﻿12 
  

  

  Mr. 
  A. 
  J. 
  Ellis 
  on 
  Musical 
  Duodenes. 
  [Nov. 
  19, 
  

  

  modulation. 
  The 
  First 
  of 
  the 
  tonic 
  cell 
  is 
  called 
  the 
  tonic 
  of 
  the 
  decad, 
  

   and 
  gives 
  its 
  name 
  to 
  it. 
  The 
  example, 
  therefore, 
  is 
  a 
  C 
  decad. 
  

  

  Harmonic 
  Trichordals 
  consist 
  of 
  three 
  triads, 
  one 
  from 
  each 
  cell 
  in 
  a 
  

   decad, 
  and 
  form 
  eight 
  groups. 
  Contracting 
  major 
  triad 
  and 
  minor 
  triad 
  

   into 
  ma 
  and 
  mi 
  respectively 
  (with 
  Italian 
  vowels), 
  and 
  naming 
  the 
  three- 
  

   cell 
  triads 
  in 
  order 
  from 
  bottom 
  to 
  top, 
  these 
  8 
  trichordals 
  are 
  distinguished 
  

   as 
  follows 
  in 
  the 
  C 
  decad. 
  The 
  triads 
  are 
  spread 
  out 
  and 
  marked 
  by 
  + 
  

   and 
  — 
  , 
  and 
  the 
  terminal 
  triads 
  are 
  repeated 
  in 
  part 
  with 
  an 
  interposed 
  | 
  

   to 
  indicate 
  the 
  dissonant 
  interval 
  of 
  a 
  Pythagorean 
  minor 
  Third= 
  

  

  ~ 
  • 
  |j=^> 
  so 
  that 
  all 
  the 
  harmonies, 
  consonant 
  and 
  dissonant, 
  peculiar 
  to 
  

  

  any 
  trichordal, 
  may 
  be 
  collected 
  at 
  a 
  glance. 
  

  

  i. 
  Mamama 
  B 
  — 
  D 
  | 
  F+ 
  A 
  -0+ 
  E 
  -G+ 
  B 
  — 
  D 
  | 
  F-f 
  A 
  

  

  ii. 
  Miniama 
  B 
  — 
  D 
  | 
  F-tAb 
  + 
  C 
  + 
  E 
  -G+ 
  B 
  — 
  D 
  | 
  F-tAb 
  

  

  iii. 
  Mamima 
  B 
  -D 
  | 
  F+ 
  A 
  _C-tEb+G+ 
  B 
  -D 
  | 
  F+ 
  A 
  

  

  iv. 
  Mimima 
  B 
  — 
  D 
  | 
  F-tAb 
  + 
  C-tEb+G+ 
  B 
  — 
  D 
  | 
  F-tAb 
  

  

  v. 
  Mamami 
  tBb+D 
  | 
  F+ 
  A 
  -C+ 
  E 
  -G-tBb+D 
  | 
  F+ 
  A 
  

  

  ri. 
  Mimami 
  tBb+D 
  | 
  F-tAb+C+ 
  E 
  -G-tBb+D 
  | 
  F-tAb 
  

  

  vii. 
  Mamimi 
  tBb 
  + 
  D 
  | 
  F 
  + 
  A 
  -C-tEb+G- 
  tBb+D 
  | 
  F+ 
  A 
  

  

  viii. 
  Mimimi 
  tBb+D 
  | 
  F-tAb 
  +0-tEb 
  + 
  G- 
  tBb+D 
  | 
  F-tAb 
  

  

  Each 
  of 
  these 
  8 
  trichordals 
  contains 
  7 
  tones, 
  and 
  when 
  these 
  are 
  reduced 
  

   to 
  one 
  Octave 
  and 
  sounded 
  in 
  order 
  of 
  pitch, 
  they 
  form 
  that 
  particular 
  

   scale 
  in 
  which 
  a 
  piece 
  of 
  music 
  is 
  usually 
  written. 
  But 
  in 
  repeating 
  them 
  

   each 
  may 
  begin 
  on 
  any 
  tone 
  of 
  the 
  seven, 
  giving 
  7 
  modes 
  (in 
  the 
  ancient 
  

   Greek 
  sense) 
  to 
  each 
  trichordal. 
  To 
  distinguish 
  these, 
  change 
  the 
  m 
  of 
  

   the 
  name 
  of 
  the 
  triad 
  containing 
  the 
  initial 
  tone 
  intop 
  when 
  it 
  is 
  its 
  Eirst 
  

   (jo 
  riina), 
  t 
  when 
  it 
  is 
  its 
  Third 
  (t 
  ertia), 
  and 
  qu 
  when 
  it 
  is 
  its 
  Fifth 
  

   (qu 
  inta), 
  which 
  last 
  is 
  of 
  course 
  required 
  for 
  the 
  highest 
  or 
  dominant 
  

   triad 
  only. 
  The 
  final 
  cadence 
  fully 
  distinguishes 
  the 
  56 
  resulting 
  harmonic 
  

   scales. 
  Of 
  these 
  I 
  append 
  such 
  as 
  are 
  usually 
  acknowledged, 
  making 
  them 
  

   all 
  begin 
  with 
  C, 
  and 
  changing 
  the 
  decad 
  accordingly. 
  Between 
  the 
  

  

  tones 
  I 
  use 
  (.) 
  for 
  the 
  Semitone 
  j|, 
  (:) 
  for 
  the 
  high 
  Semitone 
  (..) 
  for 
  

  

  10 
  • 
  9 
  

  

  the 
  minor 
  Tone 
  -q-, 
  (...) 
  for 
  the 
  major 
  Tone 
  g, 
  and 
  (.-.) 
  for 
  the 
  augmented 
  

  

  75 
  

  

  tone 
  g^. 
  

  

  1. 
  C 
  mapdma, 
  or 
  ordinary 
  scale 
  of 
  C 
  major. 
  

  

  c 
  . 
  . 
  . 
  d 
  . 
  . 
  e 
  . 
  f 
  . 
  . 
  . 
  g 
  . 
  . 
  a 
  . 
  . 
  . 
  b 
  . 
  c 
  '. 
  

  

  2. 
  F 
  mdmajpa, 
  one 
  of 
  Helmholtz's 
  modes 
  of 
  the 
  Fourth, 
  or 
  Quartenge- 
  

  

  schlecht. 
  

  

  c 
  . 
  . 
  id 
  . 
  . 
  . 
  e 
  . 
  f 
  . 
  . 
  . 
  g 
  . 
  . 
  a 
  . 
  b\) 
  . 
  . 
  . 
  c. 
  

  

  3. 
  C 
  mijjdina^ 
  Helmholtz's 
  minor-major 
  mode, 
  or 
  Moll-Durycschlccht 
  . 
  

  

  c 
  . 
  . 
  . 
  d 
  . 
  . 
  e 
  . 
  / 
  . 
  . 
  . 
  g 
  . 
  t«|? 
  .'. 
  b 
  . 
  c' 
  . 
  

  

  