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

  

  Table 
  I. 
  

  

  Limits 
  of 
  Duodenation 
  and 
  Number 
  of 
  Tones. 
  

  

  

  

  

  I. 
  

  

  II. 
  

  

  III. 
  

  

  IV. 
  

  

  V. 
  

  

  VI. 
  

  

  

  

  

  1. 
  

  

  2. 
  

  

  3. 
  

  

  4. 
  

  

  5. 
  

  

  6. 
  

  

  7. 
  

  

  8. 
  

  

  9. 
  

  

  

  1 
  

  

  m 
  

  

  tttBbb 
  

   tttEbb 
  

  

  ttDb 
  

   ttGb 
  

  

  ttF 
  

   ttBb 
  

  

  ttA 
  

   tD 
  

  

  to* 
  

  

  tFtf 
  

  

  tE# 
  

   tAjf 
  

  

  GSS 
  

  

  ess 
  

  

  BSS 
  

   ESS 
  

  

  jDSSS 
  

   tGSSS 
  

  

  i 
  

  

  m 
  

  

  n 
  

  

  t 
  ttAbb 
  

  

  ttCb 
  

  

  ttEb 
  

  

  tG 
  

  

  tB 
  

  

  m 
  

  

  ESS 
  

  

  ASS 
  

  

  jcsss 
  

  

  n 
  

  

  P 
  

  

  ttDbb 
  

   ttGbb 
  

  

  ttFb 
  

   ttBbb 
  

  

  ttAb 
  

   tDb 
  

  

  tc 
  

  

  tF 
  

  

  tE 
  

   tA 
  

  

  Gtf 
  

  

  cs 
  

  

  BS 
  

   ES 
  

  

  jDSS 
  

   |GSS 
  

  

  |FSSS 
  

   JBSS 
  

  

  P 
  

   <l 
  

  

  r 
  

   s 
  

   t 
  

   u 
  

  

  ttCbb 
  

  

  1 
  I 
  J? 
  W 
  

  

  ttBbbb 
  

   ttEbbb 
  

  

  ttEbb 
  

  

  + 
  + 
  A 
  hh 
  

  

  1 
  1 
  V 
  V 
  

  

  tDbb 
  

   tGbb 
  

  

  tGb 
  

  

  tFb 
  

   tBbb 
  

  

  tBb 
  

  

  tAb 
  

   Db 
  

  

  D 
  

  

  c 
  

  

  F 
  

  

  TD 
  

   JJ 
  

  

  E 
  

   A 
  

  

  AS 
  

  

  }GS 
  

   ICS 
  

  

  jess 
  

  

  +BS 
  

   |ES 
  

  

  tESS 
  

   UDSS 
  

  

  tm* 
  

  

  r 
  

   s 
  

   t 
  

   u 
  

  

  w 
  

  

  X 
  

  

  ttAbbb 
  

   tDbbb 
  

  

  tCbb 
  

   tFbb 
  

  

  tEbb 
  

   tAbb 
  

  

  Gb 
  

   Cb 
  

  

  Bb 
  

   Eb 
  

  

  to 
  

  

  JG 
  

  

  m 
  

  

  *B 
  

  

  JAS 
  

   «BS 
  

  

  ttcss 
  

  

  «FSS 
  

  

  w 
  

  

  X 
  

  

  y 
  

  

  tGbbb 
  

  

  tBbbb 
  

  

  Dbb 
  

  

  Fb 
  

  

  Ab 
  

  

  to 
  

  

  JE 
  ' 
  

  

  tm 
  

  

  ++BS 
  

  

  y 
  

  

  z 
  

  

  tCbbb 
  

  

  tEbbb 
  

  

  Gbb 
  

  

  Bbb 
  

  

  +Db 
  

  

  |F 
  

  

  JA 
  

  

  UCS 
  

  

  tm 
  

  

  z 
  

  

  The 
  tones 
  in 
  the 
  small 
  central 
  oblong 
  form 
  the 
  duodene 
  of 
  which 
  C 
  is 
  the 
  root. 
  

  

  The 
  tones 
  in 
  the 
  large 
  central 
  oblong 
  form 
  all 
  the 
  duodenes 
  which 
  have 
  at 
  least 
  one 
  

   tone 
  in 
  common 
  with 
  the 
  central 
  duodene 
  of 
  C, 
  forming 
  the 
  limits 
  of 
  radical 
  duodena- 
  

   tion 
  from 
  C. 
  

  

  The 
  complete 
  Table 
  contains 
  all 
  the 
  duodenes 
  which 
  have 
  at 
  least 
  one 
  tone 
  in 
  com- 
  

   mon 
  with 
  duodenes 
  whose 
  roots 
  are 
  tones 
  in 
  the 
  duodene 
  of 
  C, 
  forming 
  the 
  limits 
  of 
  

   general 
  radical 
  duodenation. 
  

  

  The 
  48 
  tones 
  in 
  columns 
  I. 
  to 
  VI., 
  between 
  the 
  dotted 
  lines, 
  are 
  those 
  considered 
  

   sufficient 
  for 
  instruments 
  with 
  fixed 
  tones 
  in 
  skhistic 
  or 
  unequally 
  just 
  intonation. 
  

  

  