﻿1874.] 
  Mr. 
  A. 
  J. 
  Ellis 
  on 
  Musical 
  Duodenes. 
  19 
  

  

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  5 
  

  

  Since, 
  then, 
  the 
  duodene 
  of 
  C 
  is 
  precisely 
  adapted 
  for 
  placing 
  on 
  our 
  

   ordinary 
  manuals, 
  and 
  no 
  corresponding 
  tones 
  which 
  have 
  to 
  be 
  intro- 
  

   duced 
  within 
  these 
  limits 
  will 
  be 
  more 
  than 
  two 
  or 
  three 
  commas 
  sharper 
  

   or 
  natter 
  than 
  these, 
  such 
  corresponding 
  tones 
  (owing 
  to 
  our 
  habits 
  of 
  

   reading 
  musical 
  notes 
  into 
  directions 
  for 
  usiug 
  digitals) 
  will 
  be 
  all 
  fitted 
  

   for 
  being 
  played 
  on 
  the 
  same 
  digitals. 
  This 
  is 
  the 
  most 
  important 
  point 
  

   in 
  the 
  practical 
  construction 
  of 
  instruments, 
  and 
  is 
  for 
  the 
  first 
  time 
  

   pointed 
  out 
  in 
  this 
  paper. 
  

  

  Another 
  important 
  result 
  is, 
  that 
  if 
  we 
  take 
  any 
  12 
  consecutive 
  skhistic 
  

   tones 
  in 
  order 
  of 
  Fifths, 
  or 
  8 
  consecutive 
  tones 
  in 
  that 
  order, 
  and 
  4 
  

   others 
  separated 
  from 
  them 
  by 
  24 
  or 
  48 
  Fifths, 
  although 
  such 
  tones 
  will 
  

   not 
  form 
  a 
  duodene, 
  they 
  will 
  be 
  12 
  tones 
  suitable 
  for 
  our 
  manuals, 
  

   and 
  will 
  therefore 
  afford 
  the 
  means 
  of 
  temporarily 
  supplementing 
  other 
  

   arrangements. 
  

  

  In 
  skhistic 
  intonation, 
  then, 
  the 
  modulational 
  peculiarities 
  of 
  just 
  

   intonation 
  are 
  preserved 
  ; 
  and 
  it 
  will 
  be 
  convenient 
  in 
  future 
  to 
  consider 
  

   modulation 
  as 
  taking 
  place 
  by 
  duodenes, 
  and 
  hence 
  consisting 
  of 
  duodena- 
  

   tion. 
  "We 
  shall 
  therefore 
  have 
  in 
  just 
  intonation 
  both 
  vertical 
  and 
  

   lateral 
  duodenation 
  to 
  consider 
  ; 
  but 
  in 
  skhistic 
  intonation 
  it 
  will 
  be 
  seen 
  

   by 
  Table 
  II. 
  that 
  one 
  right 
  lettered 
  duodenation, 
  as 
  from 
  root 
  f 
  B[? 
  to 
  root 
  

   D, 
  is 
  the 
  same 
  as 
  eight 
  descending 
  vertical 
  duodenations, 
  for 
  these 
  would 
  

   in 
  just 
  intonation 
  lead 
  to 
  the 
  root 
  which, 
  as 
  shown 
  in 
  the 
  last 
  Table, 
  

   is 
  skhistically 
  identical 
  with 
  D. 
  Hence 
  in 
  skhistic 
  intonation 
  we 
  have, 
  so 
  

   far 
  as 
  instruments 
  are 
  concerned, 
  only 
  to 
  render 
  vertical 
  duodenation 
  

   possible 
  and 
  easy. 
  

  

  c 
  2 
  

  

  