﻿20 
  

  

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

  

  And 
  in 
  writing 
  music, 
  if 
  we 
  note 
  at 
  the 
  top 
  of 
  any 
  bar 
  the 
  name 
  of 
  the 
  

   duodene 
  to 
  which 
  the 
  notes 
  to 
  be 
  played 
  belong, 
  and 
  suppose 
  this 
  duodenal 
  

   (as 
  the 
  mark 
  may 
  be 
  called, 
  in 
  contradistinction 
  to 
  the 
  signature, 
  which 
  

   will 
  remain 
  as 
  before) 
  to 
  hold 
  till 
  a 
  new 
  one 
  is 
  written 
  (according 
  to 
  the 
  

   custom 
  of 
  musical 
  signatures), 
  we 
  shall 
  be 
  able 
  precisely 
  to 
  mark 
  the 
  pitch 
  

   of 
  every 
  tone 
  in 
  just 
  or 
  skhistic 
  intonation, 
  tuithout 
  introducing 
  any 
  change 
  

   or 
  any 
  additional 
  sign 
  into 
  the 
  staff-notation 
  of 
  music 
  1 
  . 
  This 
  is 
  again 
  an 
  

   entirely 
  new 
  practical 
  principle 
  resulting 
  from 
  the 
  present 
  theory. 
  The 
  

   duodenal 
  will 
  direct 
  the 
  player 
  to 
  the 
  mode 
  of 
  arranging 
  the 
  manual 
  he 
  

   has 
  to 
  use. 
  It 
  should 
  be 
  the 
  duty 
  of 
  the 
  composer 
  to 
  insert 
  the 
  duodenals 
  

   himself 
  ; 
  but 
  in 
  respect 
  of 
  existing 
  compositions, 
  which 
  were 
  composed 
  for 
  

   some 
  commatic 
  system 
  of 
  temperament, 
  it 
  will 
  be 
  often 
  difficult 
  to 
  deter- 
  

   mine 
  which 
  of 
  two 
  adjacent 
  vertical 
  duodenes 
  it 
  would 
  be 
  best 
  to 
  use 
  ; 
  

   and 
  it 
  will 
  probably 
  be 
  necessary 
  to 
  introduce 
  commatic 
  changes, 
  when 
  

   they 
  can 
  be 
  made 
  within 
  the 
  limits 
  of 
  a 
  single 
  heptadecad. 
  Also 
  in 
  the 
  

   case 
  of 
  compositions 
  in 
  a 
  major 
  scale, 
  which 
  do 
  not 
  change 
  into 
  the 
  minors 
  

   of 
  the 
  same 
  decad, 
  and 
  hence 
  use 
  only 
  two 
  quaternions 
  of 
  a 
  duodene, 
  but 
  

   will 
  necessarily 
  and 
  frequently 
  modulate 
  to 
  the 
  right, 
  it 
  is 
  more 
  convenient 
  

   to 
  consider 
  the 
  music 
  as 
  performed 
  in 
  the 
  first 
  and 
  second 
  quaternions 
  of 
  

   a 
  duodene 
  having 
  for 
  its 
  root 
  the 
  Third 
  of 
  the 
  major 
  scale, 
  because 
  the 
  

   third 
  quaternion 
  of 
  that 
  duodene 
  contains 
  the 
  tones 
  required 
  for 
  right 
  

   lateral 
  modulation. 
  Thus 
  C 
  major 
  will 
  be 
  assigned 
  to 
  the 
  duodene 
  of 
  E, 
  

   No. 
  19 
  of 
  Table 
  II., 
  and 
  E 
  major 
  to 
  the 
  duodene 
  of 
  A, 
  No. 
  20 
  of 
  Table 
  II., 
  

   &c. 
  This 
  makes 
  the 
  modulation 
  from 
  the 
  major 
  into 
  the 
  relative 
  minor 
  

   as 
  simple 
  and 
  direct 
  as 
  vertical 
  modulation, 
  for 
  C 
  major 
  passes 
  into 
  any 
  

   form 
  of 
  A 
  minor 
  or 
  major 
  by 
  descending 
  vertically 
  from 
  the 
  duodene 
  of 
  

   E 
  to 
  that 
  of 
  A. 
  All 
  pieces 
  in 
  any 
  minor 
  scale 
  pass 
  into 
  each 
  of 
  the 
  three 
  

   quaternions 
  of 
  a 
  duodene, 
  and 
  hence 
  their 
  duodenal 
  will 
  be 
  the 
  tonic 
  of 
  

   their 
  decad, 
  which 
  gives 
  its 
  name 
  to 
  the 
  duodene. 
  The 
  duodene 
  is 
  then 
  

   prepared 
  for 
  playing 
  the 
  synonymous 
  major 
  of 
  that 
  minor 
  scale. 
  Such 
  

   duodenals 
  might 
  be 
  distinguished 
  by 
  an 
  added 
  star. 
  

  

  It 
  often 
  happens 
  that 
  passing 
  tones, 
  changing 
  notes 
  and 
  apjpoggiature, 
  

   are 
  introduced 
  which 
  do 
  not 
  belong 
  to 
  the 
  harmony. 
  They 
  are 
  written 
  

   usually 
  after 
  the 
  laws 
  of 
  Pythagorean 
  temperament, 
  but 
  their 
  pitch 
  is 
  

   really 
  indeterminate. 
  Eor 
  these 
  there 
  is 
  no 
  occasion 
  to 
  change 
  the 
  duo- 
  

   denal 
  at 
  all. 
  They 
  will 
  then 
  be 
  played 
  in 
  the 
  duodene 
  of 
  the 
  other 
  

  

  1 
  For 
  theoretical 
  and 
  experimental 
  purposes 
  it 
  may 
  be 
  sometimes 
  convenient 
  to 
  use 
  

   signs 
  equivalent 
  to 
  t 
  $ 
  in 
  the 
  staff-notation 
  itself. 
  The 
  signs 
  h 
  ^ 
  for 
  t, 
  tt, 
  and 
  

  

  I 
  £ 
  for 
  J, 
  XI, 
  being 
  the 
  tails 
  of 
  quavers 
  and 
  semiquavers, 
  are 
  well 
  adapted 
  for 
  this 
  pur- 
  

   pose. 
  The 
  direction 
  of 
  the 
  angles 
  show 
  ascent 
  and 
  descent, 
  and 
  the 
  forms 
  exist 
  as 
  

   types 
  for 
  every 
  required 
  position 
  on 
  the 
  staff 
  ; 
  thus 
  ta, 
  td, 
  tbb, 
  and 
  jg#, 
  would 
  be 
  

  

  