﻿24 
  

  

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

  

  2. 
  Just 
  Harmonium 
  (exhibited 
  when 
  this 
  paper 
  was 
  read). 
  Tor 
  

  

  ordinary 
  lecture 
  and 
  illustrative 
  purposes, 
  this 
  is 
  

   tF 
  the 
  cheapest 
  and 
  best 
  instrument. 
  It 
  contains 
  the 
  

  

  fBf> 
  D 
  portion 
  of 
  a 
  heptadecad 
  shown 
  in 
  the 
  margin, 
  and 
  

  

  t~E\) 
  Gr 
  B 
  hence 
  contains 
  the 
  duodene 
  of 
  C 
  with 
  the 
  exception 
  

   tA\} 
  C 
  E 
  of 
  E#, 
  the 
  whole 
  decad 
  of 
  C, 
  and 
  the 
  major 
  scales 
  

   D\> 
  F 
  A 
  of 
  tE[> 
  and 
  tA\}. 
  The 
  two 
  last 
  show 
  vertical 
  

  

  modulation. 
  Again, 
  tEJ? 
  major 
  or 
  tAf> 
  major 
  to 
  C 
  

   decad 
  shows 
  right 
  lateral, 
  and, 
  inversely, 
  C 
  decad 
  to 
  tE[? 
  major 
  or 
  t 
  A\} 
  

   major 
  shows 
  left 
  lateral 
  modulation. 
  The 
  E 
  and 
  f 
  E 
  show 
  the 
  influence 
  

   of 
  a 
  comma, 
  and 
  the 
  difference 
  between 
  the 
  just 
  triad, 
  D^ 
  + 
  E 
  — 
  fA[>, 
  and 
  

   the 
  Pythagorean 
  triad, 
  D\> 
  with 
  fE 
  and 
  fA\). 
  Also 
  in 
  the 
  key 
  of 
  tE[> 
  

   major 
  the 
  difference 
  can 
  be 
  shown 
  between 
  the 
  minor 
  chord, 
  E 
  — 
  fA[? 
  -f- 
  C, 
  

   and 
  the 
  chord 
  of 
  the 
  added 
  Sixth, 
  tA\) 
  + 
  C 
  | 
  tE. 
  It 
  also 
  contains 
  the 
  

   German 
  Sixth, 
  D|? 
  + 
  E 
  — 
  fAlp 
  with 
  B 
  (which 
  is 
  a 
  close 
  imitation 
  of 
  the 
  

   chord 
  of 
  the 
  natural 
  Seventh), 
  the 
  Italian 
  Sixth, 
  D|?+E 
  with 
  B, 
  and 
  the 
  

   Erench 
  Sixth, 
  D[> 
  + 
  E 
  . 
  . 
  . 
  Gr+B. 
  Using 
  capitals 
  and 
  small 
  letters 
  for 
  

   the 
  black 
  and 
  white 
  keys, 
  they 
  are 
  arranged 
  thus 
  : 
  — 
  

  

  d[> 
  D 
  te[> 
  E 
  E 
  ff 
  G 
  taj) 
  A 
  fb\> 
  B. 
  

  

  The 
  tE 
  is 
  placed 
  on 
  the 
  E# 
  digital, 
  and 
  the 
  fingering 
  is 
  normal 
  in 
  other 
  

   respects. 
  The 
  five 
  tones, 
  d|? 
  x 
  ta|? 
  x 
  fe]p 
  x 
  fh\> 
  x 
  tf, 
  will 
  then 
  enable 
  us 
  

   to 
  play 
  all 
  Scotch 
  and 
  other 
  music 
  containing 
  only 
  five 
  tones, 
  in 
  perfectly 
  

   just 
  intonation, 
  on 
  the 
  black 
  digitals, 
  and 
  to 
  show 
  that 
  such 
  music 
  can- 
  

   not 
  be 
  harmonized. 
  The 
  practical 
  direction 
  for 
  tuning 
  is, 
  "tune 
  the 
  

   following 
  7 
  major 
  chords 
  without 
  beats, 
  putting 
  tE 
  on 
  the 
  E£ 
  digital, 
  

   E 
  A 
  C, 
  C 
  E 
  Gr, 
  G 
  B 
  D 
  ; 
  D\) 
  E 
  tA[>, 
  tA\> 
  C 
  tE|?, 
  tE[> 
  G 
  tB^, 
  tB[> 
  D 
  tE." 
  

   A 
  four-Octave 
  instrument 
  was 
  thus 
  tuned 
  in 
  two 
  hours. 
  

  

  3. 
  Hejohthannonium. 
  This 
  requires 
  two 
  rows 
  of 
  vibrators 
  and 
  Mr. 
  

   Saunders's 
  " 
  tilting 
  action," 
  already 
  described. 
  The 
  vibrators 
  are 
  dis- 
  

   posed 
  thus 
  : 
  — 
  

  

  Back 
  . 
  . 
  . 
  . 
  tDb 
  tc$ 
  £D 
  ±d£ 
  tEt> 
  tE 
  £f# 
  fG\> 
  tg% 
  %A 
  b\> 
  tq> 
  

   Front 
  .... 
  C 
  &\> 
  D 
  teb 
  B 
  , 
  E 
  f# 
  Gr 
  ta[> 
  A 
  fb\> 
  B. 
  

  

  This 
  harmonium 
  contains 
  all 
  the 
  tones 
  in 
  a 
  heptadecad 
  (whence 
  its 
  

   name), 
  and 
  consequently 
  illustrates 
  every 
  kind 
  of 
  modulation 
  in 
  the 
  first 
  

   degree, 
  and 
  becomes 
  a 
  most 
  valuable 
  instrument 
  for 
  the 
  lecturer 
  and 
  

   teacher 
  of 
  singing. 
  The 
  front 
  vibrators, 
  to 
  which 
  correspond 
  the 
  digitals 
  

   when 
  the 
  stops 
  are 
  all 
  pushed 
  in, 
  contain 
  the 
  whole 
  duodene 
  of 
  C, 
  and 
  

   the 
  stops 
  enable 
  the 
  player 
  to 
  exchange 
  their 
  tones 
  for 
  those 
  in 
  the 
  six 
  

   other 
  decads. 
  All 
  lie 
  on 
  the 
  usual 
  digitals 
  except 
  fD\} 
  and 
  tG\), 
  which 
  

   are 
  placed 
  on 
  the 
  long 
  white 
  digitals 
  of 
  C 
  and 
  Gr, 
  in 
  place 
  of 
  the 
  short 
  

   black 
  digitals 
  next 
  to 
  their 
  right, 
  as 
  these 
  were 
  wanted 
  for 
  Jc# 
  and 
  Jgjf. 
  

   This 
  makes 
  a 
  slight 
  difference 
  in 
  the 
  fingering 
  of 
  tE[? 
  minor 
  and 
  

   similar 
  scales. 
  

  

  