﻿Sharpness 
  of 
  Resonance 
  under 
  Sustained 
  Forcing. 
  141 
  

  

  three-valved 
  brass 
  instruments 
  of 
  any 
  pitch, 
  the 
  second 
  valve 
  

   alone 
  adds 
  sufficient 
  tubing- 
  to 
  lower 
  the 
  pitch 
  a 
  semitone, 
  

   and 
  the 
  first 
  valve 
  alone 
  adds 
  sufficient 
  to 
  lower 
  it 
  a 
  whole 
  

   tone. 
  The 
  two 
  used 
  together 
  accordingly 
  lower 
  the 
  pitch 
  

   approximately 
  a 
  tone 
  and 
  a 
  half. 
  The 
  third 
  valve 
  is 
  usually 
  

   employed 
  only 
  in 
  conjunction 
  with 
  one 
  or 
  both 
  of 
  the 
  others. 
  

   It 
  is 
  often 
  tuned 
  so 
  that 
  with 
  the 
  second 
  valve 
  the 
  pitch 
  is 
  

   lowered 
  two 
  tones. 
  If 
  now 
  a 
  total 
  lowering 
  of 
  three 
  tones 
  

   is 
  desired, 
  it 
  is 
  obvious 
  that 
  the 
  simultaneous 
  use 
  of 
  the 
  first 
  

   valve 
  is 
  unable 
  to 
  effect 
  this. 
  For, 
  with 
  the 
  second 
  and 
  third 
  

   valves 
  already 
  down, 
  the 
  tubing 
  is 
  a 
  quarter 
  longer 
  than 
  

   originally, 
  hence 
  the 
  first 
  valve 
  needs 
  to 
  be 
  itself 
  a 
  quarter 
  

   longer 
  than 
  originally 
  in 
  order 
  to 
  be 
  able 
  to 
  depress 
  by 
  a 
  

   whole 
  tone 
  the 
  pitch 
  which 
  is 
  already 
  depressed 
  by 
  two 
  

   tones. 
  It 
  may 
  thus 
  easily 
  happen 
  that 
  the 
  note 
  with 
  all 
  

   three 
  valves 
  down 
  (immediately 
  above 
  note 
  No. 
  2, 
  written 
  as 
  

   C 
  t) 
  is 
  about 
  a 
  quarter 
  of 
  a 
  tone 
  sharp, 
  and 
  needs 
  u 
  coaxing 
  " 
  

   by 
  the 
  lips 
  and 
  breath 
  of 
  the 
  player 
  to 
  be 
  blown 
  in 
  tune. 
  

  

  But 
  the 
  three 
  valves 
  are 
  not 
  needed 
  for 
  any 
  higher 
  note 
  

   than 
  this 
  C 
  J 
  (between 
  the 
  notes 
  Nos. 
  2 
  and 
  3, 
  which 
  are 
  a 
  

   musical 
  fifth 
  apart). 
  And 
  at 
  this 
  low 
  pitch 
  the 
  considerable 
  

   range 
  of 
  resonance 
  available 
  makes 
  the 
  requisite 
  coaxing 
  

   comparatively 
  easy 
  on 
  a 
  small 
  instrument 
  like 
  the 
  trumpet 
  

   or 
  cornet. 
  An 
  octave 
  higher, 
  where 
  the 
  same 
  mistiming 
  

   would 
  be 
  difficult 
  or 
  impossible 
  to 
  achieve 
  by 
  coaxing, 
  it 
  is 
  

   not 
  needed. 
  For 
  there 
  the 
  first 
  and 
  second 
  valves 
  suffice 
  to 
  

   give 
  the 
  chromatic 
  scale 
  in 
  the 
  gap 
  of 
  two 
  tones 
  between 
  

   notes 
  Xos. 
  4 
  ami 
  5. 
  

  

  On 
  large 
  instruments 
  like 
  the 
  euphonion 
  and 
  bombardon, 
  

   this 
  coaxing 
  or 
  forcing 
  is 
  not 
  so 
  easy. 
  It 
  is 
  accordingly 
  

   desirable 
  in 
  them 
  to 
  use 
  the 
  special 
  compensated 
  valves 
  

   which 
  give 
  a 
  very 
  close 
  approximation 
  to 
  the 
  lengths 
  of 
  

   tubing 
  theoretically 
  required 
  for 
  the 
  notes 
  to 
  be 
  produced 
  by 
  

   any 
  combination 
  of 
  the 
  valves. 
  But 
  the 
  present 
  theory 
  

   shows 
  why 
  these 
  compensated 
  valves 
  have 
  acquired 
  so 
  little 
  

   vogue 
  on 
  the 
  smaller 
  instruments. 
  For 
  the 
  faulty 
  intonation 
  

   due 
  to 
  the 
  combination 
  of 
  ordinary 
  valves 
  occurs 
  only 
  in 
  the 
  

   lower 
  part 
  of 
  the 
  compass, 
  and 
  there 
  the 
  proportionately 
  

   greater 
  range 
  of 
  resonance 
  enables 
  the 
  player 
  to 
  force 
  into 
  

   tune 
  the 
  comparatively 
  small 
  mass 
  of 
  air 
  contained 
  in 
  the 
  

   instrument. 
  

  

  Possible 
  Electrical 
  Examples. 
  — 
  In 
  the 
  case 
  of 
  forced 
  

   electrical 
  vibrations, 
  which 
  might 
  be 
  supposed 
  to 
  be 
  the 
  

   most 
  complicated 
  of 
  all, 
  it 
  is 
  easy 
  to 
  see 
  that 
  many 
  of 
  the 
  

   factors 
  of 
  the 
  case 
  are 
  entirely 
  at 
  our 
  own 
  disposal. 
  Thus, 
  

   by 
  modifying 
  the 
  values 
  of 
  the 
  inductance, 
  resistance, 
  and 
  

  

  