﻿1874.] 
  

  

  Mr. 
  A. 
  J. 
  Ellis 
  on 
  Musical 
  Duodenes. 
  

  

  13 
  

  

  4. 
  C 
  mapima, 
  Helrtiholtz's 
  mode 
  of 
  the 
  minor 
  Seventh 
  with 
  the 
  leading 
  

  

  note, 
  or 
  SeptimengeschlecTit 
  mit 
  clem 
  Leittone, 
  a 
  very 
  usual 
  form 
  

   of 
  the 
  modern 
  ascending 
  scale 
  of 
  C 
  minor. 
  

  

  c 
  . 
  . 
  . 
  d 
  . 
  fe\} 
  . 
  . 
  f 
  . 
  .. 
  g 
  . 
  . 
  a 
  . 
  . 
  . 
  b 
  . 
  c' 
  ". 
  

  

  5. 
  C 
  mipima, 
  the 
  theoretical 
  modern 
  ascending 
  scale 
  of 
  C 
  minor. 
  

  

  c 
  . 
  . 
  . 
  d 
  . 
  f 
  4> 
  . 
  . 
  / 
  . 
  . 
  . 
  g 
  . 
  fa\) 
  b 
  . 
  c 
  . 
  

  

  6. 
  F 
  mamapi, 
  considered 
  by 
  Helmholtz 
  {op. 
  cit. 
  p. 
  434. 
  no. 
  6) 
  as 
  a 
  

  

  variant 
  of 
  the 
  mode 
  of 
  the 
  minor 
  Seventh. 
  

  

  c 
  . 
  . 
  %d 
  : 
  fe\} 
  . 
  . 
  / 
  . 
  . 
  . 
  g 
  . 
  . 
  a 
  . 
  b\> 
  . 
  . 
  . 
  c\ 
  

  

  7. 
  C 
  mapimi, 
  Helmholtz's 
  mode 
  of 
  the 
  minor 
  Seventh 
  without 
  the 
  

  

  leading 
  note. 
  

  

  c 
  ... 
  d 
  . 
  fe\} 
  ../... 
  g 
  . 
  . 
  a 
  : 
  ffy 
  . 
  . 
  c'. 
  

  

  8. 
  C 
  mipimi, 
  Helmholtz's 
  mode 
  of 
  the 
  minor 
  Third, 
  or 
  Terzenge- 
  

  

  schlecht, 
  the 
  ordinary 
  form 
  of 
  the 
  modern 
  descending 
  scale 
  of 
  

   C 
  minor. 
  

  

  c 
  ... 
  d 
  . 
  f 
  4? 
  ../.... 
  g 
  . 
  t«b 
  . 
  . 
  . 
  f 
  &fc> 
  . 
  . 
  c\ 
  

  

  9. 
  F 
  mimipi, 
  Helmholtz's 
  mode 
  of 
  the 
  minor 
  Sixth, 
  or 
  Sextenge- 
  

  

  schlecht. 
  

  

  c 
  . 
  d\> 
  ... 
  f 
  ../... 
  <7 
  - 
  t«[> 
  . 
  . 
  &t> 
  • 
  • 
  • 
  c 
  '- 
  

  

  These 
  56 
  harmonic 
  scales 
  are 
  all 
  that 
  can 
  be 
  produced 
  without 
  modu- 
  

   lation. 
  

  

  To 
  retain 
  old 
  names 
  as 
  much 
  as 
  possible, 
  C 
  mapdma 
  will 
  be 
  called 
  

   C 
  major, 
  and 
  all 
  three, 
  C 
  mipimi, 
  miptma, 
  mapima, 
  will 
  be 
  considered 
  as 
  

   making 
  up 
  C 
  minor, 
  whilst 
  other 
  forms 
  will 
  be 
  termed 
  unusucd 
  minor 
  

   scales. 
  All 
  these, 
  however, 
  and 
  more 
  of 
  the 
  56 
  scales 
  mentioned 
  above, 
  

   actually 
  occur 
  in 
  modern 
  music, 
  at 
  least 
  for 
  short 
  phrases, 
  although 
  the 
  

   usual 
  major 
  and 
  minor 
  alone 
  characterize 
  whole 
  compositions. 
  

  

  D. 
  Modulation 
  and 
  Duodenation. 
  

  

  Although 
  a 
  decad 
  consists 
  of 
  complete 
  triads 
  and 
  cells, 
  yet 
  it 
  is 
  evident 
  

   that 
  one 
  or 
  two 
  of 
  the 
  cells 
  may 
  be 
  made 
  parts 
  of 
  other 
  decads, 
  and 
  that 
  

   the 
  union 
  triads 
  may 
  be 
  regarded 
  as 
  parts 
  of 
  cells 
  left 
  incomplete. 
  The 
  

   tones 
  forming 
  these 
  cells 
  and 
  unions 
  are 
  therefore 
  ambiguous, 
  and 
  there 
  

   is 
  always 
  a 
  tendency 
  to 
  complete 
  them 
  in 
  a 
  different 
  way 
  from 
  that 
  in 
  

   the 
  original 
  decad, 
  or, 
  in 
  other 
  words, 
  to 
  proceed 
  to 
  the 
  other 
  decads 
  of 
  

   which 
  they 
  form 
  a 
  part. 
  By 
  an 
  extension 
  of 
  the 
  term 
  modulation, 
  

   which 
  originally 
  referred 
  to 
  a 
  mere 
  change 
  of 
  mode, 
  this 
  change 
  of 
  

   decad 
  might 
  still 
  be 
  called 
  modidation, 
  although 
  decadation 
  might 
  be 
  more 
  

   appropriate. 
  

  

  