﻿1874.] 
  

  

  Mr. 
  A. 
  J. 
  Ellis 
  on 
  Musical 
  Daodenes. 
  

  

  15 
  

  

  chordal, 
  with 
  the 
  fullest 
  and 
  best 
  harmonies, 
  is 
  undoubtedly 
  the 
  mamama 
  

   or 
  major, 
  consisting 
  of 
  the 
  central 
  and 
  right 
  columns 
  of 
  the 
  decad 
  con- 
  

   taining 
  it, 
  modulation 
  (or 
  decadation) 
  to 
  the 
  right 
  is 
  more 
  common 
  than 
  

   modulation 
  to 
  the 
  left-, 
  and, 
  owing 
  to 
  the 
  closer 
  relationship, 
  modulation 
  

   to 
  the 
  right 
  relative 
  is 
  more 
  common 
  than 
  into 
  the 
  right 
  correlative, 
  which 
  

   generally 
  occurs 
  as 
  a 
  vertical 
  (dominant) 
  modulation 
  from 
  the 
  latter. 
  

   Vertical 
  (dominant 
  or 
  subdominant) 
  modulations 
  are, 
  however, 
  the 
  most 
  

   common 
  of 
  all, 
  unconsciously 
  (owing 
  to 
  commatic 
  temperament) 
  into 
  

   the 
  subdominant 
  (when 
  the 
  minor 
  chord, 
  id— 
  f+a, 
  is 
  used 
  for 
  the 
  chord 
  

   of 
  the 
  added 
  Sixth, 
  f+a 
  | 
  d), 
  and 
  consciously 
  into 
  the 
  dominant 
  (in 
  

   which, 
  however, 
  only 
  fjf, 
  and 
  not 
  fa, 
  is 
  commonly 
  recognized). 
  

  

  The 
  vertical 
  modulation 
  is 
  so 
  common 
  that 
  it 
  influences 
  scales, 
  producing 
  

   actual 
  tetrachordals, 
  which 
  are 
  disguised 
  in 
  melody 
  by 
  being 
  occasionally 
  

   deprived 
  of 
  their 
  extreme 
  tones, 
  so 
  as 
  to 
  reduce 
  their 
  apparent 
  number 
  at 
  

   any 
  time 
  to 
  7. 
  The 
  fourth 
  chord 
  may 
  be 
  added 
  on 
  to 
  the 
  name 
  by 
  a 
  

   hyphen. 
  Thus 
  we 
  have 
  

  

  C 
  ma-majpama 
  hH> 
  + 
  id 
  — 
  f 
  + 
  a 
  — 
  c 
  + 
  e 
  — 
  g 
  + 
  b 
  — 
  d, 
  

  

  in 
  which 
  the 
  h\> 
  is 
  seldom 
  touched 
  except 
  in 
  the 
  chord 
  of 
  the 
  dominant 
  

   Seventh, 
  c 
  + 
  e 
  — 
  g 
  | 
  b|?, 
  and 
  then 
  not 
  in 
  melody, 
  but 
  id 
  often 
  comes 
  into 
  

   melody. 
  Similarly 
  we 
  have 
  

  

  C 
  mapama-ma 
  f 
  + 
  a 
  — 
  c 
  + 
  e 
  — 
  g 
  + 
  b 
  — 
  d 
  + 
  f# 
  — 
  ta, 
  

  

  where 
  fa 
  is 
  not 
  touched 
  in 
  the 
  melody. 
  But 
  in 
  minor 
  scales 
  this 
  is 
  more 
  

   marked, 
  as 
  

  

  A 
  mimipa-ma 
  id 
  — 
  f 
  + 
  a— 
  c 
  + 
  e 
  + 
  igjf 
  — 
  b 
  + 
  ±d# 
  — 
  f 
  J, 
  

  

  where 
  +d 
  and 
  f 
  # 
  are 
  not 
  touched 
  in 
  the 
  melody 
  ; 
  so 
  that 
  the 
  scale 
  reads 
  

  

  «•/•'• 
  ■ 
  +## 
  . 
  « 
  • 
  h 
  . 
  d 
  .\ 
  %d'$ 
  . 
  e\ 
  

  

  with 
  4 
  semitones 
  and 
  2 
  augmented 
  tones, 
  which 
  has 
  an 
  extremely 
  strange 
  

   effect 
  1 
  . 
  Another 
  scale 
  of 
  this 
  kind 
  is 
  

  

  A 
  mimipi-ma 
  id 
  — 
  f 
  +a 
  — 
  c+e— 
  g+b 
  + 
  id# 
  — 
  f 
  #, 
  

  

  which 
  occurs 
  in 
  the 
  modern 
  treatment 
  of 
  Helmholtz's 
  mode 
  of 
  the 
  minor 
  

   Sixth 
  (No. 
  9, 
  above). 
  The 
  apparent 
  scale 
  is 
  

  

  e 
  . 
  / 
  . 
  . 
  . 
  g 
  . 
  . 
  a 
  . 
  . 
  . 
  b 
  . 
  c 
  .'. 
  td'ft 
  . 
  e, 
  

  

  which 
  has 
  3 
  Semitones. 
  These 
  are, 
  in 
  fact, 
  all 
  cases 
  of 
  vertical 
  modula- 
  

   tion 
  (or 
  decadation) 
  ; 
  and 
  it 
  is 
  only 
  by 
  recognizing 
  this 
  fact 
  that 
  we 
  are 
  

   able 
  to 
  reduce 
  them 
  to 
  just 
  intonation. 
  They 
  have 
  not 
  been, 
  however, 
  

   hitherto 
  so 
  conceived, 
  and 
  hence 
  it 
  became 
  necessary, 
  for 
  the 
  purposes 
  of 
  

  

  1 
  This 
  scale 
  and 
  its 
  Iwmonies 
  are 
  taken 
  from 
  C. 
  Child 
  Spenser's 
  ' 
  Rudimentary 
  and 
  

   Practical 
  Treatise 
  on 
  Music,' 
  vol. 
  ii. 
  p. 
  42. 
  He 
  does 
  not 
  acknowledge 
  either 
  \d 
  or 
  fjf 
  ; 
  but 
  

   he 
  really 
  uses 
  |d 
  in 
  his 
  second 
  chord, 
  \cl 
  a 
  \d' 
  f, 
  and 
  he 
  only 
  avoids 
  f 
  $ 
  by 
  using 
  

   f+a. 
  .. 
  b 
  + 
  jdj? 
  for 
  the 
  usual 
  chord 
  of 
  the 
  dominant 
  Seventh, 
  b+{d# 
  — 
  fjf 
  | 
  a. 
  

  

  