﻿Vibration 
  Curves 
  of 
  Violin 
  G 
  String 
  and 
  Belli/. 
  239 
  

  

  length 
  from 
  the 
  bridge, 
  so 
  as 
  to 
  sound 
  middle 
  c^ 
  (saj 
  271*1 
  

   per 
  second). 
  

  

  Curves 
  25-28. 
  — 
  As 
  the 
  strings 
  of 
  a 
  violin 
  are 
  occasionally 
  

   tuned 
  to 
  other 
  pitches, 
  either 
  to 
  agree 
  with 
  accompanying 
  

   instruments 
  or 
  for 
  special 
  effects, 
  the 
  g 
  string 
  was 
  tuned 
  a 
  

   semitone 
  down 
  and 
  up, 
  also 
  a 
  tone 
  and 
  a 
  tone 
  and 
  a 
  half 
  up. 
  

   The 
  effects 
  obtained 
  are 
  shown 
  in 
  curves 
  25-28 
  respectively, 
  

   the 
  bo 
  win 
  o' 
  throuo-hout 
  beino- 
  at 
  one-seventh 
  of 
  the 
  strinor's 
  

   length 
  from 
  the 
  bridge. 
  It 
  can 
  be 
  seen 
  from 
  the 
  prints 
  that, 
  

   when 
  the 
  string 
  was 
  sharpened 
  more 
  and 
  more, 
  the 
  belly 
  

   responded 
  so 
  powerfully 
  that, 
  to 
  avoid 
  an 
  undue 
  amplitude, 
  

   the 
  string 
  needed 
  bowing 
  more 
  and 
  more 
  gently. 
  In 
  fact, 
  

   for 
  the 
  61? 
  the 
  string's 
  motion 
  is 
  barely 
  visible 
  in 
  the 
  original 
  

   plate, 
  though 
  the 
  belly's 
  motion 
  is 
  so 
  large. 
  (See 
  also 
  notes 
  

   on 
  curves 
  38-40.) 
  

  

  Curves 
  29-30 
  show 
  the 
  vibrations 
  from 
  the 
  g 
  string 
  when 
  

   flattened 
  and 
  sharpened 
  a 
  semitone 
  and 
  plucked 
  with 
  the 
  

   finger 
  at 
  one-seventh. 
  

  

  Cu7Tes 
  31-33 
  show 
  the 
  vibrations 
  from 
  the 
  combined 
  

   effect 
  of 
  the 
  g 
  string 
  at 
  concert-pitch 
  and 
  the 
  d' 
  string 
  

   (normally 
  at 
  305 
  per 
  second) 
  tuned 
  to 
  h, 
  J 
  and 
  at 
  concert- 
  

   pitch 
  respectively. 
  The 
  excitation 
  is 
  by 
  bowing 
  both 
  strings 
  

   at 
  one-seventh. 
  The 
  curious 
  character 
  of 
  these 
  curves, 
  

   amounting 
  in 
  one 
  place 
  to 
  an 
  undercutting 
  (curve 
  31) 
  is 
  due 
  

   to 
  the 
  fact 
  that 
  the 
  vibrations 
  of 
  the 
  d' 
  string 
  caused 
  the 
  

   mirror 
  to 
  rotate 
  slightly 
  about 
  a 
  vertical 
  axis, 
  thus 
  moving 
  

   the 
  spot 
  of 
  light 
  horizontally 
  on 
  the 
  photographic 
  plate. 
  

   Hence 
  these 
  curves 
  have 
  not 
  the 
  true 
  character 
  of 
  displace- 
  

   ment-time 
  curves. 
  Accordingly, 
  no 
  curve 
  is 
  given, 
  with 
  the 
  

   present 
  arrangement, 
  from 
  the 
  vibrations 
  of 
  the 
  d' 
  string 
  

   alone. 
  But 
  it 
  is 
  easily 
  seen 
  that 
  a 
  small 
  motion, 
  whether 
  

   vertical 
  or 
  horizontal, 
  superposed 
  upon 
  a 
  displacement-time 
  

   g-raph 
  of 
  much 
  larger 
  amplitude 
  gives 
  very 
  similar 
  results 
  ; 
  

   these 
  combined 
  effects 
  are 
  therefore 
  included 
  now. 
  

  

  Curves 
  31-35 
  show 
  the 
  combined 
  effects 
  of 
  d' 
  string 
  at 
  

   concert 
  pitch, 
  (i.) 
  with 
  the 
  g 
  string, 
  also 
  at 
  concert 
  pitch, 
  and 
  

   both 
  plucked 
  at 
  ^, 
  and 
  (ii.) 
  with 
  the 
  g 
  string 
  sounding 
  its 
  

   octave 
  harmonic, 
  and 
  both 
  bowed 
  at 
  ^q. 
  

  

  Curves 
  36-37. 
  — 
  Since 
  the 
  d' 
  string 
  vibratino- 
  alone 
  failed 
  

   to 
  act 
  satisfactorily 
  with 
  the 
  present 
  arrangement, 
  it 
  was 
  at 
  

   first 
  thought 
  that 
  the 
  same 
  would 
  apply 
  still 
  more 
  to 
  the 
  a' 
  

   and 
  e" 
  strings, 
  which 
  are 
  thinner 
  and 
  higher 
  in 
  pitch. 
  It 
  

   was 
  indeed 
  true 
  of 
  the 
  e" 
  string. 
  But 
  the 
  a^ 
  string, 
  on 
  the 
  

   contrary, 
  evoked, 
  by 
  bowing, 
  such 
  powerful 
  vibrations 
  of 
  

   this 
  particular 
  spot 
  of 
  the 
  belly 
  that 
  it 
  was 
  very 
  difiicult 
  to 
  

   bow 
  so 
  lightly 
  as 
  to 
  keep 
  these 
  vibrations 
  within 
  reasonable 
  

  

  