﻿1874.] 
  

  

  Mr. 
  A. 
  J. 
  Ellis 
  on 
  Musical 
  Duodenes. 
  

  

  11 
  

  

  The 
  Harmonic 
  Elements 
  are 
  the 
  Fifth, 
  CxGr 
  (=f), 
  the 
  major 
  Third, 
  

  

  C 
  + 
  E 
  ( 
  = 
  5)5 
  an( 
  i 
  the 
  minor 
  Third, 
  — 
  tE[> 
  (=|j)> 
  using 
  a 
  notation 
  which 
  

   I 
  have 
  found 
  practically 
  very 
  convenient 
  for 
  representing 
  the 
  intervals 
  

   between 
  two 
  tones 
  ; 
  the 
  symbols 
  x 
  , 
  + 
  , 
  — 
  are 
  not 
  to 
  be 
  employed 
  with 
  

   any 
  other 
  meaning 
  between 
  the 
  names 
  of 
  tones. 
  In 
  these 
  elements 
  it 
  is 
  

   supposed 
  that 
  either 
  note 
  may 
  be 
  raised 
  or 
  depressed 
  by 
  any 
  number 
  of 
  

   Octaves, 
  or 
  be 
  accompanied 
  by 
  such 
  Octaves 
  of 
  itself. 
  

  

  The 
  Harmonic 
  Cell, 
  or 
  Unit 
  of 
  Concord, 
  consists 
  of 
  a 
  major 
  triad, 
  

  

  C 
  + 
  E 
  — 
  Gr, 
  and 
  a 
  minor 
  triad, 
  C— 
  tE|? 
  + 
  Gr, 
  arranged 
  as 
  in 
  

   fEf) 
  Gr 
  the 
  margin, 
  and 
  having 
  the 
  same 
  First 
  C, 
  and 
  hence 
  the 
  

  

  C 
  E 
  same 
  Fifth 
  Gr. 
  The 
  Fifth 
  C 
  x 
  Gr 
  is 
  placed 
  vertically, 
  the 
  

  

  two 
  major 
  thirds, 
  C+E 
  and 
  tE[? 
  + 
  Gr, 
  are 
  horizontal, 
  and 
  

   the 
  two 
  minor 
  Thirds, 
  C— 
  fE|> 
  and 
  E— 
  Gr, 
  slope 
  obliquely 
  from 
  the 
  

   bottom 
  upwards 
  to 
  the 
  left. 
  These 
  positions, 
  then, 
  replace 
  the 
  symbols 
  

   x 
  , 
  + 
  , 
  — 
  . 
  Allowing 
  any 
  one 
  of 
  the 
  tones 
  to 
  be 
  altered 
  by 
  any 
  number 
  

   of 
  Octaves, 
  or 
  to 
  have 
  Octaves 
  of 
  itself 
  added, 
  and 
  any 
  tone 
  to 
  be 
  taken 
  

   as 
  the 
  First, 
  this 
  cell, 
  whence 
  all 
  harmony 
  is 
  developed, 
  contains 
  every 
  

   chord 
  recognized 
  by 
  musicians 
  as 
  a 
  concord 
  in 
  Tertian 
  Harmony 
  — 
  that 
  is, 
  

   harmony 
  depending 
  on 
  Octaves, 
  Fifths, 
  and 
  Thirds 
  alone, 
  excluding 
  

  

  natural 
  Sevenths 
  (=5)' 
  which 
  form 
  Septimal 
  Harmony. 
  By 
  Table 
  I. 
  

  

  cells 
  can 
  be 
  readily 
  constructed 
  on 
  any 
  tone 
  as 
  a 
  First. 
  

  

  The 
  Harmonic 
  Heptad, 
  or 
  Unit 
  of 
  Chord-relationship, 
  consists 
  of 
  two 
  

  

  cells, 
  the 
  First 
  of 
  one 
  being 
  the 
  Fifth 
  of 
  the 
  other, 
  as 
  

   tE|? 
  G- 
  in 
  the 
  margin. 
  Allowing 
  Octave 
  variations 
  as 
  before, 
  this 
  

  

  f 
  A|? 
  C 
  E 
  contains 
  all 
  the 
  three 
  major 
  and 
  three 
  minor 
  triads 
  which 
  

   F 
  A 
  have 
  C 
  as 
  one 
  of 
  their 
  constituents, 
  and 
  are 
  thus 
  related 
  

  

  in 
  the 
  first 
  degree. 
  Two 
  of 
  these 
  chords, 
  the 
  minor 
  triad 
  

   A 
  — 
  C 
  + 
  E 
  on 
  the 
  right 
  or 
  major 
  side, 
  and 
  the 
  major 
  triad 
  fA|p 
  + 
  C— 
  fE|j 
  

   on 
  the 
  left 
  or 
  minor 
  side, 
  connecting 
  the 
  two 
  cells 
  and 
  due 
  to 
  their 
  

   union, 
  may 
  be 
  called 
  union 
  triads, 
  to 
  distinguish 
  them 
  from 
  the 
  four 
  cell 
  

   triads. 
  The 
  heptad 
  also 
  contains 
  all 
  con-dissonant 
  triads 
  (as 
  I 
  term 
  them), 
  

   consisting 
  of 
  three 
  tones, 
  two 
  of 
  which 
  are 
  consonant 
  with 
  C 
  but 
  dissonant 
  

   with 
  each 
  other. 
  Of 
  these 
  the 
  trine 
  f 
  A|> 
  + 
  C 
  + 
  E, 
  which 
  forms 
  the 
  central 
  

   horizontal 
  line, 
  is 
  most 
  important 
  for 
  future 
  work. 
  

  

  The 
  Harmonic 
  Decad, 
  or 
  Unit 
  of 
  Harmony, 
  consists 
  of 
  two 
  heptads 
  

   having 
  a 
  common 
  cell, 
  and 
  hence 
  of 
  three 
  cells, 
  the 
  Fifth 
  

   t~B\) 
  D 
  of 
  the 
  first, 
  lowest, 
  or 
  subdominant 
  cell, 
  and 
  the 
  Fifth 
  of 
  the 
  

  

  tE|? 
  G- 
  B 
  second, 
  middle, 
  or 
  tonic 
  cell, 
  being 
  the 
  First 
  of 
  the 
  second 
  

   tAJ> 
  C 
  E 
  cell, 
  and 
  First 
  of 
  the 
  third, 
  highest, 
  or 
  dominant 
  cell, 
  

   F 
  A 
  respectively. 
  The 
  decad 
  contains 
  three 
  major 
  and 
  three 
  

   minor 
  cell 
  triads, 
  and 
  two 
  major 
  and 
  two 
  minor 
  union 
  triads 
  

   —that 
  is, 
  ten 
  triads 
  in 
  all, 
  together 
  with 
  all 
  the 
  discords 
  possible 
  without 
  

  

  