﻿Sharpness 
  of 
  Resonance 
  under 
  Sustained 
  Forcing, 
  139 
  

  

  fresh, 
  obtains 
  the 
  continuous 
  resonance 
  for 
  the 
  pedal 
  antici- 
  

   pated 
  by 
  me 
  and 
  thus 
  confirms 
  the 
  theory 
  here 
  put 
  forward. 
  

   It 
  also, 
  however, 
  supports 
  Mr. 
  Blaikley's 
  own 
  view 
  as 
  to 
  the 
  

   upper 
  partial 
  resonance. 
  For 
  he 
  felt 
  the 
  low 
  "F" 
  and 
  pedal 
  

   "0" 
  to 
  be 
  better 
  notes 
  than 
  those 
  between. 
  In 
  other 
  words, 
  

   in 
  his 
  experience, 
  the 
  resonance 
  was 
  spread 
  continuously 
  over 
  

   a 
  considerable 
  range 
  of 
  pitch 
  but 
  had 
  pimples 
  on 
  the 
  curve 
  

   at 
  two 
  special 
  pitches 
  whose 
  upper 
  partials 
  agree 
  with 
  some 
  

   of 
  the 
  natural 
  tones 
  of 
  the 
  instrument. 
  

  

  In 
  reporting 
  the 
  above 
  test 
  Mr. 
  Blaikley 
  also 
  expressed 
  

   his 
  agreement 
  with 
  my 
  view 
  as 
  to 
  the 
  pitch 
  of 
  the 
  pedal 
  

   being 
  sharp 
  on 
  some 
  instruments 
  and 
  flat 
  on 
  others. 
  He 
  

   writes: 
  '* 
  It 
  is 
  pretty 
  evident 
  that 
  on 
  the 
  large 
  conical 
  

   instruments 
  the 
  range 
  of 
  forced 
  notes 
  is 
  greater 
  upwards 
  

   than 
  downwards, 
  and 
  that 
  the 
  reverse 
  holds 
  good 
  on 
  instru- 
  

   ments 
  of 
  the 
  trombone 
  type, 
  and 
  I 
  quite 
  agree 
  with 
  you 
  as 
  

   to 
  the 
  cause 
  of 
  this." 
  

  

  It 
  may 
  be 
  noticed 
  that 
  in 
  Table 
  V. 
  only 
  two 
  low 
  ranges 
  

   of 
  resonance 
  are 
  usually 
  dealt 
  with 
  for 
  each 
  instrument. 
  

   The 
  higher 
  notes 
  did 
  not, 
  as 
  a 
  rule, 
  permit 
  of 
  flattening 
  or 
  

   sharpening 
  to 
  an 
  extent 
  measurable 
  by 
  semitones, 
  hence 
  their 
  

   omission 
  from 
  the 
  scheme. 
  But, 
  to 
  test 
  this 
  smaller 
  range 
  

   of 
  the 
  higher 
  notes 
  in 
  a 
  somewhat 
  closer 
  way, 
  a 
  B 
  \} 
  cornet 
  

   was 
  tuned 
  about 
  a 
  quarter 
  of 
  a 
  tone 
  sharper 
  than 
  the 
  piano 
  

   used 
  lor 
  comparison. 
  The 
  various 
  open 
  notes 
  of 
  the 
  instru- 
  

   ment 
  were 
  then 
  blown 
  with 
  an 
  endeavour 
  to 
  flatten 
  or 
  sharpen 
  

   their 
  pitches 
  so 
  as 
  to 
  elicit 
  a 
  resonance 
  from 
  the 
  corresponding 
  

   piano 
  strings, 
  whose 
  digitals 
  were 
  quietly 
  put 
  down 
  and 
  held. 
  

   In 
  this 
  manner, 
  from 
  the 
  pedal 
  note 
  of 
  the 
  cornet 
  four 
  strings 
  

   of 
  the 
  piano 
  were 
  set 
  in 
  vibration, 
  viz., 
  A 
  [?, 
  A, 
  B 
  [?, 
  and 
  B. 
  

   Thus 
  the 
  note 
  could 
  be 
  flattened 
  and 
  sharpened 
  by 
  about 
  

   three-fourths 
  of 
  a 
  tone 
  from 
  its 
  pitch 
  of 
  best 
  resonance, 
  say, 
  

   between 
  A 
  and 
  B 
  \>, 
  to 
  the 
  extremes 
  of 
  A\} 
  and 
  B. 
  With 
  

   note 
  Xo. 
  3 
  on 
  the 
  cornet 
  only 
  two 
  strings 
  could 
  be 
  made 
  to 
  

   vibrate 
  audibly, 
  viz., 
  F 
  and 
  F#. 
  Thus 
  this 
  note 
  could 
  only 
  

   be 
  flattened 
  and 
  sharpened 
  about 
  one-fourth 
  of 
  a 
  tone. 
  But 
  

   the 
  note 
  in 
  question 
  has 
  nominally 
  three 
  times 
  the 
  frequency 
  

   of 
  the 
  pedal. 
  It 
  might 
  accordingly 
  be 
  theoretically 
  expected 
  

   to 
  have 
  only 
  one-third 
  the 
  range 
  of 
  resonance, 
  as 
  appears 
  to 
  

   be 
  the 
  case. 
  

  

  As 
  to 
  the 
  absolute 
  values 
  of 
  the 
  range 
  and 
  sharpness 
  of 
  

   resonance 
  for 
  these 
  instruments, 
  more 
  exact 
  data 
  are 
  needed 
  

   for 
  their 
  determination 
  than 
  are 
  at 
  present 
  to 
  hand. 
  It 
  must, 
  

   suffice 
  now 
  to 
  make 
  a 
  rough 
  estimate 
  in 
  the 
  case 
  of 
  one 
  

   instrument, 
  the 
  cornet 
  in 
  B 
  \). 
  

  

  The 
  theoretical 
  values 
  are 
  the 
  quotients 
  of 
  k 
  and 
  p, 
  which 
  

  

  