opera,  on  the 
other  hand,  the  orchestra  was  very  badly  arranged,  being 
near  the  ground  and  enclosed  all  around  with  massive 
wood  and  iron,  which  destroyed  all  resonance.  At  the 
present  time,  the  principles  of  construction  so  much  praised 
by  Rousseau  are  adopted  in  the  majority  of  theatres  specially 
devoted  to  music ;  but  it  is  true  that  many  competent  archi- 
tects consider  them  useless  or  even  injurious. 


102  ACOUSTICS. 

Vitruvius  tells  us  that  the  Greeks  put  inverted  brass 
bells  over  conical  supports  in  the  niches  of  the  wall,  to 
increase  the  resonance  in  their  theatres.  They  were  used 
especially  in  Corinth,  from  whence  Nummius  carried  them 
to  Rome.  Sometimes  vases  of  baked  clay  were  used  for 
cheapness.  Vitruvius  says  that  the  bells  were  suited  to  cer- 
tain notes  of  the  gamut.  He  explains  at  length  the  way  of 
making  and  placing  them,  as  represented  in  the  drawing  by 
Kircher,  Fig.  36.  He  recommends  that  the  bells  should  be 
so  constructed  as  to  give  the  fourth,  fifth,  octave,  eleventh, 
twelfth,  and  double  octave,  or  the  series  of  notes — 

sol,  doh,  re,  sola,  doha,  rev  soly 

Kircher  thinks  this  contrary  to  the  laws  of  harmony,  and 

Substitutes — 

sol,  si,  re,  sola,  si,,  rea,  sol,, 

which  seems  to  us  correct.  Probably  the  brass  bells  emitted 
no  sound,  and  the  resonance  was  produced  by  the  air  con- 
tained in  them  and  the  niches  of  the  walls.  Sounding- 
boards  in  musical  instruments  are  intended  to  intensify  the 
feeble  sounds  emitted  from  the  strings,  whose  surface  is 
too  small  to  put  a  mass  of  air  in  motion— they  divide  it 
without  making  it  vibrate ;  it  is  necessary,  therefore,  to 
stretch  them  across  a  sounding-board,  which  receives  the 
vibrations,  and  propagates  them  with  more  effect.  A  tuning- 
fork  becomes  very  audible  when  it  rests  on  wood.  For 
this  reason  diapasons  are  attached  to  a  wooden  case  to 
increase  the  sound ;  the  case  also  causes  the  air  in  it 
to  resound,  and  thus  adds  to  the  effect.  It  is  necessary 
that  the  size  of  the  case  should  be  proportioned  to  the  note 
to  which  it  belongs,  or  the  effect  would  not  be  produced. 


RESONANCE.  105 

Elastic  bodies  of  a  certain  form — sticks,  chords,  mem- 
branes, strings,  &c. — have  their  own  peculiar  notes,  which 
they  give  when  struck,  or  which  they  prefer  to  reinforce  by 
resonance.  The  volume  of  air  contained  in  the  case  of  a 
diapason  has  its  own  particular  note,  which  must  accord  with 
the  cound  which  it  is  capable  of  reinforcing.  M.  Helmholtz 
applied  this  principle  to  make  an  instrument  for  analysing 
sounds,  called  the  sonorous  globe  (Fig.  37).  It  consists  of  a 


Fig.  37. — Sonorous  Globe. 


hollow  sphere  of  glass  or  metal,  with  openings  at  two  oppo- 
site points  :  one  of  a  form  to  receive  the  sound,  while  in  the 
other  a  tube  is  inserted  of  ivory  and  india-rubber,  to  apply 
to  one  ear  while  the  other  is  closed.  The  volume  of  this 
globe,  and  the  size  of  its  orifice,  determine  the  note  which 
it  is  adapted  to  reinforce.  *  If  that  note  exist  in  any 
noise,  it  will  be  heard  resounding  in  the  globe,  but  no  other 
note  will  produce  any  effect.  In  this  way,  a  note  can  be 
distinguished  in  the  midst  of  confused  sounds,  which  veil  it 
entirely  from  the  naked  ear.  A  series  of  these  globes,  of 
different  sizes,  supplies  an  apparatus  for  analysing  sounds, 


106  ACOUSTICS. 

of  much  importance  in  acoustic  researches.  If  two  dia- 
pasons of  the  same  note  are  placed  even  at  a  considerable 
distance,  with  their  openings  facing  each  other,  then,  if  one 
be  struck,  and  the  sound  arrested  by  laying  the  hand  on  it, 
the  note  will  be  heard  from  a  distance  carried  on  by  the 
other  diapason — 

"  Et  sese  lampada  tradunt." 

Here  the  vibrations  are  sent  through  the  communicating 
column  of  air,  the  atmosphere  transmitting  the  vibration  in 
the  air  contained  in  one  case  to  the  other,  which  responds. 
A  violin  or  stringed  instrument  will  sound  if  the  note  to 
which  it  accords  is  given  at  a  distance ;  but  sounds  which  it 
does  not  render  produce  no  effect  on  it. 

Kircher  mentions  a  large  stone  which  vibrated  to  a  cer- 
tain organ-pipe.  We  have  often  heard  of  the  famous  pillar 
in  a  church  at  Rheims,  which  vibrates  perceptibly  at  the 
sound  of  a  bell,  while  all  the  others  are  immovable.  Boyle 
asserts  that  he  has  often  felt  with  his  hand  the  pews  in 
church  vibrating  at  the  sound  of  the  organ,  or  at  the  human 
voice,  certain  notes  producing  more  intense  effects  than 
others. 

A  glass  may  be  broken  by  the  voice.  Every  glass  has 
its  own  note,  heard  when  it  is  tapped  or  broken ;  so  that 
if  a  man  with  a  true,  strong  voice,  pronounces  the  note  on 
the  edge  of  the  glass,  it  will  break  in  a  few  seconds.  The 
octave  of  the  note  is  said  to  be  equally  effectual.  Thin  convex 
glasses  are  the  best  for  trying  the  experiment.  The  sound 
of  a  violin  would  answer,  while  the  blast  of  a  trumpet  would 
not.  A  German  physician  saw  it  done  in  an  inn  by  a  man 
who  made  it  his  trade.  Several  glasses  were  ranged  before 
him;  he  struck  them  in  succession  with  a  key  to  get  the 


RESONANCE.  IO7 

note,  then  bending  down  sounded  the  same  note  vigorously, 
and  the  glasses  broke.  There  was  no  proof  that  the  glasses 
had  not  been  prepared :  a  slight  scratch  with  a  diamond 
would  have  made  success  more  certain. 

It  is  curious  that  the  earliest  mention  of  this  class  of 
facts  should  be  in  the  Talmud.  "  It  was  said  by  Rame, 
the  son  of  Jacheskel :  If  a  cock  shall  put  his  head  into  a 
vessel,  and  break  it  by  his  crowing,  the  owner  must  pay  the 
whole  price.  Rabbi  Joseph  says,  '  These  are  the  words  of 
the  Master :  If  a  horse  by  neighing,  or  an  ass  by  braying, 
break  a  vessel,  the  owner  shall  pay  the  half  of  the  price.' " 
The  writers  of  the  Talmud  who  invented  these  niceties  of 
law  must  have  had  exuberant  imaginations. 

We  have  just  seen  that  the  phenomena  of  resonance  are 
always  produced  by  vibrations  in  elastic  bod:es.  Gene- 
ralising from  this,  we  perceive  that  all  sound  results  from  the 
vibration  of  elastic  matter,  so  that  sound  may  be  denned 
as  a  vibratory  movement,  perceptible  by  the  ear.  But 
before  enlarging  on  this,  we  have  a  few  words  to  say  on  the 
acoustics  of  churches,  theatres,  &c. — a  difficult  problem, 
which  has  been  but  little  studied.  How  should  a  hall  be 
constructed,  so  that  the  sound  emanating  from  one  point 
may  be  transmitted  distinctly  in  all  directions  ? 

The  ancients  built  circular  amphitheatres,  with  the  seats 
in  raised  circles,  and  semi-circular  theatres,  with  the  stage,  not 
extending  far  back,  enclosed  in  thick,  solid  walls.  But  the 
only  roof  was  a  covering  to  keep  off  the  sun's  rays,  which, 
though  it  could  not  fail  to  reflect  sound,  was  not  taken  into 
account  by  the  architects.  They  succeeded  in  so  disposing 
the  seats  that  the  actor's  voice  should  proceed  directly 
to  all  the  hearers,  numbering  often  some  thousands.  Even 
in  the  ruins  of  such  theatres,  we  can  see  that  this  end  was 


io3 


ACOUSTICS. 


generally  attained.  Every  word  spoken  in  the  arena  can 
be  heard  at  the  farthest  seats.  The  theatre  of  Hadrian's 
villa  atTivoli,  the  circus  of  Murviedro,  and  the  amphitheatre 
at  Nismes  (Fig.  38)  are  remarkable  in  this  respect. 

The  only  means  employed  by  ancient  architects  to  aug- 
ment sound  were  the  vases  or  bells   already   mentioned. 


Fig-  38-  —  Amphitheatre  of  Nisme*. 

Public  affairs  were  transacted  in  an  open  building  called 
a  forum.  Under  the  blue  heavens  they  enjoyed  their 
amusements,  took  counsel,  and  listened  to  harangues.  But 
now  that  civilisation  has  left  its  cradle  to  find  a  home  under 
ruder  skies,  for  this  simple  architecture  various  kinds  of 
halls,  circuses,  concert-rooms,  theatres,  houses  of  legislation, 
&c.,  are  substituted.  Platforms,  pillars,  stalls,  boxes, 
pews,  introduce  great  difficulties  into  the  propagation  of 


RESONANCE.  IO9 

sound,  by  their  powers  of  resonance  and  reflection.  We 
must  proceed  on  a  new  plan  to  discover  the  method  of 
applying  the  science  of  acoustics  to  modern  buildings. 
Domes  are  generally  unfortunate  in  their  effect;  they  pro- 
duce a  too  powerful  and  too  prolonged  resonance.  Under 
the  dome  of  St.  Paul's  the  sound  seems  to  run  along  the 
Avails.  In  the  Rotunda  at  Rome  this  resonance  produces 
such  singular  effects,  that  it  is  said  many  people  go  to 
church  for  the  sake  of  hearing  them.  In  the  circular  con- 
cert-room of  the  Fine  Arts  Society  in  Berlin,  where  the 
walls  are  broken  by  a  large  number  of  deep  embrasures, 


Fig.  39-  Fi«-  «* 

this  inconvenience  is  not  met  with.  The  dome  of  St.  Mary's 
at  Dresden  is  remarkable  for  the  same  absence  of  resonance. 
There  is  no  advantage  in  elliptic  arches  or  halls,  the 
ellipse  only  serving  to  concentrate  sound  at  a  particular 
point.  The  parabola,  which  makes  diverging  rays  parallel, 
has  some  recommendation.  The  speaker's  desk  should  be 
at  the  focus  of  the  curve.  Chladni  proposes  to  terminate 
a  rectangular  hall  with  a  parabola.  This  arrangement 
(Fig.  39)  is  found  in  some  ancient  basilicas.  It  might  be 
completed  by  giving  a  parabolic  form  to  the  roof  over  the 
platform.  A  sounding-board  of  this  nature  is  sometimes 
placed  over  the  pulpit ;  its  mode  of  action  is  the  same  as 
that  of  the  apparatus  for  reflecting  in  lighthouses.  In  a 
concert-room  or  hall  it  might  be  an  advantage  to  construct 


no 


ACOUSTICS. 


over  the  platform  a  spherical  dome,  with  its  axis  directed  to 
the  centre  of  the  hall.    Another  idea  of  Chladni's  is  to  place 

the  speaker's  platform  in  a 
semi-conical  space  at  the  ex- 
tremity of  the  hall  (Fig.  40), 
but  he  admits  that  this  arrange- 
ment would  be  unsightly  and 
difficult  of  construction.  In 
theatres,  of  course,  no  reflector 
could  be  placed  behind  the 
actors.  The  only  suggestion 
deserving  attention  is  to  em- 
ploy, like  the  ancients,  triangular  columns  turning  on  their 
axes,  instead  of  the  folding  screens  through  which  so  much 
sound  is  lost  (Fig.  41).  The  arrangement  of  the  seats  in 
a  semi-circular  form  would  not  suit  the  exigencies  of  the 


Fig.  4«. 


Fig.  43. 


Fifi  43- 


modern  drama.  An  advantageous  form  is  given  in  Fig.  42. 
The  theatre  of  Parma,  which  is  celebrated  for  its  acoustic 
properties,  is  given  in  Fig.  43.  The  boxes  in  front  of  the 
stage  are  the  great  defect  in  modern  theatres.  Zamminer 
compares  them  to  monster  traps  for  strangling  sound. 


RESONANCE.  Ill 


Unfortunately  the  architect  is  compelled  to   consult  the 
wishes  of  those  who  come  not  to  hear,  but  to  see. 

In  the  construction  of  our  churches  and  amphitheatres, 
the  simplest  laws  of  acoustics  are  neglected,  and  conse- 
quently very  imperfect  effects  obtained.  The  commonest 
defect  is  an  excessive  sonorousness,  which  prevents  words 
from  being  distinctly  perceived.  The  semi-circular  room 
of  the  Fine  Arts  School  in  Paris,  though  beautifully  deco- 
rated, is  miserable  in  this  respect.  The  great  Amphitheatre 
of  Physics  and  Chemistry  in  the  Jardin  des  Plantes,  and  the 
Amphitheatre  of  Physics  in  the  College  of  France,  are 
inconveniently  sonorous.  They  have  tried  to  remedy  it  by 
using  drapery  to  deaden  the  walls,  and  pieces  of  wood  to 
impede  the  vibrations  of  the  raised  seats  ;  but  this  modi- 
fication is  of  little  use.  In  the  church  of  St.  Paul,  Boston, 
which  has  the  same  defect,  the  preacher's  voice  can  only 
be  heard  once  a  year,  on  Christmas  Day,  when  it  is  deco- 
rated in  such  a  way  that  the  arches  are  less  sonorous. 

The  semi-circular  form,  so  often  given  to  amphitheatres, 
produces  great  inequality  between  the  seats  at  the  centre 
and  those  at  the  extremities,  as  in  the  Amphitheatre  of 
Physics  of  the  Sorbonne,  and  that  of  the  Conservatory  of 
Arts  and  Trades,  but  there  the  inconvenience  is  lessened 
by  the  chair  being  differently  placed.  The  most  advan- 
tageous form  is  that  approaching  the  quarter  of  a  circle, 
because  the  walls  direct  the  sound  to  the  hearers. 

For  placing  the  raised  seats,  the  general  rule  is  to  follow 
a  line  direct  from  the  platform  to  the  beginning  of  the  roof. 
A  concave  curve  would  be  more  advantageous,  as  it  would 
obviously  allow  of  the  back  rows  hearing  better.  Mr.  Scott 
Russell,  M.  Lacheze,  and  others  have  proposed  several 
curves  for  this  purpose. 


112  ACOUSTICS. 

The  most  original  project  for  improving  the  acoustics  of 
theatres  is  that  suggested  to  Chladni  by  Langhaus,  of  Berlin. 
He  would  direct  from  the  stage  to  the  spectators  a  slight 
current  of  air,  which  should  carry  the  words  of  the  actors. 
It  would  be  produced  by  skilful  ventilation. 


CHAPTER  VIII. 

SOUND     IS     A    VIBRATION. 

Trevelyan's  Instrument — Singing  Flames — Pendulum — Undulations  of 
Water — Progressive  and  Stationary  Waves — Vibration  of  Rods, 
Strings,  Boards,  and  Tubes — Graphic  Method. 

UP  to  the  present  we  have  only  considered  the  phenomena 
of  sound  as  affecting  the  senses.  It  is  now  time  to  consider 
what  produces  them.  The  phenomena  of 
resonance  point  to  the  conclusion  that  sound 
can  only  originate  in  the  vibrations  of  a 
ponderable  body. 

Common  experience  shows  us  that  a 
sound  of  any  force  is  always  accompanied  by 
vibrations  perceptible  to  the  touch.  Drums 
beaten  in  the  streets  shake  the  window-panes. 
The  report  of  a  cannon  makes  the  earth 
tremble  ;  those  near  enough  feel  a  shock  in 
the  chest.  In  a  concert-room,  turning  the 
opening  of  a  hat  toward  the  orchestra,  you 
may  feel  the  trembling  of  the  air  by  placing 
your  finger-ends  on  the  crown.  In  many 
cases  it  is  easily  proved  that  sound  cannot 
be  produced  without  a  concurrent  vibratory 
movement.  A  stretched  chord  when  struck 
makes  oscillations  which  are  visible,  and,  owing  to  the  per- 
sistence of  luminous  impressions,  it  takes  the  form  of  Fig.  44. 

I 


H4 


ACOUSTICS. 


The  outline  of  a  diapason  becomes  indistinct  while  it  sounds, 
because  of  the  rapid  motion.  A  glass  bell,  rung  by  means  of 
a  fiddle-stick  or  wooden  hammer, 
will  communicate  violent  shocks 
to  a  little  ivory  ball  hung  beside 
it.  Each  time  that  it  touches 
the  bell,  the  ball  is  thrown  away, 
returning  again  and  again  as  by 
an  irresistible  impulse,  only  to 
rebound  once  more.  If  the  edge 
of  the  bell  be  touched  with  a 
pencil,  it  grates  against  the  vi- 
brating glass ;  or  if  a  horizontal 
bar  of  steel  be  rubbed  between 
the  thumb  and  fore-finger  with 
a  little  colophony,  it  gives  a 
sharp  sound ;  and  if  the  ivory 
pendulum  touch  either  extremity, 
it  rebounds  with  great  force. 

Plates  of  brass,  wood,  or  glass 
give  different  sounds,  according 
to  the  manner  of  striking  them. 
Sand  sprinkled  on  the  surface 
assumes  regular  curves,  marking 
the  lines  of  repose.  A  membrane 
stretched  upon  a  cardboard  frame, 
and  hung  by  three  threads  in  the 
pipe  of  an  organ,  will  throw  to 

a  distance  the  powder  scattered  upon  it.     The  better  to 
show  this,  a  glass  pipe  can  be  used  for  the  organ  (Fig.  45). 

It   is   always  easy  to   produce   sounds  by  mechanical 
action  repeated  at  short  intervals.     The  buzzing  of  a  fly's 


Fig-  45- 


SOUND   IS   A  VIBRATION.  Ilg 

wings,  the  chirp  of  a  cicada  or  grasshopper,  are  examples  of 
this  kind  of  sound.  A  flexible  card  pressed  against  the 
edge  of  a  cog-wheel  makes  a  sound,  which  grows  sharper  as 
the  rotation  becomes  more  rapid  ;  this  is  the  principle  of  the 
rattle.  In  the  siren  (an  apparatus-  that  will  be  described 
further  on)  a  stream  of  air  or  liquid  is  directed  against  a 
perforated  revolving  disc ;  this  stream  either  passes  or  is 
arrested  alternately,  thus  giving  birth  to  a  remarkable  sound. 
In  the  reed  stop  of  an  organ  the  sound  is  produced  by  the 
vibrations  of  an  elastic  tongue.  The  lips  tremble  while 
playing  on  the  oboe  or  clarinet. 

It  sometimes  seems  as  though  sound  might  be  produced 
by  a  continuous  movement ;  the  flute  and  the  common  whistle 
seem  influenced  by  the  action  of  an  uninterrupted  current  of 
air.  But  in  these  cases  the  current  is  broken  and  divided 
into  two  streams  by  the  orifice,  one  part  entering  the 
mouth-piece,  the  other  escaping  into  the  outer  air.  The 
current  first  compresses  that  portion  of  the  air  next  the 
orifice ;  this  latter,  reacting  by  its  elasticity,  resists  the 
current,  then  gives  place  again,  repeatedly;  so  there  is, 
in  reality,  a  continued  series  of  vibrations.  Wertheim  suc- 
ceeded in  playing  upon  pipes  submerged  in  liquid,  by  the 
injection  of  a  stream  of  the  same  liquid.  The  sounds  he 
obtained  had  the  same  musical  character  as  when  the  pipes 
were  played  upon  by  air.  Cagniard  de  Latour  had  pre- 
viously to  this  made  glass  tubes  vibrate  in  water  by  means 
of  friction,  so  that  the  water  became  sonorous. 

We  must  here  mention  the  "rocker"  of  Trevelyan,  in 
which  the  sound  results  from  the  contact  of  two  metals 
unequally  heated. 

In  1805  M.  Schwartz,  inspector  of  one  of  the  foundries  of 
Saxony,  having  placed  a  silver  cup,  still  hot,  upon  a  cold  anvil, 

I    2 


1 1 6  ACOUSTICS. 

heard,  to  his  great  astonishment,  musical  sounds  coming 
from  the  metal.  Professor  Gilbert,  of  Berlin,  repeated  this 
experiment,  and  described  how  the  cup  vibrated  so  long  as 
the  sound  was  heard,  but  grew  quiet  as  it  cooled  and  the  sound 
ceased  ;  he  did  not  attempt  to  explain  the  phenomenon. 

About  1829  Mr.  Arthur  Trevelyan,  wishing  to  melt  resin 
with  an  iron,  found  the  iron  was  too  hot,  and  laid  it  against  a 
block  of  lead  to  cool.  Scarcely  had  the  iron  touched  the 
lead,  when  a  sharp  note  was  heard  coining  from  it,  some- 
thing like  a  Northumberland  flute ;  at  the  same  time  he 
saw  the  iron  moving  in  rapid  vibration.  Mr.  Trevelyan  set 
himself  then  to  study  these  facts,  and  he  gave  an  explanation 
of  them  which  seems  to  be  the  true  one.  The  vibrations  he 
supposes  to  be  caused  by  the  sudden  expansion  of  a  cold 
body  when  brought  into  contact  with  a  warmer.  At  the 
moment  when  the  hot  iron  touches  the  lead  at  a  given 
point,  the  lead  expands  and  repulses  the  iron ;  the  iron  then 
touches  at  some  other  point,  where  the  same  thing  occurs, 
whilst  the  point  first  touched  cools  and  contracts.  By  this 
play  of  alternate  expansion  and  contraction  the  "rocker" 
is  able  to  produce  music.  It  is  usually  made  in  brass,  of 
a  prismatic  bar,  the  lower  angle  having  a  hollow  groove. 
This  is  fixed  on  a  round  handle.  When  heated  to  about  the 
temperature  of  boiling  water,  or  a  little  more,  it  is  placed  on 
a  piece  of  lead.  Mr.  Tyndall  made  the  same  experiment 
with  a  heated  shovel,  which  he  balanced  on  two  pieces  of 
sheet  lead  fixed  in  a  vice.  It  immediately  took  a  see-saw 
motion,  and  gave  out  a  musical  sound,  which  could  be 
modified  by  lightly  touching  the  handle. 

Sometimes  a  musical  vibration  may  be  obtained  by  a 
simple  coin  or  ring  laid  upon  a  piece  of  lead,  after  having 
been  sufficiently  heated. 


SOUND    IS   A  VIBRATION. 


When  a  current  of  air  is  heated  and  cooled  periodically 
at  a  certain  point,  there  results  a  succession  of  alternate 
dilatations  and  contractions,  which  may  prove  a  source  of 
sonorous  vibrations.  This  is  illustrated  by  the  apparatus 
of  Fig.  46.  It  is  composed  of  a  glass  tube,  in  which  is  fixed 
a  small  metallic  web.  This  is  heated  red-hot  by  a  spirit- 
lamp.  After  a  few  moments  a  plaintive  sound — a  sort 
of  low  moaning — seems  to  float  around 
the  tube ;  gradually  it  swells,  increases, 
becomes  very  loud;  then,  as  the  web 
cools,  the  sound  dies  away,  and  the 
tube  becomes  silent  again.  The  sound 
is  caused  by  the  ascending  current  of 
air  becoming  heated  as  it  passes  through 
the  web,  and  cooling  as  it  leaves  it 
Indeed,  by  lowering  the  tube  towards 
a  horizontal  position  it  may  be  stopped 
momentarily,  because  of  the  interruption 
of  the  current  of  air.  The  mysterious 
sounds  which  were  heard  to  procee$ 
from  the  statue  of  Memnon  at  sunrise 
were,  very  probably,  caused  by  the 
currents  of  air  in  the  hollows  of  the  stone  being  heated  by 
the  sun's  rays  (Fig.  47), 

We  often  hear  the  gas  sing  when  the  jet  is  stopped  by 
an  obstacle  which  prevents  the  free  passage  of  the  current. 
The  jet,  instead  of  being  continuous,  is  intermittent,  and 
the  gas  escapes  by  pulsations.  A  current  of  hydrogen  in  a 
glass  tube  would  produce  the  same  effect.  This  little  cir- 
cumstance has  given  rise  to  a  number  of  beautiful  expert 
ments  by  Count  Schaffgotsch  and  others.  Introduced  into 
a  glass  tube  is  a  small  brass  burner,  with  a  gas  flame  (Fig.  48). 


Fig.  46. 


u8 


ACOUSTICS. 


If  then  a  note  be  sounded  at  a  distance,  in  harmony  with 
the  glass  tube,  the  air  within  begins  to  vibrate,  and  communi- 
cates its  pulsation  to  the  flame,  which  grows  tall,  and  trem-' 
bles,  and  begins  to  sing  in  its  turn.  It  may  be  silenced  by 


Fig.  47.— Statue  of  Memnon. 

pressing  a  finger  on  the  opening  of  the  tube,  but  will  sound 
again  for  another  call  of  the  voice ;  only  the  true  note  must 
be  produced,  or  the  flame  will  not  respond.  With  four 
flames  and  four  tubes,  a  little  organ  may  be  made  to  give 
the  chord  doh,  mi,  sol,  doh,  in  perfect  harmony,  whose 


SOUND   IS   A   VIBRATION.  II 9 

music  is  sustained  as  long  as  the  flame  continues  to  burn. 
Sometimes,  too,  it  will  happen  that  the  flame  will  begin  to 
sing  spontaneously,  if  its  point  be  placed  at  a  certain  part 
of  the  tube. 

It  is  easily  proved  that  the  sound  of  singing  flames  is 
produced  by  a  pulsation  of  gas  burning  in  the 
tube.     The  flame  changes  alternately  from  yellow 
to  blue,  according  to  the  quantity  of  gas  which 
comes  to  feed  it.     If  the  head  be  moved  quickly 
from  right  to  left,  the  flame  will  seem  to  separate 
into  a  number  of  blue  and  white  images,  which 
being  received  on  different  points  of  the  retina, 
are  not  confused  in  the  eye.     The  result  may 
be  better   obtained   by  using  an    opera    glass 
during   the   experiment       The  best  means  of 
separating   the    successive   appearances   of  the 
flame   is,  however,  furnished  by  the  revolving 
mirror.     This  is  a  mirror  with  two,  three,  or  four 
faces,  rotating  round  a  vertical  axle.     It  causes 
the  flame   to  appear  every  moment  in  a  new 
direction,  the  result  of  which  is  a  kind  of  lu- 
minous ribbon,  continuous  so  long  as  the  flame       Fig.  48. 
remains   still,   but   breaking   into  a  chaplet   of 
brilliant  pearls  when  it  begins  to  vibrate.     There  is  a  suc- 
cession of  little  stars,  followed  by  luminous  trails  of  a  rich 
blue,  such  as  we  see  in  jets  of  gas  when  the  wind  blows 
on  them.      These  trails  terminate  in  spaces   of  complete 
darkness,  which  seem  to  indicate  that  the  flame  is  momen- 
tarily extinguished,  though  immediately  rekindled. 

Sonorous  flames  may  also  be  studied  by  means  of  a 
revolving  disc,  perforated  with  a  circular  row  of  holes.  A 
vibrating  body,  looked  at  through  such  an  apparatus  (called 


120  ACOUSTICS. 

a  stroboscope),  appears  to  move  with  diminished  velocity. 
It  is  as  if  we  had  a  microscope  to  magnify  time.  The 
vibratory  movement  is  a  motion  of  going  and  coming, 
reproduced  at  equal  intervals,  in  a  uniform  rhythm.  The 
oscillations  of  the  pendulum  give  a  curious  example  of  this. 
Moved  from  its  position  of  repose,  the  pendulum  imme- 
diately returns  because  of  its  weight.  It  falls,  but  in  falling 
it  acquires  an  increase  of  velocity,  and  passes  the  starting- 
point.  It  mounts  to  an  equal  height  on  the  opposite  side. 
It  cannot  mount  higher,  for  the  weight 
draws  it  back  while  it  swings,  thus 
gradually  destroying  its  velocity,  which 
becomes  nothing  as  at  the  moment 
of  first  setting  it  off.  Then  the  pen- 
dulum is  found  exactly  in  the  same 
condition  as  at  first ;  and  the  action 
recommences  in  an  opposite  manner: 
it  descends,  passing  the  point  of  equi- 
Fig.  49.-The  Pendulum.  ijbrjum  at  [ts  maximum  speed,  and 

returning  to  its  starting-point  with  no 
velocity.  Thus  it  has  accomplished  a  complete  oscillation, 
going  and  returning,  or  two  simple  oscillations  in  a  contrary 
direction.  Should  nothing  stop  it,  it  will  continue  indefinitely 
to  move  thus  from  side  to  side  of  its  vertical ;  but  the  re- 
sistance of  the  air,  and  the  friction  of  the  thread  at  the  point 
of  suspension,  together  with  other  causes,  diminish  by  degrees 
the  scope  of  the  oscillations,  and  so  bring  the  pendulum  at 
last  to  rest.  It  is  ascertained  that  all  oscillations  are  accom- 
plished in  a  definite  time.  A  pendulum  a  little  over  a  yard 
long  performs  one  oscillation  in  a  second. 

The  motion  of  the  pendulum  is  kept  up  by  the  force  of 
gravitation.     The  vibrations  of  a  sonorous  body  are  usually 


SOUND    IS   A  VIBRATION.  121 

sustained  by  the  force  of  elasticity.  Like  the  vibrations  of 
a  pendulum,  they  are  finally  extinguished  by  the  action  of 
different  resisting  forces  which  are  constantly  tending  to 
destroy  them.  The  duration  of  the  vibration  of  perceptible 
sounds  varies  from  the  tenth  to  the  twenty-thousandth  part 
of  a  second. 

As  to  the-  particular  nature  of  these  vibratory  move- 
ments, they  may  be  of  different  kinds.  In  the  air  they  form 
alternate  condensations  and  dilatations.  A  prismatic  body 
may  contract  and  dilate  lengthwise,  or  bend  transversely,  or 
even  perform  rotatory  vibrations. 

When  sound  is  propagated  the  vibrating  air-particles  do 
not  sensibly  change  their  place,  but  only  move  near  their 
positions  of  rest  for  a  short  space,  and  the  motion  or  pulse 
only  is  transmitted  to  a  distance.  Therefore  it  is  that  water 
scarcely  seems  to  be  displaced  when  traversed  by  an  ordi- 
nary wave.  To  prove  this,  throw  a  stone  into  a  piece  of 
quiet  water.  Around  the  point  of  commotion  we  see  con- 
centric rings,  which  are  propagated  to  the  shore,  describing 
larger  and  larger  circles.  On  their  way  they  meet  with 
many  floating  bodies — pieces  of  wood,  withered  leaves,  and 
straws.  Light  as  they  are,  these  are  not  carried  away.  We 
see  them  rise  at  the  approach  of  the  wave,  and  sink  as  it 
passes,  but  they  do  not  perceptibly  change  their  place.  It 
is  not  then  a  material  wave  which  is  carried  on  the  surface 
of  the  water ;  that  which  appears  to  be  carried  is  merely  the 
shock  or  impulse,  and  the  deformation  that  results  from  it. 
The  rings  dissolve  each  moment,  and  each  moment  are 
formed  anew,  with  fresh  particles,  which  in  their  turn 
quickly  come  to  repose.  Let  us  now  imagine,  instead  of  a 
single  stone,  a  number  thrown  in  one  after  another,  at 
regular  intervals,  to  the  same  place;  the  waves  that  they 


122 


ACOUSTICS. 


excite  will  also  break  upon  the  shore  at  regular  intervals, 
but  they  will  not  carry  the  particles  of  water  very  far ;  they 
mount  and  fall  continually,  and  pass  on  the  impulse  they 
have  themselves  received. 

The  interesting  experiments  of  Ernest  Henry  and  Wil- 
liam Weber  showed  that  liquid  particles  generally  move  in 


Fig.  50.— Undulations  of  Water. 

circles,  while  the  wave  travels  onwards.  To  make  this 
plain,  let  us  suppose  that  each  particle  makes  a  complete 
circle  in  the  time  that  the  wave  takes  to  go  from  the  point  o 
to  the  point  12  in  Fig.  50 :  it  will  make  the  twelfth  part  of 
a  circle  as  the  wave  clears  each  of  the  twelve  spaces 


Fig.  51.— The  Quarter  of  an  Undulation. 


between  the  points  o  and  12.  At  the  moment  the  wave 
touches  point  3  (Fig.  5 1)  the  particle  o  will  already  have 
had  time  to  accomplish  three-twelfths  or  one-quarter  of  its 
circle ;  the  particle  i  two-twelfths  or  one-sixth,  and  the  par- 
ticle 2  one-twelfth  of  the  circle,  while  particle  3  will  scarcely 
have  begun  its  movement.  At  this  moment  the  particle  o 
will  have  reached  the  lowest  point  of  its  course,  and  then 
will  begin  to  mount  the  opposite  side. 


SOUND   IS   A  VIBRATION. 


123 


The  next  figure  (Fig.  52)  represents  the  situation  of  the 
particles  by  the  time  the  wave  has  reached  point  6.  The 
particle  o  has  finished  the  half-circle,  particle  3  a  quarter, 
and  so  on.  It  is  now  3  which  is  at  the  base  of  its  path, 


Fig.  52. — Half  of  an  Undulation. 

whilst  o  is  again  on  the  general  level.     Between  o  and  6  is 
a  hollow. 

In  Fig.  53  the  first  particle  has  described  three-quarters 
of  a  circle,  and  is  seen  on  the  culminating  point  of  its 
course ;  the  particle  3  has  made  half  its  journey,  and  re- 
gained its  first  level;  the  whole  set  from  3  to  9  form  a 


Fig.  53. — Three-quarters  of  an  Undulation. 


hollow  undulation,  just  as  the  set  between  o  and  6  did 
formerly. 

Finally,  in  Fig.  54  the  hollow  is  displaced  for  three 
points — that  is,  from  6  to  12.  The  point  3  is  now  at  the 
summit  of  its  course ;  while  point  o,  having  described  an 
entire  circle,  has  returned  to  its  primary  position.  Between 
o  and  6  there  is  a  crest.  This  elevation,  and  the  depression 


124 


ACOUSTICS. 


which  extends  from  6  to  12,  taken  together  form  an  entire 
wave,  and  the  interval  it  fills  is  called  the  wave-length.  It 
will  be  noticed  that  at  the  depth  of  the  hollow  the  particles 
are  at  a  distance  from  one  another,  while  towards  the  crest 
of  the  wave  they  are  close  together.  The  same  thing  is 


Fig.  54.— Complete  Undulation. 

repeated  at  regular  intervals  afterwards.  When  the  particle 
o  has  finished  its  second  revolution,  the  particle  1 2  has  only 
accomplished  its  first ;  there  is  one  complete  wave  between 
o  and  12,  and  another  between  12  and  24  (Fig.  55).  When 
the  particle  o  has  made  three  turns  the  waves  are  propa- 
gated up  to  the  point  36  ;  when  it  has  made  four  turns  the 


Fig.  55- 

waves  have  reached  point  48,  and  so  on,  advancing  a  wave- 
length at  each  oscillation. 

Particles  may  travel  in  ellipses  instead  of  circles,  and 
these  ellipses  may  become  so  elongated  as  to  be  transformed 
into  straight  lines.  Then  the  liquid  particles  only  rise  and 
fall  vertically ;  they  simply  make  transverse  vibrations,  as  we 
may  see  them  do  in  chords,  metal  plates,  and  membranes. 


SOUND    IS   A   VIBRATION.  125 

The  general  form  of  the  wave  remains  the  same,  but  the 
trough  and  the  crest  become  symmetrical,  the  one  being 
always  the  reverse  of  the  other,  as  is  shown  in  the  following 
curves  (Fig.  56),  which  represent  the  progress  of  a  trans- 
verse vibration.  Such  are  the  undulations  of  the  ether 
which  produce  light 


Fig.  56.— Progression  of  a  Transverse  Vibration. 

If  the  orbits  of  the  particles,  instead  of  becoming  ver- 
tical lines,  changed  into  horizontal  lines  (the  propagation  of 
the  wave  being  always  supposed  horizontal),  we  should  have 
longitudinal  vibrations,  analogous  to  those  of  gaseous  bodies. 
The  particles  then  can  only  separate  and  approach  by  turns, 
whence  result  alternate  dilatations  and  compressions,  as  may 
be  seen  in  the  curves  in  Fig.  57,  which  represent  the  pro- 
gression of  a  longitudinal  wave. 


126  ACOUSTICS. 

In  a  body  of  cylindrical  form  another  class  of  vibrations 
may  be  seen — tortuous  or  revolving  vibrations.  The  par- 
ticles circulate  round  the  axis  of  the  cylinder,  and  the  motion 
is  propagated  in  the  same  manner  as  in  other  cases.  Each 
particle  begins  its  excursion  a  little  after  the  preceding  one, 
and  therefore  remains  a  little  behind  it,  in  all  the  phases  of 
the  oscillations,  which  they  pass  through  together. 


Fig.  57. — Progression  of  a  Longitudinal  Vibration. 

In  this  way  the  progressive  waves  are  propagated  in  an 
unlimited  medium.  Thus  sound  is  transmitted  in  the  open 
air,  light  through  the  ether,  and  undulations  in  an  unbounded 
sheet  of  water.  We  observe  these  waves  to  move  along  as 
if  each  phase  of  the  movement  of  the  first  particle  were  trans- 
mitted successively  to  all  the  file.  In  transverse  vibrations 
we  see  the  summit  of  the  wave  displaced,  and  travelling 
along  the  chord.  In  longitudinal  vibrations  it  is  the  compres- 
sions and  dilatations  which  are  transmitted  (Fig.  57).  An 
india-rubber  tube,  fixed  at  one  end  and  held  by  the  hand  at 


SOUND   IS   A  VIBRATION. 


127 


the  other,  is  shown  in  Fig.  56.  A  slight  stroke  at  one  end 
will  send  a  transverse  wave  undulating  along  the  tube,  thus 
forming  the  curve.  It  may  be  followed  with  another  wave, 
by  striking  again  on  the  end  of  the  tube  the  moment  it 
becomes  still ;  then  with  a  third,  and  a  fourth,  and  so  on, 
till  the  first  has  reached  the  wall  against  which  the  tube  is 
fixed.  From  this  instant  the  phenomenon  changes  its  aspect ; 
die  waves  being  unable  to  advance  are  obliged  to  return, 


ii. 


in. 


B  ABA 

Fig.  58.-Shock  of  Elastic  Balls. 


and  the  returning  waves  meet  the  later,  which  are  still 
advancing  ;  hence  the  result  known  as  "  fixed  waves.' 

The  fixed  waves  characterise  the  sonorous  vibrations  of 
elastic  bodies,  whether  they  give  out  their  own  sounds,  or 
only  resound  under  the  influence  of  repeated  shocks.  They 
can  be  easily  distinguished  from  progressive  waves.  In 
the  one  the  particles  vibrate  one  after  another,  whilst  in  the 
fixed  waves  they  vibrate  altogether.  These  waves  do  not 
travel ;  they  are  born,  live,  die,  and  rise  again- always  in  the 
same  place. 

This  change  is  owing  to  the  intervention  of  reflected 
waves.  The  laws  which  govern  these  phenomena  are  com- 


128  ACOUSTICS. 

plicated  enough.  To  give  an  idea  of  them,  let  us  consider 
what  happens  at  the  meeting  of  two  elastic  bodies.  Suppose 
A  and  B  (Fig.  58)  to  be  two  billiard-balls  hung  by  two  parallel 
threads.  Raise  the  ball  A,  and  let  it  fall  against  ball  B  ;  if 
their  size  be  equal  (I.),  A  will  remain  in  repose  after  the 
shock,  giving  up  all  its  velocity  to  B,  and  B  will  be  thrown 
forwards.  If  the  ball  A  be  larger  than  B  (II.),  it  will  pass  the 
vertical  line  with  a  velocity  scarcely  diminished,  chasing  the 
smaller  ball  before  it.  Finally,  if  A  be  smaller  than  B  (III.), 
it  will  be  thrown  back  with  more  or  less  force ;  the  greater 
the  resistance  opposed  by  the  mass  B,  the  stronger  will  be 
the  rebound. 

The  same  thing  takes  place  when  a  vibration  is  propa- 
gated in  an  elastic  medium.  The  balls  A,  B,  in  Fig.  58  (I.), 
represent  two  neighbouring  particles  which  transmit  a  pro- 
gressive wave.  B  receives  all  the  velocity  from  A,  and  A 
remains  in  repose  till  another  impulse  comes  to  disturb  it. 
But  if  A  and  B  are,  so  to  say,  the  bordering  columns  of 
two  media  of  differing  density,  we  fall  into  one  of  the  two 
cases  represented  by  II.  and  III.  If,  for  example,  the  me- 
dium B  be  less  resistant  than  the  medium  A,  the  particle  A 
will  pass  forward  while  communicating  its  velocity  to  par- 
ticle B  (II.).  If,  on  the  contrary,  the  second  medium  be 
more  resistant  than  the  first — if,  for  example,  B  represent  a 
fixed  obstacle — the  particle  A  will  be  thrown  back,  and  B 
will  be  scarcely  stirred. 

Now,  in  these  cases  what  must  follow  ?  The  particle  A 
not  being  at  rest  will  become  a  source  of  movement  for  all 
the  particles  behind.  The  result  will  be  a  reflected  wave, 
which  will  carry  back  the  movement  given  by  A,  either  in 
the  direction  that  A  was  pursuing  before  the  shock  (II.), 
or  in  the  contrary  direction  (III.). 


SOUND   IS   A  VIBRATION.  129 

These  comparisons  will  serve  to  give  an  approximate 
idea  of  the  phenomena  accompanying  the  reflection  of  a 
sonorous  wave.  The  first  case  (II.)  represents  the  re- 
flection of  a  sound  in  the  interior  of  a  solid  body  which 
vibrates  in  the  air,  A  being  a  point  of  the  surface,  and  B  a 
particle  of  air. 

A  reflection  of  the  same  nature  takes  place  at  the  ex- 
tremity of  a  tube  filled  with  air,  opening  into  the  atmos- 
phere ;  for  the  surrounding  air,  because  it  moves  more  freely, 
has  less  resistance  than  the  air  inside.  Therefore  the  sound 
which  comes  from  an  open  tube  is  partially  reflected  by  the 
surrounding  air,  and  returns  to  the  tube.  This  result,  indi- 
cated by  theory,  may  be  verified  by  experiment :  at  the  end 
of  a  very  long  open  tube  a  faint  echo  is  formed.  Biot 
observed  that  when  he  spoke  at  one  end  of  the  water-pipes 
of  the  aqueduct  at  Arcueil,  the  sound  was  echoed  back  tc 
him  six  times. 

The  case  shown  in  Fig.  58  (III.)  is  the  same  as  we  have 
in  fixed  obstacles.  Sound  is  reflected  in  this  manner,  in  the 
interior  of  a  closed  tube,  from  one  end  to  the  other.  A 
simple  apparatus,  which  we  have  not  time  to  notice  now, 
would  show  how,  in  either  case,  the  direct  waves  and  the 
reflected  combine  so  as  to  produce  fixed  waves,  separated 
by  points  of  repose,  called  nodes. 

The  particles  comprised  between  two  consecutive  nodes 
form  what  is  called  a  simple  wave.*  Agitated  by  a  common 
motion,  they  all  rush  forward  in  the  same  direction,  and 
return  in  a  contrary  one.  The  centre  of  each  wave  is  also 
a  centre  of  vibration.  There  the  commotion  is  at  its 

*  The  simple  wave  is  equivalent  to  the  half  of  a  complete  or  double 
wave,  just  as  a  simple  vibration  is  the  half  of  a  complete  or  double 
vibration. 


'3°  ACOUSTICS. 

maximum ;  from  the  centre  to  the  nodes  it  diminishes,  the 
extent  of  the  excursions  decreases,  and  at  the  nodes  all 
movement  has  ceased. 

The  particles  of  two  consecutive  waves  always  vibrate  in 
opposite  directions.  If  they  rise  in  one,  they  sink  in  the 
other,  and  vice  verscL  (Fig.  59) ;  if  on  the  one  side  they 


Fig  59.—  Nodes  and  Centres. 

approach  or  depart  from  the  node  that  separates  the  two 
waves,  they  approach  or  depart  equally  on  the  other  side. 

The  interval  between  two  nodes  or  two  centres  is  a 
simple  wave-length,  which  is  half  an  entire  wave-length. 
The  length  of  a  fixed  wave  is  equal  to  that  of  a  progressive 
wave ;  it  is  the  measure  of  the  advance  made  during  the 
time  a  single  vibration  lasts ;  in  other  words,  it  is  the  space 
traversed  by  sound  during  one  vibration.*  Thus  when  a 

*  A  simple  wave-length  corresponds  to  a  simple  vibration,  as  a 
double  or  entire  wave-length  corresponds  to  a  double  or  complete  vi- 
bration. Sometimes  one  and  sometimes  another  of  these  quantities  is 
employed,  therefore  it  is  necessary  not  to  confuse  tl  em. 


SOUND   IS   A  VIBRATION.  1*1 

ta9  o  ^ 

vibration  lasts  the  millionth  part  of  a  second,  the  corre- 
sponding wave-length  is  thirteen  inches  if  the  sound  be  pro- 
pagated in  the  air,  and  fifty-six  in  water,  &c.,  since  these 

numbers   represent   the   spaces   traversed   in   the   different 

LQ.OO  <K.  .  , 

media  during  the  mi  m  oath  of  a  second. 

In  the  reflection  from  a  fixed  obstacle,  a  node  is  formed 
close  against  it,  since  the  direct  and  the  reflected  shock, 
being  in  contrary  directions,  neutralise  one  another.  Nodes 
are  therefore  found  at  the  points  of  suspension  of  a 
vibrating  body — at  the  ends  of  a  string,  for  instance,  or  the 
points  where  a  metal  plate  is  held  in  a  vice.  The  position 
of  the  other  nodes  depends  on  the  shape  of  the  sonorous 
body,  and  the  sound  given  out  by  it. 

Any  elastic  body  will  generally  return  all  the  sounds 
which  meet*  it,  but  the  resonance  varies  greatly  in  intensity. 
It  is  strong  only  when  the  nodes  of  the  fixed  waves,  resulting 
from  the  interior  reflection  of  sound,  follow  certain  regular 
directions,  and  in  this  case  they  continue  after  the  producing 
cause  has  ceased  to  act.  The  sounds  which  develop  such 
a  peculiar  resonance  in  a  body  are  such  as  are  produced  by 
a  mechanical  shock — in  other  words,  they  are  the  sounds 
properly  belonging  to  a  body.  Any  other  sound  finds  but 
a  feeble  echo. 

Let  us  now  consider  the  fixed  vibrations  of  some 
sonorous  bodies,  and  find  out  the  arrangement  of  the  nodes 
which  characterise  their  specific  sounds.  Take  first  a 
string,  fastened  at  both  ends.  In  this  case  there  is  a  node 
at  either  end,  since  the  extremities  are  motionless ;  there 
may  be,  besides,  any  number  of  nodes  at  intervals  from 
one  end  of  the  string  to  the  other.  If  it  vibrates  trans- 
versely in  all  directions,  all  its  points  will  simultaneously 
describe  the  same  kind  of  orbits,  but  of  different  dimensions, 

J    2 


132 


ACOUSTICS. 


that  of  the  centre  of  the  chord  being  the  widest.  This  orbit 
may  be  a  right  line,  vertical  or  horizontal,  an  ellipse,  a 
circle,  or  any  other  curve,  according  to  the 
mode  employed  to  produce  the  vibrations. 
If  it  be  a  right  line,  the  string  will  vibrate 
in  a  plane ;  if  it  be  a  circle,  it  will  form  a 
spindle  (Fig.  60).  To  make  it  vibrate  with 
three  nodes,  we  have  only  to  touch  the 
middle  of  the  string  lightly  with  the  finger 
while  striking  one  of  the  two  halves  with 
the  bow;  the  string  then  divides  into  two 
conical  spindles  or  segments,  separated  at  c 
by  a  node,  and  vibrating  in  contrary  directions 
(Fig.  61).  Touching  it  in  the  same  way  at 
different  points,  we  may  obtain  three,  four, 
or  even  five  segments  of  the  string,  in  each 
case  giving  a  different  sound  according  to 
the  manner  in  which  it  is  divided.  The 
immobility  of  the  starting-points  may  be 
demonstrated  by  placing  slips  of  paper  upon  them,  which 
will  remain  perfectly  quiet  while  on  the  nodes,  but  at  any 
other  point  will  be  thrown  off  immediately  (Fig.  62). 


Fig.  60. 


6i. 


By  rubbing  the  chord  lengthways  with  a  little  resin 
Fig.  63),  the  longitudinal  vibrations  are  shown,  consisting 
of  alternate  dilatations  and  contractions.  When  there  are 
only  two  nodes  at  the  extremities  A,  B,  the  section  A,  c, 
dilates,  while  B,  c,  contracts,  and  vice  versa;  the  middle 


SOUND   IS   A  VIBRATION.  133 

C  becomes  a  centre  of  vibrations  where  the  movement 
of  translation  is  a  maximum,  but  where  the  density  remains 
the  same.  In  the  nodes  A,  B,  the  density,  on  the  contrary, 
changes  most,  and  there  is  no  translation.  It  could  not 
possibly  be  otherwise,  for  since  those  particles  at  C  move 


more  than  the  others  they  will  trench  upon  those  in  front, 
forcing  them  to  a  compression  ;  at  the  same  time  distancing 
those  behind,  which,  consequently,  must  separate  more  and 
more. 

Now  the  chord  may  be  again  subdivided  into  portions  of 
an  equal  length,  separated  by  nodes  which  will  become  the 


Fig.  63. 

centres  of  successive  compression  and  dilatation.  From  the 
two  sides  of  each  node  the  particles  move  in  contrary  di- 
rections ;  compression  takes  place  when  the  node  be- 
comes the  meeting-place  of  two  files,  and  dilatation  when 
it  is  the  starting-point  of  two  files  moving  away  again  (Fig.  64). 
It  often  happens  that  a  string  is  stirred  at  the  same 
time  by  longitudinal  and  transverse  vibrations,  more  or 
less  complicated,  to  which  may  be  also  added  rotating 


J34  ACOUSTICS. 

vibrations.  *  Each  particle  then  describes  an  orbit  in  the 
form  of  a  spiral  slightly  distorted.  If  you  picture  a  poor 
fiddle-string  tortured  by  the  bow  of  the  fiddler,  who  strokes 
it  and  strikes  it,  pinches  and  stretches  it  by  turns,  you  will 


Fig.  64. 

not  marvel  to  see  it  execute  curves  such  as  no  geometer 
has  ever  dreamed  of. 

To  get  transverse  vibrations  from  a  prismatic  metal 
plate,  it  may  be  either  fixed  by  one  end  or  laid  upon  two 
triangular  wedges  (Fig.  65).  A  series  of  centres  and  nodes 


Fig  65. 

will  then  be  seen,  whose  distribution  depends  on  the 
manner  in  which  the  rod  is  supported.  The  general  rule 
is  that  there  are  always  centres  at  the  free  extremities,  and 
nodes  at  the  fixed  points.  The  nodes  are  shown  under  the 
form  of  straight  lines,  which  cross  the  plate,  and  which 

*  A  chord  cannot  vibrate  transversely  without  lengthening  slightly, 
and  this  occasions  longitudinal  vibrations.  This  longitudinal  sound  is 
sometimes  recognisable  in  the  la  of  the  violoncello. 


SOUND    IS   A  VIBRATION. 


135 


may  be  rendered  visible  by  throwing  sand  upon  the  plate 
while  it  vibrates.  The  grains  of  sand  unable  to  remain  at 
the  centres,  where  the  tumult  is  at  its  height,  take  refuge 
at  the  nodes,  which  afford  them  a  quiet  asylum,  and  group 
themselves  in  fine  right  lines,  called  the  lines  of  repose,  or 
nodal  lines. 

Tuning-forks  belong  to   the  same  category  as  the  pris- 
matic metal  plates  ;    they  vibrate  so    that   there  are   two 
centres  at  the  extremities  of  the  branches, 
which  alternately  approach  and  separate, 
two  nodes  close  to  the  base,  and  a  third 
centre  in  the  midd'e  of  the  fork.      This 
lower  centre  makes  the  stem  rise  and  fall, 
so  that  when  placed  upon  a  wooden  table 
it  causes  it  to  resound  by  the  incessant 
vibration  (Fig.  66) 

The  longitudinal  vibrations  of  prismatic 
or  cylindrical  bars  develop  a  wonderful 
force.  Savart,  having  secured  a  steel  rod  (Fig.  67),  placed 
a  spherometer  opposite  the  free  end,  not  touching.it  when 
at  rest,  but  near  enough  to  be  struck  at  each  vibration. 
The  shocks  were  heard  when  the  sphero- 
meter was  at  a  distance  of  Y^^Q-  of  an 
inch ;  the  total  variation  in  the  length 
of  the  rod  (dilatation  and  contraction) 
being  then  at  least  double,  or  equal 
to  -2^-  of  an  inch.  It  would  have 
needed  a  weight  of  3,740  pounds,  hung  to  the  end  of  the 
rod,  to  lengthen  it  to  this  extent.  This  proves  that 
during  its  longitudinal  vibrations,  a  steel  wire  is  subject 
to  a  traction  which  might  become  strong  enough  to  break 
it  Thus,  when  a  weight  is  not  sufficient  to  break  a  metal 


Fig.  66. 


Fig.  67. 


136  ACOUSTICS. 

wire,  or   even   lo   get   a  permanent  elongation,  either  of 
these  results  may  be  obtained  by  making  the  wire  vibrate 


Fig 


throughout  its  length  while  the  weight  hangs  from  it.  For 
this  reason  it  is  always  necessary  to  avoid  a  regular  oscil- 
lation of  the  chains  of  a  suspension  bridge.  In  America, 
and  other  countries  where  there  are  great  suspension 


SOUND    IS   A  VIBRATION. 


137 


bridges,  they  forbid  regiments  of  soldiers  walking  in  time, 
or  even  herds  of  cattle,  to  pass,  fearing  the  effect  of  the 
vibration  on  the  chains. 

To  make  a  thin  plate  of  metal,  wood,  or  glass  vibrate 
transversely,  the  edge  should  be  struck  with  a  bow.  The 
simplest  means  of  holding  it  during  this  operation  is  to  take 


Fig.  69.— ChladnPs  Figures. 


it  between  the  thumb  and  the  fore-finger,  if  it  be  small 
enough,  or  to  let  it  rest  on  three  fingers.  The  best  way, 
however,  is  to  fix  it  with  four  screws  covered  with  cork, 
at  four  points,  through  which  the  nodes  will  pass.  The 
bow  is  then  drawn  vertically  across  the  edge  of  the  plate. 

If  the  plate  be  previously,  or  during  the  vibrations, 
sprinkled  with  fine  dry  sand,  the  grains  of  sand  will  be  seen  first 
to  dance  tumultuously,  and  at  last  to  range  themselves  in 
regular  and  symmetrical  figures.  The  nodal  lines  on  the 


138 


ACOUSTICS. 


plate  mark  the  places  where  there  is  no  vibration.  Each 
line  separates  two  vibrating  segments,  where  the  vibrations 
are  opposite,  the  surface  falling  in  one  while  it  rises  in 
the  other.  Figs.  68  and  69  represent  some  of  the  nodal 
lines  which  may  be  seen  on  plates  of  different  forms — 
square,  triangular,  circular,  &c. 


Fig.  70.-  ChladnL 

These  beautiful  phenomena  were  discovered  and  pub- 
lished by  Ernest  Florens  Frederic  Chladni,  Doctor  of  Phi- 
losophy, in  1767.  He  passed  the  greater  part  of  his  life 
in  illustrating  acoustics  in  the  different  towns  of  Germany, 
France,  and  Italy,  wherever  his  erratic  humour  led  him. 
To  him  we  are  also  indebted  for  the  first  catalogue  of  ae'ro- 
ites,  and  the  earliest  affirmation  of  their  ex-terrestrial  for- 


SOUND    IS   A   VIBRATION.  IJ9 

mation.  Chladni's  figures  long  puzzled  the  philosophers, 
who  looked  upon  them  as  an  unanswerable  enigma.  Savart 
endeavoured  to  explain  them,  but  as  usual  he  only  involved 
the  matter  in  deeper  obscurity.  The  only  useful  discovery 
which  he  contributed  -,vas  one  made  by  his  assistant,  of  using 
a  powder  of  heliotrope  in  place  of  sand,  and  laying  a  sheet 
of  damp  paper  over  the  figures,  by  which  means  they  may 
be  printed  and  kept  for  reference. 

Bells,  discs,  and  glasses  vibrate  with  nodal  lines  which 
divide  the  surface  like  seams.  If  the  bell  or  glass  be  turned 
mouth  upwards  and  filled  with  water,  these  vibrations  will 
express  themselves  in  beautiful  ripples  upon  the  surface. 
On  pouring  the  water  in,  it  will  be  thrown  away  from  the 
vibrating  segments,  and  remain  motionless  in  contact  with 
the  nodes.  The  nodes  may  also  be  discovered  by  suspend- 
ing a  little  ball  by  a  string,  and  letting  it  gently  touch  the 
vibrating  surface;  when  the  ball  remains  still  we  may  know 
that  it  is  on  a  nodal  line. 

The  same  experiments  may  be  shown  on  a  drum,  or  a 
sheet  of  paper  or  collodion  stretched  upon  a  frame.  Owing 
to  its  flexibility,  a  thin  membrane  will  easily  resound  under 
the  impression  of  any  sound  whatever.  The  tympanum  of 
the  ear  affords  a  striking  instance  of  this.  Therefore  we 
may  ascertain  the  position  of  the  nodes  and  vibrating 
segments  in  a  vibrating  column  of  air  by  the  ear,  or  by  a 
little  drum  covered  with  sand. 

We  have  already  said  that  the  vibrations  of  the  air  are 
longitudinal.  In  the  vibrating  segments  there  is  agitation; 
in  the  nodes,  complete  repose  ;  with  alternate  compression 
and  dilatation.  The  motion  of  the  air  in  the  segments  may 
be  communicated  to  a  membrane,  if  it  be  struck  perpendi- 
cularly; the  compressions  and  dilatations  that  take  place  in 


MO  ACOUSTICS. 

the  nodes  will  cause  it  to  vibrate,  if  they  act  on  one  side 
only.  The  ear  is  especially  sensitive  to  the  changes  of 
density  in  the  nodes. 

The  flames  of  Koenig  (noticed  more  fully  hereafter) 
allow  us  to  make  use  of  this  property  belonging  to  mem- 
branes, to  exhibit  the  changes  in  the  density  of  the  air. 
These  flames  are  supplied  by  a  stream  of  gas,  vibrating  under 
the  pressure  of  a  membrane  inserted  in  the  pipe.  Observed 
in  a  revolving  mirror  they  have  the  appearance  of  a  row 


of  tongues,  separated  by  black  spaces  (Fig.  71),  which 
depend  upon  the  nature  of  the  sonorous  vibrations.  An 
admirable  means  of  studying  the  vibrations  of  sonorous 
bodies  is  afforded  by  the  "  phonography  "  first  conceived  by 
William  Weber.  Imagine  a  pendulum  ending  in  a  point, 
swinging  exactly  over  a  sheet  of  paper  blackened  with 
smoke.  Evidently,  the  point  will  clear  a  white  line  for 
itself  through  the  black  powder,  in  which  it  will  pass  from 
right  to  left,  and  from  left  to  right.  But  if  the  paper  be 
drawn  slowly  back,  it  will  touch  a  different  point  each 
moment,  and,  instead  of  a  straight  line,  there  will  appear 
an  undulating  curve. 

The  same  result  may  be  obtained  by  using  a  vibrating 


SOUND   IS   A  VIBRATION. 


141 


rod  in  place  of  the  pendulum,  which  shall  mark  its  way 
upon  a  piece  of  smoked  glass.  If  the  tube  have  a  fine  and 
flexible  point  it  will  trace  every  vibration  by  a  zigzag  on 
the  glass.  It  is  still  better  to  use  a  rotating  cylinder  for 
this  purpose,  with  a  sheet  of  blackened  paper  fastened  to 
it.  When  the  tracing  is 
finished,  the  paper  is  taken 
off  and  steeped  in  alcohol, 
which  fixes  the  pattern. 

In  Fig.  72  we  are  able  to 
see  how  the  tuning-fork  may 
be  made  to  write.  Fixed 
to  one  of  its  prongs  is  a 
bit  of  pointed  copper  wire 
or  a  pen-nib.  Observing 
the  direction  in  which  it 
vibrates,  this  is  brought  up 
to  the  cylinder  in  such  a 
way  that  its  oscillations  are 
parallel  to  the  axis.  Be- 
fore any  vibration  takes 
place  the  point  will  trace 

upon  the  revolving  cylinder  a  fine  straight  line,  but  as 
soon  as  the  vibration  begins  the  line  grows  tremulous, 
and  each  sinuous  curve  corresponds  to  an  oscillation  of  the 
sonorous  body.  The  same  experiment  may  be  also  tried 
with  a  plate  or  membrane  on  to  which  is  fix^d  a  perpen- 
dicular point  of  some  kind — a  horse-hair  or  hog's  bristle,  or 
a  bit  of  tinsel.  Fig.  73  represents  different  curves  obtained 
in  one  or  other  of  these  ways. 

Leon  Scott  had  a  very  ingenious  idea  for  visibly  tracing 
the  vibrations  of  the  voice,  or  any  other  sound  transmitted 


Fig.  72. 


142 


ACOUSTICS. 


by  the  air,  with  a  membrane  arranged  after  this  manner. 
This  is  the  principle  of  the  instrument  that  Koenig  called 
the  phonautograph :  A  membrane  furnished  with  a  flexible 
point  is  stretched  over  the  end  of  a  kind  of  ear-trumpet ;  it 


rig  73- 

resounds  loudly  when  a  note  is  sounded  at  the  other  end  of 
the  apparatus  by  the  voice  or  an  organ-pipe,  and  the  point 
will  write  its  vibrations  on  a  turning  roller.  Koenig  wrote  a 
musical  air  of  seven  notes  by  this  means ;  but  it  is  hardly 
likely  that  anything  more  complicated  could  be  written,  for 
the  tracings  are,  in  general,  not  very  intelligible. 


CHAPTER  IX. 

PITCH      OF      SOUNDS. 

Measure  of  Notes  —  Chladni— Mersenne — Pythagoras — Sonometer — 
Savart's  Rattle — Sirens — Limits  of  Sound — Extent  of  the  Kcale 
of  Musical  Sounds — Limits  of  the  Human  Voice. 

WE  have  seen  that  the  origin  of  sound  must  be  sought  in 
the  vibrations  of  elastic  bodies.  These  vibrations  are  essen- 
tially isochronous — that  is  to  say,  the  same  phase  con- 
tinually returns  at  the  end  of  the  same  interval,  and 
each  oscillation  lasts  exactly  the  same  time  as  the  preceding. 
It  will  be  easy  now  to  define  the  pitch  of  sounds,  or  that 
which  distinguishes  a  low  tone  from  a  sharp  one,  as  the 
duration  of  their  vibrations,  or  the  number  of  vibrations  ac- 
complished during  a  certain  time. 

Sounds  of  the  same  pitch,  whatever  they  proceed  from, 
correspond  in  the  number  of  their  vibrations.  Two  notes 
produced  with  different  instruments  are  always  in  unison,  if 
they  have  the  same  number  of  vibrations.  When  a  note 
is  higher  than  another  it  is  because  of  its  more  rapid  vibra- 
tions. Therefore,  to  appreciate  the  exact  pitch  of  a  note, 
the  number  of  variations  it  executes  in  a  second  must  be 
counted.  One  of  the  simplest  means  of  ascertaining  this  is 
as  follows  : — The  sonorous  body  is  furnished  with  a  point 
wherewith  to  write  upon  and  a  rotating  cylinder  covered  with 
blackened  paper,  and  is  then  sounded.  By  the  side  is  placed 
a  registering  chronometer,  which  marks  each  second  on  the 
same  cylinder.  The  number  of  zigzags,  counted  between 


A\VVvV^/<//Vl 


144  ACOUSTICS 

the  two  marks,  gives  the  pitch  of  the  note.  If  the  tone  of  a 
tuning-fork  were  known  exactly  beforehand,  it  would  answer 
instead  of  the  chronometer  ;  as  writing  side  by  side  with  the 
sonorous  body,  whose  vibrations  are  to  be  counted,  each 
bend  of  its  course  represents  a  known  fraction  of  time. 
Suppose,  for  example,  that  the  tuning-fork  makes  100  vibra- 
tions in  a  second,  and  that  side  by  side  with  50  of  its  oscil- 

lations  220   are   found  in   the 
parallel  tracing:  from  this  we 

condude  that  the  tracin§  win 
give  440  vibrations  in  the  time 

. 

which  the  tuning-fork  takes  to 

*     *'  accomplish  100  —  that  is  to  say, 

Fis  74-  in  a  second  (Fig.  74). 

Chladni  discovered  a  clever 

plan  for  ascertaining  the  number  of  vibrations,  by  starting 
from  oscillations  slow  enough  to  be  discernible,  but  too 
slow  to  act  upon  the  ear.  He  took  a  metallic  bar,  long 
and  thin  enough  to  give  only  four  oscillations  a  second 
—  easy  to  count,  watch  in  hand.  According  to  the  theory, 
a  bar  of  half  the  length  must  give  sixteen  vibrations  ; 
a  bar  one-fourth  the  length,  sixty-four,  and  so  on.  Con- 
tinually shortening  the  bar,  in  the  given  proportion,  we 
enter  at  last  the  region  of  sonorous  vibrations.  But  all 
this  only  holds  good  in  theory  ;  in  practice  it  is  full  of  error. 
Mersenne  measured  the  pitch  of  notes  by  the  length  of 
the  string  required  to  produce  them.  He  had  noticed  that 
when  two  strings  of  different  lengths,  but  otherwise  identical, 
were  made  to  vibrate,  the  number  of  the  vibrations  was 
always  in  the  inverse  ratio  to  their  length.  Thus  a  chord  of 
fifteen  feet,  stretched  by  a  weight  of  seven  pounds,  gave  ten 
vibrations  a  second  ;  these  were  too  slow  to  be  heard,  but 


PITCH    OF   SOUNDS. 


'45 


by  shortening  the  chord  to  one-twentieth  of  its  length  Mer- 
senne  obtained  a  sound  twenty  times  sharper,  or  200  vibra- 
tions a  second,  which  he  took  as  the  starting-point  for  his 
measurements. 

The  sonometer  or  monochord  (Fig.  75)  acts  on  this  prin- 
ciple. Its  use  is  to  ascertain  the  pitch  of  a  note.  On  a 
wooden  box  are  fixed  two  bridges  a,  b,  over  which  a  string 


75- 


or  wire  is  passed.  One  end  is  firmly  attached  to  a  pin; 
the  other,  being  carried  over  the  pulley  /,  is  stretched  by 
a  weight.  Between  the  two  bridges  is  a  divided  scale, 
along  which  passes  a  movable  bridge  g,  which  is  used  to 
reduce  the  length  of  the  string,  if  so  required,  till  it  is  in 
unison  with  the  given  note  ;  then  the  scale  will  show  to  a 
fraction  the  length  of  the  chord,  and  a  very  simple  calculation 
gives  the  corresponding  note,  provided  only  the  note  of  the 
entire  string  is  first  known.  This  is  settled  by  comparison  with 
a  tuning-fork,  and  we  shall  presently  see  how  that  is  fixed. 


146  ACOUSTICS. 

By  the  sonometer  it  has  been  demonstrated  that  the 
half  of  the  string  gives  the  upper  octave  of  the  note  ren- 
dered by  the  whole  length  of  the  string ;  that  if  its  length  is 
reduced  to  two-thirds  the  sound  mounts  to  the  fifth ;  that 
taking  three-fourths  we  obtain  the  fourth,  &c.  When  the 
entire  length  gives  doh,  the  three-fourths  will  give  fa,  the 
two-thirds  sol,  the  half  the  octave  doh,  and  so  forth.  These 
relations  existing  between  the  length  of  the  strings  and  the 
notes  of  the  scale  were  not  unknown  to  the  Pythagoreans  ; 
and  we  may  interpret  them  by  saying  that  the  octave,  the 
fifth,  and  the  fourth  are  intervals  characterised  by  the  rela- 
tions of  -f-,  |,  -f  of  the  number  of  vibrations.  Hence  a 
note  is  the  upper  octave  of  another  when  it  makes  twice 
as  many  vibrations  in  the  same  time;  also  two  notes 
have  the  interval  of  a  fifth  when  three  vibrations  of  the 
one  correspond  to  two  of  the  other;  and  they  form  a 
fourth  when  one  makes  four  vibrations  while  the  other 
makes  three. 

The  sonometer  also  gives  us  a  true-  idea  of  the  value  of 
the  anecdote  told  by  so  many  authors.  One  day,  it  is  said, 
Pythagoras  passed  a  forge  where  four  blacksmiths  were  at 
work,  and  to  his  surprise  he  heard  that  the  four  hammers 
beating  in  measured  time  on  the  anvil  gave  the  intervals  of 
the  fourth,  the  fifth,  and  the  octave.  He  had  them  weighed, 
and  found  that  their  relative  weights  were  as  the  numbers 
I?  4^  ^  2.  On  his  return  home  the  great  philosopher  resolved 
to  test  this  result  by  another  experiment.  He  took  a  chord, 
and  strained  it  successively  by  four  weights  equal  to  these 
of  the  hammers.  The  four  notes  produced  under  these 
circumstances  gave  the  intervls  of  the  fourth,  the  fifth, 
and  the  octave.  Unfortunately,  however,  the  notes  of 
a  chord  do  not  vary  in  true  proportion  to  the  weight  at- 


PITCH  OP  SOUNDS.  147 

tached ;  to  obtain  the  octave,  for  instance,  we  must  not 
only  double  but  quadruple  the  amount  of  tension.  With 
the  four  weights  of  the  hammers  Pythagoras  would  never 
have  been  able  to  get  these  intervals  from  his  string.  Again, 
it  would  be  very  difficult  to  find  hammers  giving  notes  pro- 
portioned to  their  weight;  the  circumstance  is  merely  a 
coincidence.  Finally,  it  must  be  allowed  that  in  a  forge 
we  do  not  hear  the  blow  of  the  hammer  on  the  bar  so  much 
as  that  of  the  bar  on  the  anvil. 

Modern  scientific  men  have  applied  another  principle  to 
the  measurement  of  the  number  of  vibrations.  It  consists 
in  producing  sounds  by  a  succession  of  periodical  impulses 
given  by  a  wheel,  whose  turns  are  registered  by  a  mechani- 
cal contrivance.  This  idea  was  first  put  in  practice  by 
Stancari.  He  took  a  wheel  three  feet  in  diameter,  and 
fixed  on  its  outer  circle  200  iron  points.  Thus  prepared, 
the  wheel  was  set  on  a  horizontal  axle,  and  turned  with 
great  rapidity.  The  points  whistled  through  the  air,  and 
the  pitch  of  the  sound  thus  obtained  was  in  proportion  to 
the  rapidity  of  its  rotation. 

About  the  year  1830,  Savart  found  another  method  of 
illustrating  this  by  a  kind  of  huge  rattle.  The  sounds 
were  produced,  by  causing  the  teeth  of  a  rotating  wheel  to 
strike  in  quick  succession  against  a  flexible  metal  plate. 
The  wheel  was  set  in  motion  by  a  leather  band  passing  over 
a  large  fly-wheel,  which  was  turned  by  a  handle.  A  register- 
ing apparatus  fixed  to  the  axle  marked  the  number  of  turns 
made  in  a  given  time.  Multiplying  this  by  the  number  of 
teeth,  we  have  the  number  of  the  vibrations  executed  by  the 
edge  of  the  plate,  and  consequently  the  pitch  of  the  note 
sounded.  The  difficulty  of  turning  the  wheel  with  uniform 
velocity,  and  the  bad  quality  of  the  sounds  emitted  by 

K2 


I48 


ACOUSTICS. 


this  cumbrous  apparatus,  have   long  ago  brought  it  into 

disfavour. 

Savart  thought  to  supersede  the  siren   of  Cagniard  de 

Latour  by  his  great  rattle.  The  plan  of  the  siren  is  as  fol- 
lows : — A  disc,  perforated  with  holes 
placed  in  concentric  circles,  is  rotated 
in  such  a  way  that  a  current  of  air 
is  directed  against  a  point  of  the  per- 
forated circle  j  the  air  passes  whenever 
it  meets  a  hole,  and  is  interrupted 
when  it  strikes  upon  the  plate.  If 
the  disc  turns  ten  times  in  a  second, 
and  the  holes  are  twelve  in  number, 
the  jet  of  air  will  pass  120  times  in  a 
second,  and  this  will  also 'be  the  num- 
ber of  vibrations  of  the  sound  produced. 
This  arrangement,  first  invented  by 
Seebeck,  is  valuable  in  many  re- 
searches. By  it,  for  instance,  it  is 
proved  that  sound  can  only  be  engen- 
dered by  puffs  or  impulses,  succeeding 
one  another  at  regular  intervals,  for 
the  holes  must  be  equi-distant  on  the 
disc  if  we  want  to  obtain  a  sound  cor- 
responding to  their  number.  Holes 
irregularly  distributed  only  give  a 
noise  of  high  and  low  sounds. 
The  disc  may  be  turned  by  a  fly-wheel,  or  by  a  kind  of 

clockwork,  which  also  registers  the  number  of  turns.     The 

improved    siren    of   Cagniard    de   Latour    (Fig.   76)    was 

worked  by  the  very  current  of  air  which  caused  the  sound. 

The  wind  coming  from  a  bellows  (Fig.  77)  enters  through 


Fig.  76. -Siren 
of  Cagniard  de  Latour. 


PITCH   OF   SOUNDS.  149 

0,  into  a  brass  cylinder,  closed  at  the  top  by  a  perforated  disc. 
On  this  disc  rests  another,  perforated  in  the  same  manner, 
which  turns  on  an  axis  c\   when  the  holes  coincide  the 
air   passes,    but   it  is   periodically   intercepted.     The    per- 
forations  are  made   obliquely   through   the   two   discs,   in 
such  a  way  that  when  the  holes  meet  they  are  at   right 
angles  one  with  the  other.     Thus  the  current  urged  from 
below  suddenly  changes  its  direction  in  passing  from  the 
lower  to  the   upper  hole,   and  gives  an   impulse    to    the 
movable  disc  sufficient  to  turn  it.     The  velocity  of  the  rota- 
tion increases  continually,   and  the  note  rises  in  pitch,  so 
that  if  the  pressure  of  the  bellows  were  kept  up  the  shrillness 
would  become  almost  unbearable.     It  is  true  that  the  speed 
and  the  pitch  may  be  adjusted  by  arranging  the  pressure,  but 
it  is  very  rarely  that  a  perfectly  regular  note  is  obtained 
from  the  siren.     When  the  note  in  unison  with  the  one  to 
be  measured  is  reached,  the  pressure  is  maintained  constant, 
while  the  index  is  consulted  for  the  number  of  turns.     This 
reckoner,  shown  uncovered  in  the  figure,  is  set  in  motion 
by  an  endless  screw,  fixed  upon  the  axis  of  the  moving  disc 
c\  this  works  into  two  toothed  wheels,  which,  by  indices 
on   the  dials,   mark  respectively  the  hundreds,  tens,  and 
units.     If,  at  the  end  of  five  minutes,  the  first  dial  points  to 
66,  and  the  other  to  30,  the  number  of  turns  accomplished 
would  be  6,630 ;  supposing,  then,  the  disc  has  twenty  holes, 
that  would  give  132,600  puffs  of  the  sonorous  current  in 
five  minutes,  or  300  seconds,  or  442  a  second ;  from  which 
we  conclude  that  the  note  obtained  corresponds  to  442 
double  vibrations 

The  siren  can  sing  under  water,  and  therefore  gained 
its  name.  Plunged  in  any  liquid,  it  can  be  made  to  sing  by 
forcing  a  powerful  jet  of  the  same  through  the  aperture. 


ACOUSTICS. 


Thus  water,  oil,  and  mercury  will  sing.  The  sounds  are 
distinguished  by  a  peculiar  quality,  but  the  notes  are  the 
same  as  in  the  air. 


Fig-  77.— The  Bellows. 


We  must  plainly  confess  that  the  tone  of  the  siren  is 
not  so  pleasant  to  the  ear  as  its  name  would  lead  one  to 
suppose;  these  shrill  and  piercing  sounds  would  scarcely 


PITCH    OF   SOUNDS.  151 

set  us  dreaming  of  the  Siren's  songs  which  Homer  says 
allured  travellers  by  their  wondrous  spell,  and  if  we  stop 
our  ears,  it  is  certainly  not  for  fear  of  being  bewitched. 

To  produce  the  current  of  air  requisite  for  working  these 
instruments,  an  apparatuses  used  (Fig.  77)  composed  of  a 
double  pair  of  bellows,  acted  upon  by  a  pedal  /,  a  rod  ty 
and  an  air  compartment  c,  perforated  with  a  certain  num- 
ber of  holes.  By  these  holes  the  siren,  or  the  tubes  which 
are  to  be  sounded,  receive  the  wind.  They  can  be  opened 
and  shut  at  pleasure  by  pressing  different  buttons. 

A  natural  question  arises  here  as  to  the  limit  of  audible 
sound.  What  are  the  very  lowest  and  the  highest  notes 
appreciable  by  the  ear  ? 

In  1700,  Sauveur  pronounced  the  lowest  sound  to  be 
that  produced  in  a  pipe  of  iorty  feet,  corresponding  to 
twenty-five  vibrations  per  second. 

The  deepest  bass-pipe  yet  constructed  by  organ-builders 
is  thirty-two  feet  in  length.  It  should  give  the  doh-2,  cor- 
responding to  thirty-two  simple  vibrations.  On  the  other 
hand  they  make  very  short  pipes,  which  should  give  10,000 
vibrations,  or  more.  But  is  it  proved  that  these  sounds 
actually  exist? 

The  lowest  notes  of  the  octave  of  sixteen  feet,  the  doh 
of  sixty-five,  and  the  re  of  seventy-three  vibrations,  are  heard 
only  as  a  kind  of  rumbling,  in  which  the  most  practised  ear 
can  scarcely  distinguish  the  musical  pitch ;  and  the  pipes 
that  produce  these  notes  can  only  be  tuned  by  indirect 
means.  On  the  piano,  where  they  constitute  the  lower 
extremity  of  the  key-board,  their  musical  character  is  very 
undecided ;  and  orchestral  music  but  rarely  descends 
below  the  mi  of  the  double-bass,  which  has  eighty-two 


152  ACOUSTICS. 

vibrations.  In  these  regions  the  ear  already  begins  to 
apprehend  the  vibrations  of  the  air  as  separate  shocks. 
This  sensation  becomes  more  distinct  as  we  advance  to 
the  octave  of  thirty-two  feet,  and  as  we  approach  the  doh 
of  thirty-two  vibrations  we  no  longer  hear  a  sound,  properly 
speaking ;  that  which  strikes  the  ear  is  only  a  series  of 
disconnected  explosions.  Many  people,  nevertheless,  ima- 
gine that  they  have  heard  the  notes  of  this  octave  ;  but  this 
is  because  the  organ-pipes  produce,  simultaneously  with  their 
fundamental  note,  other  higher  notes  of  which  we  shall  speak 
presently;  a  pipe  of  thirty-two  feet  causes  the  notes  be- 
longing to  a  higher  octave  to  resound  slightly,  and  this  in 
all  probability  deceives  the  listener. 

The  same  illusion  is  doubtless  present  in  the  con- 
clusions Savart  has  drawn  from  his  experiments  on  the 
limits  of  hearing.  He  arranged  a  bar  of  iron  to  turn  round 
a  horizontal  axis  in  such  a  manner,  that  at  each  half  revo- 
lution it  should  pass  through  a  chink  hollowed  in  a  plank. 
At  the  moment  of  its  entrance  the  bar  forced  the  air  like 
a  piston,  producing  a  sort  of  explosion,  and  if  the  wheel 
turned  fast  enough  a  deep  sound  was  heard,  accompanied 
by  a  loud  rumbling.  Seven  or  eight  revolutions  a  second 
still  gave  an  audible  sound,  wherefore  Savart  concluded 
that  the  deepest  note  distinguishable  by  the  ear  might  be 
fixed  at  seven  or  eight  double,  or  fourteen  to  sixteen  simple 
vibrations.  But  Despretz  has  without  difficulty  shown 
the  error  of  this,  for  by  arranging  two  chinks  instead  of  one 
for  the  iron  bar  to  pass  through,  we  do  not  get  the  octave 
as  we  ought  by  doubling  the  number  of  the  explosions. 
It  must  then  be  admitted  that  the  note  of  thirty-two  vibra- 
tions, corresponding  to  sixteen  rotations,  has  already  been 


PITCH    OF   SOUNDS.  153 

obtained  by  eight;  and  this  is  not  surprising  if  we  remember 
that  natural  sounds  are  almost  always  accompanied  by 
higher  notes,  called  harmonics,  as  we  shall  presently  see. 
At  the  most,  Savart's  instrument  gives  a  note  of  about  thirty 
semi  or  simple  vibrations  a  second. 

Helmholtz  had  recourse  to  another  plan.  He  used  a 
wooden  case  closed  at  both  ends,  and  having  a  small 
opening  into  which  was  fitted  a  gutta-percha  tube,  in- 
tended to  be  introduced  into  the  auditive  canal.  On  this 
sounding-board  he  stretched  a  wire,  weighted  in  the  middle 
by  a  brass  coin  with  a  hole  in  it ;  owing  to  this  precaution 
the  string  could  not  give  the  upper  octaves  of  its  fundamental 
note,  which  was  very  deep. 

Under  these  circumstances,  the  sound  of  a  string  which 
gives  a  medium  note  becomes  insupportable  through  its 
strength ;  but  that  employed  in  these  experiments,  giving 
the  re  of  seventy-three  vibrations,  produced  only  a  faint  and 
slightly  growling  noise.  Coming  down  to  si  of  sixty-one 
vibrations,  Helmholtz  scarcely  heard  anything.  From  these 
experiments  he  concluded  that  audible  sounds  began  at 
about  sixty  semi-vibrations,  and  took  a  musical  character 
at  about  eighty,  in  the  octave  already  mentioned  of  sixteen 
feet.  But  the  limits  of  hearing  may  perhaps  vary  in  different 
persons,  and  depend  in  some  degree  on  experience  and  on 
the  intensity  of  sounds. 

The  higher  limit  of  hearing  is  certainly  not  the  same  for 
every  one.  Many  people  cannot  distinguish  certain  high 
notes  that  others  hear  perfectly.  Savart  tells  us  that  a 
sound  of  31,000  semi-vibrations,  produced  by  the  longi- 
tudinal vibrations  of  a  glass  cylinder,  was  heard  by  the 
greater  part  of  his  audience,  whilst  the  33,000  vibrations 


154  ACOUSTICS. 

of  a  cylinder  a  little  smaller  were  scarcely  heard  at  alL 
With  large  toothed  wheels  he  produced  a  very  intense 
sound,  which  was  not  lost  till  the  moment  when  it  appeared 
to  perform  48,000  vibrations  per  second;  but  it  is  difficult 
to  prove  in  this  case  that  the  flexible  plate  touched  all  the 
teeth  of  the  wheel. 

Despretz  thought  to  extend  this  limit  by  means  of  tuning- 
forks  which  should  give  73,000  semi -vibrations.  There  are 
some  miniature  tuning-forks  still  preserved  at  the  Sorbonne, 
and  shown  on  special  occasions.  But  how  are  the  notes 
determined  ?  M.  Marloye  first  adjusted  tuning-forks  to  the 
ear.  He  began  by  making  a  scale  which  passed  from 
16,000  to  32,000  vibrations,  guiding  himself  by  ear;  then 
in  the  same  manner  he  tuned  a  fork  to  an  octave  higher 
than  the  last,  giving  consequently  64,000  vibrations,  and  cor- 
responding to  doh10;  then  he  went  to  re10  of  73,000  vibra- 
tions. These  tuning-forks  can  only  be  heard  by  very 
sensitive  ears ;  the  very  shrill  notes  produce  a  painful 
impression,  an  indefinable  uneasiness  which  lingers  for 
some  time ;  it  is  very  difficult  to  perceive  their  musical 
relations.  Till  further  light  dawns  on  the  subject,  we  do 
not  deem  these  conclusions  very  important. 

Recently  Kcenig  resumed  these  experiments.  The  highest 
notes  that  he  could  distinguish  corresponded  to  40,000 
vibrations ;  but,  as  we  have  already  said,  the  limit  varies 
with  different  persons.  Very  high  notes  cease  to  be  appre- 
ciable by  many  ears.  Has  not  Wollaston  told  us  that  many 
people  are  quite  incapable  of  hearing  the  sharp  chirp  of 
grasshoppers,  or  even  the  twittering  of  sparrows  ?  Perhaps 
there  are  animals  who  can  distinguish  notes  beyond  the 
reach  of  human  ears. 


PITCH   OF   SOUNDS.  155 

To  resume  :  appreciable  sounds  are  limited  to  a  range 
of  from  about  60  to  40,000  semi-vibrations  per  second, 
which  range  may  be  sometimes  passed  for  ears  of  excep- 
tional power  and  delicacy.  The  undulations  of  the  ether 
produced  by  light  and  heat  are  infinitely  more  rapid. 
Heat  begins  at  65,000,000  vibrations,  visible  colours 
range  from  400  to  900  trillions,  1lhd  chemical  rays  attain  as 
much  as  a  quadrillion.  Heat  is  not  produced  simply  by 
the  vibrations  of  the  fluid  ether ;  it  is  certain  that  ponderous 
bodies  themselves  vibrate  when  they  are  heated ;  therefore 
we  must  admit  that  molecules  can  accomplish  vibrations  of 
wondrous  rapidity.  But  what  becomes  of  those  vibrations 
which  are  too  rapid  to  be  audible,  and  too  slow  to  be  felt  as 
heat?  Have  we  senses  that  can  appreciate  them,  organs 
that  can  be  affected  by  them  ?  May  we  seek  in  these  un- 
classified vibrations  the  explanation  of  galvanism  and  elec- 
tricity, which  everything  leads  us  to  suppose  a  form  of 
motion  ?  Who  can  tell  ? 

It  will  not  be  uninteresting  to  mention  here  the  compass 
of  the  notes  given  by  the  commonest  musical  instruments. 
First  stands  the  organ,  the  grandest  and  richest  of  all, 
which  occupies  the  whole  field  of  audible  vibrations — nearly 
ten  octaves.  The  piano  has  almost  seven  octaves,  com- 
prising all  the  notes  from  la-a  to  doh7,  or  from  54  to  8,400 
vibrations. 

The  sounds  of  the  violin  properly  extend  from  400  to 
6,000,  along  four  octaves,  but  much  higher  sounds  can  be 
drawn  from  this  instrument.  The  violoncello,  or  violone,  is 
confined  to  a  scale  of  between  80  and  350  vibrations ;  but 
the  octo-basso  of  M.  Villaume  embraced  vibrations  as  low 
as  64.  The  cornet,  trombone,  and  other  brass  instruments 


156  ACOUSTICS. 

give  very  varied  sounds.  The  highest  note  used  in  the 
orchestra  is  probably  the  re7,  which  corresponds  to  9,400 
vibrations. 

We  may  take  as  the  extreme  limits  of  the  human  voice 
the  fa-,  of  87,  and  the  doh6  of  4,200  vibrations — 


I 


CHAPTER    X. 

THE   NOTES. 

Relation  of  the  Notes— Scale— Names  of  the  Notes — Hymn  of  St. 
John—  Musical  Notation— Major  and  Minor  Keys— The  Waves  of 
the  Tempered  Scale — Galin  and  Cheve —  Choir  and  Concert  Pitch 
— Natural  Tuning-fork— M.  Lissajous'  Method. 

Music  is  not  so  much  concerned  with  the  absolute  pitch 
of  notes,  as  with  their  relation  one  to  another,  or  the  inter- 
vals between  them.  The  pleasure  we  derive  from  the  com- 
bination of  certain  sounds  depends  on  this  relation.  When 
two  notes  are  in  the  mutual  relation  of  two  simple  whole 
numbers,  they  form  a  concord  or  harmony ;  discords  are 
produced  by  complex  relations.  In  this  sense  we  may  say 
that  music  is  a  matter  of  numbers. 

Pythagoras  was  aware  that  a  string  divided  into  two 
unequal  sections  would  give  two  perfectly  harmonious 
sounds,  when  the  lengths  of  the  two  sections  hold  a  simple 
relation  to  one  another,  expressible  by  whole  numbers. 
The  relation  i  :  2  corresponds  to  the  octave ;  the  relation 
2  :  3  to  the  fifth  ;  3  : 4  to  the  fourth,  and  so  on.  Most  pro- 
bably the  Greek  philosopher  had  learnt  this  law  from  the 
Egyptian  priests,  which  is  equivalent  to  saying  that  it  was 
known  in  the  earliest  times. 

Harmonious  intervals,  therefore,  are  based  on  the  re- 
lations of  the  pitch  of  the  notes.  Take,  for  example, 
the  fifth  doh,  sol.  The  ear  tells  us  that  this  harmony 
may  be  found  between  very  high  as  well  as  between  very 


15  ACOUSTICS. 

low  notes,  not  at  all  depending  on  the  absolute  number 
of  vibrations.  Measurements  show  that  any  two  notes 
having  this  interval  hold  always  the  mutual  proportion  of 
3  :  2,  and  consequently  this  interval  is  always  caught  by 
the  ear  when  two  notes  are  as  3  :  2.  From  this  it  is  easy 
to  see  that  the  more  nearly  this  relation  is  consummated, 
the  purer  and  sweeter  will  be  the  harmony ;  and  therefore 
this  interval  is  called  a  true  fifth.  We  shall  presently  see 
that  it  is  seldom  realised  in  all  its  purity. 

The  simple  intervals  adopted  by  musicians  are  charac- 
terised by  the  following  relations  :— 

Octave 

Fifth 

Fourth 

Major  third  •  •  .  . 
Minor  third  •  •  •  . 
Major  sixth  •  •  •  • 
Minor  sixth  •  .  .  . 

A  note  is  said  to  be  the  upper  octave  of  another  when  it 
makes  twice  as  many  vibrations  in  a  given  time,  and  vice 
versa.  The  successive  octaves  of  a  note  are  distinguished 
by  figures  placed  below  or  in  a  bracket,  thus  :  doh2  means 
the  upper  octave  of  doh  (we  never  write  doh,) ;  doh3  is  the 
upper  octave  of  doh2,  or  the  double  of  doh,  £c.  Descend- 
ing to  the  lower  octaves  we  write  them  thus :  doh-,  is  the 
lower  octave  of  doh,  doh-2  the  double  octave,  and  so  on. 

It  is  easy  to  see  that  two,  three,  or  four  notes  which 
harmonise  when  taken  two  and  two,  will  still  accord  when 
united  altogether.  The  two  chords  of  three  notes  most  plea- 
sant to  the  ear  are  the  perfect  major  chord,  characterised  by 
the  numbers  4,  5,  6,  and  the  perfect  minor  chord,  represented 
by  the  fractions  \,  \,  {-.  They  both  contain  a  fifth,  a  major 
third,  and  a  minor  third,  the  only  difference  being  that  in 


THE    NOTES. 


159 


the  major  chord  the  major  third  is  the  lower,  while  in 
the  minor  it  is  the  upper  interval.  To  realise  the  different 
harmonies  a  musical  scale  has  been  adopted,  composed 
of  seven  degrees  (the  octave  of  the  first  note  making  an 
eighth),  which  may  be  expressed  by  the  following  syllables  : — 

Doh,  re,  mi,  fa,  sol,  la,  si,  doh ; 

the  relation  amongst  them  being  as  the  numbers — 
24,  27,  30,  32,  36,  40,  45,  48. 

The  first  scale  is  followed  by  another,  and  so  on,  each  being 
formed  by  raising  all  the  notes  of  the  preceding  scale  one 
octave.  We  have  already  described  how  the  successive 
octaves  are  written.  The  relations  which  the  different  notes 
of  the  scale  bear  to  the  first,  constitute  their  musical  in- 
tervals, and  are  expressed  by  the  following  numbers : — 

Doh— doh 
Doh— re  . 
Doh — mi. 
Doh— fa  . 
Doh— sol. 
Doh— la  . 
Doh — si  . 
Doh— doha 
Doll— re2 . 
Doh — mia 
Doh— faa . 
Doh — so!2 
* 

Doh— doh, 


unison 

i  :    I 

second 

8 

9 

third  . 

4 

5 

fourth 

3 

4 

fifth   . 

2 

3 

sixth  . 

3 

5 

seventh 

8 

15 

octave 

2 

ninth  . 

4 

9 

tenth  . 

2 

5 

eleventh 

3 

8 

twelfth 

i 

3 

*                      * 

* 

•        double  octave     .         I 

4 

Doh — mi, 
&c. 


seventeenth 
&c. 


:    5 

&c. 


The  names  of  the  intervals  simply  recall  the  position  of 
the  notes  in  the  scale.  The  twelfth,  the  double  octave, 
and  the  seventeenth  make  perfect  harmonies,  which  fact 


I  Go  ACOUSTICS. 

presupposes  the  simplicity  of  the  relations  which  characterise 
them ;  it  is  needless  to  particularise  them  further,  since  they 
are  but  the  counterparts  of  the  fifth,  the  octave,  and  the  third. 

Associating  the  notes  of  the  scale  by  twos,  we  do  not 
always  obtain  a  harmony.  A  suitable  choice  must  be  made. 
But  even  discords  are  important  in  music.  The  interval 
from  cloh  to  re,  called  a  major  tone ;  the  interval  from  re  to 
mi,  called  a  minor  tone ;  the  intervals  mi — fa  and  si — doh,,, 
known  as  diatonic  semitones,  are  very  characteristic  discords. 

The  scale  just  explained  does  not  suppose  any  know- 
ledge of  the  absolute  pitch  of  the  notes  ;  it  merely  depends 
upon  the  relationship  they  bear  one  to  another.  The  first 
note  may  be  anything ;  but  its  value  once  determined,  that 
of  all  the  other  notes  is  fixed  also.  This  may  be  noticed 
in  the  exercises  of  solfeggio,  which  consists  in  singing  the 
notes  of  the  scale  on  the  syllables  doh,  re,  mi,  fa,  sol,  la,  si. 
The  sound  represented  by  doh  may  be  chosen  arbitrarily ; 
but  by  this  choice  the  pitch  of  all  the  notes  is  decided.  If, 
for  example,  the  doh  has  240  vibrations,  the  re  must  have 
270,  the  mi  300.  the  fa  320,  and  so  on. 

The  names  of  the  first  six  notes  were  introduced  in  1026, 
by  Guido  TAretino,  or  Guy  of  Arezzo  ;  they  are  the  beginnings 
of  words  taken  from  the  hymn  of  John  the  Baptist: — 
"  Ut*  queant  laxis  ?rsonare  fibris 
Jlftra  gestorumyfzmuli  tuorum, 
•Sb/ve  polluti  /abii  reatum, 

Sancte  loannes." 

The  air  to  which  this  hymn  is  now  sung  at  St.  Jean  is  not 
exactly  the  same  as  the  ancient  air,  in  which  the  six  syllables 
chosen  by  L'Aretino  really  fall  upon  the  notes  they  name. 
That  air,  found  in  a  MS.  in  the  library  of  the  Chapter  of 
Sens,  has  been  copied  in  old  style,  as  follows  : — 
*  Ut  is  the  first  syllable  in  French,  but  is  replaced  by  doh  in  English. 


THE   NOTES.  l6l 

HYMN  OF  ST.  JOHN 

Ancient  Melody. 


Rat  que-ant  la  -  xis  re-son  -a-  re   fi-bris    Mi  -  ra      ges-to-rum  fa-  mu-H     tu 
-  o-rum      Sol  -  ve  pol-ln-ti    la  -  bi  -  i     re  -  a-tum.  Sane  -  te       lo-an-ness. 

The  seventh  syllable,  si,  was  not  added  till  1684,  by 
Lemaire.  In  Italy  they  soon  substituted  doh  in  place  of  ut, 
as  being  a  more  vocal  syllable.  The  names  proposed  by  Guy 
did  not  come  quickly  into  general  use,  for  in  the  time  of 
Jean  de  Muris,  in  the  fourteenth  century,  they  still  used  the 
syllables  pro,  to,  no,  do,  tu,  a,  in  Paris;  but  at  last  they 
were  accepted  pretty  generally,  excepting  in  England  and 
Germany,  where  they  kept  for  the  notes  the  names  of  the 
letters  C,  D,  E,  F,  G,  A,  B,  or  H. 

Here  is  the  history  of  the  letter  designation.  Since  the 
time  of  Gregory  the  Great,  perhaps  even  before  the  sixteenth 
century,  a  series  of  scales  of  fixed  notes  corresponding  to 
the  limits  of  the  voice  and  to  the  sounds  of  the  principal 
instruments  had  been  used.  They  were  called  after  the  first 
seven  letters  of  the  alphabet,  in  this  way  :  — 

A,  B,  C,  D,  E,  F,  G,  a,  b,  c,  d,  e,  f,  g,  aa,  bb,  cc,  &c. 
At  a  latex  date,  a  note  having  been  added  below,  it  was 
designated  by  the  Gamma,  or  Greek  G,  whence  comes  the 
common  name  of  the  scale,  Gamut. 

Guido  1'Aretino  substituted  for  these  letters  points  set 
upon  parallel  lines  (les  portees\  to  each  of  which  a  letter 
served  as  key.  The  key  fixed  the  value  of  the  line  ;  thus, 
when  F  was  written  upon  the  beginning  of  a  line,  all  points 

L 


l62  ACOUSTICS. 

placed  upon  this  line  represented  the  note  F.  Afterwards 
they  enlarged  these  points,  and  determined  to  place  them 
in  the  intermediate  spaces,  and  multiplied  both  lines  and 
spaces,  as  it  was  found  necessary. 

The  signs  of  the  notes  only  served  at  first  to  mark  the 
difference  of  intonation,  without  respect  to  the  duration. 
Jean  de  Muris,  or  Mceurs,  invented  square  figures  to  dis- 
tinguish the  relative  value  or  duration  of  the  notes.  This 
was  about  the  year  1338,  and  in  1502  the  invention  was 
perfected  by  Octavio  Petrucci,  who  discovered  a  way  of 
printing  music  with  movable  type.  The  longest  note  accord- 
ing to  the  old  notation  was  called  a  Long,  ^  ;  the  next  in 
duration  was  a  Breve,  r  or  M.  Of  these,  the  latter  is  occa- 
sionally found  in  church  music,  the  former  but  seldom.  The 
moderns  have  gradually  confined  themselves  almost  entirely 
to  the  following,  which,  since  the  fifteenth  century,  have 
been  indicated  by  the  accompanying  signs  : — 

o     j    j    ;     ;     ; 

Semibreve.         Minim.           Crotchet.     Quaver.     Semiquaver.    Demisemiquaver. 
We  also  find  Occasionally P  Hemidemisemiquaver. 

A  long  is  equal  in  duration  to  two  breves,  a  breve  to  two 
semibreves,  a  semibreve  to  two  minims,  a  minim  to  two 
crotchets,  and  so  on.  These  notes  may  be  replaced  by 
equivalent  rests : — 

EEE  ~r~  r          *  ^  ^ 

Long  Breve  Semibreve  Minim  Crotchet  Quaver  Semiquaver  Demisemiquaver 
Rest.  Rest  Re^t.  Rest.  Rest.  Rest  Rest.  Rest 

To  fix  the  absolute  duration  of  a  note,  a  metronome  is 
employed.  3- 

The  letter  G  has  become  the  key  of  sol,  gj;  the  letter  F, 
the  key  of  fa,  §i;  the  letter  C,  the  key  of  doh,  JL  &c. 


THE   NOTES.  163 

The  syllables  doh,  re,  mi,  fa,  sol,  la  did  not  originally 
designate  any  fixed  notes,  but  only  the  degrees  of  a  scale ; 
they  represent  the  hexachord  of  Guido  I'Aretino.  They 
used  to  be  written  underneath  the  letters  which  marked  the 
fixed  scales,  beginning  with  C,  F,  or  G. 

CDEFGABcdef... 

doh  re    mi    fa    sol   la    

..     ..      ..  doh   re    mi   fa    sol  la    ..   .. 

doh  re   mi   fa  sol  la  .. 

doh  re  mi  fa 

The  same  fixed  note  might  then  occupy  different  places  in 
the  movable  scale,  and  this  was  sometimes  found  to  be 
incompatible  with  the  preservation  of  the  intervals  adopted 
for  the  notes  doh,  re,  mi,  fa,  sol,  la.  This  led  to  different 
plans  for  harmonising,  and  there  was  a  great  confusion  in 
the  musical  system.  The  necessity  was  soon  felt  of  altering 
some  of  the  fixed  notes,  when  the  movable  scale  was  so 
transposed,  that  the  intervals  of  the  fixed  corresponding 
notes  did  not  realise  the  intervals  first  intended  by  the 
notes  doh,  re,  mi,  fa,  sol,  la.  Thus,  when  doh  was  written 
below  F,  and  fa  below  B,  the  interval  from  F  to  B  should 
have  been  a  fourth;  but  as  it  was  in  reality  greater,  it  was 
lessened  by  lowering  B  a  semitone.  This  note  then  became 
B  flat,  while  it  remained  B  natural  in  the  scale  beginning 
with  C.  This  double  part  it  had  to  play  was  indicated  by 
writing  the  B  in  different  ways,  and  it  is  also  the  origin  of 
the  signs  f )  flat,  and  (1)  natural.* 

It  was  only  after  a  thousand  changes  and  attempts  that 
the  modern  musical  system  took  form.  The  principal  rule 
which  directs  it  is  this :  Whatever  note  be  fixed  upon  for 

*  This  is  more  clearly  shown  by  the  French  words  bemol  and  becarre. 

L   -A 


1 64  ACOUSTICS. 

beginning  the  scale,  the  other  notes  must  all  follow  in  the 
intervals  already  decided  on.  To  provide  for  this  necessity 
the  sounds  are  altered,  either  by  raising  them  a  semitone, 
which  is  called  sharpening,  and  this  is  expressed  in  the 
notation  by  the  sign  ft;  or  by  lowering  them  a  semitone, 
which  is  called  flattening,  and  is  expressed  by  the  sign  °. 
For  the  value  of  this  semitone  the  ratio  ff  is  used,  which 
is  less  than  ^-f ,  the  value  of  the  interval  from  mi  to  fa.* 

The  words  doh,  re,  mi,  fa,  sol,  la,  si  are  now  used  for 
the  principal  fixed  notes  of  the  piano  and  other  instruments, 
and  following  the  sign  "  or  It  they  become  changed  notes, 
in  such  instruments  as  the  organ  and  pianoforte.  In  vocal 
music  and  fidicinal  instruments,  the  ratios  of  the  diatonic 
scale  are  preserved  in  every  key.  The  scales  always  bear 
the  name  of  their  first  note  or  tone.  All  the  major  scales 
are  modelled  on  the  scale  of  doh,  formed  by  the  set  of 
natural  notes — 

Doh,  re,  mi,  fa,  sol,  la,  si,  doh. 

The   intervals  are  reproduced   with    tolerable    exactitude, 

owing  to  the  alterations  applied   to  certain  notes.      The 

scale  of  sol  is  composed  of  the  notes- 
Sol,  la,  si,  doh,  re,  mi,  fajf,  scl; 

the  scale  of  fa,  of  the  notes — 

Fa,  sol,  la,  si!?,  doh,  re,  mi,  fa ; 

and   so   forth.      These   scales  belong  to  the   major   key. 

There  have  been  many  other  scales  used  in  music  which, 

from  having  the   third   minor,  have   given   rise  to  minor 

scales,  as,  e.g. — 

La,  si,  doh,  re,  mi,  fa,  sol,  la. 

The   chief  difference  between   the  two  scales  lies  in  the 
•  The  semitone  is  nearer  fa  than  mi. 


THE  NOTES.  165 

introduction  of  the  minor  third,  la — doh  (5  : 6),  in  place  of 
the  major  third,  doh — mi  (4:5) ;  they  are  each  characterised 
by  a  perfect  harmony  formed  with  the  third  and  the  fifth 
of  the  tonic. 

Perfect  major  chord    .     .     •     doh,  mi,  sol. 

Perfect  minor  chord    »     .    •     la,  doh,  mi,  or 
doh,  mi!?,  soL 

The  minor  scale  is  still  further  varied  by  raising  the  seventh, 
and  sometimes  also  the  sixth  note  of  the  scale  a  semi- 
tone,  for  certain  harmonic  reasons. 

It  would  singularly  complicate  the  construction  of  all 
instruments  with  fixed  sounds,  if  it  were  attempted  to  make 
them  realise  the  scales  in  their  theoretical  purity.  It  was 
necessary  to  make  a  compromise,  and  this  was  done  in  the 
tempered  or  adjusted  scale.  The  ear  will  tolerate  a  slight 
deviation  from  perfect  harmony,  and  this  allows  a  simplifi- 
cation of  the  scale  in  instruments  with  fixed  notes,  by 
employing  only  one  sound  for  two  notes  nearly  alike,  from 
the  inverse  alteration  of  two  neighbouring  notes.  Thus  doh& 
and  re&  have  but  one  pipe  or  string  for  both,  &c.  &c.  In  this 
way  it  is  managed  on  a  keyed  instrument  to  interpolate  five 
black  keys  with  the  seven  white  of  each  octave,  thus 
forming  the  chromatic  scale,  which  is  composed  of  twelve 
equal  semitones,  adapting  themselves  to  all  the  exigencies 
of  the  musical  system.  It  follows  that  we  are  thereby  led 
to  alter  more  or  less  sensibly  the  natural  notes  represented 
by  the  white  keys,  and  so  to  modify  all  musical  intervals. 

The  adjusted  semitones  may  be  approximately  rendered 
by  the  relation  ~\\  and  an  adjusted  whole  tone  scarcely 
differs  from  a  major  tone  £.  The  fifth  and  the  fourth  are 
only  falsified  to  an  inappreciable  extent  by  the  adjustment, 
but  the  thirds  are  so  much  so  that  they  are  painful  to  an 


1 66  ACOUSTICS. 

ear  educated  to  pure  harmony,  which  is  wonderfully  more 
exquisite.  Some  authors  of  the  last  century  gave  the  name 
of  "wolves"  to  these  lost  intervals,  where  the  discords 
seemed  to  meet  and  growl. 

A  natural  voice,  guided  only  by  instinct,  always  gives 
true  intervals;  and  violinists  whose  ears  have  not  been 
spoilt  by  the  orchestra  will  play  true  thirds  and  sixths  much 
more  delightful  than  the  adjusted  intervals.  Unfortunately 
the  free-toned  instruments,  which  play  in  the  orchestra  with 
tempered  or  adjusted  instruments,  are  forced  to  follow  their 
lead  and  acknowledge  the  false  intervals;  and  thus  those 
violinists  who  have  all  their  lives  been  forced  to  play 
falsely  in  the  orchestra,  become  accustomed  to  the  change 
of  tone.  Under  the  overwhelming  influence  of  the  or- 
chestra the  accuracy  of  the  voice  also  suffers.  Singers  end 
by  adapting  themselves  to  the  adjusted  notes,  and  lose  the 
power  of  singing  a  simple  air  with  that  true  intonation  which 
constitutes  its  charm.  Still,  if  a  singer  have  true  ear  and 
taste,  Nature  reasserts  her  rights  as  soon  as  she  is  relieved 
from  the  requirements  of  the  accompaniment. 

The  inconveniences  arising  from  the  equal  adjustment 
have  given  rise  to  numberless  attempts  to  return  to  natural 
harmony,  even  in  instrumental  music.  Erard's  harp  with 
a  double  movement ;  Poole's  enharmonic  organ,  and  that 
of  Gen.  Perronet  Thompson ;  the  harmonium  devised  by 
Helmholtz — all  give  the  different  scales  without  the  aid  of 
adjusting  or  tempering.  The  vocal  systems  adopted  in 
France  by  Galin  and  Cheve',  and  in  England  by  the 
numerous  Tonic  Sol-fa  Associations,  hold  to  the  natural 
scales  in  their  purity.  The  English  societies  employ  the 
syllables  doh,  re,  mi,  fa,  sol,  la,  ti,  doh,  and  reduce  them  in 
writing  to  the  letters  d,  r,  m,  f,  s,  1,  t,  d.  Galin  and  Chev^ 


THE   NOTES.  167 

employed  the  figures  i,  2,  3,  4,  5,  6,  7,  for  this  purpose,  the 
successive  octaves  being  indicated  by  points  placed  over  or 
under  the  figures.  It  is  only  needful  to  give  the  absolute 
pitch  of  the  first  note,  or  tonic,  for  all  the  other  notes  to  be 
determined.  This  plan  is  believed  to  give  greater  facilities 
for  reading  music  than  the  old  notation,  and  has  had  many 
advocates.  Rousseau  recommended  it  most  highly. 

"  Music,"  says  J.  J.  Rousseau,  "  has  shared  the  fate  of 
all  arts  which  are  only  brought  to  perfection  slowly.  The 
inventors  of  notes  thought  merely  of  the  state  of  the  art  in 
their  own  day,  not  looking  on  to  the  future ;  and,  therefore, 
the  nearer  the  art  draws  to  perfection,  the  more  defective 
are  their  signs  found  to  be.  As  it  advances,  new  rules  are 
established  to  obviate  present  inconveniences;  in  multiplying 
the  signs,  the  difficulties  also  are  multiplied;  and  what  with 
additions  and  alterations,  they  have  formed  out  of  a  simple 
principle  a  most  cumbrous  and  ill-arranged  system.  Mu- 
sicians, it  is  true,  do  not  admit  this.  Custom  is  everything. 
Music  is  not  for  them  the  science  of  sounds;  it  is  but  a 
science  of  crotchets  and  quavers  and  minims.  As  soon  as 
these  are  lost  to  sight,  they  think  that  music  is  done  with. 
Besides,  why  should  that  be  made  easy  for  others  which 
they  have  acquired  with  such  difficulty  ?  The  musician  is 
not  the  one  to  be  consulted  on  this  subject,  but  a  man  who 
understands  music,  and  has  reflected  on  the  art." 

When  a  piece  is  to  be  played  by  several  performers, 
it  is  necessary  for  the  instruments  to  agree ;  therefore,  in 
the  orchestra  they  are  tuned  by  means  of  a  tuning-fork, 
whose  note  remains  constant.  Formerly,  the  pitch  used  to 
be  given  to  an  orchestra  by  a  kind  of  whistle,  furnished  with 
a  graduated  piston,  whereby  the  pipe  could  be  lengthened 
or  shortened  at  will,  so  as  to  draw  different  fixed  sounds 


1 68  ACOUSTICS. 

from  it.  There  was  the  choir-pitch  for  the  plain  song  and 
for  secular  music,  the  chapel-pitch,  and  the  orchestra  or 
concert -pitch.  The  latter  was  never  fixed:  they  raised  or 
lowered  it,  according  to  the  compass  of  the  voices.  The 
chapel-pitch,  on  the  contrary,  was  fixed,  at  least  in  France, 
and  generally  higher  than  concert-pitch.  As  for  the  choir- 
pitch,  which  agreed  with  the  organ,  it  is  hard  to  say  whether 
it  was  higher  or  lower  than  the  chapel-pitch,  for  authors 
contradict  one  another  on  this  point ;  it  would  seem  that 
after  all  they  only  set  the  organ  to  chapel-pitch. 

Since  the  science  has  been  possessed  of  means  for 
measuring  the  absolute  pitch  of  notes,  musicians  have  been 
able  otherwise  to  determine  the  pitch  of  the  different  lead- 
ing orchestras  of  Europe,  and,  very  curiously,  it  has  been 
discovered  that  it  is  everywhere  rising  rapidly.  Sauveur, 
who  appears  to  have  first  studied  the  question,  found  in 
1700  that  the  lowest  note  in  the  harpsichord,  la,  made  202 
vibrations ;  and  the  low  doh  of  the  harpsichord,  244  vibra- 
tions, which  gave  Ia3  810.  Other  determinations  of  the 
last  century  vary  from  820  to  850.  In  1833,  Henri  Scheibler 
examined  the  tuning-forks  of  the  principal  theatres,  and 
found  that  at  the  Opera  they  had  two  of  853  and  868 ;  at 
the  Italian  and  Conservatoire,  others  of  870  and  88 1  vibra- 
tions ;  at  Berlin  he  found  a  la  of  883  ;  at  Vienna  they  varied 
from  867  to  890.  In  1857,  M. 'Lissajous  declared  a  new 
progression  in  the  orchestra-pitch.  Here  are  the  results  of 
his  measurements  : — 

Opera  of  Paris 896 

Opera  of  Berlin 897 

Theatre  of  San  Carlo,  Naples      .         .         .  890 

Theatre  clella  Scala,  Milan  •        •        •  903 

Italian  Opera,  London        ....  904 

Maximum  in  London  .        «         .        .        .  910 


THE   NOTES.  169 

This  increasing  elevation  in  the  pitch  of  instruments  is 
proved  by  the  ancient  organs  found  in  some  basilicas. 
What  is  the  reason  that  musicians  and  authors  have  made 
this  change?  It  is  supposed  that  most  instruments  show- 
greatest  brilliancy  in  their  high  notes,  and  therefore  the 
makers  have  by  little  and  little  heightened  the  pitch.  Singers 
generally  follow  the  same  inclination,  to  the  detriment  of 
their  voices.  But  we  must  not  go  too  far  in  attributing  the 
ruin  of  so  many  fine  voices  to  this  solely ;  it  would  be  fairer 
to  seek  the  cause,  as  M.  Berlioz  does,  in  the  tendency  of 
modern  composers  to  write  higher  parts  for  vocal  music  than 
the  ancient  composers.  Whatever  the  height  of  the  pitch 
may  be,  it  is  easy  for  the  composer  to  keep  within  reason- 
able limits. 

It  is  none  the  less  true,  however,  that  the  progressive 
variation  must  at  last  trouble  the  musicians,  and  it  is  very 
important  to  return  to  a  natural  and  absolutely  settled 
pitch.  Sauveur  insisted  on  the  necessity  of  this  so  long 
ago  as  1700.  He  first  proposed  for  this  purpose  the  sound 
which  makes  200  vibrations  per  second.  Finding  subse- 
quently that  his  calculation  was  erroneous,  he  modified  his 
views,  and  so  proposed  to  take  a  doh  of  512  vibrations  for 
his  starting-point.  This  number  is  one  of  the  series 
i,  2,  4,  8,  &c.,  whose  terms  may  be  regarded  as  the  suc- 
cessive octaves  of  unity.  Chladni  afterwards  adopted  the 
same  doh  of  512  vibrations,  corresponding  to  the  natural 
la,  853,  and  this  was  generally  employed  by  scientific  men. 
However,  as  the  pitch  of  the  orchestras  continued  to  rise, 
the  German  philosophers  meeting  at  Stuttgard  in  1834 
decided  on  choosing  a  normal  la  more  in  harmony  with  the 
custom  of  musicians,  and  they  fixed  definitively  on  the  la 
of  880  vibrations ;  this  is  the  German  la,  most  useful  for 


17°  ACOUSTICS. 

numerical  calculations.  Unhappily,  this  congress  could  not 
reach  the  rest  of  the  world,  and  the  pitch  still  mounted  in 
a  very  disorderly  manner.  Then  it  was  that  the  decree  of 
February  16,  1859,  fixed  an  official  diapason  for  France. 
This  pitch  gives  the  normal  la  with  870  vibrations;  it 
scarcely  differs  from  the  German,  yet  it  is  much  less  useful 
for  calculations. 

Here  follow  the  numbers  of  the  simple  vibrations  of  the 
adjusted  scale  based  upon  Ia3  (French  style),  and  of  the 
natural  scale  beginning  with  the  same  doh.  The  octaves  are 
obtained  by  doubling,  or  by  dividing  by  two. 

Notes.  Adjusted  Scale.        Natural  Scale.  Natutal  Ratio 

or  Relation. 

Doh  ...  517.3  ...  517.3  ...  24 

Re  ...  580.7  ...  582.0  ...  27 

Mi  ...  651.8  ...  6^6.6  ...  30 

Fa  ...  690.5  ...  689.7  ...  32 

Sol  ...  775.1  ...  7760  ...  36 

La  ...  870.0  ...  862.2  ...  40 

Si  ...  976.5  ...  970.0  ...  45 

^\  Doh  ...  1034.6  ...  1034.6  ...  48 

The  middle  octave  of  the  piano  is  represented  by  ths 
following  notes  : — 


Henceforth,  in  France  all  musical  instruments  will  be 
tuned  by  a  tuning-fork  set  to  the  official  standard  of  the 
Conservatoire.  Concord  is  thus  ensured,  and  there  is  no 
more  to  fear  from  the  tendency  of  orchestras  to  raise  the 
pitch. 

The  piano,  violin,  and  other  instruments  are  generally 


THE   NOTES.  17 1 

timed  by  ear.  One  string  is  set  to  the  note  of  the  tuning, 
fork,  and  the  others  are  regulated  by  the  musical  intervals, 
chiefly  by  octaves  and  fifths.  According  to  Weber's  experi- 
ments, a  very  fine  ear  can  appreciate  a  difference  of  a 
thousandth  part,  or  one  vibration  in  a  thousand,  but  that 
is  the  limit.  The  study  of  beats,  however  (a  phenomenon 
which  we  shall  soon  notice),  leads  us  much  further.  It  is 
by  this  means  that  organs  are  tuned.  When  extreme  pre- 
cision is  required  we  have  recourse  to  a  later  method 
invented  by  M.  Lissajous.  the  principle  of  which  will 
now  be  explained. 

A  prismatic  rod  can  vibrate  transversely,  so  that  its  free 
end  describes  a  right  line.  If  a  steel  bead  be  fastened  at 
this  end,  the  continuance  of  the  luminous  impressions  will 
appear  as  a  line  of  brilliancy.  The  eye  has  the  power 
of  preserving  the  most  fugitive  impressions  for  about  the 
fifteenth  part  of  a  second.  If  then  the  luminous  point  run 
its  course  in  less,  time  than  ^  of  a  second,  the  whole  track 
will  appear  illuminated.  Thus  a  burning  stick  or  piece  of 
charcoal  swung  round  in  the  air  will  make  a  fiery  circle. 
When  the  section  of  the  rod  is  rectangular,  it  can  be  made 
to  vibrate  either  in  its  thickness  or  its  breadth.  In  either 
case  the  bead  will  draw  a  line  of  light,  but  in  the  former 
the  route  will  be  perpendicular  to  that  which  it  takes  in  the 
latter.  But  we  may  agitate  the  rod  in  yet  another  way  by 
striking  it  obliquely.  It  is  then  moved  simultaneously  in 
two  directions  crossing  at  right  angles.  Will  it  decide  to 
follow  one  impulse  rather  than  the  other?  The  rod  takes 
a  middle  course  between  the  two  roads,  and  follows  first 
one  impulse  and  then  the  other,  changing  momentarily. 
The  little  bead  takes  a  tortuous  road,  and  its  luminous  track 
allows  us  to  follow  the  rod  in  its  rapid  evolutions. 


172 


ACOUSTICS. 


The  number  of  straight  vibrations  depends  on  the 
direction  in  which  the  rod  vibrates.  When  the  section  of 
the  rod  is  square,  its  thickness  and  breadth  being  equal, 
the  number  of  vibrations  will  evidently  be  the  same  in 
both  directions.  In  this  case  the  little  bead  will  describe 
an  ellipse,  which  may  either  pass  into  a  circle  or  flatten 
to  a  straight  line.  Calculation  proves  this.  The  line  may 

be  understood  a  priori  by 
supposing  that  the  rod 
moves  diagonally  from  its 
position  of  repose,  always 
making  little  equal  steps 
forwards  and  to  the  right, 
forwards  and  to  the  right ; 
then,  in  returning,  back- 
wards and  to  the  left 
backwards  and  to  the  left, 
as  shown  in  Fig.  78.  To 
explain  the  ellipses,  it 
would  be  necessary  to 
enter  upon  some  rather  abstruse  propositions. 

When  the  two  dimensions  of  the  rod  are  as  1:2,  the 
corresponding  numbers  of  vibrations  will  evidently  be  in 
the  relation  of  the  octave  ;  if  the  measurements  are  as  2:3, 
the  vibrations  will  be  the  fifth,  &c.  The  bead  and  the 
reflected  ray  then  will  describe  the  curves  given  later  on 
in  Figs.  84  and  85.  It  may  therefore  be  said  that  these 
figures  characterise  the  musical  intervals. 

Wheatstone's  kaleidophone  (Fig.  79)  is  on  this  principle. 
This  is  an  apparatus  composed  of  several  metal  rods,  to 
the  end  of  which  are  fixed  light  glass  beads,  silvered  within. 
When  illuminated  by  the  sun  or  the  light  of  a  lamp,  the 


Fig.  78.— Vibration  of  a  Square  Rod. 


THE  NOTES. 


373 


bright  spots  will  describe  curves  as  shown  in  the  figures, 
while  the  rods  vibrate.  Wheatstone  made  this  known  in 
1827,  and  the  kaleidophone  is  now  found  very  frequently  in 
the  studios  of  scientific  men.  Let  us,  then,  examine  some 
other  conclusions  drawn  from  the  same  principle.  Imagine 
an  upright  mirror  fixed  at  the  end  of  a  horizontal  bar,  which 
can  be  made  to  vibrate  alternately  vertically  and  horizon- 
tally (Fig.  80).  On  this  mirror  we  throw  a  luminous  ray, 
by  placing  it  before  a  lamp  covered  with  a  shade,  from 


7Q- — The  .Kaleidophone. 


which  a  single  ray  escapes  by  a  small  hole  pierced  for  the 
purpose.  While  the  mirror  remains  motionless  the  reflected 
ray  will  form  upon  the  wall  a  simple  point  of  light ;  looking 
straight  into  the  glass  for  the  image  of  the  lamp,  we  see  the 
tiny  light  shining  like  a  fixed  star.  Now,  if  the  bar  be 
struck  so  as  to  oscillate,  the  reflected  ray  shares  the  move- 
ment of  the  mirror,  and  the  image  on  the  wall  is  displaced. 
As,  at  first,  the  bar  only  vibrates  in  a  vertical  plane,  we  see 
upon  the  wall  a  luminous  track,  drawn  straight  down ;  and 
looking  into  the  vibrating  mirror,  we  see  there  also  a  perpen- 
dicular line.  If,  on  the  contrary,  a  horizontal  motion  be 
given  to  the  bar.  the  reflected  line  will  be  horizontal  too. 


174  ACOUSTICS. 

Finally,  if  the  bar  be  made  to  vibrate  obliquely,  we  shall  see 
both  upon  the  wall  and  mirror  the  fanciful  curves  of  the 
kaleidophone.  It  will  even  be  sufficient  to  hold  before  the 
mirror  a  metal  button,  a  pin's  head,  or  any  small  bright 
object.  Its  reflection  will  form  a  luminous  curve  as  soon  as 
the  bar  is  set  in  motion.  The  form  of  the  curves  will 
always  depend  on  the  rate  of  the  vibrations  executed  by  the 
bar  in  a  straight  line,  if  it  oscillates  first  in  «.  vertical,  and 
then  in  a  horizontal  plane. 


Fig.  80. 

The  same  curve  may  be  obtained  by  a  double  reflection 
on  two  mirrors,  each  vibrating  in  a  different  plane  (Fig.  81). 
They  are  placed  opposite  one  another,  so  that  a  ray  of 
light  reflected  by  the  first  will  fall  upon  the  second,  which 
throws  it  back  in  its  turn  against  the  wall.  If,  then,  one 
only  of  the  mirrors  be  made  to  vibrate,  the  brilliant  point 
upon  the  wall  will  change  into  a  luminous  line,  drawn  in  the 
direction  of  the  vibrations,  because  the  reflected  ray  shares 
the  motion  of  the  reflecting  surface.  But  if  the  first  mirror 
be  made  to  vibrate  horizontally,  and  the  second  vertically, 
the  reflected  ray  will  receive  from  the  first  a  horizontal 
movement,  to  which  is  added  a  vertical  movement  by  the 


THE    NOTES. 


'75 


second  reflection ;  the  two  movements  combine,  as  in  the 
kaleidophone,  to  give  birth  to  the  different  curves  already 


Fig.  81. 

described.  They  may  be  seen  either  by  looking  directly  into 
the  second  mirror,  or  by  receiving  the  image  of  the  luminous 
point  upon  a  screen  of  any  kind.  Greater  clearness  and 


Fig.  82.— The  Optical  Method  of  M.  Lissajous. 

brilliancy  is  given  to  this  experiment  by  passing  the  luminous 
rays  through  a  lens.  A  simple  inspection  of  the  curves  will 
shew  the  n.tio  of  the  respective  numbers  of  the  vibrations 


!76 


ACOUSTICS. 


made  by  the  two  mirrors.      A.  straight  line  or  an  ellipse 
indicates  unison,  the  figure  8  the  octave,  and  so  on. 

Instead   of  fixing   the   two   mirrors   to  horizontal  and 


Phase 


Fig.  83. — Unison  i :  i. 


Pliatc 


f  i 

Fig.  84.—  Octave  i:  a. 


vertical  rods,  they  may  be  fastened  against  the  branches  of 
two  tuning-forks,  placed  at  right  angles,  one  horizontally 
and  the  other  vertically,  as  in  Fig.  82.  The  first  gives 
to  the  reflected  ray  a  horizontal  movement,  the  second 
imparts  to  it  a  vertical  impulse,  and  thus  are  obtained  curves 
which  reveal  at  once,  by  their  aspect,  the  musical  relation  of 


THE   NOTES. 


I7JT 


the  two  forks.  Herein  consists  the  optical  method  for  com- 
paring sonorous  vibrations,  made  known  by  M.  Lissajous  in 
1855.  It  enables  us  to  ascertain  the  musical  interval  of 


Fig.  86.— Fourths  3:4. 


two  vibrating  bodies,  with  a  certainty  unknown  before  this 
beautiful  discovery. 

It  may  be  asked  why  the  same  ratio  should  produce 
different  figures.  This  is  due  to  the  difference  of  phase.  If 
one  of  the  two  mirrors  be  slightly  behind  the  other  in  first 
beginning  to  vibrate,  this  delay  (which  is  called  difference  of 


178  ACOUSTICS. 

phase,  or  simply  phase)  modifies  the  appearance  of  the 
figure  resulting  from  the  combination  of  the  two  movements. 
Thus,  when  two  tuning-forks  in  perfect  unison  begin  and 
end  their  course  together  (when  there  is  no  phase),  the 
trajectory  of  the  luminous  image  is  a  right  line;  in  any 
other  case  it  is  an  ellipse  or  a  circle.  Under  each  figure 
will  be  found  written  the  difference  of  phase  as  a  fraction 
of  the  entire  vibration. 

When  the  vibrations  of  two  tuning-forks  are  in  the  ratio 
of  two  whole  numbers,  the  optical  figure  drawn  at  the 
beginning  of  their  movement  will  continue  unchanged 
as  to  form,  but  will  diminish  slightly  in  size  as  the  vibrations 
die  away.  In  this  case,  only  one  of  the  curves  which 
characterise  the  musical  interval  in  question  will  be  seen. 
But  if  there  be  the  slightest  discordance  between  the  two 
tuning-forks,  the  figure  does  not  remain  steady,  but  changes 
gradually,  so  as  to  pass  through  a  complete  cycle  of  the 
different  curves  which  correspond  to  the  same  interval. 
This  is  because  the  delay  (or  phase)  continually  increases, 
and  the  figure  consequently  changes  in  the  same  way.  The 
more  decided  the  discord,  the  more  rapid  the  changes.  So 
it  happens  that  the  ellipse  which  characterises  unison  will 
pass  into  an  oblique  ellipse  crossing  the  line,  then  narrowing 
into  the  form  of  a  straight  line,  it  passes  on  to  a  reversed 
obliquity.  This  variation  of  the  figures  betrays  the  slightest 
discord  immediately,  and  also  helps  to  an  appreciation  of 
its  value. 

By  this  means  the  tuning-forks  are  tested  in  the  Con- 
servatoire ;  once  corrected  by  the  standard  there,  they 
are  stamped  and  fully  recognised.  But  the  fork  to  be  tested 
has  no  mirror  attached  j  its  own  polished  surface  serves  the 
purpose. 


THE   NOTES.  179 

M.  Lissajous  has  added  to  his  beautiful  inventions 
that  of  the  "vibration  microscope."  The  object-glass  is 
held  by  one  branch  of  a  tuning-fork  placed  at  right  angles 
with  the  tube.  When  the  fork  vibrates  the  object-glass 
oscillates  before  the  tube,  and  the  objects  upon  the  field 
of  the  microscope  seem  to  oscillate  in  the  same  direction. 
If,  then,  one  of  the  objects  itself  vibrates  in  a  different  di- 
rection, the  real  and  the  apparent  vibrations  blend,  and  the 
curve  thereby  formed  will  show  the  number  of  vibrations  of 
the  body  under  consideration. 


M  a 


CHAPTER    XI. 

TIMBRE   OR   QUALITY   OF   SOUND, 

Form  of  Waves— Simple  and  Complex  Sounds — Harmonics— Timbre 
of  Voices  and  Musical  Instruments — Musical  Sounds — Vowels. 

WE  have  seen  that  the  pitch  of  a  note  depends  on  the 
rapidity  with  which  the  vibrations  succeed  one  another. 
Is  that  the  only  difference  which  can  exist  between  sounds  ? 
Evidently  not ;  for  we  never  confuse  sounds  having  a 
different  origin,  even  when  they  are  in  unison ;  they  are 
distinguished  by  what  has  been  called  timbre.  The  sounds 
of  the  cornet,  for  instance,  do  not  resemble  those  of  the 
harp,  nor  does  the  violin  sound  like  the  organ.  The  same 
note,  even,  has  a  different  character  according  as  it  is 
sung  on  a  or  o\  whence  it  follows  that  the  vowels  only 
represent  the  changing  timbre  of  the  human  voice.  We 
may  even  classify  the  differences  in  the  timbre  of  musical 
instruments  by  determining  which  vowels  they  seem  most 
to  resemble. 

What,  then,  causes  the  timbre?  How  can  the  same 
note  produce  such  different  impressions  ?  These  questions 
have  long  occupied  philosophers,  and  it  is  but  latterly 
that  they  have  been  satisfactorily  answered,  owing  to  the 
researches  of  Helmholtz. 

It  had  always  been  supposed,  and  with  reason,  that  the 
timbre  must  have  some  connection  with  the  particular  form 
of  the  vibrations  of  the  sonorous  body.  Their  number 


TIMBRE   OR   QUALITY   OF   SOUND.  l8l 

simply  determined  the  pitch;  no  other  possible  difference 
remained  than  that  which  might  be  presented  by  each 
vibration  taken  separately.  Such  a  difference  was  easily 
discoverable  in  liquid  waves,  which  may  be  pointed,  crested, 
or  flattened,  while  still  keeping  the  same  rate  of  vibration. 
A  puff  of  wind  ruffling  the  surface  of  the  water  causes 
numberless  little  ripples,  which  change  the  form  of  the 
waves  without  hastening  or  retarding  their  motion.  But 
what  is  the  form  of  a  fixed  vibration  (like  that  of  a  chord), 
where  each  of  the  points  of  the  vibrating  body  simply 
rises  and  falls,  and  therefore  always  remains  in  the  same 
straight  line  ?  Nothing  is  simpler.  Just  as  a  man  might  go 
from  one  place  to  another  in  a  thousand  different  ways 
during  a  quarter  of  an  hour,  loitering  the  first  five  minutes, 
then  running  a  little  way,  and  again  dawdling  at  the  end 
of  the  journey,  so  a  vibrating  particle  may  change  in  more 
than  one  manner  during  the  hundredth  part  of  a  second 
which  it  takes  to  run  its  course.  It  can  go  first  slowly, 
then  very  fast,  and  again  slacken  its  speed ;  and  it  may  do 
this  two  or  three  times  along  its  route.  The  revolving 
mirror  enables  us  to  record  the  alterations  of  velocity  which 
take  place  during  one  simple  oscillation.  A  sheet  of 
smoked  paper,  which  is  moved  rapidly  under  the  vibrating 
point,  will  show  in  visible  tracery  all  the  irregularities  of  the 
oscillating  motion;  by  looking  at  the  curve  so  obtained, 
it  may  be  known  at  once  how  many  times  during  each 
oscillation  the  andante  alternates  with  the  presto.  The 
revolving  mirror  reflects  a  bead  fixed  at  the  end  of  a  hori- 
zontal bar,  in  a  series  of  different  perspectives,  giving  the 
appearance  of  a  luminous  ribbon  ;  if,  then,  the  bar  vibrate 
perpendicularly  to  this  ribbon,  the  bead  rises  and  falls,  and 
the  shining  band  changes  into  a  chain  of  serpentine  folds. 


1 82  ACOUSTICS. 

The  curve  is  exactly  analogous  to  that  shown  by  the  graphic 
tracery. 

When  the  particular  nature  of  a  periodical  motion  is 
known  beforehand,  the  curves  may  be  traced  without  having 


Fig.  87. 


been  seen.  On  a  horizontal  line  the  successive  seconds 
must  be  marked ;  at  each  division  an  upright  line  is  raised 
to  the  height  where  the  vibrating  body  should'  be  found 
at  this  moment ;  the  extremities  of  these  lines  give  the  curve 
of  the  vibration.  Thus  Fig.  87  represents  the  periodic 


Fig.  88. 

motion  of  a  hammer  worked  by  a  hydraulic  wheel :  first  it 
rises  slowly,  then  suddenly  falls ;  at  the  first  point  it  is  quite 
low,  up  to  the  ninth  it  lazily  rises,  between  the  ninth  and 
tenth  it  comes  down  with  a  sudden  fall.  The  motion  of 
the  bow-string  of  an  archer  is  just  the  same.  Fig.  88 
shows  in  like  manner  the  course  of  an  india  rubber  ball 


TIMBRE   OR   QUALITY   OF   SOUND.  183 

which  rebounds  vertically  after  having  touched  the  ground. 
A  revolving  mirro"  would  show  it  describing  this  curve, 
which  is  formed  of  successive  arches. 

The  simplest  or  most  regular  periodical  movement  is 
that  of  the  pendulum.  It  is  represented  by  a  curve  having 
the  sinuous  form  of  Fig.  89.  Thus  a  pendulum  ending  in  a 
point  will  trace  its  oscillations  on  a  sheet  of  paper  slipped 
underneath  it.  The  straight  line  indicates  the  direction  in 
which  the  paper  is  drawn ;  the  oscillations  are  perpendicular 


Fig.  89 


to  this  line,  as  pointed  out  by  the  arrows.  It  is  easy,  by 
the  aid  of  this  curve,  to  reproduce  the  remarkable  movement 
of  the  well-known  simple  pendulum.  Take  a  card,  and  after 
cutting  a  slit  in  it  with  a  penknife,  hold  it  against  the  curve 
in  such  a  position  that  the  slit  shall  be  vertical ;  then  move 
it  slowly  from  right  to  left.  You  will  never  see  more  than 
one  point  of  the  curve,  and  it  will  seem  to  oscillate  in  the 
slit  just  like  a  pendulum. 

The  mathematical  law  of  pendular  motion  may  be  in 
some  degree  explained  by  illustration.  Let  us  imagine  a 
luminous  point — a  small  lantern,  for  instance — fastened  to 
the  edge  of  a  vertical  wheel  revolving  with  a  uniform  velo« 


I84 


ACOUSTICS. 


city  (Fig.  90).  Placing  yourself  opposite  this,  you  will  see  the 
light  describe  a  perfect  circle.  The  appearance  would  be 
very  different  viewed  sideways.  Take  a  somewhat  distant 
position,  where  you  see  only  the  edge  of  the  wheel,  and  the 
light  will  seem  to  travel  up  and  down  exactly  in  a  perpen- 
dicular line,  only  it  will  have  the  appearance  of  going  much 
faster  in  the  centre  of  the  line  than  at  the  top  or  bottom. 
At  these  two  points,  indeed,  it  will  seem  to  stop  for  a 
moment  before  turning.  Now  this  apparent  movement  will 


Fig.  s<x 


be  the  exact  imitation  of  a  pendular  movement,  which 
would  make  the  luminous  point  swing  the  length  of  the 
vertical  diameter  of  the  wheel. 

A  "  pendular  vibration  "  is  any  periodical  movement  of 
the  same  character  as  that  of  the  pendulum,  the  velocity 
being  zero  at  the  two  extremities,  and  increasing  towards 
the  middle,  where  it  reaches  its  maximum.  A  simple  sound 
is  produced  by  a  pendular  vibration.  The  motion  of  the 
branches  of  a  common  tuning-fork  approach  this  type  of 
vibration ;  it  gives  a  note  very  nearly  simple,  and  so  also 
does  the  flute. 

All  simple  sounds  at  2  exceedingly  sweet,  and  seem  softer 


TIMDRE   OR   QUALITY   OF    SOUND.  185 

than  they  really  are.  Their  timbre  has  something  mournful, 
recalling  the  timbre  of  the  vowel  combination  ou;  this  is 
quite  independent  of  the  material  of  the  sonorous  body. 
We  shall  soon  see  what  is  necessary  to  produce  a  simple 
sound;  it  is  a  ram  avis  of  nature,  seldom  if  ever  met 
with. 

The  sounds  we  find  in  nature  are  complex,  that  is  to 
say,  they  are  composed  of  several  simple  sounds  differing  in 
height.  Each  body  forms  a  little  orchestra  to  itself  when  it 
vibrates  freely.  The  lowest  sound  gives  the  pitch,  the 
others  accompany  it.  This  it  is  that  gives  the  timbre  or 
tone.  A  rich,  full  timbre  is  like  a  nest  of  harmonious 
sounds,  whose  warblings  please  us,  we  know  not  why. 

It  had  long  been  known  that  many  bodies  give  fainter 
sounds  at  the  same  time  with  the  fundamental  one ;  and 
these  were  called  harmonics  ;  but  no  one  understood  the 
part  they  played,  nor  was  it  suspected  that  they  are  the 
principal,  if  not  the  only,  cause  of  the  tone  distinguishing 
different  instruments,  and  that  the  numberless  vibratory 
curves  are  explained  by  their  intervention. 

Sauveur  gave  the  name  of  harmonics  of  a  fundamental 
sound  to  those  sounds  which  make  2,  3,  4,  5  vibrations, 
whilst  the  other  makes  only  one  ;  together  they  form  the 
natural  series  of  i,  2,  3,  4,  5.  The  first  harmonic  is  the 
octave  of  the  fundamental  sound,  and  the  second  is  its 
twelfth,  or  the  octave  of  the  fifth  ;  then  follow  the  double 
octave  ;  the  seventeenth,  or  the  double  octave  of  the  third ; 
the  nineteenth,  or  double  octave  of  the  fifth,  &c. 

In  order  to  indicate  the  ratio  of  the  height  of  the  har- 
monics by  their  designations,  the  fundamental  sound  has  been 
included  with  them,  as  the  harmonic  i  ;  the  octave  will  be 
the  harmonic  2 ;  the  twelfth,  the  harmonic  3,  &c.  Taking 


1 86  ACOUSTICS. 

doha  for  the  fundamental   sound,  we  have  the  following 

series : — 


doh,  doh,  so!3  doh.  im\    sol,    latf,    dohs     to.     mi,    faJt. 

8345678          9        10       ii 

Notwithstanding  their  names,  these  notes  do  not  in- 
variably form  harmonious  chords.  The  first  six,  however, 
do  so;  7  and  n,  approximately  represented  by  latt  and 
faj,  do  not  even  belong  to  the  musical  scale ;  they  are  dis- 
cordant notes,  and  so  is  9,  the  re.  When  these  notes  are 
perceived  in  a  compound  sound  they  mar  its  beauty,  giving 
it  somewhat  of  a  harsh  or  jarring  tone. 

In  1700,  Sauveur  thus  notices  the  phenomenon  of  har- 
monics or  "overtones :" — 

"  On  striking  a  harp-string,"  says  he,  "  besides  the  funda- 
mental sound,  a  number  more  may  be  heard  at  the  same 
time  by  a  delicate  and  educated  ear,  sharper  than  that  of  the 
entire  chord,  produced  by  some  portions  of  the  string  which, 
freeing  themselves  in  some  way  from  the  general  vibration, 
take  one  of  their  own.  These  complex  vibrations  may  be 
explained  by  the  example  of  a  slack-rope,  such  as  dancers 
use ;  for  while  the  rope-dancer  gives  the  rope  a  violent 
swing,  he  may  with  his  two  hands  give  two  different  im- 
pulses to  the  two  halves." 

"  Each  half,  each  third,  each  quarter  of  a  string  has  its 
own  special  vibrations,  while  the  general  vibration  of  the 
whole  string  is  going  on.  It  is  the  same  with  a  bell  when  it 
is  very  good  and  tuneful." 

After  enumerating  the  successive  harmonics  which  ac- 


TIMBRE   OR   QUALITY   OF   SOUND.  187 

company  the  fundamental  sound  of  a  string,  he  adds : 
"  It  would  appear,  then,  that  whenever  Nature  makes  for 
herself,  as  we  may  say,  a  musical  system,  she  employs  sounds 
of  this  kind ;  and  yet  they  have  been  hitherto  unknown 
to  the  theory  of  musicians.  When  they  were  heard,  they 
were  treated  as  irregular  and  of  no.  consequence,  the 
musicians  thinking  thereby  to  prevent  a  breach  in  the  im- 
perfect and  limited  system  then  in  vogue." 

Twenty-five  years  later,  Rameau  used  these  ideas  as  the 
base  of  a  new  musical  system. 


Fig.  91.— Fundamental  Sound  and  Octave. 

The  fundamental  sound  and  its  harmonics,  taken  singly, 
are  simple  sounds  with  pendular  vibration.  Their  inter- 
mixture constitutes  a  complex  sound,  whose  vibrations  take 
a  form  more  or  less  complicated.  Each  of  these  compounded 
vibrations  is  composed — ist,  of  one  vibration  of  the  fundamen- 
tal sound ;  2 nelly,  of  two  vibrations  of  the  octave  ;  3rdly,  of 
three  vibrations  of  the  twelfth  ;  4thly,  of  four  vibrations  of  the 
double  octave,  and  so  on.  The  general  form  of  the  curve 
which  represents  this  compound  vibration,  is  determined  by 
the  fundamental  sound  ;  but  the  harmonics  make  its  contour 


1 28  ACOUSTICS. 

shrink  and  swell  by  their  vibrations.  In  Fig.  91,  the  dotted 
line  represents  the  curve  of  the  fundamental  sound,  and  the 
white  line,  the  curve  resulting  from  the  addition  of  the 
octave.  It  is  a  curve  of  this  species  which  characterises  the 
timbre  or  quality  of  a  compound  sound ;  it  changes  form 
according  to  the  relative  intensity  of  the  harmonics  ;  but 
the  number  of  the  great  curves  or  periods  is  always  the 
same,  and  for  this  reason,  the  pitch  of  the  mixed  sound  is 
that  of  the  fundamental  note. 

Inversely,  a  periodical  vibration,  of  whatever  form,  may 
always  be  separated  into  a  series  of  simple  harmonic  vibra- 
tions of  pendular  form.  In  other  words,  all  complex  sound 
of  a  definite  pitch  may  be  resolved  into  an  harmonic  series 
of  simple  sounds,  beginning  with  the  fundamental,  which  has 
the  same  pitch  as  the  complex  sound.  This  is  a  theorem 
of  Fourier's,  and  one  of  the  most  interesting  ever  drawn 
from  analysis ;  but  we  cannot  make  more  than  a  passing 
reference  to  it.  From  it  we  conclude,  that  if  quality  depend 
on  the  form  of  vibrations,  this  form  in  its  turn  depends  upon 
harmonics,  so  that  in  reality  quality  is  given  by  the  super- 
position of  simple  sounds.  This  is  no  mathematical  fiction, 
no  subtle  definition  devoid  of  reality;  experience  confirms 
these  deductions  in  the  most  striking  manner. 

In  order  thoroughly  to  understand  a  compound  move- 
ment, let  us  refer  once  more  to  the  undulations  of  a  liquid 
surface.  Suppose  the  water  be  agitated  by  two  stones,  in  two 
different  places ;  there  are  then  two  centres  of  commotion, 
whence  two  systems  of  circular  and  concentric  rings  spread 
out,  till  they  meet  and  interpenetrate  ;  but  the  eye  can  still 
follow  their  separate  circles.  It  is  beautiful  to  watch  this 
kind  of  motion  at  the  sea-side.  The  waves  as  they  come 
in,  easily  distinguished  by  their  foaming  crests,  break  in  a 


TIMBRE   OR   QUALITY  OF   SOUND.  189 

regular  succession,  and  thrown  back  in  different  ways,  ac- 
cording to  the  form  of  the  coast -line,  they  intermingle,  cross- 
ing obliquely  in  all  directions.  A  steam-boat  leaves  behind 
her  in  the  water  two  divergent  breaks  of  dancing  waves  ;  a 
bird  plunging  after  a  fish  will  make  a  succession  of  tiny 
circular  waves,  which  work  their  way  across  the  general 
commotion.  It  is  rarely  that  an  attentive  observer  fails  to 
follow  the  differ jnt  partial  movements  which  give  a  special 
form  and  direction  to  each. 

In  the  same  way  the  ear  can  perfectly  distinguish  the 
different  sonorous  movements  transmitted  to  it  simultane- 
ously by  the  air.  Let  us  transport  ourselves  in  thought  to 
the  midst  of  a  ball  room,  at  the  moment  when  the  orchestra 
bursts  forth  with  a  merry  dance.  What  a  mixture  of  sounds, 
which  can  nevertheless  be  disentangled  more  or  less !  The 
strings  of  the  bass  violin  and  the  mouths  of  men  give  out 
sonorous  waves  twelve  or  fourteen  feet  long ;  the  rosy  lips 
of  women  give  shorter  and  more  rapid  undulations ;  the 
silken  rustle  of  dresses,  and  the  noise  of  footsteps,  produce 
small  tempests  of  tiny  crowded  waves;  and  all  these  mingle 
without  losing  their  identity,  for  the  ear  can  still  distinguish 
their  different  origin.  The  auditory  canal,  however,  which 
receives  all  these  impressions  at  once,  is  but  a  speck  in  com- 
parison with  the  mass  of  air  in  the  room  where  all  these 
vibratory  motions  are  going  on  The  ear  cannot  follow  the 
sonorous  waves  throughout  their  course,  as  the  eye  observes 
the  motions  in  a  sheet  of  water. 

If  a  stone  be  thrown  into  water  already  agitated  by 
undulations  of  a  certain  extent,  little  concentric  circles  will 
be  seen  spreading  over  the  undulated  surface,  just  the  same 
as  in  quiet  waters.  At  the  moment  when  the  little  circular 
ring  coincides  with  the  crest  of  one  of  the  great  waves,  the 


I QO  ACOUSTICS. 

height  of  this  wave  is  suddenly  augmented  by  the  height  of  the 
little  one;  so  too  its  tiny  depression,  added  for  a  moment  to 
the  depression  already  existing  between  the  large  waves,  will 
hollow  it  yet  a  little  more.  On  the  contrary,  when  a  de- 
pression meets  with  an  elevation,  the  principal  effect  will 
be  weakened.  Thus  the  addition  of  smaller  waves  to 
greater  simply  increases  the  height  of  the  hollow ;  and  if 
we  can  imagine  the  little  wavelets  raised  out  of  our  vision 
for  a  moment,  we  shall  see  nothing  but  the  large  waves, 
slightly  modified. in  their  outline. 

The  separation  of  elementary  notes,  found  associated 
in  any  noise  whatever,  may  nevertheless  be  effected  by  the 
ear  with  the  aid  of  the  resonant  globes  already  described. 
We  have  seen  that  these  globes  each  reinforce  a  particular 
note  of  which  they  are  constituted  guardians ;  they  respond 
to,  echo,  and  draw  it,  so  to  say,  out  of  the  general  tumult. 
With  a  set  of  these  globes,  each  made  for  a  special  note, 
it  will  be  easy  to  single  out  the  notes  from  any  medley, 
however  slight  their  existing  force.  Thus  also  it  is  proved 
that  the  harmonics  of  musical  sounds,  far  from  being  a 
fanciful  illusion,  a  merely  subjective  phenomenon,  have  a 
true  existence.  With  a  little  practice,  they  may  be  caught 
by  the  ear  alone. 

Once  accustomed  to  listen,  the  ear  listens  almost  uncon- 
sciously. Thus  when  a  drum  is  heard  at  some  little  dis- 
tance, a  low  dull  sound  is  first  noticed,  which  is  caused 
by  the  air  imprisoned  in  the  hollow ;  then  a  succession  of 
sharp  notes,  clearer  and  more  defined,  produced  by  the 
stretched  parchment  or  head ;  other  harsh  sounds  are  due 
to.  the 'jarring  of  the  strings  on  the  lower  parchment ;  and 
finally  there  is  a  metallic  ring,  coming  from  the  sides  of  the 
cylinder. 


TIMBRE   OR   QUALITY  OF   SOUND.  IQI 

The  Human  voice  is  very  rich  in  harmonics,  taking  very 
complex  timbres.  With  the  sympathetic  resonant  balls, 
sixteen  harmonics  or  overtones  can  be  reckoned  in  a  bass 
voice  singing  a  or  e,  on  a  very  low  note.  Rameau  was 
not  unaware  of  this  phenomenon,  and  many  musicians  have 
noticed  it  since.  Seiler  tells  us  how,  in  listening  during 
sleepless  nights  to  the  voice  of  the  watchmen  telling  the 
hours  in  Leipsig,  he  often  seemed  to  hear  first  the  twelfth, 
and  then  the  note  itself.  M.  Garcia  says  that,  listening  to 
his  own  voice  in  the  silence  of  night  upon  a  bridge,  he  has 
been  able  to  distinguish  the  octave  and  the  twelfth  of  the 
note  he  gave.  We  seldom  notice  the  existence  of  these 
parasite  notes  in  the  sound  of  the  voice,  because  we  do  not 
look  for  them  ;  but  we  may  easily  convince  ourselves  of  the 
fact  in  this  way.  Ask  a  singer  to  sing  the  vowel  o  on  the  mil? 
in  the  bass,  then  gently  strike  the  si*  of  the  middle  octave 
on  the  piano,  so  as  to  fix  attention  on  this  note.  You  will 
continue  to  hear  the  sit?  after  the  finger  has  left  the  piano 
and  the  string  has  ceased  to  vibrate.  This  is  because  the 
si?,  resounding  in  the  mil?  of  the  voice,  will  replace  the 
sound  of  the  string.  If  you  wish  to  tiy  the  sol  of  the 
following  octave,  or  the  seventeenth  of  mitr,  in  this  way,  it 
will  be  better  to  take  the  vowel  a. 

Let  us  mention  here  that  the  notes  from  mi6  to 
so!6,  belonging  to  the  last  octave  of  the  piano,  are  always 
heightened  in  tone  by  a  peculiar  resonance  they  excite  in 
the  auditory  canal:  thus  acquiring  a  fictitious  intensity, 
which  gives  a  piercing  character  to  the  sounds  they  ac- 
company as  overtones.  To  a  sensitive  ear  it  is  actually 
painful.  We  know  that  even  dogs  are  very  sensitive  to  this 
kind  of  impression  ;  a  high  mi  on  the  violin  will  make 
them  howl.  This  irritability  of  the  ear  in  regard  to  very 


1Q2  ACOUSTICS. 

high  notes,  renders  it  particularly  sensitive  to  those  disagree- 
able dissonances  that  always  strike  us  in  choirs,  especially 
when  the  voices  are  at  all  forced.  Above  the  lower  notes  we 
really  hear  a  crowd  of  little  screaming  notes,  accompanying 
the  harmony  like  an  orchestra  of  castanets  and  cymbals. 

Fine  strings  also  abound  in  overtones.  Helmholtz  has 
counted  as  many  as  eighteen.  The  harmonics  7,  9,  n,  13, 
14,  17,  1 8,  are  more  or  less  discordant;  if  they  had  more 
intensity  they  would  produce  a  most  unpleasant  effect. 
Happily  the  ear  only  catches  the  first  upper  notes,  which 
agree  with  the  fundamental  note,  and  even  these  can  only 
be  seized  by  close  attention. 

These  facts  seem  to  show  that  all  sonorous  vibration, 
having  a  peculiar  timbre,  is  reduced  by  the  ear  to  simple 
sounds  which  form  an  harmonious  series.  This  conclusion 
may  seem  at  first  sight  too  absolute,  and  contrary  to  our 
senses,  since  we  are  not  accustomed  to  take  note  of  the 
existence  of  several  notes  in  a  musical  sound.  At  most, 
musicians  only  distinguish  in  a  chord  the  notes  that  form  it, 
but  that  are  produced  separately.  The  difficulty  seems  to 
augment  when  the  chord  is  formed  with  compound  intervals, 
such  as  the  twelfth,  repeat  of  the  fifth,  and  the  seventeenth, 
triplique  of  the  third  (as  Sauveur  calls  it).  Kcenig  made 
a  pretty  experiment  in  this  way.  On  the  sounding-board  of 
an  enormous  tuning-fork  he  arranged  a  whole  orchestra  of 
small  ones,  which  gave  amongst  them  the  first  four  or  five 
harmonics  of  their  leader.  Then  with  a  vigorous  stroke  he 
set  the  great  patriarch  in  vibration,  and  afterwards  all  his 
attendants  :  the  air  was  filled  with  a  deep  harmonious  sound, 
very  full,  but  seeming  to  the  unpractised  ear  a  single  note, 
the  voices  of  the  sharper  forks  not  being  heard.  He  then 
suddenly  stifled  the  deepest  by  placing  his  hand  upon  it, 


TIMBRE   OR  QUALITY  OF   SOUND.  193 

and  the  others  were  heard  immediately — clearly  separating 
themselves,  as  soon  as  the  deep  tone  which  had  sustained 
and  bound  them  together  was  subdued. 

Thus,  in  ordinary  circumstances,  the  ear  seems  unable  to 
accomplish  the  dissection  necessary  for  reducing  the  timbre 
to  its  constituent  parts.  But  this  is  a  mistake.  It  is  only 
necessary  to  understand  the  words  we  use.  Indeed,  we 
must  here  distinguish  between  perception  or  sensation,  which 
is  complex,  and  the  impression  received  by  the  mind,  which 
is  simple.  The  ear  really  perceives  several  notes  when  fa  is 
given  by  the  violin,  but  the  whole  of  these  notes  only  recall 
to  our  mind  a  fa  having  a  peculiar  timbre ;  we  have  no 
particular  reason  for  analysing  our  impression  further.  The 
hearing  apparatus  dissects  the  complex  sounds  that  strike  it, 
but  the  separate  elements  are  reunited  in  the  nervous  im- 
pression made  on  the  mind.  Physiology  gives  us  many 
instances  of  similar  illusions.  Thus  we  take  for  simple 
colours,  tin's  which  the  prism  divides  into  numberless  tints. 
The  theory  of  binocular  vision  shows  how  during  our  whole 
lives  we  see  all  objects  double,  and  nevertheless  it  needs  a 
strong  effort  of  attention  to  be  convinced  of  it.  Few  people 
know  that  in  the  retina  there  is  a  little  blind  spot,  the  punc- 
tum  ctcctim,  and  that  consequently  in  one  direction  we 
cannot  see  at  all.  This  blank  is  so  large  that  there  would 
be  room  in  it  for  seven  lunar  images  in  a  row,  and  at  a 
distance  of  a  few  feet  a  human  face  would  be  lost  in  it , 
yet  it  is  not  inconvenient.  When  Mariotte  illustrated  the 
fact  by  experiments  in  the  court  of  Charles  II.,  he  was 
greatly  amused  at  the  astonishment  occasioned  among  his 
illustrious  audience.  There  are  some  well-authenticated 
instances  of  people  who  have  only  discovered  by  chance 
that  they  had  lost  the  sight  of  one  eye  years  ago.  Such  is 

N 


194  ACOUSTICS. 

our  indifference  to  a  phenomenon  always  present  with  us. 
We  do  not  notice  the  complexity  of  a  sound  any  more  than 
the  double  image  of  an  object  that  we  look  at  with  both 
eyes ;  yet  it  is  this  very  duplicity  that  gives  the  effect  of 
relief,  as  shown  by  the  stereoscope.  Timbre  is  the  relief  of 
sounds. 

We  manage  to  distinguish  the  sounds  of  different  instru- 
ments, or  the  voices  of  different  people ;  and  in  these  cases 
there  are  many  things  to  help  us  besides  the  timbre — those 
little  noises  which  precede  and  follow  the  emission  of  the 
sound,  its  duration  and  power,  its  intermissions  and  varia- 
tions. But  the  ear  must  be  educated  to  the  task  of  dissecting 
the  timbre,  in  order  to  be  conscious  of  its  complexity. 

Helmholtz  has  corroborated  these  deductions  by  com- 
posing different  artificial  timbres  with  the  notes  they  were 
supposed  to  contain.  Here  is  an  experiment  that  any  one 
can  easily  try  :  Raise  the  hammers  of  a  piano  so  as  to  have 
all  the  wires  at  liberty,  then  sing  loudly  the  vowel  a  upon 
any  note  you  choose,  standing  near  the  instrument.  The 
resounding  of  the  strings  exactly  reproduces  the  a.  The 
resemblance  is  much  less  complete  when  the  hammers  are 
not  all  lifted  from  the  strings  ;  because  the  vowel  a  is 
characterised  by  a  peculiar  timbre,  depending  on  certain 
sharp  notes ;  the  strings  corresponding  to  these  notes 
vibrate  through  sympathy,  and  their  intervention  gives  to 
the  echo  of  the  voice  the  timbre  it  had  in  singing  the  a. 
In  the  same  way  the  timbre  of  the  clarionet,  the  cornet,  and 
so  on,  may  be  imitated. 

The  height  of  a  musical  sound,  then,  is  always  that  of 
the  dominant  note  in  this  harmonic  medley,  and  this  is 
generally  the  lowest  of  all.  But  the  presence  of  the  upper 
notes  is  not  without  its  influence  on  our  judgment  of  a 


TIMBRE   OR   QUALITY  OF   SOUND.  1 95 

complex  sound — it  sharpens  it,  slightly  raising  the  musical 
scale.  For  this  reason  even  practised  musicians  sometimes 
mistake  an  octave  in  comparing  notes  of  different  timbre. 

We  have  already  said  that  the  ear  does  not  depend 
solely  upon  timbre  in  discerning  the  origin  of  sounds,  but 
is  guided  by  certain  accessory  noises.  In  many  cases  these 
characteristic  noises  are  only  heard  at  the  first  moment,  or 
as  the  sound  dies  away. 

The  preparation  for  the  emission  of  a  sound  is  almost  as 
important  as  its  timbre.  With  the  human  voice  the  noises 
preceding  the  emission  of  the  vowels  are  so  very  distinct, 
that  they  are  called  after  the  explosive  consonants,  ^,  /,  d, 
t,  £,  k.  They  give  to  the  vowel  following  a  peculiar 
character  quite  apart  from  its  timbre. 

In  any  loud  note  given  by  a  brass  instrument,  we  can 
distinguish  between  the  hautbois,  clarionet,  &c.,  without 
regard  to  the  timbre.  Then,  too,  the  greater  or  lesser 
rapidity  with  which  the  fundamental  sound  and  its  har- 
monics die  away,  constitutes  a  sensible  difference  between 
catgut  strings  and  wires,  even  when  they  are  equally  struck. 
The  vibrations  of  the  first  being  unsustained,  their  sound 
is  somewhat  poor  and  dry ;  while,  the  vibrations  of  the  metal 
wires  enduring  much  longer,  their  sound  is  fuller,  though 
less  penetrating. 

In  other  cases  the  sound  is  accompanied  by  noises 
throughout.  Thus,  in  wind  instruments  there  is  a  sort 
of  whistling,  caused  by  the  action  of  the  air  on  the  edge 
of  the  opening.  The  scraping  of  the  bow  is  always  heard 
more  or  less  with  the  violin.  Noises  of  this  kind  are  ex- 
pressed by  the  letters/,  v,  s,  j,  z,  /,  r. 

The  vowels,  too,  are  constantly  accompanied  by  little 
noises,  that  help  us  to  guess  them  even  when  they  are 

N    2 


i96 


ACOUSTICS. 


whispered.  These  sounds  are  heard  more  in  speaking  than 
in  singing,  for  in  singing  the  timbre  or  the  musical  part  of 
the  vowel  is  most  dwelt  upon,  and  this  is  heard  to  a  much 
greater  distance.  This  is  why  consonants  are  not  heard 
so  far  away  as  vowels,  and  why  a  distant  voice  may  be  mis- 
taken for  a  cornet.  The  consonants  n  and  m,  however,  by 
their  mode  of  formation,  have  somewhat  of  the  nature  of 
vowels,  and  the  accessory  noises  play  a  very  subordinate 

part.  If  you  stand  at  the 
foot  of  a  hill  and  listen  to 
voices  speaking  some  way 
up,  you  will  scarcely  catch 
any  words  except  those 
formed  with  ;;/  or  n. 

A  few  further  remarks 
may  be  made  about  diffe- 
rent timbres.  In  the  first 
place,  we  can  obtain  simple 
sounds  by  strengthening 
the  fundamental  sound  of 

a  tuning-fork  by  a  resounding  box  (A,  Fig.  92),  whose  upper 
notes  do  not  harmonise  with  those  of  the  fork.  The  timbre 
of  simple  sounds  is  sweet  and  subdued,  not  brilliant  enough 
for  music. 

Sounds  accompanied  by  upper  notes  that  are  not  harmo- 
nious, are  not  included  in  our  definition  of  musical  sound  : 
we  can  only  use  them  in  music  when  the  upper  notes  die 
away  so  quickly  that  we  may  forget  them,  and  notice  only 
the  principal  note.  In  this  category  we  place  rods,  discs, 
tuning-forks,  bells,  parchment  skins,  &c.  Tuning-forks 
have  very  high  upper  notes,  heard  at  the  moment  of  striking 
the  metal.  The  first  is  at  an  interval  of  a  twelfth  from  the 


Fig.  92. — Mounted  Tuning-fork. 


TIMBRE   OR   QUALITY  OF   SOUND.  197 

fundamental  sound.  The  ear  always  separates  these  sharp 
quickly  passing  notes  from  the  principal  notes,  and  has  no 
tendency  to  blend  them  with  it,  as  it  does  the  harmonious 
elements  of  a  musical  sound. 

The  sound  of  common  bells  can  hardly  be  ranked  as  a 
musical  sound :  but  it  appears  that  a  skilful  founder  is 
able  to  make  the  first  upper  notes  of  a  bell  harmonious, 
and  then  the  timbre  is  tolerably  good.  This  explains  the 
pleasant  effect  of  chimes.  There  are  eight  at  Amsterdam, 
one  of  which  numbers  forty-two  bells,  and  has  a  compass 
of  three  octaves  and  a  half  (between  doh2  and  fa.).  The 
most  celebrated  is  that  of  Ghent  Paris  is  going  to  have 
one  at  Saint  Germain  1'Auxerrois. 

The  fundamental  sound  of  bells  is  lowered  by  an 
increase  of  weight  or  diameter.  The  largest  bell  in  the 
world  is  that  cast  at  Moscow,  in  1736.  Its  weight  is  about 
193  tons.  Unfortunately  it  was  cracked  before  ever  it  was 
rung.  Still,  there  is  one  at  Moscow,  weighing  63  tons, 
that  dates  from  1307.  The  great  bells  of  our  cathedrals 
seldom  weigh  more  than  10  tons.  That  of  Notre  Dame  de 
Paris,  founded  in  1680,  weighs  nearly  13  tons. 

Franklin's  harmonica  is  composed  of  a  number  of  glass 
bells,  which  are  sounded  by  rubbing  round  the  edges  with 
damp  fingers.  The  effect  is  rather  irritating  to  the  nerves, 
the  sound  being  too  penetrating,  because  of  the  prevalence 
of  harmonic  overtones. 

Instruments  that  are  played  upon  by  striking,  such  as 
timbrels,  tambourines,  castanets,  triangles,  and  cymbals,  are 
classed  together  with  bells  and  tuning-forks.  They  have 
discordant  upper  notes.  The  tam-tam  or  gong  of  the 
Chinese  is  a  circular  disc  with  a  raised  edge,  made  of  well- 
tempered  and  hammered  bronze.  It  is  struck  with  quick 


198  ACOUSTICS. 

light  taps  from  the  rim  to  the  centre,  and  wonderful  effects 
are  got  from  the  multiplied  sounds,  which  gather  and  seem 
to  burst  out  with  great  violence.  It  is  as  if  a  struggle  were 
going  on  in  the  metal  of  sounds  which  make  frantic  efforts 
to  escape  from  their  prison.  The  sheet  iron  with  which 
the  sound  of  thunder  is  imitated  in  theatres,  produces  effects 
somewhat  similar. 

The  skins  of  the  drum  and  tambourine  do  not  give 
true  musical  sounds,  but  the  resistance  of  the  frame  or 
body  stifles  the  higher  notes  considerably.  All  these  noisy 
instruments  are  employed  chiefly  to  mark  the  time,  and 
they  are  in  high  favour  among  savages.  There  is  not  a 

nation  on  the  earth  that 
has  not  invented  a  drum 
of  some  kind  to  beat  a 
measure,  and  animate  the 
dancers.  Amongst  the  Es- 
quimaux, the  Patagonians 
and  Hottentots,  and  the 
New  Zealanders,  they  are 
to  be  found.  An  earthen 

Fig.  93.— Sistra  of  the  Ancients.  ,.       r.      „  ,  , 

pot  or  bit  of  hollowed  wood, 

or  a  calabash,  with  an  ass's  or  crocodile's  skin,  form  the 
materials  of  these  rough  resounding  boxes.  The  tambourine 
and  the  castanets,  which  Southern  nations  use  so  gracefully, 
are  of  very  ancient  origin.  The  crotalon  of  the  priestesses 
of  Bacchus  (Fig.  94)  was  nothing  more. 

Strings  and  pipes  are  pre-eminent  as  the  true  source  of 
musical  instruments.  Their  timbre  is  harmonious.  A 
homogeneous  string  vibrating  completely  gives,  besides  its 
fundamental  sound,  the  series  2,  3,  4,  as  harmonics  ;  but 
it  may  be  made  to  vibrate  in  such  a  way  as  only  to  give  one 


FIG.  94.— PRIESTESS  Of  BACCHUS  (from  a  Bas-relief). 


TIMBRE   OR   QUALITY   OF   SOUND.  2OI 

of  its  harmonics,  dividing  itself  into  different  segments, 
separated  by  nodes. 

The  quality  or  timbre  varies,  according  as  they  are 
played  upon  by  pulling,  as  in  the  harp ;  by  striking  with  a 
hammer,  as  in  the  piano ;  by  drawing  a  bow  across,  as  in 
the  violin  ;  or  by  the  wind  blowing  over  them,  as  in  the 
./Eolian  harp. 

In  the  construction  of  pianos,  the  experience  of  two 
centuries  led  to  the  foundation  of  a  number  of  rules,  which 
are  now  justified  by  theory.  Thus  the  hammers  of  the 
middle  strings  have  been  made  to  strike  them  at  the 
seventh  or  the  ninth  of  their  length,  because  the  best  quality 
or  timbre  was  thus  obtained.  Theory  shows  that  by  this 
arrangement  the  harmonics  7  and  9,  the  first  which  will  not 
harmonise  with  the  fundamental  sound,  are  suppressed.  The 
time  during  which  the  hammer  remains  in  contact  with  the 
string  also  influences  the  timbre. 

Strings  of  cat-gut  have  very  little  persistency  of  sound, 
though  their  harmonics  are  very  high ;  so  the  disagreeable 
effect  of  these  is  neutralised.  In  the  violin  their  timbre  is 
slightly  modified  by  the  resonance  of  the  instrument,  whose 
own  proper  sound  is  generally  doh3.  The  first  harmonics 
are  less  distinct  in  the  violin  than  in  the  piano,  but  the 
sharp  harmonics  are  more  strongly  marked. 

Open  pipes  are  much  like  strings,  having  a  fundamental 
sound,  with  a  timbre  comprising  the  natural  series  of  notes, 
i>  2,  3,  4>  5  ;  and  the  fundamental  sound  can  be  got  rid  of, 
and  nothing  left  but  a  harmonic,  by  forcing  the  wind.  In 
the  closed  pipes  some  of  the  harmonics  are  wanting :  they 
give  only  the  notes  I,  3,  5,  7. 

A  closed  pipe  has  always  the  same  fundamental  sound 
as  an  open  one  of  double  the  length ;  this  may  be  seen  by 


2C2 


ACOUSTICS. 


closing  an  open  pipe  midway  with  a  slide  (/,  Fig.  95),  so 
reducing  it  to  a  closed  pipe  of  half  its  former  length,  when 
the  sound  will  remain  the  same.  In  short,  the  law  that  ex- 
plains the  names  of  the  register  (or  draw-stop)  of  an  organ  is 
this  :  The  height  of  the  fundamental  sound  is  in  inverse  ratio 
to  the  length  of  the  pipes.  An  open  pipe  of  1 6  feet  gives 
the  lower  octave  of  the  open  pipe  of  8  feet,  but 
is  in  unison  with  the  closed  pipe  of  8  feet ;  the 
open  pipe  of  8  feet  is  the  lower  octave  of  the 
open  pipe  of  4  feet,  and  in  unison  with  the 
closed  pipe  of  4  feet,  &c. 

In  the  organ  there  is  a  pipe  for  every  note, 
each  one  giving  only  its  fundamental ;  but  in 
other  wind  instruments  there  are  many  plans 
for  getting  all  the  notes  of  the  scale  out  of  the 
same  pipe.  Thus  the  horn  is  made  of  a  very 
long  brass  pipe,  curled  round :  its  only  harmonics 
are  8,  9,  10  ;  but  these  will  give  the  actual  scale 
by  a  little  modification,  which  is  done  by  intro- 
ducing the  hand  into  the  end.  In  the  trombone 
the  length  of  the  pipe  is  varied  by  a  slide ;  in 
the  cornet-a-piston,  by  supplementary  pipes.  In 
Fig.  95.  other  instruments,  like  the  flute  and  clarionet, 
the  pipe  is  pierced  with  holes,  that  are  opened 
and  closed  by  keys.  The  column  of  air  in  the  pipe  is  made 
to  vibrate  in  such  a  way  as  to  form  centres,  in  relation  to 
the  open  holes,  wherefore  these  openings  produce  the  same 
effect  as  if  the  pipe  were  cut  at  the  places  where  they  are 
situated.  Owing  to  this  mechanism,  the  musician  has  in 
his  hands  a  whole  set  of  pipes  of  different  lengths,  from 
which  he  can  draw  the  most  varied  sounds. 

In  all  wind  instruments  one  of  the  most  important  parts 


TIMBRE   OR    QUALITY   OF   SOUND.  203 

is  the  mouth  or  opening.  The  most  simple  is  such  as  we 
find  in  flutes  and  the  generality  of  organ-pipes  ;  it  is  repre- 
sented by  the  whistle  (Fig.  96),  which  is  a  simple  mouth- 
piece without  a  pipe.  The  wind  strikes  upon  the  lip  of  the 
mouth  with  a  rustling  that  may  be  considered  as  a  medley 
of  feeble  sounds.  The  column  of  air  in  the  pipe  strengthens 
some  of  these  by  a  sympathetic  resonance,  and  these  are 
the  harmonics  the  pipe  will  utter.  In  the  reed 
mouth-pieces  the  stream  of  air  first  sets  in  vibra- 
tion a  metal  key,  which  interrupts  it  periodically 
This  trembling  of  the  key  gives  birth  to  a  num- 
ber of  notes,  among  which  the  column  of  air 
makes  its  choice ;  but  the  sound  is  not  the  same 
as  when  the  pipe  is  played  with  an  ordinary 
mouth-piece.  To  this  list  belong  the  reed-stop 
pipes  of  organs,  and  the  notes  of  the  harmonium, 
clarionet,  hatitbois,  bassoon,  cornet,  and  cor 
anglais.  Our  lips  act  as  reed  mouth-pieces  when  playing 
upon  such  instruments  as  the  horn,  trumpet,  or  trombone, 
their  position  and  their  tension  influencing  one  or  other 
of  the  harmonics  of  the  tube  of  the  instrument. 

In  the  production  of  the  voice  there  are  vocal  chords 
which  play  the  same  part,  but  their  mode  of  action  is  quite 
different  from  that  of  the  lips.  They  determine  the  height  of 
the  note  for  singing  or  speaking.  In  the  clarionet  and 
horn  the  note  depends  on  the  volume  of  air  in  the  pipe ; 
but  here,  on  the  contrary,  it  only  depends  on  the  tension  of 
the  vocal  chords,  and  not  at  all  on  the  volume  of  air 
which  is  made  to  resound  by  their  action.  But  this  reso- 
nance becomes  very  important  from  another  point  of  view. 
It  modifies  the  timbre  by  favouring  certain  sounds.  This 
is  the  origin  of  vowels. 


204  ACOUSTICS. 

A  vowel  is  nothing  more  than  the  particular  timbre 
taken  by  any  note,  if  the  resonance  of  the  mouth  streng- 
thens, amongst  the  harmonics  of  this  note,  that  which  ap- 
proaches nearest  to  a  certain  fixed  note.  Thus,  for  example, 
the  vowel  a  is  produced  by  the  resonance  of  sit?4.  To 
articulate  a,  the  mouth  is  placed  in  such  a  position  as  to 
sound  si&4 ;  and  whatever  be  the  fundamental  of  the  sound 
we  emit,  it  is  always  the  harmonic  nearest  to  sil?.,  which  will 
be  made  prominent. 

If  when  the  mouth  be  opened  to  articulate  some  such 
vowel  a  number  of  tuning-forks  of  various  pitch  be  passed 
before  it,  one  will  always  be  found  to  answer  to  it  by  increase 
of  sound  :  its  note  is  the  one  that  answers  to  the  proper 
volume  of  air  contained  in  the  mouth.  In  this  way  Helm- 
holtz  found  that  each  vowel  is  characterised  by  one  or  two 
notes,  usually  the  same,  but  sometimes  modified,  according 
to  the  accent  in  which  the  vowel  is  spoken. 

It  is  easy  to  understand  how  this  occurs.  The  defini- 
tion of  the  vowels  as  five  letters  of  the  alphabet  is  alto- 
gether insufficient,  as  they  are  indeed  numberless,  if  we  take 
heed  of  all  shades  of  pronunciation.  We  must  at  least  dis- 
tinguish seven  principal  vowel  sounds  which  group  them- 
selves in  this  way  : — 

>    e i 


Therefore  if  a  vowel  be  defined  by  its  specific  note,  the  note 
varies  with  the  language  in  which  the  vowel  is  spoken.  The 
notes  decided  on  by  Helmholtz  for  the  German  vowels,  differ 


TIMBRE   OR   QUALITY   OF  SOUND. 


205 


from  those  that  M.  Bonders  attributes  to  the  same  vowels 
pronounced  in  Dutch. 

The  vowels  a,  o,  and  ou  have  always  only  one  single 
specific  note,  but  for  the  others  two  are  found ;  and  this  two- 
fold expression  is  explained  if  we  remember  that  the  mouth 
in  their  case  takes  the  form  of  a  bottle,  the  wide  part  being 
represented  by  the  mouth,  and  the  narrow  neck  by  the 
tongue  and  the  lips.  These  two  cavities  vibrate  separately. 
Here  are  the  notes  which,  according  to  Helmholtz,  answer 
to  the  vowels  spoken  in  the  accent  of  North  Germany : — 


f 

P     "- 

s-f- 

H-                    P- 

k 

M 

PI 

—  U 

—  f  — 

1          . 

? 

e 

—  j_  — 

-   1 

—  r 

|h 

T 

r 

OU         O          A         AI  B  I  EU         U 


The  intensity  of  the  partial  sounds  of  a  vowel  does  not, 
then,  depend  on  the  place  they  occupy  in  the  harmonic 
scale,  but  only  on  their  absolute  pitch ;  and  it  is  this  which 
distinguishes  the  timbre  of  vowels  from  that  of  musical 
instruments.  Take,  for  example,  a  flute :  whatever  note  it 
gives,  it  is  always  the  octave  which  resounds  simultaneously. 
But  if  a  be  sung  upon  any  note  whatever,  one  cannot  foresee 
what  harmonic  will  be  strengthened  :  sometimes  it  will  be 
the  octave,  sometimes  the  twelfth  or  the  seventeenth,  or 
some  other  note  of  the  harmonic  series.  Thus  if  a  be  sung 
upon  the  note  sit>3,  the  octave  will  be  given,  for  the  specific 
note,  of  the  vowel  a  is  the  octave  of  sit>3 ;  but  if  the  fun- 


200 


ACOUSTICS. 


damental  note  be  fa%,  the  ninth  harmonic  la&4,  which  is 
the  nearest  to  sit>4,  will  be  heard  above  all.  There  is  ^a 
slight  analogy  here  with  the  violin,  which  always  strengthens 
the  neighbouring  notes  of  doh3,  the  sound  belonging  to  the 
volume  of  air  imprisoned  within  it. 


Fig.  07.— Vowels  observed  by  the  aid  of  Koenig's  Flames. 


Kcenig  obtained  a  visible  image  of  the  timbre  of  vowels 
by  means  of  his  flames,  upon  which  the  voice  was  made  to 
act  by  a  gutta-percha  tube  furnished  with  a  funnel  (Fig.  97). 
They  are  fed  by  a  jet  of  gas,  which  crosses  a  hollow  capsule 
closed  on  one  side  with  a  membrane,  which  is  made  to 
vibrate  by  the  voice.  This  membrane  acts  upon  the  flame 


TIMBRE   OR   QUALITY   OF   SOUND. 


207 


as  a  bellows,  which  makes  it  by  turns  flare  up  and  grow 
dim ;  if  the  shocks  be  too  violent,  and  the  flame  small,  it  is 
extinguished  altogether;  even  if  it  be  able  to  resist,  it  becomes 


jfejyj 

>  A  .  .    J  , 


w^,  m  --'•  -f^-s  •••-"-  y  --^^  i  -;',^^/'-^^—  x^--?^ 

^^"^^^5a^^B^^^^^^^^»^^^BM^':'  -^3i: — '.  -  /£^gssi^g 


Fig.  98.— The  Timbre  of  Vowels. 

bluish.  A  flame  palpitating  thus  would  appear  in  the  re- 
volving mirror  under  the  form  of  a  serrated  ribbon,  whose 
changing  appearance  reveals  the  number  and  relative 
strength  of  its  harmonics,  as  shown  in  Fig.  98. 

After   having    accomplished    the   analysis   of   timbres, 


208  ACOUSTICS. 

Helmholtz  tried  to  reproduce  them  by  means  of  synthesis, 
reuniting  the  notes  that  had  been  separated  by  analysis. 
He  constructed  an  harmonic  series  of  eight  tuning-forks, 
which  were  mounted  between  the  branches  of  a  set  of 
electro -magnets,  so  as  to  be  able  to  maintain  them  in 
vibration  by  the  action  of  a  periodical  current  of  electricity. 
In  front  of  each  tuning-fork  was  placed  a  sounding-box, 
which  could  be  shut  more  or  less  completely  by  pressing 
upon  the  key-board.  When  the  box  was  closed  the  tuning- 
fork  gave  hardly  any  perceptible  sound,  but  it  grew  stronger 
as  the  box  was  opened  wider.  With  this  apparatus,  an  o 
was  distinctly  produced  by  strongly  sounding  the  sit?3,  more 
feebly  sit?2,  and  fa4;  a  was  obtained  by  giving  sit>2,  sii?3,  and 
fa,  moderately,  and  sifr4  and  res  with  full  force.  The  tuning- 
fork  having  siir2  for  its  fundamental  gives,  when  sounding 
alone,  a  very  faint  ou.  Kcenig  made  a  like  apparatus  with 
ten  tuning-forks.  But  we  must  always  remember  that  com- 
pared with  true  vowels  the  resemblance  is  generally  some- 
what doubtful.  Once,  and  only  once,  we  heard  a  perfect  a. 

How  is  it  possible  to  describe  the  marvellous  power 
possessed  by  the  ear  for  separating  such  complex  sounds 
into  simple  vibrations?  We  have  seen  that  the  strings  of 
a  piano  effect  this  dissociation  of  harmonics,  since  they 
answer  to  all  the  notes  which  are  united  together  in  the 
sound  examined.  Imagine  a  series  of  musical  strings  giving 
the  scale  of  all  possible  notes,  and  then  we  shall  have  some- 
thing with  which  to  reproduce  faithfully  all  varieties  of  timbre 
or  composite  sounds. 

Helmholtz  thinks  that  the  ear  possesses  just  such  a 
series.  This  is  the  wonderful  organ  discovered  by  Corti, 
and  called  after  him.  It  is  situated  in  the  labyrinth,  and 
may  be  described  as  the  terminal  fibres  of  the  auditory 


TIMBRE  OR  QUALITY  OF  SOUND.          209 

nerve.  There  are  above  3,000  fibres  spread  over  the  mem- 
brane of  this  labyrinth ;  and,  supposing  that  each  one 
answers  to  a  particular  note,  we  have  an  instrument  of  3,000 
strings — more  than  enough  to  gather  and  reunite  all  the 
sounds  in  creation.  There  must  be  at  least  400  for  each 
octave. 

In  the  same  manner  the  perception  of  colours  may  be 
explained  by  the  existence  of  fibres  of  the  optic  nerve,  each 
appropriated  to  a  simple  colour.  This  hypothesis  was  put 
forward  by  Thomas  Yo:mg.  It  cannot  be  denied  that  by 
this  ingenious  theory  all  the  phenomena  of  our  perception 
of  colour  and  sound  are  explained  in  a  very  natural  way. 
It  is  now  understood  that  the  ear  must  act  as  a  prism,  which 
decomposes  the  timbre  into  its  primary  elements,  although 
the  complex  impression  made  upon  the  brain  is  seldom 
analysed  by  the  mind  accustomed  to  judge  of  its  impressions 
only  as  a  whole. 

The  most  pleasant  and  musical  qualities  of  timbre  are 
the  harmonics  i,  2,  3,  4,  5,  6.  Compared  with  simple  sounds, 
musical  sounds  are  richer,  fuller,  and  more  magnificent — 
more  coloured,  so  to  say ;  they  seem  soft  and  mellow,  too, 
so  long  as  the  sharp  upper  notes  do  not  trouble  the  har- 
mony. In  this  list  we  may  place  the  sounds  of  the  piano 
and  organ,  the  human  voice  and  the  cornet,  unless  they  are 
forced.  The  flute  belongs  rather  to  simple  sounds.  With 
such  sounds  only  very  little  music  can  be  produced :  they 
must  be  sustained  by  others.  An  instrument  composed  of 
tuning-forks  (which  also  give  sounds  almost  simple)  would 
not  be  pleasant  to  listen  to  alone. 

The  large  pipes  of  an  organ  give  very  faint  harmonics 
of  the  fundamental  sound,  and  are  therefore  very  nearly 
simple.  This  is  especially  true  of  the  closed  pipes.  When 


210 


ACOUSTICS. 


a  sound  only  contains  the  odd  notes  of  the  harmonic  series 
(the  fundamental,  the  twelfth,  &c),  as  happens  in  the 
narrow  and  closed  organ-pipes,  the  clarionet,  and  strings 


Fig.  99. — Voices  of  Birds. 

struck  in  the  middle,  the  timbre  becomes  hollow;  when  the 
number  of  higher  sounds  increases,  it  becomes  nasal;  when 
the  fundamental  sound  governs,  it  is  full;  when  this  is  too 
feeble,  it  becomes  //////.  The  sound  of  a  string  is  fuller 
when  struck  with  a  hammer  than  when  pulled  by  the 
fingers. 


TIMBRE    OR   QUALITY   OF   SOUND.  211 

When  the  harmonics  above  6  are  very  distinct,  the 
sound  becomes  harsh  and  piercing,  because  of  the  discords 
caused  by  these  high  notes  ;  but  if  they  are  heard  in  mode- 
ration, they  rather  add  brilliancy  and  colour  to  the  tone  of 
an  instrument. 

This  subtle  and  changeful  element  which  we  have 
spoken  of  under  the  name  of  timbre  plays  an  important  part 
in  the  relations  of  voice  and  feeling.  It  is  the  timbre  which 
renders  a  voice  sympathetic,  persuasive,  and  loving;  or 
sharp,  quarrelsome,  and  disagreeable.  The  timbre  of  a 
bird's  song  serves  instead  of  speech,  expressing  ail  the 
emotions  that  stir  its  little  heart  (Fig.  99). 


CHAPTER  XII. 

INTERFERENCE    OF    SOUND. 

Beats— Resultant  Sounds  — Sonometers  of  Scheibler  and  Koenig — In- 
fluence of  the  Movement  of  the  Source  of  Sound  on  its  Pitch. 

HOWEVER  paradoxical  it  may  appear,  we  shall  see  in  this 
chapter  how  sounds  quarrel,  fight,  and  when  they  are  of 
equal  strength  destroy  one  another,  and  give  place  to  silence. 
The  phenomena  of  resonance  revealed  a  sort  of  sympathetic 
reciprocal  bond  existing  between  sounds.  The  strings  of  a 
violin  hanging  on  a  wall  resound  without  being  touched 
when  another  violin  is  tried  in  the  same  room.  Every 
sonorous  body  harbours  a  family  of  notes,  which  readily 
respond  to  the  call  of  a  friend.  We  are  now  about  to  study 
the  warfare  of  notes,  to  spy  out  their  enmities  and  discords. 
We  shall  see  how  the  whole  crowd  of  harmonics  take  sides 
when  two  declare  war.  Often,  indeed,  we  hear  them  skir- 
mishing when  as  yet  the  two  chiefs  are  quiet. 

Two  notes  are  said  to  "  beat"  when  their  union  gives  rise 
to  periodical  alternations  of  strength  and  weakness.  This 
phenomenon  is  well  known  in  organ-pipes.  When  two 
slightly  discordant  pipes  are  sounded  together  there  is  a 
beating  effect  produced ;  the  sound  alternately  swells  and 
dies  away,  and  when  the  strong  swells  follow  very  quickly 
there  is  quite  a  little  tumult. 

Sauveur  was  also  the  first  to  study  this  curious  pheno- 
menon, and  he  found  that  important  deductions  might  be 
made  from  it  From  his  experiments  he  had  concluded 


INTERFERENCE   OF   SOUND.  213 

that  the  number  of  beats  is  always  equal  to  the  difference  of 
height  of  the  two  notes ;  for  each  double  vibration  that 
the  one  accomplishes  more  than  the  other  there  is  a  beat ; 
therefore  nothing  is  easier  than  to  determine  the  absolute 
height  of  two  notes  by  counting  their  beats.  Suppose,  for 
instance,  that  two  pipes  are  tuned  for  the  notes  doh  and  re  : 
the  interval  being  a  major  tone,  the  first  will  always  make 
eight  vibrations  while  the  other  makes  nine ;  the  difference 
being  one,  there  will  always  be  one  beat  for  eight  vibrations 
of  one  and  nine  of  the  other.  If  we  now  count  four  beats 
a  second,  we  shall  conclude  that  in  the  second  the  first  tube 
has  made  four  times  eight,  or  thirty-two  vibrations,  and  the 
other  four  times  nine,  or  thirty-six ;  and  thus  the  absolute 
pitch  is  at  once  determined.  The  beats  may  be  also  observed 
in  tuning-forks,  or  in  any  other  sonorous  bodies,  if  only 
their  vibrations  be  sufficiently  slow. 

What  is  the  producing  cause  of  this  phenomenon  of 
beats  ?  According  to  Sauveur,  "  the  sound  of  two  pipes 
must  have  more  power  when  their  vibrations,  after  having 
been  separated,  reunite  and  coincide,  and  strike  simul- 
taneously upon  the  ear."  "  It  even  seems,"  he  says,  "  that 
the  common  expression  of  musicians,  that  the  pipes  beat 
when  their  sound  is  thus  redoubled,  originates  in  this  idea." 

The  explanation  of  beats  rests  upon  the  phenomena  of 
interference.  Two  vibrations  are  said  to  interfere  when 
they  urge  the  air-particles  in  opposite  directions.  This  is  a 
case  of  "union  is  strength  ;"  for  when  two  vibratory  motions, 
acting  on  a  point,  coincide,  they  assist  and  strengthen 
each  other;  when  they  are  in  opposition  they  Aveaken,  and 
even  annul  the  sound  of  both.  In  the  same  way  it  has 
been  demonstrated  that  light  added  to  light  will  produce 
darkness. 


214  ACOUSTICS. 

We  have  already  seen  the  composition  of  vibratory 
motions,  and  how  they  may  be  examined  by  means  of  curves. 
Let  us  imagine  two  identical  vibrations  starting  from  the 
same  point  at  the  same  time :  they  pass  on  uniformly,  and 
acting  together  assist  one  another,  and  augment  the  motion 
of  the  particles,  the  result  being  a  vibration  in  the  same  time, 


Fig.  too. — Coincidence.  Fig.  101.— Opposition. 

but  much  more  energetic  (Fig.  100).  If  the  two  vibrations 
be  so  disposed  that  one  generates  a  condensation  where  the 
other  generates  a  rarefaction,  they  act  against  one  another, 
and  if  their  power  be  equal,  completely  neutralise  one 
another  (Fig.  101).  Two  sounds  of  the  same  pitch  and 
intensity  thus  meeting  produce  silence.  This  startling  effect 
may  be  shown  with  two  organ-pipes,  exactly  similar  in  all 
respects,  and  mounted  side  by  side  on  the  same  bellows. 
While  one  only  is  played  upon  it  sounds  loudly ;  when  both 
are  made  to  sound  together  there  is  scarcely  any  sound, 


INTERFERENCE   OF   SOUND.  215 

although  they  vibrate,  as  may  be  proved  by  placing  a  feather 
near  the  opening,  where  the  current  of  air  is  broken ;  but 
they  vibrate  in  opposition.  When  the  air  on  entering  one 
tube  is  condensed,  it  is  rarefied  in  the  other ;  the  surround- 
ing air  is  also  urged  in  contrary  directions  by  the  two 
different  actions ;  and  since  there  is  no  reason  why  it  should 
obey  one  rather  than  another,  it  remains  motionless,  and  the 
sound  is  never  produced. 

This  curious  fact  may  be  directly  proved.    A  communica- 
tion is  made  between  the  two  pipes  with  two  of  Kcenig's 


Fig   102. —Interference. 

flames,  so  arranged  that  the  point  of  one  passes  a  little 
mirror  which  hides  its  base,  but  shows  by  reflection  the  base 
of  the  other.  This  produces  the  illusion  of  a  single  flame. 
If,  now,  this  flame  be  seen  in  the  revolving  mirror  while  the 
two  pipes  are  played  upon,  the  point  will  separate  from  the 
base,  which  proves  that  the  two  flames  shine  alternately 
(Fig.  102).  If  both  pipes  act  on  the  same  flame,  the  effect  is 
neutralised,  and  the  flame  remains  motionless.  Two  equal 
vibrations,  then,  either  strengthen  or  weaken  one  another, 
according  to  the  manner  in  which  they  combine ;  but  the 
same  effect,  whichever  it  be,  continues  throughout  the  move- 
ment. If  there  be  the  slightest  inequality  the  case  is  very 
different.  In  such  a  case  one  soon  gains  on  the  other,  and 
passes  on,  then  slackens,  and  is  in  its  turn  overtaken  and 
passed,  and  so  on.  The  encounters  will  take  place  in  all 


2l6  ACOUSTICS. 

manner  of  ways.  Sometimes  there  will  be  an  augmentation, 
sometimes  a  falling  off,  of  sound ;  the  two  notes  alter- 
nating more  or  less  completely  between  brilliancy  and  ex- 
tinction. If  one  should  make  exactly  nine  vibrations  while 
the  other  made  eight,  and  if  the  two  vibrations  started  in 
opposition,  they  would  at  first  weaken  one  another ;  then  as 
one  took  the  lead  (nine  simple  vibrations  having  been  ac- 
complished on  one  side  to  eight  on  the  other),  they  would 
coincide  for  an  instant,  thus  supporting  one  another ; 
then,  after  eight  or  nine  simple  vibrations  more,  they  would 
again  be  in  opposition,  and  weakened  as  at  first.  In  the 
interval  of  eight  and  nine  double  vibrations,  there  would 
always  be  an  augmentation  of  power  or  a  beat.  This  would 
occur  each  time  that  the  more  rapid  note  gained  a  double 
vibration  on  the  other  (Fig.  103). 

An  illustration  will  explain  this.      Let  us  imagine  two 


Fig.  103.— Beats. 

rivers  subject  to  periodical  high-tides,  rising  in  one  at  the 
beginning  of  each  month,  that  is  to  say  twelve  times  a  year, 
and  in  the  other  every  twenty-eight  days,  or  thirteen  times 
a  year.  Suppose  further  that  between  the  high  tides  there 
intervened  low  ones  :  a  high  and  a  low  tide  would  be  equi- 
valent to  a  complete  undulation  or  double  vibration.  If  these 
two  rivers  flowed  into  the  same  lake  they  must  cause  great 


INTERFERENCE    OF    SOUND.  21 7 

commotion  at  certain  times,  whilst  at  others  they  would 
exert  scarcely  any  influence  over  the  state  of  the  waters.  It 
is  indeed  clear  that  if  at  any  given  moment  the  full  tides  co- 
incide, the  low  tides  must  also  fall  together ;  and  since  the 
difference  between  the  two  rivers  is  but  two  days,  this  must 
happen  for  two  or  three  months ;  and  at  these  times  their 
united  action  on  the  open  waters  would  make  a  sensible  rise 
and  fall.  But  when  the  high  tide  of  one  happened  at  the 
same  time  as  the  low  tide  of  the  other,  there  would  be  no 
variation  in  the  level  of  the  lake.  This  period  of  calm 
would  also  last  some  months.  Say  that  the  two  rivers  rise 
together  January  ist,  they  fall  the  i4th  or  i5th,  mount 
again  towards  the  end  of  the  month,  and  fall  in  the  middle 
of  February.  At  the  end  of  six  months  the  river  which  rises 
every  four  weeks  will  be  about  fifteen  days  in  advance  of 
the  other,  and  therefore  will  have  a  full  tide  in  the  middle 
of  July,  just  as  the  other  has  a  low  one.  This  state  of  things 
will  begin  about  June,  and  last  till  August.  During  this 
time  there  will  be  no  effect.  The  summer  then  will  be  a 
period  of  great  calm  for  the  lake.  Towards  the  end  of  the 
year,  the  second  river  being  a  whole  month  in  advance,  its 
thirteenth  tide  will  coincide  with  the  twelfth  of  the  other, 
and  the  lake  will  again  be  agitated  by  a  great  flux  and  reflux. 
Thus  each  winter  the  lake  will  be  stormy,  and  each 
summer  will  find  it  calm.  In  ten  years,  the  120  high  tides 
of  the  one,  combined  with  the  130  of  the  other,  would 
have  produced  ten  periods  of  maximum  agitation.  It  is 
thus  that  two  notes,  making  respectively  120  and  130 
complete  vibrations  in  a  second,  will  give  at  the  same  time 
ten  beats. 

This   phenomenon  may  be  exhibited  in  various  ways. 
By   transcribing    faithfully   the   vibrations   of  the   air,   the 


218 


ACOUSTICS. 


varying  intensity  will  also  be  revealed  if  there  have  been 
any  beats.  To  obtain  a  tracing  with  two  slightly  discordant 
tuning-forks,  it  is  only  necessary  to  fasten  on  one  a  piece  of 
blackened  glass,  and  on  the  other  a  flexible  point ;  then 
make  them  vibrate  horizontally,  and  hold  them  so  that  the 
point  rests  on  the  glass  (Fig.  104).  The  curve  then  drawn 


shows  the  augmentation  as  often  as  the  one  fork  has  gained 
on  the  other  a  complete  vibration.  Fig.  105  shows  two 
tracings  obtained  in  this  way  with  two  notes,  which  were  at 
first  in  the  ratio  24:25,  and  afterwards  in  that  of  So:8i. 
The  flames  of  Kcenig  furnish  another  means  for  observing 
beats. 

The  physiological  perception  of  beats  seems,  at  first 
sight,  irreconcilable  with  the  hypothesis,  according  to  which 
the  ear  always  separates  notes  of  unequal  pitch.  If  the 
two  sounds  do  not  act  upon  the  same  fibre,  how  can  their 
vibrations  combine  in  the  auditory  apparatus?  The  answer 
is  simple.  It  must  not  be  forgotten  that  the  nervous  fibres, 
like  all  elastic  bodies,  are  influenced,  though  in  a  less  degree, 
by  vibrations  a  little  out  of  unison,  so  that  the  sphere  of 
action  of  two  neighbouring  sounds  spreads  over  a  large  sur- 
face of  fibres,  instead  of  embracing  only  two.  A  note  that 
is  a  semitone  higher  or  lower  than  thf  note  of  a  given  fibre, 


INTERFERENCE   OF   SOUND. 


219 


makes  it  resound  ten  times  less  than  a  note  in  unison; 
still  the  resonance  is  percep'ible.  Ac- 
cording to  that,  we  see  that  the  unison 
of  two  neighbouring  notes,  which  beat, 
must  be  manifested  in  all  the  inter- 
mediate fibres,  and  the  ear  must  be 
affected  by  them. 

When  the  augmentations  follow 
rapidly,  the  effect  of  the  beats  becomes 
very  disagreeable,  like  the  burr  of  an 
r,  or  the  grating  of  a  scythe  on  wood. 
The  harshness  is  at  its  height  when 
there  are  thirty  or  forty  beats  per 
second ;  beyond  that  it  becomes 
difficult  for  the  ear  to  separate  them, 
and  the  impression  is  not  so  strong. 
Helmholtz  declares  that  he  has  been 
able  to  distinguish  up  to  132  beats 
per  second  (between  the  sis  and  doh6) 
— without  counting  them,  be  it  un- 
derstood. Since  the  lowest  sound 
perceptible  by  the  ear  comprises  about 
thirty  double  vibrations,  it  is  therefore 
possible  to  hear  beats  at  least  four 
times  as  rapid  as  the  lowest  notes. 

This  observation  contradicts  the 
common  opinion,  that  very  rapid  beats 
are  perceived  by  the  ear  as  a  very 
low  note.  The  reason  of  this  hypo- 
thesis was,  that  two  notes  resounding 
forcibly  toge'h?r  engender  a  third  note,  called  the  resultant 
tone,  which  is  expressed  simply  by  the  difference  of  the  two 


105. 


2  20  ACOUSTICS. 

primitive  notes,  or,  which  comes  to  the  same  thing,  by  the 
beats  produced  by  their  concurrence. 

The  resultant  sounds  were  known  before  they  were 
understood.  The  German  organist  Sorge  speaks  of  them  in 
a  work  published  in  1745.  The  celebrated  violinist  Tar- 
tini  set  himself,  nine  years  later,  to  found  a  new  musical 
system  thereupon;  but  his  book  is  so  abstruse  that  even 
D'Alembert  admits  he  could  not  understand  it. 

It  has  long  been  thought  that  the  resultant  sounds  must 
always  be  lower  than  the  sounds  which  cause  them ;  but 
Helmholtz  foretold  by  theory  resultant  sounds  which  should 
be  sharper,  and  experiment  has  fulfilled  his  prophecy. 

There  are,  then,  two  kinds  of  resultant  sounds  :  first, 
the  differential  sounds,  whose  pitch  is  given  by  the  difference 
in  the  number  of  vibrations  of  the  primary  sounds.  These 
are  the  easiest  to  observe.  Secondly,  the  additive  sounds, 
the  pitch  of  which  is  found  by  adding  the  vibrations  of  the 
primitive  sounds.  Let  us  suppose,  for  example,  that  two 
pipes  are  sounded  together,  giving  a  fifth.  Their  notes 
will  be  in  the  ratio  of  2:3,  and  the  difference  being  unity, 
the  differential  sound  will  be  one,  the  octave  below  the  lower 
of  the  two  sounds.  The  sum  of  two  and  three  is  five  ;  one 
might,  therefore,  also  hear  a  note  which  would  be  the  major 
sixth  of  the  sharper  of  the  two  sounds.  With  doh2  and 
so!2  we  can  obtain  doht  and  mi3,  but  we  shall  hardly  hear 
anything  beyond  the  doh — unless,  indeed,  the  generating 
sounds  are  very  strong.  If  (as  generally  happens)  the  latter 
are  accompanied  by  harmonics,  the  intermingling  of  the 
respective  harmonics,  the  fundamental  notes,  and  the  first 
resultant  sound,  may  give  birth  to  new  resultant  sounds  ; 
but  these  superfluities  are  difficult  to  observe,  on  account  of 
their  weakness. 


INTERFERENCE    OF    SOUND.  221 

The  resultant  sounds  of  a  major  third  are  these.  The 
minims  represent  the  primary,  the  crotchet  the  first  diffe- 
rential, the  quavers  the  cross  products,  and  the  barred  note 
the  additive  sounds  : — 


^E 


To  hear  the  resultant  sounds,  it  is  only  necessary  to 
force  the  generating  sounds.  Theory  shows  that  this 
phenomenon  must  be  considered  as  a  kind  of  disturbance 
of  the  vibratory  motion,  which  becomes  too  violent  to  follow 
the  simple  laws  of  ordinary  elastic  vibrations.  *  It  is  by  an 
analogous  perturbation  that  tuning-forks  and  bells  give  the 
upper  octave  of  their  fundamental  sound  whenever  they  are 
violently  set  in  motion  ;  whilst  vibrating  moderately  they 
would  only  produce  upper  sounds  not  harmonic. 

Resultant  sounds  and  beats  render  important  aid 
in  tuning  organ-pipes,  &c.,  indicating  with  great  precision 
the  difference  in  the  pitch  of  two  notes.  Koenig  was  thus 
enabled  to  tune  a  doh9  of  32,000  vibrations,  and  a  re9  of 
36,000,  by  their  differential  sound  —  the  doh6  of  4,000 
vibrations. 

Henri  Scheibler,  a  silk  manufacturer  at  Cre'feld,  did 
much  to  utilise  the  employment  of  beats  for  tuning 
musical  instruments.  This  man,  who  had  a  passion  for 
acoustics,  devoted  not  less  than  twenty-five  years  to  per- 
fecting his  method.  He  constructed,  with  inconceivable 
trouble,  considering  the  state  of  science  at  that  time,  a  set 


222  ACOUSTICS. 

of  fifty-six  tuning-forks,  giving  the  scale  from  la  of  440  to  la 
of  880,  embracing  an  entire  octave  by  degrees  of  eight 
simple  vibrations.  This  set  of  forks  formed  what  he  called  a 
sonometer.  Taken  two  and  two  in  the  order  in  which  they 
succeed  one  another,  they  always  give  four  beats  a  second. 
They  are  thus  tuned  by  differences,  and  the  last  will,  of 
course,  give  the  exact  octave  of  thi  first.  If  this  result  has 
been  attained  we  are  sure  that  the  first  made  440,  and  the 
last  880  vibrations  per  second,  for  the  beats  prove  a  diffe- 
r.nce  of  440,  and  we  know,  on  the  other  hand,  that  they 
are  as  i  :  2.  We  understand  that  these  fifty -six  tuning-forks, 
the  notes  of  which  are  perfectly  certain,  allow  any  note 
whatever,  contained  within  the  limits  of  their  octave,  to  be 
tuned  by  them  with  mathematical  precision ;  we  have  only 
to  count  the  beats  that  this  note  gives  with  the  tuning-fork 
to  which  it  stands  in  the  nearest  relation.  If  the  note  be  in 
another  octave  it  is  set  by  means  of  a  supplementary  tuning- 
fork,  which  gives  its  true  octave. 

Scheibler  published  his  method  in  1834.  He  also  went 
to  Paris,  to  try  and  make  his  sonometer  known ;  but  the 
difficulty  of  construction  frightened  the  manufacturers. 
Thanks  to  the  progress  of  science,  this  valuable  method  is 
now  within  reach  of  every  one.  Kcenig  made  sonometers  of 
sixty-five  tuning-forks,  embracing  the  middle  octave  of  the 
piano  (from  512  to  1,024  simple  vibrations).  He  even  went 
beyond  this,  filling  in  the  same  way  the  whole  scale  of  per- 
ceptible sounds.  In  the  bass  octaves  great  forks  are  used, 
furnished  with  movable  weights  that  slide  along  the 
branches  ;  according  to  their  position  the  fork  gives  different 
notes.  In  the  very  high  octaves  Kcenig  replaces  the  tuning- 
forks  by  straight  rods.  The  sonometer  that  he  exhibited  in 
1867  was  composed,  first,  of  eight  large  tuning-forks,  for 


INTERFERENCE   OF   SOUND  223 

the  four  octaves  comprised  between  the  doh  of  32  and  that 
of  512  simple  vibrations.  Each  of  these  could  give  thirty-two 
notes,  so  that  they  represented  a  scale  of  2  5 6  notes.  Secondly, 
the  middle  octave  (512  to  1,024)  is  represented  by  sixty- 
four;  the  next  octave  (1,024  to  2,048)  by  eighty-six ;  and  the 
next  (^2,048  to  4,096)  by  172  tuning-forks,  making  a  total  of 
330.  Thirdly,  from  doh6  of  4.096  vibrations,  Kcenig  employed 
steel  rods,  the  length  of  which  is  inversely  proportional  to 
the  pitch  of  their  longitudinal  sound.  Ninety-six  rods  thus 
represent  the  four  octaves  from  doh6  to  doh,0  (64,000). 
This  last  octave  is  almost  beyond  the  limit  of  perceptible 
sound ;  few  people  can  hear  the  sol9  (48,000)  that  Kcenig 
obtained  by  transverse  vibrations  of  a  rod  about  three 
inches  long. 

Two  tuning-forks  with  an  exact  difference  of  two  simple 
vibrations  will  beat  the  seconds  just  like  a  pendulum ;  if 
they  vary  more,  they  will  beat  a  fraction  of  a  second  as 
small  as  is  wished  for.  In  counting  these  beats  we  may 
also  see  another  very  curious  phenomenon — the  influence  of 
a  movement  of  the  sonorous  source  on  the  pitch  of  its  note. 
Kcenig  took  two  tuning-forks,  doh4,  giving  four  beats  per 
second  when  left  in  their  places  ;  he  placed  himself  about 
two  feet  distant  from  the  sharper  one,  and  moved  the  other 
backward  and  forward  between  it  and  his  ear,  keeping  his 
eyes  fixed  on  a  pendulum.  When  the  to-and-fro  movement 
was  synchronous  with  that  of  the  pendulum,  the  listener  only- 
heard  three  beats  in  the  second  when  the  low  tuning-fork 
approached  his  ear;  but  there  were  five  when  it  receded. 
It  follows  that  the  tone  of  this  fork  was  raised  a  double 
vibration  during  the  first  second,  and  was  equally  lowered 
during  the  following  one.  In  fact,  by  moving  it  two  feet 
nearer  (which  represents  the  length  of  its  wave)  a  complete 


224 


ACOUSTICS. 


vibration  is  gained,  and  by  moving  it  an  equal  distance  the 
same  is  lost — just  as  navigators  who  sail  round  the  world 
gain  or  lose  a  day,  accordingly  as  they  travel  with  the  sun, 
or  in  a  contrary  direction. 

Railways  often  afford  opportunities  for  observations  of 
this  kind.  Thus  the  whistle  of  the  engine-driver  seems  more 
shrill  when  the  train  approaches  than  when  it  is  passing 


Fig.  106 — Influence  of  Motion  on  the  Pitch  of  Sounds. 


away.  Taking  thirty-one  miles  an  hour  as  the  speed  of  a 
train,  we  find  that  it  moves  about  forty-six  feet  per  second, 
which  is  •£•%  of  the  velocity  of  sound  ;  a  calculation  based 
upon  this  shows  that  for  an  observer  placed  on  the  railroad, 
the  note  of  the  whistle  will  be  changed  in  the  ratio  of 
24  :  25  ;  he  will  either  estimate  it  too  high  or  too  low 
by  a  semitone,  according  to  the  direction  of  the  motion. 
If  it  is  a  la  for  the  engine-driver,  it  will  be  latt  for  the  signal- 
man at  the  approach  of  the  train,  aM  la^  after  it  has  passed. 
A  stationary  whistle  would  have  the  same  effect  for  passengers; 


INTERFERENCE   OF   SOUND.  £25 

they  would  only  hear  the  true  note  at  the  moment  of  pass- 
ing. If  the  observer  and  the  whistle  were  carried  in  opposite 
directions,  the  effect  would  be  still  more  striking — the  note 
would  appear  alternately  a  whole  tone  higher,  and  a  whole 
tone  lower  than  the  reality.  At  the  moment  the  trains  met 
it  would  leap  a  major  third. 

In  1845,  M.  Buys-Ballot  made  some  experiments  of  this 
kind  on  the  railroad  between  Utrecht  and  Maarsen.  Three 
groups  of  musicians  were  placed  as  close  as  possible  to  the 
rails,  and  distant  from  one  another  about  half  a  mile.  A 
musician  placed  upon  the  locomotive  blew  a  trumpet,  first 
on  leaving  Utrecht,  then  between  the  three  groups,  and 
finally  after  having  passed  them.  The  others  estimated  the 
varying  pitch  of  the  note,  and  it  was  always  found  conform- 
able to  theory. 

Mr.  Scott  Russell  tells  us  that  the  reflection  of  the  noises 
of  a  train  on  the  piles  of  a  bridge  should  produce  the 
same  effect  as  the  contrary  movement  of  two  trains,  and  thus 
the  notes  which  are  echoed  back,  altered  by  a  whole  tone, 
mix  very  discordantly  with  those  which  are  heard  directly. 
To  obtain  minor  thirds  by  reflection,  the  train  should  move 
at  a  speed  of  seventy-three  miles  an  hour. 

A  German  philosopher,  named  Doppler,  has  inquired 
into  these  facts,  applying  them  to  luminous  vibrations,  and 
the  explanation  of  the  colours  of  the  stars ;  but  these  are 
only  speculations. 


CHAPTER  XIIL 

THE   VOICE. 

Organ  of  the  Voice— Bass — Tenor — Alto  — Soprano — Celeorated 
Voices— Song  and  Speech— Vowels  and  Consonants— Ventrilo- 
quism. 

THE  sublime  effects  of  the  human  voice  are  produced  by  a 
very  puny  instrument.  Some  cartilages,  a  pair  of  ligaments, 
a  group  of  muscles — that  is  all  which  Nature  needed  to  create 
a  musical  instrument,  the  sweetness  and  moving  power  of 
which  no  human  invention  has  rivalled.  This  vocal  appa- 
ratus is  a  reed  with  two  lips.  It  is  composed  of  the  larynx, 
a  cartilaginous  tube,  which  forms  the  "  Adam's  apple  "  in 
the  throat ;  the  vocal  chords,  flexible  ligaments  with  only  a 
narrow  slit,  the  opening  of  the  glottis,  between  them ; 
the  lungs,  which  furnish  the  wind ;  and  the  cavities  of  the 
^nwiith,  where  the  first  rude  sound  of  the  voice  is  fashioned 
into  vowels  and  consonants. 

The  vocal  chords  can  meet  and  separate,  contract  and 
expand,  by  the  action  of  certain  muscles  ;  the  current  of  air 
proceeding  from  the  lungs  makes  them  vibrate,  and  this 
vibration  causes  the  sound.  Thanks  to  that  ingenious  in- 
strument, the  laryngoscope,  by  means  of  which  the  inside 
of  the  mouth  is  made  visible  and  the  formation  of  the 
voice  may  be  observed,  the  different  conditions  which 
modify  it  are  well  known. 

For  the  production  of  a  chest-voice  a  very  complete 
action  is  necessary,  and  a  very  close  contact  of  the  two 


THE  VOICE.  £27 

sides  of  the  glottis  ;  and  the  vocal  chords  vibrate  throughout 
their  whole  extent.  In  falsetto  notes  they  only  vibrate 
partially,  and  the  glottis  opens  so  as  to  form  an  elliptical 
orifice.  Practised  singers  can  sound  the  same  note  alter- 
nately in  chest-tone  and  falsetto,  without  taking  breath ;  but 
as  for  Garcia's  story  of  the  Russian  peasants,  who  sang 
an  air  simultaneously  with  chest-voice  and  falsetto,  we  must 
class  it  among  the  miracles. 

If  the  voices  of  women  be  shriller  than  those  of  men, 
it  is  because  of  the  smaller  dimensions  of  the  larynx.  The 
opening  of  the  glottis  is  nearly  twice  as  large  with  men  as 
with  women  and  children.  At  the  age  of  puberty  the 
glottis  of  a  man  suddenly  enlarges,  and  his  voice  generally 
drops  an  octave  ;  it  is  then  said  to  "  break." 

Men's  voices  are  divided  into  bass,  barytone,  tenor,  and 
counter-tenor.  The  last-mentioned  is  at  the  present  day 
extremely  rare.  Women's  voices  are  contralto,  mezzo- 
soprano,  and  soprano.  In  the  following  table  is  shown 
the  compass  usually  assigned  to  these  different  voices. 


fa — 

Basse.      Bar?ton.         Tenor.       Cnntral'o.    Mezzosonrano.  S-i>rano. 
(rr  lenor.) 


This  shows  that  ordinary  voices  do  not  compass  two  full 
octaves.  The  difference  between  the  lower  fa  in  the  bass 
(174  simple  vibrations)  and  the  upper  sol  of  the  soprano  (1,5  66 
vibrations)  is  a  little  over  three  octaves.  But  these  limits 

P    2 


223 


ACOUSTICS. 


are  passed  by  exceptional  voices.  On  the  one  hand  we 
hear  of  bass  voices  reaching  the  fa  of  87  vibrations;  and 
on  the  other,  of  sopranos  that  can  touch  fa  in  the  fifth 
octave  of  2,784  vibrations,  and  even  higher. 


i 


The  voice  of  Gaspard  Forster,  a  Dane,  extended  over 
three  octaves,  while  that  of  the  youngest  of  the  sisters  Sessi 
embraced  three  and  a  half.  Catalani  could  also  command 
three  octaves  and  a  half. 


Forster. 


Farioelli. 


At  the  Bavarian  Court  there  were  in  the  sixteenth 
century  three  remarkable  basses,  who,  according  to  Prae- 
torius  in  his  "  Syntagma  Musicum,"  reached  the  fa-x. 

Christine  Nilsson  and  Carlotta  Patti  attain  a  mar- 
vellous height.  When  acting  the  Queen  of  Night  in  The 
Magic  Flute,  Mdlle.  Nilsson  gives  the  fa5.  But  the 
highest  voice  ever  known  seems  to  have  been  that  of 
Lucrezia  Ajugari,  whom  Mozart  heard  in  Parma,  1770.  In 
a  letter  addressed  to  his  sister  Marianne,  he  transcribes 


THE  VOICE.  229 

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


Trills  were  given  on  the  rec,  and  other  adornments  of  a 
similar  kind.  The  father  of  Mozart  adds  that  La  Bastar- 
della  sang  these  passages  with  a  little  less  power  than  the 
lower  notes,  but  her  voice  remained  pure  as  a  flute.  She 
descended  easily  as  low  as  sol . 

Oulibicheff  tells  of  a  Madame  Becker,  who  astonished 
St.  Petersburg  in  1823  by  her  wonderful  roulades.  Kuhlau 
composed  the  part  of  Adelaide,  in  his  opera  Le  Chateau  des 
Brigands,  for  her.  The  grand  air  in  the  third  act  goes  up  to 
las.  On  one  occasion,  at  the  moment  of  giving  this  dan- 
gerous note,  the  leader  of  the  orchestra  looked  so  fixedly  at 
her  that  she  was  frightened,  and  gave  doh6. 

The  quality  of  the  voice  depends,  as  before  explained, 
on  the  number  and  force  of  its  harmonics.  A  "  true  voice  " 
is  one  that  passes  without  hesitation  from  one  note  to 
another.  Practice  will  do  much  to  produce  it,  but  a  musical 
memory  is  also  necessary.  The  absolute  pitch  of  the  notes 
is  difficult  to  fix  in  the  memory ;  but  it  is  by  no  means  un- 
common to  find  people,  especially  professional  musicians, 
who  can  give  any  note  as  it  is  asked  for  by  name. 

The  difference  between  the  singing  and  the  speaking 
voice  consists  in  this :  the  first  bounds  from  interval  to 
interval,  while  the  conversational  voice  rises  and  falls  by  a 


230  ACOUSTICS. 

continuous  motioii.  The  singing  voice  is  sustained  on  the 
same  tone,  as  on  an  indivisible  point,  which  is  not  the  case 
in  simple  pronunciation,  where  the  sounds  are  not  sufficiently 
united  to  be  appreciated  from  a  musical  point  of  view. 

The  dramatic  declamation  of  the  ancients  was  an  approach 
to  song,  and  often  had  an  accompaniment  on  the  lyre.  We 
find  a  relic  of  it  in  the  peculiar  intonation  of  the  Italian 
orators,  and  in  the  monotone  recitation  heard  in  cathe- 
drals. Recitative  forms  the  link  in  modern  music  between 
speech  and  song.  It  might  even  be  said  that  up  to  a  certain 
point  song  is  but  an  idealised  imitation  of  the  accents  of  im- 
passioned speech.  One  may  cry  and  complain  without 
singing,  but  both  may  be  imitated  by  song.  With  a  little 
attention,  too,  we  may  find  the  vestiges  of  musical  intona- 
tion in  common  speech.  The  accented  syllables  and  the 
fall  of  phrases  are  marked  by  a  change  of  tone.  In  an 
affirmative  German  sentence,  Helmholtz  says,  the  point  is 
indicated  by  a  fall  of  a  fourth,  while  in  an  interrogation  it 
rises  a  fifth.  Indications  of  this  kind  are  to  be  found  in 
the  Gregorian  chant. 

Sic    can  -  ta    com  -  ma  ,      sic     du  -          pun  -  eta  : 


FZi*~*^^*_.*__.f_-,_*    ' 

i  r  i  r-i3r-f-H 


f 

sic  ve-  ro  punctum     Sic  signum  in-ter-ro- ga-  ti-  o-  nis? 


In  Chinese,  intonation  is  a  grammatical  element 

"  If,"  said  M.  Ch.  Beauquier,  "  we  could  translate  into 
musical  sounds  all  the  most  singing  sentences,  such  as  in- 


THE   VOICE.  231 

terrcgations,  menaces,  ironical  sayings,  &c.,  we  should  find 
a  national  similarity,  amongst  different  individuals,  in  accent- 
ing the  same  phrases.  The  Italian  modulates  much,  the 
German  less,  the  Englishman  not  at  all." 

The  sounds  of  speech  are  divided  into  vowels  and 
consonants  ;  the  timbre  of  the  vowels  varies  according  to 
the  resonance  of  the  mouth,  but  the  consonants  are,  as  we 
have  explained  already,  little  more  than  noises.  The  lips, 
the  tongue,  the  palate,  the  teeth,  bear  a  part  in  the  pro- 
duction of  these  characteristic  sounds,  which  make  up  the 
framework  or  scaffolding  of  speech,  and  which  are  alone 
written  by  the  Orientals,  to  the  utter  neglect  of  the  vowels. 
The  child  commences  with  the  vowels,  only  gradually  learn- 
ing the  consonants,  and  only  when  he  does  so  can  his 
speech  become  intelligible. 

The  letters  of  the  alphabet  have  been  thought  by  some 
to  have  certain  physiological  characters.  Listen  to  Mer- 
senne.  He  writes  as  follows  : — 

"  The  vowels  a  and  o  signify  what  is  grand  and  full ;  and 
because  a  is  pronounced  with  a  widely  opened  mouth,  it 
signifies  clear  things,  and  actions  which  are  used  in  opening 
or  beginning  some  work.  Therefore  it  was  that  Virgil  com- 
menced his  '^Eneid'  by  the  word  Anna. 

"  The  vowel  e  expresses  something  subtle,  and  is  pro- 
perly used  in  mourning  and  sorrow  : 

'  Heu  quoe  miserum  tellus,  quoe  me  zequora  possunt !' 

"The  vowel  /  means  very  small  and  slight  things. 
Thence  comes  the  word  minim.  It  expresses  also  something 
penetrating. 

"O  is  expressive  of  strong  passions  :  O  patria  /  O  tern- 


232  ACOUSTICS. 

pora  !  O  mores !  and  to  represent  rotundity,  because  the 
mouth  must  form  a  circle  while  uttering  it. 

"£/ belongs  to  things  secret  and  hidden." 

Then  he  proceeds  to  classify  the  consonants.  He  makes 
the  /  indicate  a  breath,  a  wind  (flatus) ;  s  and  x,  bitter 
things  (stridor) ;  r,  rough,  hard,  disorderly  things,  violent 
and  impetuous  actions,  which  have  earned  it  the  title  of 
the  canine  letter ;  m,  all  that  is  great  (magnus,  monstre)  ; 
n,  things  dark,  hidden,  and  obscure,  and  so  on. 

Boiste,  in  his  "  Observations  on  Pronunciation,"  says  the 
f  is  the  soul  of  the  French  language  ;  it  is  the  most  variable 
of  all  the  letters,  the  one  most  capable  of  modulation,  and 
having  most  shades.  According  to  the  same  author,  "  the 
doubling  of  the  f  denotes  either  sharpness  or  vanity, 
pedantry  or  satire ;  it  irritates,  it  domineers,  it  bites;  in  such 
words  as  en  cffct,  qu'ai-je  affaire,  cela  suffit,  c'est  affreux. 
None  but  a  born  and  educated  Frenchman  can  truly  pro- 
nounce this."  Words  formed  by  onomatopreia  imitate 
natural  noises ;  the  great  poets  often  get  very  happy  effects 
from  the  different  characters  of  consonants  and  vowels.  In 
the  well-known  verse  of  Virgil  the  clatter  of  horses'  hoofs 
is  rendered  by  a  succession  of  vigorous  dactyls  : 

"  Quadrupedante  putrem  sonitu  quatit  ungula  campum." 

It  has  been  remarked  that  each  of  the  vowels  has  its 
favourite  place  in  the  musical  scale.  Helmholtz  says  that 
the  vowels  which  belong  to  a  given  note  are,  first,  those 
whose  characteristic  is  a  little  higher  than  the  note  in 
question,  and  afterwards  those  whose  characteristic  is  the 
octave  or  twelfth  of  the  same  note.  The  ou,  whose  charac- 
teristic is  fa.,,  is  produced  with  greatest  ease  on  the  notes  163, 


THE  VOICE.  -33 

mi2,  fa2,  and  fa.     The  e  prefers  re3,  mi^  fa, :  then  again  fa, 
and  sifr,  because  of  its  characteristic  fa^ 


This  affinity  of  the  vowels  for  certain  fixed  notes  is  prin- 
cipally verified  in  the  limits  of  falsetto  and  chest-voices.  A 
woman's  voice  giving  a  lower  note  than  doh3  turns  involun- 
tarily to  the  o  or  on.  Above  mi4,  the  most  easy  note  to 
sound  is  a.  Passing  si4,  i  takes  the  ruling  place.  Such 
facts  are  very  important  to  composers,  and  to  those  who 
write  words  intended  for  a  musical  setting. 

Jean  M filter  and  other  physiologists  have  studied  the 
mechanism  of  the  human  voice,  by  means  of  the  artificial 
larynx,  made  of  india-rubber  bands  fixed  to  the  end  of  a 
tube,  and  acted  upon  by  pincers,  which  give  a  variable 
tension.  By  blowing  into  tlvs  apparatus,  sounds  can  be 
produced  closely  resembling  those  of  the  human  voice. 

To  imitate  the  vowels,  the  theory  of  timbre  shows  that 
it  is  necessary  to  strengthen  certain  fixed  notes  in  these 
sounds.  Thus  it  is  that  Mr.  Willis  produces  the  vowels  by 
the  help  of  a  whistle  mounted  on  a  tube,  which  he  could 
lengthen  or  shorten  at  pleasure.  By  adding  to  such  an 
apparatus  sensitive  membranes  to  produce  the  characteristic 
sounds  of  consonants,  it  is  possible  to  imitate  speech.  We 
have  all  heard  of  the  dolls  who  say  papa  and  mamma.  Mr. 
Wheatstone  had  a  kind  of  bag-bipe  which  could  pronounce 
short  phrases.  Mersenne  tells  us  of  an  organ  that  gave 
vowels  and  consonants.  In  1791  Van  Kempelen  exhibited 


234  ACOUSTICS. 

a  speaking  automaton,  but  the  spectators  did  not  speak  very 
enthusiastically  of  the  resemblance  of  the  artificial  sounds 
to  the  human  voice. 

The  vocal  apparatus  found  in  birds  is  placed  very  low  in 
the  throat.  This  is  the  reason  that  Cuvier  was  able  to  cut 
the  neck  of  a  singing  bird  without  preventing  its  song. 
With  men  an  accidental  opening  in  the  larynx  renders  the 
formation  of  the  voice  impossible.  Magendie  tells  us  of  a 
man  he  knew  who  was  always  obliged  to  wear  a  cravat 
with  a  valve,  to  stop  a  leakage  in  his  throat. 

The  organ-stop  called  vox  humana  is  only  a  set  of  very 
short  zinc  pipes,  which  often  give  a  harsh  and  screaming 
sound,  and  is  seldom  effective. 

Ventriloquists  only  talk  like  ordinary  mortals,  but  they 
avoid  opening  the  mouth  so  as  to  be  seen  to  speak,  and 
they  scarcely  move  their  lips,  and  breathe  as  little  as  possible. 
Their  voice  then  appears  changed,  and  as  if  coming  from  a 
great  distance.  This  is  not  done  without  a  great  effort  of 
the  lungs,  which  fatigues  the  chest,  and  obliges  the  ventrilo- 
quist from  time  to  time  to  resume  his  natural  voice ;  there- 
fore dialogue  is  easy  to  them,  while  at  the  same  time  it 
helps  to  mislead  the  audience.  They  speak  also  while 
breathing,  and  the  stifled  sound  thus  produced  seems  to 
come  through  a  thick  wall.  The  illusion  is  completed  by 
an  imitation  of  the  inflexions  used  when  people  call  from  a 
distance.  But  when  one  becomes  familiar  with  the  voice  of 
a  ventriloquist  the  illusion  is  dispelled.  Robertson  proved 
this  with  a  servant  of  his,  who  was  a  famous  ventriloquist. 

Ventriloquists  generally  find  it  very  easy  to  imitate  the 
voice  of  a  child ;  but  they  can  rarely  sing  in  a  borrowed 
voice. 

This  art  was  known  in  the  earliest  ages ;  the  sorcerers 


THE   VOICE.  235 

made  use  of  it.  Amongst  the  celebrated  ventriloquists  we 
may  mention  Louis  Brabant,  valet-de-chambre  of  Francis  I., 
Saint  Gille,  Baron  van  Mengen,  Charles,  Comte,  &c.  Of 
this  last  they  tell  a  number  of  odd  stories.  Once  at  Tours 
he  made  them  break  open  a  closed  shop,  in  which,  from  the 
groans  they  heard,  they  supposed  some  one  was  starving. 
At  Nevers  an  ass  suddenly  declared,  with  strong  invectives, 
that  he  would  carry  his  rider  no  further.  He  cured  people 
possessed  with  devils,  exorcising  the  demons,  who  were 
heard  to  fly  away  howling.  In  a  church  invaded  by  revolu- 
tionists greedy  of  destruction,  he  made  the  statues  speak, 
reproaching  the  iconoclasts  for  their  Vandalism ;  and  they 
took  to  flight,  wild  with  terror.  Once  he  saved  himself  from 
the  peasants  of  Fribourg,  who  were  going  to  burn  him  as  a 
sorcerer,  by  making  a  voice  of  thunder  come  from  the 
furnace  towards  which  they  led  him,  whereupon  they  fled  in 
disorder. 


CHAPTER  XIV. 

THE   EAR. 

The  External  and  Internal  Ear — The  Ossicles— The  Mechanism  of 
Hearing — The  Fibres  of  Corti — Inequality  of  the  Two  Ears — 
Perception  of  the  Direction  of  Sound. 

ON  either  side  of  the  head  Nature  has  placed  the  ears, 
commissioning  them  to  receive  and  introduce  to  the  presence 
of  the  mind  tlie  sounds  which  arrive  as  invisible  messengers 
from  Nature.  It  is  not  because  there  is  no  other  way  in 
which  the  auditory  nerve  can  be  reached.  We  have  seen 
that  it  is  possible  to  hear  through  the  teeth.  Deaf  people 
have  even  been  known  to  hear  by  the  epigastrium  ;  but  the 
natural  road  for  sonorous  impressions  is  by  the  auditory 
canal. 

With  men  and  all  the  mammalia,  the  hearing  organ 
comprises  three  successive  compartments  —  the  external 
orifice,  the  middle  ear,  and  the  inner  ear.  The  external  ear 
is  composed  of  a  passage  c  (Fig.  107),  opening  out  at  the 
base  of  the  temporal  bone,  and  a  cartilaginous  funnel. 
This  is  a  sort  of  hearing-trumpet,  for  gathering  and  con- 
centrating the  sonorous  waves.  When  this  is  wanting,  or  is 
flattened  against  the  head,  the  hearing  loses  much  of  its 
delicacy.  In  many  animals  this  concha  is  movable  ;  horses 
and  dogs  prick  their  ears,  in  order  to  hear  better.  The 
motion  is  produced  by  the  cutaneous  muscle  of  the  head. 
It  is  a  very  rare  faculty  among  men,  though  individuals 
possessing  it  are  occasionally  met  with. 


THE   EAR.  237 

The  middle  ear  is  separated  from  the  external  by  the 
tympanic  membrane,  which  closes  a  kind  of  hollow  cavity 
in  the  hardest  part  of  the  temporal  bone.  This  membrane 
receives  the  sonorous  vibrations,  and  transmits  them  to  the 
interior.  With  birds  and  reptiles  it  is  placed  near  the 
crown  of  the  head.  The  passage  E  forms  a  free  communica- 
tion between  the  membrane  and  the  back  of  the  mouth, 


Fig.  107. -The  Ear. 

by  which  means  an  equilibrium  is  maintained  between  the 
outer  air  and  that  imprisoned  in  the  cavity.  One  can  easily 
experience  the  reality  of  this  communication,  by  stopping 
the  mouth  and  the  nose,  and  then  blowing.  The  tympanic 
membrane  swells  under  the  pressure  of  the  imprisoned  air, 
and  one  who  tries  to  breathe  under  these  conditions  feels  it 
to  be  drawn  inwards.  This  explains  why  we  should  open 
the  mouth  when  standing  near  a  cannon  as  it  is  fired.  The 
pressure  upon  the  tympanum  caused  by  the  detonation  is 
thm  diminished,  by  being  equalised  on  both  sides. 


238  ACOUSTICS. 

The  bony  partition  opposite  the  tympanum  is  perforated 
by  two  small  holes,  the  one  round  and  the  other  oval ; 
they  are  both  closed  by  fine  membranes.  The  oval  orifice, 
which  is  above  the  other,  communicates  with  the  tympanic 
membrane  by  a  series  of  little  bones.  These  are— the 
hammer  (m,  Fig.  1 08),  which  is  fastened  to  the  middle  of  the 
tympanum ;  the  anvil  (ri},  resembling  a  molar  tooth,  and 
supporting  the  head  of  the  hammer;  the  little  lenticular 
bone  (/)  joining  the  anvil  to  the  stirrup-bone,  which  adheres 
by  its  base  to  the  membrane  of  the  oval 
orifice.  Some  tiny  muscles  attached  to  the 
sides  of  the  concha  can  act  upon  the  hammer 
and  anvil,  making  them  turn  together  round 
a  horizontal  axis ;  the  end  of  the  hammer 
then  either  draws  or  pushes  the  tympanic 
Fig  108  —Ossicles  membrane,  and  the  end  of  the  anvil  acts  on 

the  stirrup. 

The  internal  ear,  or  labyrinth,  is  composed  of  the 
vestibule  v  (Fig.  107),  surmounted  by  three  semi-circular 
canals  R,  and  the  cochlea  L,  which  has  the  form,  both  outside 
and  inside,  of  a  turbinated  shell.  The  vestibule  opens  on 
the  oval  orifice,  the  cochlea  on  the  round  one ;  but  they 
communicate  by  means  of  a  pretty  large  opening.  The 
bony  labyrinth  has  a  lining  membrane,  which  takes  nearly 
the  same  form,  and  is  generally  a  counterpart  of  the  ex- 
ternal surfaces.  It  is  filled  with  a  liquid  called  the 
vitreous  fluid,  and  over  it  are  spread  the  terminations  of  the 
acoustic  nerve  N. 

The  process  of  hearing  is  as  follows : — The  vibrations 
of  the  tympanum  are  communicated  by  the  air  in  the 
concha  to  the  round  orifice,  and  by  the  ossicles  to  the  oval 
orifice.  The  membranes  which  close  these  orifices  make 


THE    EAR.  239 

the  fluid  in  the  labyrinth  vibrate,  and  consequently  the  float- 
ing filaments  of  the  acoustic  nerve ;  and  thus  the  sensation 
of  sound  is  produced. 

The  hammer,  probably,  serves  also  to  give  a  variable 
tension  to  the  tympanic  membrane  when  we  listen  atten- 
tively. The  movement  of  the  muscles  which  control  it  may 
be  voluntary.  Fabrice  d'Aquapendente  could  produce  a 
little  noise  in  his  ear  by  acting  on  the  hammer,  and  Miiller 
could  make  his  ossicles  crack,  so  as  to  be  heard  by  another 
person.  M.  Daguin  observed,  when  he  was  handling  some 
veiy  small  objects  in  perfect  silence,  and  let  one  fall  by 
accident,  a  slight  tinkling,  due  in  all  probability  to  the  same 
cause.  These  facts  prove  that  the  hammer  strains  the  tym- 
panic membrane  when  one  "  gives  ear,"  just  as  the  pupil 
adjusts  itself  to  look  fixedly  at  an  object. 

The  tympanum  is  not  absolutely  necessary  to  hearing. 
When  it  is  torn  the  hearing  is  impaired,  but  not  destroyed, 
since  the  surrounding  air  then  acts  directly  upon  the  mem- 
branes of  the  two  orifices. 

The  inner  membrane  of  the  cochlea  is  lined  with  elastic 
fibres,  discovered  by  the  illustrious  Corti,  and  bearing  his 
name.  They  apparently  form  the  terminations  of  the 
filaments  of  the  auditory  nerve.  Helmholtz  thinks  that 
each  one  is  attuned  to  a  special  note,  and  as  they  are  above 
3,000  in  number,  there  must  be  above  400  for  each  octave. 
The  interval  from  one  to  another  would  be  ^  of  a  tone, 
and  so  they  form  a  wondrous  instrument  for  reproducing 
every  note  that  the  ear  can  distinguish.  We  have  already 
seen  its  bearing  on  timbre,  and  the  analysis  of  harmonics. 
The  cochlea  may,  then,  be  called  an  ^Eolian  harp  of  3,000 
strings,  that  move  in  sympathy  to  all  the  sounds  of  creation. 

This  idea  has  been   unexpectedly  confirmed  by  the 


240  ACOUSTICS. 

recent  researches  of  M.  V.  Hensen  on  the  hearing  of  the 
decapod  crustaceans.  Having  placed  some  of  these  animals 
in  sea-water,  charged  with  strychnine,  in  order  to  intensify 
the  action  of  the  nervous  centres,  he  has  seen  them  thrown 
into  convulsions  at  the  slightest  noise  ;  from  which  experi- 
ment he  concludes  that  with  them  audition  takes  place 
through  the  medium  of  auditory  hairs,  each  hair  vibrating 
in  unison  with  a  certain  note.  When  he  examined  the  point 
of  attachment  between  a  nervous  cord  and  one  of  these 
hairs  under  the  microscope,  whilst  a  horn  was  being  loudly 
sounded,  the  point  became  indistinct  through  the  rapid 
motion  of  the  hair  each  time  certain  notes  were  given,  the 
neighbouring  hairs  remaining  motionless.  One  of  the  hairs 
answered  to  reik  and  to  re&3,  a  little  more  faintly  to  so!2,  and 
still  less  to  sol.  Probably  it  had  for  its  fundamental  tone  an 
harmonic  common  to  these  four  notes,  and  situated  between 
re4  and  re$4.  Another  hair  vibrated  under  the  influence  of 
the  notes  la&3,  rett2,  and  lafl,  which  indicated  the  fundamental 
tone  lajfv 

In  the  vestibule  and  semi- circular  canals,  the  termina- 
tions of  the  nerves  are  found  to  be  under  other  conditions. 
There  we  find  some  little  crystalline  particles,  called  otolithes, 
and  some  fine  elastic  bristles,  which  seem  meant  to  sustain 
the  vibrations  of  the  nervous  filaments.  Scarpa  and  Trevi- 
ranus  believed  this  different  formation  of  the  various  ramifi- 
cations of  the  acoustic  nerve  must  be  for  the  purpose  of 
enabling  us  to  distinguish  the  pitch  and  timbre  of  sounds  ; 
but  our  present  knowledge  of  the  matter  does  not  allow  us 
to  define  everything  in  the  wonderful  organisation  of  the 
auditory  apparatus. 

Paralysis  of  the  auditory  nerve  causes  incurable  deaf- 
ness. Atrophy  of  certain  parts  of  the  plexus,  or  "  Corti's 


THE   EAR.  241 

organ,"  explains  the  partial  deafness  which  prevents 
sounds  of  a  certain  pitch  being  heard.  Many  ears  are 
incapable  of  hearing  very  high  sounds.  Wollaston  found 
that  several  people  were  deaf  to  the  chirping  of  crickets, 
and  some  even  to  that  of  sparrows.  Why  may  there  not  be 
animals  to  whom  sounds  beyond  the  range  of  the  human 
ear  are  still  perceptible?  There  are  certain  kinds  of  insects 
that  vibrate,  just  like  our  well-known  crickets,  without  making 
the  faintest  audible  sound  :  may  it  not  be  that  there  is,  in 
truth,  a  delicate  music  audible  only  to  its  proper  listeners  ? 

Musicians  have  been  known  to  play  in  the  orchestra, 
and  to  be  aware  of  the  slightest  falsity  in  tune,  who  yet  could 
not  join  in  a  common  conversation  without  the  help  of  an 
ear-trumpet.  Mr.  Willis  describes  a  singular  phenomenon 
under  the  name  of  paracousis.  Some  people  who  have 
imperfect  hearing,  and  cannot  in  general  hear  faint  sounds 
at  all,  hear  them  at  once  when  they  are  accompanied  by  a 
great  noise.  Mr.  Willis  knew  a  lady  who  made  her  servant 
beat  a  drum  whenever  she  wanted  to  listen  to  anything,  for 
then  she  could  hear  very  well.  Another  person  could  only 
hear  when  the  bells  were  ringing.  Holder  mentions  two 
similar  cases :  one  of  a  man  who  was  deaf  except  when 
they  beat  a  large  drum  close  beside  him,  and  another  of 
one  who  never  heard  so  well  as  when  he  was  rattling  over 
a  stony  road  in  a  carriage.  There  was  a  shoemaker's  ap- 
prentice, too,  who  only  heard  while  his  master  was  beating 
the  leather  on  the  stone.  Such  facts  may  perhaps  be 
explained  by  the  habitual  relaxation  of  the  muscles  of  the 
hammer,  which  would  render  them  incapable  of  acting  on 
the  tympanic  membrane,  except  under  the  excitement  of 
very  strong  vibrations. 

With  many  people  the  ears  are  unequal  in  their  power 

Q 


£42  ACOUSTICS. 

of  hearing.  From  M.  Fechner's  experiments  it  seems  that 
the  left  ear  generally  hears  better  than  the  right.  He 
thinks  that  the  reason  may  be  the  common  habit  of  sleeping 
on  the  right  side.  Ittard  mentions  a  remarkable  instance  of 
a  man  he  knew,  whose  two  ears  heard  different  notes  at 
the  same  time  when  a  single  one  was  given.  M.  Fessel, 
of  Cologne,  lately  discovered  the  same  peculiarity  in 
himself.  In  setting  some  tuning-forks — first  by  his  ear, 
and  then  by  a  more  exact  process — he  noticed  that  all  which 
he  had  set  by  his  right  ear,  while  holding  the  normal  or 
pattern  tuning-fork  to  his  left,  were  too  low,  while  the 
others,  set  in  the  opposite  way,  were  too  sharp.  It  follows 
that  the  same  sound  is  sharper  for  his  right  ear  than  for 
his  left.  Much  struck  by  this  circumstance,  he  examined 
the  hearing  of  many  persons,  and  found  it  a  much  more 
common  thing  than  could  have  been  imagined.  So  that 
we  might  ask  a  musician  for  the  right  la  or  the  left.  M. 
Fessel  even  supposes  that  the  phenomenon  is  objective,  and 
that  the  same  tuning-fork  really  gives  a  higher  note  when 
it  vibrates  before  the  ear  to  which  it  appears  sharper. 
This  note  of  resonance  is  heard  in  the  same  way  by  an  on- 
looker. He  asked  different  persons  of  his  acquaintance  to 
carry  alternately  to  the  right  and  left  ear  two  duplicate 
tuning-forks;  and  according  to  the  notes  they  heard,  he 
could  tell  by  which  ear  they  heard  too  high  or  too  low.  But 
such  facts  need  verification. 

As  the  two  eyes  serve  to  give  us  the  impression  of  the 
geometrical  relief  of  a  body,  so  the  two  ears  allow  us  to 
judge  of  the  direction  of  sounds.  When  the  eyes  are  blind- 
folded, and  one  ear  stopped,  all  sound  seems  to  come  in  the 
direction  of  the  free  ear;  or,  at  least,  our  inference  as  to  its 
direction  is  very  uncertain. 


THE   EAR.  243 

It  is  the  concha  of  the  ear  that  specially  helps  to  arrest 
attention,  and  to  recognise  the  direction  of  sonorous  waves. 
Diderot  tells  us  of  a  blind  man  who,  when  disputing 
with  his  brother,  took  up  something  and  threw  it  very  neatly 
at  his  head,  his  aim  being  guided  by  his  ear. 

The  hearing  of  the  blind  is  generally  very  acute  and 
delicate,  because  it  has  to  serve  them  for.  the  most  part 
instead  of  sight.  Ittard  invented  an  instrument,  which  he 
called  an  acoumeter^  to  measure  the  delicacy  of  hearing.  It  .is 
a  brass  ring,  hung  upon  a  thread,  and  struck  by  the  ball  of 
a  pendulum  which  falls  from  a  given  height.  The  distance 
at  which  different  persons  cease  to  hear  it  is  accurately 
measured.  Freycinet  used  this  instrument  for  studying  the 
hearing  of  savages.  In  nocturnal  birds  and  timid  animals, 
such  as  the  hare,  the  external  ear  is  largely  developed.  The 
ears  of  the  lower  animals  are  incomplete.  The  cavity  of 
the  tympanum  is  entirely  wanting  in  fish,  the  round  and 
oval  orifices  being  at  the  top  of  the  head.  The  articulata 
do  not  show  any  visible  auditory  apparatus.  Amongst  the 
molluscs,  the  cephalopods  are  the  only  creatures  that  possess 
a  vestige,  and  there  it  is  of  the  simplest  form,  consisting 
merely  of  a  cavity  and  acoustic  nerve. 


CHAPTER  XV. 

MUSIC     AND     SCIENCE. 

Principles  of  Music — Euler — Rameau  —  Sauveur  —  Helmholtz  —  Har- 
mony and  Discord  Explained  by  Beats — Chords — Major  and  Minor 
Keys. 

THE  disdain  with  which  the  majority  of  musicians  reject  all 
attempts  of  the  exact  sciences  to  invade  their  domain  is,  up 
to  a  certain  point,  justifiable. 

The  help  that  mathematics  has  hitherto  given  to  musical 
science  is  very  slight ;  it  has  scarcely  done  more  than  point 
out  a  few  vague  analogies  which  explain  nothing.  It  has 
travelled  in  a  defective  circle ;  the  pleasure  of  the  ear  has 
been  exalted  into  a  principle,  and  made  the  foundation  of 
all  systems. 

It  was  known  that  harmonious  chords  correspond  to  the 
relations  of  whole  numbers.  The  Pythagoreans  propounded 
and  repropounded  this  theory,  without  deducing  from  it  any 
other  conclusion  than  some  aphorisms  upon  the  harmony  of 
the  world,  and  the  occult  power  of  numbers.  Philosophers  have 
attempted  to  find  the  seven  notes  of  the  scale  repeated  in 
the  movements  of  the  celestial  bodies,  and  even  the  great 
Kepler  abandoned  himself  to  such  mystical  speculations. 

In  the  first  half  of  the  eighteenth  century,  towards  1740, 
the  great  mathematician,  Leonard  Euler,  endeavoured  to 
explain  the  relations  of  musical  intervals  by  considerations 
drawn  from  physiology.  He  reasoned  thus  :  That  which 
pleases  us  is  always  that  which  to  our  feeling  possesses  a 


MUSIC   AND   SCIENCE.  i*45 

certain  perfection ;  and  wherever  there  is  perfection  there  is 
necessarily  also  order — that  is  to  say,  some  law  which 
governs.  A  song  will  please  us  if  we  recognise  the  order  of 
the  sounds  of  which  it  is  composed  ;  and  it  will  please  us  so 
much  the  more  in  proportion  as  we  are  able  to  understand 
that  order.  Now,  there  are  in  sounds  two  ways  in  which 
order  may  manifest  itself — by  their  pitch,  as  represented  by 
high  notes  or  low  notes,  and  by  their  duration.  Pitch  is 
reckoned  by  rapidity  of  the  vibrations,  and  duration  by  the 
length  of  time  during  which  a  sound  is  heard.  Order  with 
regard  to  duration  consists  in  rhythm  or  time  ;  order  in 
pitch  is  simple  proportion  amongst  the  vibrations.  The 
degrees  of  accord  in  these  proportions — that  is  to  say,  in  the 
musical  intervals — depend  upon  their  simplicity,  for  the  ear 
appreciates  them  so  much  the  more  easily  as  they  are  ex- 
pressed by  the  most  simple  numbers,  and  the  pleasure  is 
greatest  when  it  costs  us  least.  In  developing  these  principles 
Euler  succeeded  in  establishing  the  laws  of  harmony. 

That  which  is  wanting  in  his  theory  is,  that  it  is  not 
based  upon  any  certain  fact.  Nothing  warrants  us  in 
admitting  that  the  ear  can  judge  of  the  relations  of  vibra- 
tions which  depend  on  the  thousandth  part  of  a  second. 
The  observations  of  astronomers  show  that  the  ear  separates 
at  the  most  two  strokes  of  a  pendulum  which  vibrates  in 
a  tenth  parth  of  a  second.  How  can  it  be  supposed  that  it 
can  compare  the  proportion  between  two  vibrations  num- 
bering, for  example,  5,000  and  5,050  ?  And  nevertheless  it 
easily  recognises  this  relation  in  so  many  musical  intervals. 

Ideas  analogous  to  these  of  Euler  had  been  already  put 
forward  in  1701  by  Sauveur.  "The  mind,"  he  says,  "by 
its  very  nature  loves,  at  the  same  time,  simple  perceptions 
because  they  do  not  weary  it,  and  varied  perceptions  because 


246  ACOUSTICS. 

they  spare  it  the  ennui  of  uniformity.  ....  Every 
variety  which  pleases  the  mind  is  then  confined  in  certain 
limits ;  it  must  be  guarded  from  becoming  difficult  to  per- 
ceive, confused,  complicated  .  .  ."  He  then  explains 
how  chords  are  rendered  agreeable  to  the  ear  by  the  more 
or  less  frequent  concurrence  of  vibrations.  When  these 
concurrences  become  rare,  as  in  thirds  where  they  occur 
only  once  in  five  or  six  vibrations,  the  perception  of  the 
sound  becomes  less  simple,  but  it  is  nevertheless  pleasant 
because  it  is  slightly  varied,  the  discords  putting  the  har- 
monies in  still  stronger  contrast. 

But  there  is  a  point  at  which  the  harmony  of  this  variety 
stops,  and  this  point  is  given  by  the  ratio  5  :  6.  Sauveur 
afterwards  remarks  that  harmonies  do  not  make  beats,  and 
that  discords  do.  Unfortunately,  he  has  not  developed  this 
idea  as  it  deserves. 

In  1726,  Rameau  started  another  theory,  which  D'Alem- 
bert  thought  worthy  of  notice.  It  seems,  at  first,  to  account 
for  the  pleasure  that  music  gives  us.  It  is  very  curious  to 
see  the  means  that  this  celebrated  artist  has  taken  to  dis- 
cover what  he  calls  the  principle  of  harmony. 

"  I  saw,"  said  he,  "  that  I  must  follow  in  my  researches 
the  same  order  that  exists  in  the  things  themselves ;  and 
as,  to  all  appearance,  there  must  have  been  song  before  there 
was  harmony,  I  asked  myself  in  the  first  place  how  song 
was  obtained. 

"  Enlightened  by  the  method  of  Descartes,  which  I 
had  happily  read,  and  with  which  I  had  been  struck,  I  began 
with  myself.  I  tried  some  songs,  like  a  child  who  is 
practising  singing ;  I  watched  what  took  place  in  my  mind 
and  in  my  voice,  and  it  always  seemed  to  me  that  there  was 
not  any  reason  that  decided  me,  when  I  had  uttered  a  sound. 


MUSIC  AND  SCIENCE.  247 

to  choose  one  more  than  another  of  all  the  multitude  of 
sounds  that  might  come  next.  There  were  certainly  some 
for  which  my  voice  and  my  ear  seemed  to  me  to  have  a 
predilection,  and  that  was  the  first  thing  I  noticed ;  but  this 
predilection  appeared  to  me  purely  a  matter  of  habit.  I 
imagined  that  in  a  different  system  of  music  from  ours,  with 
another  kind  of  song,  the  predilection  of  the  voice  and  sense 
would  have  been  in  favour  of  another  sound  ;  and  I  con- 
cluded that,  since  I  found  in  myself  no  good  reason  to 
justify  this  predilection  and  to  regard  it  as  natural,  I  must 
not  take  it  as  a  principle  in  my  researches,  nor  even  sup- 
pose that  it  would  exist  in  another  man  who  was  not  in 
the  habit  of  singing  or  of  hearing  it." 

He  declares,  however,  that  the  sounds  which  had  seemed 
to  him  to  succeed  each  other  most  naturally  were  the  fifths 
and  the  thirds,  or  the  sounds  which  correspond  to  the 
relations  of  2  to  3,  and  of  4  to  5.  But  this  simplicity  of 
relations  appeared  to  him  to  be  only  a  sort  of  convenient 
arrangement,  and  insufficient  to  account  for  a  phenomenon 
such  as  that  which  he  sought  to  explain. 

"  I  began,"  continued  he,  "  to  look  around  me,  hoping 
to  find  in  nature  that  which  I  could  not  discover  in  myself 
so  surely  or  so  clearly  as  I  desired.  The  search  was  soon 
rewarded  :  the  first  sound  which  struck  my  ear  was  a  clap 
of  thunder.  I  suddenly  perceived  that  it  was  not  one,  and 
that  the  impression  which  it  made  upon  me  was  complicated. 
'That,  said  I,  is  the  difference  between  noise  and  sound. 
Everything  that  produces  a  simple  impression  upon  my  ear 
is  noise,  and  everything  that  produces  an  impression  com- 
posed of  several  others  is  sound.'  I  called  the  primitive 
sound  a  fundamental  tone  ;  its  concomitants,  harmonics." 

He  afterwards  discovered  that  harmonics  are  very  sharp 


248  ACOUSTICS. 

and  very  transient,  so  that  they  cannot  strike  equally  a 
musical  ear,  and  one  lacking  in  musical  sensibility.  Then 
he  decided  that  the  complementary  sounds  of  the  funda- 
mental tone  must  be  its  twelfth  and  its  seventeenth — that  is, 
the  octave  of  the  fifth  and  the  double  octave  of  the  major 
third.  Then,  as  he  knew  by  experience,  as  he  says,  that 
the  octave  is  only  a  repeat,  he  thought  it  quite  natural  that 
his  voice  and  his  imagination  should  lower  the  harmonics 
to  the  last  point ;  and  that,  therefore,  his  fancy  should  be 
taken  by  the  third  and  the  fifth  of  the  fundamental  tone, 
and  not  by  their  repeats,  when  he  took  the  notes  that  his 
ear  suggested  to  him  after  the  fundamental  tone. 

Thus  the  multiple  resonance  of  the  sonorous  body  be- 
comes the  base  upon  which  is  built  the  musical  system. 
Rameau  deduces  from  it  the  formation  of  the  diatonic  scale 
and  the  principal  rules  of  harmony.  But  his  fertile  imagi- 
nation led  him  afterwards  to  attempt  to  draw  from  the  same 
source  the  principle  of  geometry;  and  it  is  here  that 
D'Alembert,  to  whom  is  due  the  merit  of  developing  and 
simplifying  Rameau 's  system,  ielt  himself  obliged  to  place 
his  veto,  and  to  circumscribe  clearly  the  range  of  the  musi- 
cian's discovery.  D'Alembert  continually  asserts  that  the 
demonstration  which  Rameau  pretends  to  have  given  of  the 
principles  of  harmony  is  no  demonstration,  and  that  there 
will  always  enter  into  the  theory  of  musical  phenomena  a 
sort  of  metaphysics,  which  introduces  into  the  science  an 
obscureness  natural  to  itself.  "But,"  says  he,  "if  it  be  un- 
just to  demand  here  the  unshaken  complete  assurance  which 
is  produced  only  by  the  clearest  light,  we  doubt  at  the  same 
time  whether  it  would  be  possible  to  throw  upon  these 
matters  a  stronger  light  than  that  which  we  have  already." 

The  judgment  that  D'Alembert  passes  upon  Rameau's 


MUSIC   AND   SCIENCE.  2-49 

system  proves  sufficiently  that  the  illustrious  mathematician 
understood  perfectly  well  its  weak  points,  or,  to  speak  more 
correctly,  its  insufficiency.  It  is  not  enough  to  say  that  the 
octave  is  a  repeat ;  the  word  does  not  sufficiently  account 
for  the  important  part  that  this  interval  plays  in  musical 
compositions ;  and,  on  the  other  hand,  the  phenomenon  of 
harmonic  resonance  is  not  so  general  as  Raineau  supposes. 
A  large  number  of  sonorous  bodies  produce  in  reality  en- 
tirely dissonant  simultaneous  sounds.  It  is  therefore  not 
right  to  lay  it  down  as  a  principle  that  harmonics  are  found 
by  natural  resonance ;  and  even  if  it  were  true,  we  must 
remember  that  the  ugly  has  quite  as  much  a  place  in  nature 
as  the  beautiful,  which  proves  that  a  thing  may  be  at  the 
same  time  natural  and  disagreeable. 

It  must  then  be  acknowledged  that  this  theory  has  not  a 
rational  foundation,  since  it  does  not  explain  in  any  way  the 
origin  of  discords.  Nevertheless,  we  cannot  but  admire 
the  ingenuity  with  which  Rameau  has  deduced  his  system 
from  data  so  incomplete  ;  and  it  may  be  said,  without  exag- 
geration, that  he  has  inaugurated  a  new  era  in  the  theory  of 
music. 

The  celebrated  Tartini  published  in  1754  a  treatise  on 
Harmony,  in  which  he  took  as  his  starting-point  resultant 
tones,  which  he  thought  he  had  discovered,  and  which  he 
had  observed  when  he  played  two  chords  at  once.  Tartini 
calls  such  tones  of  the  series  i,  2,  3,  &c.,  monad  harmonics y 
from  the  concurrence  of  which  results  a  sound  All  har- 
mony, he  says,  is  comprised  between  the  monad,  or  com- 
ponent unison,  and  the  full  sound,  or  compound  unison. 
He  then  enumerates  the  resultant  tones  of  musical  in- 
tervals, always  mistaking  the  octave,  and  finds  that  the 
different  intervals  may  be  so  arranged  as  to  give  the  same 


250  ACOUSTICS. 

resultant  tone,  which  may  be  considered,  therefore,  their 
common  base,  &c.  &c. 

At  this  time  the  theory  of  music  had  not  emerged 
from  a  circle  of  ideas  completely  estranged  from  natural 
philosophy  and  physiology.  Generally,  the  propounders  of 
systems  have  lost  themselves  in  mystical  speculation.  The 
German  philosopher  Herbart  travelled  in  this  track ;  ac- 
cording to  his  views  any  two  sounds  suggest  to  the  mind  two 
ideas,  which  exercise  at  once  an  attractive  and  repulsive 
force.  In  the  soul  of  the  fifth,  hate  has  just  overcome 
love  ;  in  the  major  third,  the  two  powers  keep  an  armed 
neutrality.  The  most  curious  conclusion  is,  that  the 
adjusted  scale  is  that  which  satisfies  most  fully  the  musical 
ear!  and  that  Herbart  was  the  first  to  lay  the  foundations 
of  a  mathematical  psychology. 

Aristoxenus  had  eagerly  combated  the  arithmetical  sub- 
tleties of  the  Pythagorean  school.  He  has  found  many 
imitators  among  musicians  of  modern  times.  The  Spaniard 
Eximeno  published,  towards  the  end  of  the  last  century,  a 
work  in  which  he  demonstrates  that  music  has  no  manner 
of  connection  with  mathematics.  This  must  still  be  the 
opinion  of  M.  Fetis,  to  judge  from  the  preface  to  his  "  Traite 
d' Harmonic." 

This  learned  theorist  describes  in  the  following  terms  his 
discovery  of  the  principles  of  harmony — a  discovery  which 
he  made  one  day  in  May,  1831,  as  he  was  travelling  from 
Passy  to  Paris,  and  which  caused  him  such  emotion  that  he 
was  obliged  to  seat  himself  at  the  foot  of  a  tree  : — "  Nature 
furnishes  us,  for  elements  of  music,  with  only  a  multitude  of 
sounds,  which  differ  among  themselves  in  intonation,  dura- 
tion, and  intensity,  in  a  greater  or  less  degree. 

"Amongst  these  sounds,  those  which  differ  sufficiently  to 


MUSIC   AND   SCIENCE.  25 1 

affect  the  sense  of  hearing  distinctly  become  the  objects  of 
our  attention  ;  the  idea  of  the  relations  which  exist  between 
them  becomes  present  to  the  intelligence,  and  under  the 
action  of  sensitiveness  on  the  one  hand,  and  will  on  the 
other,  the  mind  arranges  them  in  different  series,  of  which 
each  one  corresponds  to  a  particular  order  of  emotions,  of 
feelings  and  ideas. 

"These  series  become  then  the  types  of  tones  and  rhythms 
which  have  necessary  consequences,  under  the  influence  of 
which  the  imagination  comes  into  exercise,  in  the  creation 
of  the  beautiful." 

After  such  assertions,  ought  he  not  to  have  made  the 
scale  ? 

There  appeared  in  Germiny,  in  1863,  a  book  which 
made  immediately  a  great  sensation.  It  was  "  La  Theorie 
de  la  Perception  des  Sons,"  by  Helmholtz.*  The  illustrious 
author  has  succeeded  in  reducing  to  physical  phenomena, 
susceptible  of  being  submitted  to  calculation,  the  secret  re- 
lations of  sympathy  and  antipathy  which  exist  between 
natural  tones,  and  explaining  the  cause  of  the  sensations 
which  we  experience  from  them. 

M.  Helmholtz  is  Professor  of  Physiology  at  the  Univer- 
sity of  Heidelberg,  which  boasts  also  Kirchhoff  and  Bunsea 
Already  illustrious  by  the  discoveries  with  which  he  has 
enriched  physiological  optics — it  is  to  him  that  we  owe  the 
ophthalmoscope — and  by  other  scientific  researches,  he  was 
the  man  who  was  needed  to  find  the  answer  to  an  enigma 
two  thousand  years  old. 

We  have  already  spoken  at  length  of  the  researches  to 
which  M.  Helmholtz  devoted  himself,  with  the  object  of 

*  Die  Lehre  von  den  Tonenipfindungen. 


252  ACOUSTICS. 

discovering  the  true  nature  of  tone,  and  we  have  mentioned 
his  experiments  on  beats  and  resultant  tones.  It  was  in 
that  way  that  he  discovered  the  key  to  harmony,  the  true 
principle  of  concords  and  discords. 

It  is  necessary  to  fully  understand  his  ingenious  argu- 
ments, and  with  that  view  we  first  consider  beats.  The 
disagreeable  sensation  that  they  give  us  is  easily  explained. 
All  intermittent  excitement  of  the  nerves  tires  us.  We  know 
the  unpleasantness  of  unsteady  light  like  that  of  a  flame 
blown  by  the  wind.  A  strong  steady  light  soon  dulls  the 
irritability  of  ths  retina,  just  as  continued  pressure  hardens  the 
skin ;  a  flickering  light,  on  the  contrary,  or  a  rapid  and  oft- 
repeated  pressure,  allows  the  nerves  to  retain  their  sensibility, 
and  becomes  for  that  reason  a  source  of  pain.  Tickling 
excites  the  epidermis  in  the  same  way  an  intermittent  sound 
irritates  the  ear,  and  hence  it  is  that  beats  are  felt  to  be  a 
source  of  discord. 

Sauveur  had  divined  the  same  reason.  "Beats,"  he 
says,  "do  not  please  the  ear,  because  of  the  inequality  of 
the  sound,  and  it  is  very  probable  that  it  is  the  absence  of 
these  beats  which  renders  octaves  so  agreeable.  Following 
out  this  idea,  it  appears  that  the  chords  in  which  the  beats 
are  not  heard  are  just  those  that  musicians  call  harmonies, 
and  that  those  in  which  the  beats  are  perceived  are  discords; 
also  that  when  a  chord  is  discord  in  a  certain  octave,  and 
harmony  in  another,  it  is  because  it  beats  in  one  and  not  in 
the  other ;  it  is  then  called  an  imperfect  concord.  If  this 
hypothesis  be  true  it  will  reveal  the  true  source  of  the  rules 
of  composition,  till  now  unknown  to  philosophy,  which 
referred  almost  entirely  to  the  judgment  of  the  ear.  Natural 
judgments  of  this  kind,  however  foolish  they  may  some- 
times appear,  are  not  in  reality  so ;  they  have  some  very 


MUSIC  AND  SCIENCE:  253 

real  causes,  the  knowledge  of  which  belongs  to  Philosophy, 
provided  she  were  able  to  put  herself  in  possession  of  it." 

Sauveur  (or  rather  Fontenellc,  the  historian  of  the 
Academy)  adds  afterwards,  in  returning  to  this  idea,  that 
what  is  real  harmony  of  chords  has  probably  not  been 
fixed  by  Nature,  and  that  what  is  called  a  fine  ear  is  quite 
as  much  the  result  of  long  custom,  of  old  habits,  and  of 
arbitrary  prejudices,  as  of  an  inborn  faculty.  He  would 
thus  explain  the  great  difference  that  is  found  between 
nations  in  their  taste  for  music. 

These  ideas  were  not  further  developed,  and  they  fell 
into  oblivion.  It  is  only  recently  that  M.  Helmholtz  has 
entered  upon  the  same  investigation  with  all  the  resources 
of  modern  science,  and  has  unravelled  the  physical  principles 
of  harmony. 

In  studying  beats,  M.  Helmholtz  first  proves  that  the 
degree  of  roughness  which  they  give  to  a  musical  interval 
does  not  depend  solely  upon  their  frequency;  they  become 
less  irritating  in  the  bass  octaves,  where  the  same  number  of 
beats  correspond  to  a  larger  interval.  Thus,  the  minor 
second,  si3 — doh4,  is  very  discordant,  while  the  fif.h,  doh — sol, 
is  a  harmony ;  and  yet  these  two  intervals  give  alike  thirty- 
three  beats  in  a  second.  This  circumstance  is  explained  by 
the  greater  difference  of  the  strings,  which  answer  to  a  larger 
interval.  The  sol  does  not  vibrate  the  string  allotted  to 
doh,  and  the  doh  does  not  vibrate  the  string  sol,  whence  it 
follows  that  resonance  is  powerless  to  unite  the  two  notes  on 
the  same  string,  and  to  give  rise  to  beats ;  on  the  contrary, 
the  notes  si  and  doh  make  a  great  number  of  strings  vibrate 
in  common,  which  renders  their  beats  perceptible  to  the 
acoustic  nerve. 

When  the  beats  are  observed  in   two   tones   between 


254  ACOUSTICS. 

which  the  interval  is  very  great,  the  phenomenon  is  due  to 
the  harmonics,  or  rather  to  the  resultant  tones.  Thus  doh^ 
the  harmonic  of  doh,  will  beat  with  all  the  notes  which  it 
may  happen  to  approach ;  for  instance,  with  re2  or  si,  even 
when  these  notes  occur  as  harmonics  of  another  fundamental 
tone.  Two  tones,  too  far  removed  to  touch  each  other 
directly,  may  then  be  in  opposition  through  the  medium 
of  their  satellites;  thus,  mi3,  the  harmonic  of  doh,  will 
beat  with  mit?3  which  carries  the  colours  of  lat>.  But  the 
struggle  may  even  take  place  under  the  same  roof;  when 
two  harmonics  of  the  same  note  find  themselves  too  close 
together  they  quarrel.  Thus,  the  harmonics  8  and  9, 
or  9  and  10,  which  differ  only  by  a  tone,  always  beat, 
and  disturb  the  internal  harmony  of  the  tone,  wherever  they 
are  at  all  prominent.  Their  presence  explains  the  harshness 
of  the  trumpet,  and  of  strained  bass  voices. 

When  two  sounds  of  whatever  tone  make  exactly  the 
octave,  the  harmonics  of  the  sharper  note  are  superposed 
upon  the  harmonics  of  the  flat 

Doh  ...    i      2      3      4      5      6      7      8      9      10  ... 

Dohs...  2  4  6  8  ip   .    .    . 

doh  doh,     sol,   doh,   mi,  sol#3   las   doh«    re«     mi4   ... 

From  that  time  there  are  no  more  beats ;  but  however  little 
the  chord  may  be  disturbed,  we  become  aware  of  it  by  the 
great  tumult  that  the  divided  harmonics  produce.  The 
doha  will  beat  with  the  untrue  doh2,  the  doh3  with  the  untrue 
dohv  and  so  on. 

The  reason  why  the  octave  is  the  consonant  interval  par 
excellence  of  which  the  ear  has  the  most  correct  appreciation 
is  easily  seen.  The  virtual  or  eventual  beats  of  the  harmonics 


MUSIC  AND   SCIENCE.  255 

distinguish  it  by  their  energy,  the  least  discord  betraying  itself 
by  a  great  cacophony.  The  other  concords  are  much  less 
characteristic,  as  we  shall  see.  Take,  for  instance,  the 
twelfth  1:3,  and  the  following  will  be  the  order  of  the  two 
series  : — 

Doh...  I         23456789..* 

I  I  I 

Sol  ...  3  6  9    •     •    • 

doh       doh,    sola     doh,     mis     sol,      .  .  .     doh4    re*  .       •     • 

The  coincidence  of  the  harmonics  again  takes  place 
here ;  but  it  is  less  important.  If  the  doh  be  a  little  untrue, 
the  harmonics  3,  6,  9,  which  it  has  in  common  with  the  sol^ 
are  divided  and  beat ;  but  they  are  weaker  than  the  har- 
monics of  a  less  elevated  order,  which  divide  when  the 
interval  of  the  octave  is  adjusted;  their  beats  are  not  so 
perceptible,  and  then  the  concord  is  less  distinct. 

The  other  concords — fifths,  fourths,  thirds,  &c. — contain 
already  elements  of  discord ;  here  the  harmonics  are  super- 
posed only  partially,  but  there  remains  the  germ  of  discord. 
Thus,  for  example,  in  the  fifth  : — 

Doh...   2  4  6  8  10          12      .    .    . 

I  I 

Sol ...  3  6  9  12      ... 

doh    sol    doh,         sol,          doh,  re,    tnis          sol,      ... 

The  so!2  and  the  so!3  are,  at  the  same  time,  the  harmonics 
of  doh  and  sol,  and  coincident  when  the  fifth  is  exact ;  but 
the  re3  of  the  series  of  SOL  can  beat  with  the  doh3  and  the 
mi3  of  the  series  of  DOH.  The  concord  of  the  fifth  is  then 
not  absolutely  pure,  besides  which  it  is  less  characteristic 
than  the  octave;  for  a  false  fifth  only  makes  those  harmonics 


256  ACOUSTICS. 

beat  which  are  of  the  same  class  as  those  that  beat  a  false 
twelfth. 

The  same  may  be  said  of  the  other  harmonious  chords. 
The  more  slightly  raised  the  harmonics  are  which  form 
the  coincidence,  the  purer  is  the  interval,  and  the  better  dis- 
tinguished by  the  eventual  beats  of  these  harmonics. 

In  the  intervals  where  there  exist  harmonics  which  have 
the  power  to  disturb  the  chord,  it  is  necessary  to  take 
account  of  the  juxtaposition  more  or  less  close  of  these 
notes,  for  the  beats  will  be  so  much  the  more  slow  in  pro- 
portion to  their  nearness.  We  have  already  said  that  the 
impression  made  by  thirty-three  beats  in  the  second  is  very 
disagreeable ;  beats  much  more  rapid  than  this  cease  to  be 
perceptible  ;  and  very  slow  beats,  instead  of  annoying  the 
ear,  give  to  the  music  a  solemn  character,  or  an  expression 
of  trembling  emotion  like  that  produced  by  the  tremulo  of 
the  voice.*  It  follows  that  an  interval  will  be  so  much  the 
more  discordant,  as  it  supplies  a  larger  number  of  less 
elevated  harmonics  which  are  able  to  produce  beats  of  a 
certain  rapidity. 

On  these  principles  it  is  easy  to  calculate  a  priori  the 
degree  of  purity  of  different  intervals  considered  in  all  parts 
of  the  musical  scale.  M.  Helmholtz  calls  an  interval  in  which 
one  of  the  two  given  notes  coincides  with  a  partial  tone  of 
the  other,  an  absolute  or  free  consonance,  for  in  that  case 
there  is  also  coincidence  between  all  the  respective  har- 
monics. To  this  category  belong  unison,  successive  octaves, 
the  twelfth,  seventeenth,  &c.  The  intervals  which  imme- 
diately follow  in  point  of  purity  are,  first  the  fifth,  then  the 

*  There  is  found  in  modern  organs,  in  fact,  a  regular  arrange- 
ment for  making  beats.  The  effect  of  the  register  called  nnda  marts  is 
made  also  ty  slow  beats. 


MUSIC  AND   SCIENCE. 

fourth,  which  may  be  called  perfect 
concords ;  the  major  sixth  and  third 
are  medium  concords ;  the  minor  sixth 
and  third  are  but  imperfect  ones.  Yet 
the  beats  of  the  thirds  are  very  sensible 
in  the  deep  notes  of  the  scale,  and 
they  were  not  admitted  into  the  group 
of  imperfect  concords  until  the  end 
of  the  twelfth  century.  The  employ- 
ment of  minor  sixths  and  thirds  is  never 
justified  except  by  necessities  in  the 
formation  of  chords. 

If  the  intervals  be  split,  the  major 
fifth  and  third  are  improved  (they 
change  into  the  major  tenth  and 
twelfth) ;  the  fourth,  the  minor  third, 
and  the  sixth,  on  the  contrary,  become 
more  discordant. 

M.  Helmholtz  tried  to  make  these 
phenomena,  and  the  laws  which  regulate 
them,  evident  by  means  of  a  figure, 
which  represents  in  a  very  irregular 
curve  the  relative  degree  of  discord  or 
any  two  notes  of  a  violin,  calculated 
according  to  the  intensity  and  frequency 
of  the  beats  of  the  superior  tones  of 
those  notes,  supposing  that  the  highest 
effect  would  be  thirty-three  beats  in  a 
second.  Upon  a  straight  line,  by  which 
is  represented  a  note  which,  starting 
from  doh3,  rises  by  insensible  degrees  to 
the  double  octave  dohs,  stand  the  Cor- 


257 


258  ACOUSTICS. 

dillera  of  displeasure  (Fig.  109).  Valleys  mark  the  position 
of  unison  of  the  fifth,  the  octave,  the  twelfth,  and  the  double 
octave.  The  Chimborazo  of  discord  occurs  quite  close  to 
unison,  where  the  least  discord  produces  the  most  percep- 
tible beats.  More  or  less  distinct  unevenness  distinguishes 
the  other  discordant  regions  ;  and  more  or  less  deep  depres- 
sions, the  various  degrees  of  concord. 

The  influence  of  resultant  tones  is  in  every  way  analogous 
to  that  of  superior  or  harmonic  tones.  The  union,  then,  of 
two  tones  accompanied  by  their  harmonics,  the  first  differen- 
tial sounds,  produces  only  the  beats  pointed  out  as  being 
those  of  harmonics ;  and,  as  they  are  in  general  much  more 
feeble  than  harmonics,  the  consideration  of  them  is  less 
important  for  practical  purposes,  where  we  have  to  do 
only  with  musical  tones  that  have  harmonics;  but  in  treating 
of  simple  tones,  it  is  necessary  to  have  recourse  to  the  beats 
of  resultant  tones,  to  account  for  discords,  and  to  characterise 
harmonics.  Thus  the  first  differential  sound  of  the  octave 
coincides  with  the  deepest  of  two  given  notes,  and  can 
therefore  beat  with  it,  since  the  chord  is  disturbed;  and 
this  is  one  means  of  judging  of  the  accuracy  of  an  octave 
formed  by  two  simple  notes.  The  fifth  again,  and  perhaps 
also  the  fourth,  are  characterised  by  resultant  tones;  but 
the  other  intervals  lose  all  clearness  and  decision  when 
only  simple  tones  are  employed.  And  this  is,  in  fact, 
the  reason  why  empty  harmonic  tones  are  improper  in 
musical  harmony:  they  can  only  be  used  to  strengthen 
richer  tones.  This  remark  applies,  for  instance,  to  the  large 
closed  pipes  of  an  organ.  If  a  piece  of  music  be  played 
upon  an  organ  with  the  register  closed,  it  has  neither 
character  nor  energy ;  the  absence  of  harmonics  makes  it 
very  difficult  to  distinguish  harmonies  from  discords,  and 


MUSIC  AND   SCIENCE.  259 

this  want  of  clearness  renders  the  music  so  weak  and  soft 
as  to  be  tedious. 

The  sound  of  the  flute  contains,  besides  the  fundamental 
tone,  its  sharpened  octave,  and  sometimes  the  twelfth ;  the 
intervals  of  the  octave  and  the  fifth  are  well  denned ;  the 
thirds  and  sixths  only  very  indistinctly.  It  is  a  common 
saying  that  the  worst  thing  in  the  world  after  a  flute  solo  is 
a  duet  on  two  flutes  ;  yet  this  instrument  becomes  very 
useful  when  it  is  played  in  concert  with  others  which  have 
more  energy.  The  same  thing  may  be  said  of  harmoniums 
with  diapasons.  Therefore  we  see  that  the  quality  of 
musical  intervals  varies  necessarily  with  the  tone  of  the 
instruments. 

The  most  extended  analysis  of  the  sound  of  instruments 
has  shown  that  the  ear  delights,  above  all,  in  tones  in  which 
the  two  first  harmonics  (octave  and  twelfth)  are  strongly 
accentuated,  the  two  following  somewhat  modified,  and  the 
others  less  and  less  perceptible.  Taking  this  as  a  starting- 
point,  it  is  easy  to  explain  the  particular  effect  of  each 
instrument,  and  to  establish  a  priori  a  number  of  practical 
rules  known  to  musicians. 

It  is  clear  that  the  consideration  of  beats  helps  to  the 
understanding  of  the  part  that  whole  numbers  play  in  the 
fixing  of  musical  intervals.  Fourier's  law,  in  virtue  of  which 
every  sonorous  movement  is  an  accumulation  of  simple 
notes,  becomes  thus  the  true  base  of  counterpoint,  since 
concords  are  derived  from  the  superposition  of  partial  sounds, 
and  discords  from  their  antagonism. 

We  have  now  to  speak  of  sounds  with  respect  to  their 
effect  produced  when  they  are  combined  in  music ;  this 
subject  encroaches  upon  the  domain  of  aesthetics,  where  we 
have  no  longer  fixed  and  invariable  principles  to  guide  us 

R    2 


260  ACOUSTICS. 

like  those  of  purely  physical  sciences.  Musical  scales, 
modes,  &c.,  have  been  developed,  step  by  step,  in  the  course 
of  centuries;  and  the  changes  that  the  tastes  of  different 
nations  have  wrought  in  them  are  a  sufficient  proof  of  the 
instability  of  their  foundations.  The  science  of  counter- 
point is  based,  in  part  at  least,  upon  laws  capable  of  improve- 
ment, and  it  would  be  rash  to  affirm  that  it  has  yet  reached 
its  last  point  of  development.  Nevertheless,  here  again  we 
find  some  general  laws  which  seem  to  have  guided  artists 
unknown  to  themselves,  and  which  spring  naturally  from 
those  which  we  have  already  established.  These  laws  prove 
the  philosophical  necessity  of  rules  to  which  ignorant 
groping  has  led. 

Thus  the  formation  of  multiple  chords  rests  upon  the 
same  principles  as  that  of  consonant  intervals.  It  is  necessary 
that  the  three  intervals  between  the  three  notes  which  com- 
pose a  triple  chord  should  be  separately  consonant,  in  order 
that  the  chord  may  be  so.  Intervals  which  exist  in  dif- 
ferent chords  may  be  classified  under  different  degrees  of 
consonance. 

The  difference  between  major  and  minor  modes  may 
consist  in  the  resultant  tones  which  are  formed  by  the  com- 
bination of  three  notes.  In  major  chords  the  resultant 
tones  are  only  repetitions  of  notes  given  in  lower  octaves. 
It  is  found  that  in  minor  chords  this  does  not  happen ;  the 
resultant  tones  there  are  formed  by  the  harmony,  and 
form  major  chords  which  accompany  the  minor.  This 
intervention  of  a  strange  element,  and  probably  also  the 
very  feeble  beats  of  resultant  tones  of  the  second  order, 
give  to  the  minor  chord  something  mysterious  and  un- 
decided, that  all  musicians  have  felt  without  being  able 
to  account  for. 


MUSIC   AND    SCIENCE. 


26l 


In  the  accompanying  example  the  major  and  minor 
chords  are  printed  in  minims;  the  resultant  tones  of  funda- 
mental notes,  in  crotchets ;  the  resultant  tones  due  to  the 
combination  of  fundamental  notes  and  harmonics,  by  quavers 
and  semiquavers.  A  rest  placed  after  a  note  denotes  that  it 
is  slightly  higher  than  the  sound  it  ought  to  represent. 


Passing  on  to  the  melodious  combination  of  sounds,  we 
find  that  melody  depends  like  harmony  upon  the  phenome- 
non of  superior  tones,  inasmuch  as  these  tones  determine  the 
affinity  of  sounds,  just  as  the  affinity  of  chords  results  from 
the  notes  which  are  common  to  them.  Melody  is  the 
succession  of  notes  following  each  other  in  an  order  pleasant 
to  the  ear.  According  to  Rameau  and  D'Alembert,  it  springs 


262  ACOUSTICS. 

from  harmony,  and  the  effect  of  it  will  be  found  expressed 
or  unexpressed  in  the  harmony,  and  especially  in  the  un- 
expressed fundamental  bass.  But  as  homophonous  song 
existed  long  before  polyphonous  music,  or  music  in  har- 
mony, we  are  compelled  to  seek  an  independent  origin  for 
melody. 

We  notice  first  that  melody  is  a  movement  which  is 
produced  by  a  change  in  the  height  of  notes,  and  which  we 
can  conceive  imitated  by  mechanical  movements.  But  the 
mind  would  not  have  been  able  to  appreciate,  or  even  to 
feel,  these  shades  of  expression  if  the  progression  of  the 
notes  had  not  been  arranged  according  to  a  definite  value 
— that  is,  by  intervals  of  tones  or  half-tones,  and  in  a  fixed 
rhythm. 

The  bar  helps  us  to  divide  time;  the  progression  of 
notes  by  tones  or  semitones  allows  us  to  separate  the 
height  of  notes  into  fractional  parts ;  and  thus  we  understand 
movement  by  rhythm  and  melody.  The  sensations  that  we 
experience  at  the  sight  of  a  rough  sea,  when  the  waves  follow 
each  other  at  regular  intervals,  are  of  the  same  nature.  In 
the  voice  of  the  wind  the  notes  blend  without  intermission, 
therefore  they  produce  upon  us  a  painful  and  confused 
impression,  through  the  absence  of  all  proportion  and 
distinctness.  Music,  on  the  contrary,  has  a  standard  for 
measuring  the  ascending  and  descending  movement  of  tones, 
and  this  standard  is  the  scale. 

But  why  were  the  notes  of  which  the  scale  is  composed 
adopted?  Was  there  a  reason  for  it?  Why  do  we  find 
there  the  octave,  with  its  fifths,  fourths,  and  thirds?  The 
answer  is  easy,  after  what  we  have  already  remarked  concern- 
ing partial  tones  or  harmonics.  The  following  table  repre- 
sents the  harmonics  with  consonant  intervals :— 


MUSIC   AND   SCIENCE.  263 

Tonic  (i)  123456789 

Octave  (2)  —      2     —     4      —     6     —     8     — 

Twelfth  (3)  —    —      3     _    _     6     —    —     9 

Fifth  (!)—    —3—    _6—    —9 

Fourth  (|)  __—      4     _    _    _     g     — 

Third  (f)      — -5- 

Third  (f)  _____      6      —     —     — 

The  octave  with  its  attendant  harmonics  being  com- 
prised in  the  tone  of  the  voice,  it  is  clear  that  in  ascending 
the  octave  a  fractional  part  of  the  tonic  is  constantly  re- 
peated. Therefore  we  may  say,  with  Rameau,  that  the 
sharpened  octave  simply  answers  to  the  tonic,  the  harmonics 
of  which,  2,  4,  6  ...  .it  reproduces.  It  is  in  this  sense 
that  the  successive  octaves  of  a  key-board  are  only  repe- 
titions of  the  same  scale. 

The  twelfth,  being  the  third  partial  tone  of  the  tonic,  is 
equally  expressed  by  the  tonic,  but  less  completely  than  the 
octave,  because  it  only  produces  the  harmonics  3,  6  ... 
of  the  tonic.  Lowering  it  an  octave,  we  have  the  fifth,  of 
which  the  second  partial  tone  reproduces  the  harmonic 
3  of  the  tonic,  the  fourth  the  harmonic  6  of  the  tonic, 
and  so  forth.  The  fifth  is  then,  again,  a  partial  echo  of  the 
tonic  ;  but  at  the  same  time  it  contains  new  notes  which  are 
not  comprised  in  it,  and  has  therefore  less  affinity  for 
the  tonic  than  the  octave  and  the  twelfth.  The  affinity  of 
the  fourth  is  still  less,  for  there  it  is  only  the  third  partial 
sound,  which  corresponds  with  the  fourth  of  the  tonic. 
Therefore  it  was  that  the  polyphonous  songs  of  the  Middle 
Ages  were  accompanied  by  fifths.  The  thirds  and  sixths 
answer  to  the  tonic  still  less  perceptibly ;  they  were  intro- 
duced into  music  only  at  the  time  when  tnie  harmony  began 
to  develop  itself. 

M.    Helmholtz  calls   those  tones  which  have  at  least 


264  ACOUSTICS. 

one  harmonic  in  common,  affinities  of  the  first  degree ; 
and  two  sounds  which  have  an  harmonic  in  common  with  a 
third  sound,  he  calls  affinities  of  the  second  degree.  Build- 
ing upon  this  foundation,  he  succeeded  in  constructing  in  a 
very  reasonable  manner  a  diatonic  scale  of  notes,  which 
have  either  the  first  or  second  degree  of  affinity  for  the 
tonic. 

The  direct  relatives  of  the  tonic  doh  are  composed  of 
the  notes  doh2,  sol,  fa,  la,  mi,  and  mi,,  if  we  stop  at  the  first 
six  harmonics,  the  others  being  too  weak  to  determine  the 
affinity.  We  have  then  the  scales — 

Doh mi  —  fa  —  sol  — la doha  ; 

or — 

Doh mifr  —  fa  —  sol  —  la doh2 ; 

for  two  notes  so  similar  as  mi  and  mi  ?  could  not  be  intro- 
duced into  the  same  scale. 

In  order  to  divide  the  two  excessive  intervals  which  exist 
in  this  series,  it  is  necessary  to  have  recourse  to  the  rela- 
tives of  sol,  which  consist  of  the  notes  doh,  re,  mip,  si,  doh2. 
The  re  and  the  si  are  united  to  doh  by  an  affinity  of  the 
second  degree,  and  by  inserting  them  into  the  scales  given 
above,  the  diatonic  scale 

Doh  —  re  —  mi  —  fa  —  sol  —  la  —  si  —  doha 

is  obtained,  which  becomes  the  minor  ascending  scale  if  we 
put  mifr  in  the  place  of  mi.  The  re  which  would  be  taken 
amongst  the  relatives  of  fa,  would  differ  by  a  comma  from 
the  re  fixed  by  sol.  These  examples  suffice  to  render  the 
method  followed  by  M.  Helmholtz  comprehensible. 

In  studying  the  rules  of  harmony,  it  becomes  evident 
that  chords,  considered  as  complex  sounds,  have  amongst 


MUSIC  AND   SCIENCE.  265 

them  the  same  relations  of  affinity  as  the  notes  of  the  scale, 
in  consequence  of  the  coincidence  of  some  of  their  notes. 
The  importance  of  the  tonic  in  modern  music,  or  that  which 
M.  Fetis  calls  the  principle  of  tonality,  is  also  explained  by 
the  nature  of  the  superior  tones  of  the  tonic.  These  clear  and 
simple  principles  have  allowed  of  the  fundamental  rules  of 
composition  being  deduced  from  mathematical  considera- 
tions, which  M.  Helmholtz  has  done.  Nevertheless,  it 
must  be  confessed  that  the  theory  of  music  is  not  yet  com- 
pleted ;  all  the  deductions  that  M.  Helmholtz  has  drawn 
cannot  be  considered  fully  proved,  and  they  are  not  univer- 
sally admitted.  For  instance,  M.  Arthur  von  Oettingen 
has  criticised  (and  with  reason)  the  explanation  that  M. 
Helmholtz  gives  of  the  difference  between  major  and  minor, 
for  the  phenomenon  of  harmonics  is  sometimes  very  little 
apparent.  M.  d'Oettingen  traces  this  difference  to  the  re- 
ciprocal principles  of  tonics  and  phonics. 

The  tonicity  of  an  interval  or  of  a  chord  consists  in  the 
possibility  of  considering  it  as  a  group  of  harmonics  having 
the  same  fundamental  tone.  Thus,  the  major  chord  is  formed 
of  the  harmonics  4,  5,  6  of  the  tonic,  or  fundamental  bass, 
i.  The  phonicity  of  that  interval  would  be  th2  inverse 
property  of  having  an  harmonic  in  common  ;  the  minor  chord 
i>  i>  i  nas  tne  tone  I  as  its  common  harmonic  or  phonic. 
The  major  chord  has  for  its  phonic  60 ;  the  minor  chord  has 
for  its  tonic  ^.  The  relations  may  be  explained  as  follows: 


A       -  i '.  i '  1  -  *  4-5-6-6o 

Tonic     —  Minor     —    Phonic  Tonic    —    Major     —  Phonic 


chord 
fa        —  la-doh-mi — 


mi 


chord 
doh        — doh-mi-sol  — 


Musicians  call  doh  the  tonic,  and  sol  the  dominant,  of 


266  ACOUSTICS. 

the   scale  of  doh  major,  which  may  be  written   in   this 
way  :  — 

Doh        re  mi        fa        sol        la        si        doh 

i         8  I        !        i        i       ¥       2 

M.  d'Oettingen  calls  mi  the  phonic,  and  la  the  leading 

note,  of  la  minor  ;  and  writes  this  scale  in  the  following 
manner  :  — 

Mi        fa  sol        la        si         doh        re        mi 


In  developing  this  dualism  he  establishes  the  parallel  con- 
struction of  the  major  and  minor  modes.  But  we  must 
draw  to  a  close  details  which  have,  perhaps,  already  weaned 
the  reader. 

If  it  be  possible  thus  to  establish  a  priori  the  most  im- 
portant laws  of  music,  however  grand  may  be  the  result 
with  regard  to  the  philosophy  of  the  art,  it  does  not  follow 
that  the  knowledge  of  these  laws  is  all  that  is  required  in  a 
musician.  We  must  here  repeat  what  D'Alembert  has  said 
in  the  preface  to  his  book  on  music  :  "  Nature  must  do  the 
rest  ;  without  her,  no  one  will  compose  better  music  for 
having  read  these  elements,  any  more  than  he  would  write 
good  verses  for  possessing  Richelet's  Dictionary.  In  a 
word,  it  is  the  elements  of  music  that  I  pretend  to  give,  and 
not  the  elements  of  genius." 

In  the  works  of  art  that  we  admire,  we  instinctively 
divine  a  secret  law  which  the  artist  has  obeyed,  however 
ignorantly,  and  it  is  in  this  sense  that  we  must  use  the  words 
of  Leibnitz  so  often  quoted  :  Musica  est  exerdtium  arith- 
metier  occultum  nescientis  se  numerare  animi 

When  the  law  is  so  manifest  that  it  instantly  strikes  the 
eye,  we  feel  the  intention  and  the  calculation,  and  the  work 


MUSIC   AND   SCIENCE.  267 

does  not  move  us ;  for  one  essential  condition  of  admira- 
tion is,  not  to  understand  completely.  Admiration  ceases 
as  soon  as  we  feel  ourselves  on  an  equality  with  the 
artist.  This  is  the  unconscious  law  which  distinguishes  a 
work  of  art  from  a  systematic  and  calculated  production ;  it 
must  not  therefore  be  supposed  that  science  can,  or  ought 
to,  discover  and  lay  bare  all  the  resources  of  the  creative 
intellect 


THE    END. 


UNIVEI 


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