﻿10 
  

  

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

  

  bad 
  as 
  the 
  best 
  intervals 
  (Fifths) 
  in 
  equal 
  temperament, 
  and 
  all 
  the 
  other 
  

   intervals 
  absolutely 
  just. 
  Hence 
  the 
  name 
  unequally 
  just. 
  In 
  future 
  I 
  shall 
  

   consider 
  that 
  skhistic 
  intonation 
  is 
  practically 
  realized 
  by 
  unequally 
  just 
  

   intonation, 
  for 
  which 
  the 
  practical 
  rule 
  is 
  : 
  — 
  tune 
  six 
  tones 
  malting 
  just 
  

   major 
  Thirds 
  without 
  beats 
  (as 
  fF|? 
  to 
  f 
  A\> 
  to 
  C 
  to 
  E 
  to 
  t 
  Gr# 
  to 
  iB#, 
  line 
  t 
  

   in 
  Table 
  I.), 
  and 
  from 
  each 
  of 
  them 
  tune 
  seven 
  other 
  tones 
  malcing 
  just 
  Fifths 
  

   (as 
  C 
  to 
  Gr 
  to 
  D 
  to 
  f 
  A 
  to 
  f 
  E, 
  and 
  C 
  to 
  F 
  to 
  B[> 
  to 
  E[>, 
  in 
  col. 
  5 
  of 
  

   Table 
  I.). 
  

  

  Saunders's 
  "Tilting 
  Action.'" 
  — 
  Before 
  proceeding 
  to 
  show 
  that 
  48 
  skhistic 
  

   tones 
  suffice 
  for 
  modern 
  modulational 
  music, 
  it 
  will 
  be 
  useful 
  for 
  future 
  

   constructions 
  to 
  remark 
  that 
  a 
  method 
  of 
  realizing 
  all 
  the 
  effects 
  which 
  I 
  

   contemplated 
  by 
  my 
  duplex 
  finger-board 
  (Proc. 
  vol. 
  xiii. 
  p. 
  422) 
  has 
  been 
  

   invented 
  by 
  Mr. 
  T. 
  W. 
  Saunders 
  l 
  , 
  by 
  means 
  of 
  stops, 
  which 
  allow 
  the 
  

   manual 
  and 
  fingering 
  to 
  remain 
  unaltered. 
  Two 
  sets 
  of 
  harmonium 
  

   vibrators 
  are 
  arranged 
  one 
  behind 
  the 
  other, 
  tuned 
  in 
  tertian 
  intonation 
  

   (by 
  means 
  of 
  beats, 
  counted 
  by 
  a 
  pendulum, 
  which 
  gives 
  a 
  fairly 
  accurate 
  

   means 
  of 
  approximating 
  to 
  the 
  correct 
  result) 
  as 
  follows, 
  the 
  capital 
  

   letters 
  referring 
  to 
  the 
  white 
  or 
  long 
  digitals, 
  and 
  the 
  small 
  letters 
  to 
  the 
  

   black 
  or 
  short 
  digitals, 
  a 
  mode 
  of 
  distinction 
  which 
  I 
  shall 
  constantly 
  

   employ 
  : 
  — 
  

  

  Back 
  B# 
  dt> 
  CU 
  eb 
  E[> 
  E# 
  g\> 
  F## 
  a[> 
  

  

  Front 
  C 
  c# 
  D 
  d# 
  E 
  F 
  f# 
  Gr 
  g# 
  A 
  a# 
  B 
  

  

  There 
  are 
  12 
  stops 
  2 
  , 
  one 
  corresponding 
  to 
  each 
  digital 
  in 
  the 
  Octave, 
  

   which, 
  by 
  a 
  "tilting 
  action," 
  enables 
  one, 
  and 
  one 
  only, 
  out 
  of 
  the 
  two 
  

   vibrators 
  in 
  the 
  same 
  column, 
  as 
  shown 
  above, 
  to 
  be 
  " 
  damped" 
  at 
  plea- 
  

   sure 
  throughout 
  all 
  the 
  Octaves 
  of 
  the 
  instrument. 
  When 
  all 
  the 
  stops 
  

   are 
  pushed 
  in, 
  the 
  front 
  vibrators 
  only 
  are 
  free, 
  and 
  any 
  one 
  may 
  be 
  

   exchanged 
  for 
  a 
  back 
  vibrator 
  by 
  pulling 
  out 
  its 
  stop. 
  Hence 
  24 
  out 
  of 
  

   27 
  tones 
  are 
  under 
  the 
  command 
  of 
  the 
  player; 
  EJ>|^, 
  A\}\) 
  are 
  

  

  omitted. 
  

  

  C. 
  Harmonic 
  Scales. 
  

  

  A 
  series 
  of 
  tones, 
  each 
  of 
  which 
  is 
  consonant 
  with 
  two 
  other 
  tones 
  in 
  

   the 
  same 
  series 
  that 
  are 
  themselves 
  consonant 
  with 
  each 
  other, 
  forms 
  

   what 
  I 
  here 
  mean 
  by 
  an 
  harmonic 
  scale. 
  This 
  was 
  not 
  the 
  principle 
  on 
  

   which 
  scales 
  were 
  originally 
  formed 
  ; 
  but 
  this 
  is 
  the 
  way 
  in 
  which 
  the 
  pitch 
  

   of 
  the 
  tones 
  must 
  be 
  determined 
  for 
  the 
  just 
  intonation 
  of 
  modern 
  har- 
  

   mony 
  and 
  modulation. 
  

  

  1 
  As 
  Mr. 
  Saunders 
  has 
  not 
  patented 
  his 
  invention, 
  I 
  am 
  unable 
  to 
  give 
  more 
  than 
  

   the 
  indications 
  in 
  the 
  text, 
  and 
  refer 
  to 
  him 
  personally, 
  at 
  E. 
  Lachenal's 
  Concertina 
  

   Manufactory, 
  4 
  Little 
  James 
  Street, 
  Bedford 
  Row, 
  W.O. 
  His 
  invention 
  offers 
  great 
  

   facilities 
  for 
  the 
  construction 
  of 
  experimental 
  instruments 
  in 
  any 
  uniform 
  or 
  just 
  

   intonation. 
  His 
  harmonium 
  was 
  shown 
  when 
  this 
  paper 
  was 
  read. 
  

  

  2 
  In 
  the 
  specimen 
  shown 
  there 
  are 
  only 
  9 
  stops, 
  the 
  C#jf, 
  F##, 
  G## 
  having 
  been 
  

   omitted 
  ; 
  but 
  as 
  the 
  principle 
  admits 
  of 
  the 
  construction 
  of 
  12 
  stops 
  as 
  easily 
  as 
  9, 
  the 
  

   complete 
  form 
  is 
  mentioned 
  in 
  the 
  text. 
  

  

  