﻿1874.] 
  

  

  Mr. 
  A. 
  J. 
  Ellis 
  on 
  Musical 
  Duodenes. 
  

  

  23 
  

  

  The 
  48 
  tones 
  thus 
  pointed 
  out 
  form 
  the 
  32 
  trines, 
  which, 
  with 
  their 
  

   skhistic 
  synonyms, 
  are 
  shown 
  on 
  Table 
  II. 
  By 
  taking 
  these 
  in 
  quater- 
  

   nions 
  we 
  obtain 
  29 
  duodenes. 
  In 
  Table 
  II. 
  the 
  root 
  of 
  the 
  duodene 
  is 
  

   written 
  against 
  its 
  uppermost 
  trine, 
  and 
  hence 
  the 
  root 
  itself 
  is 
  found 
  in 
  

   the 
  middle 
  of 
  the 
  second 
  trine 
  below, 
  and 
  the 
  whole 
  duodene 
  extends 
  to 
  

   the 
  third 
  trine 
  below. 
  Trines 
  on 
  the 
  same 
  line 
  are 
  skhistically 
  identical, 
  

   the 
  capitals 
  indicating 
  the 
  names 
  of 
  the 
  48 
  selected 
  tones 
  of 
  cols. 
  I. 
  to 
  vi., 
  

   lines 
  j) 
  to 
  %, 
  in 
  Table 
  I. 
  In 
  Table 
  III. 
  the 
  roots 
  of 
  these 
  duodenes 
  are 
  

   arranged 
  in 
  4 
  columns, 
  of 
  which 
  each 
  tone 
  in 
  the 
  same 
  line 
  is 
  skhis- 
  

   tically 
  identical; 
  but, 
  proceeding 
  from 
  left 
  to 
  right, 
  each 
  tone 
  is, 
  in 
  

   just 
  intonation, 
  one 
  skhisma 
  natter 
  than 
  the 
  next 
  adjacent 
  tone 
  on 
  

   the 
  right. 
  

  

  In 
  Table 
  III., 
  also, 
  the 
  tones 
  in 
  each 
  of 
  the 
  duodenes 
  are 
  written 
  down 
  

   in 
  the 
  order 
  in 
  which 
  they 
  would 
  stand 
  on 
  a 
  manual 
  ; 
  but 
  the 
  skhistic 
  

   identities 
  of 
  the 
  central 
  column 
  of 
  tones 
  in 
  the 
  preceding 
  Table 
  of 
  Octs 
  

   (p. 
  19) 
  have 
  been 
  used 
  to 
  give 
  the 
  same 
  names 
  to 
  all 
  the 
  tones 
  in 
  one 
  

   column, 
  exclusive 
  of 
  the 
  prefixed 
  f 
  and 
  J, 
  We 
  thus 
  see 
  clearly 
  that 
  

   three 
  new 
  tones 
  are 
  introduced 
  by 
  each 
  new 
  successive 
  duodene, 
  two 
  

   falling 
  and 
  one 
  rising 
  by 
  a 
  skhistic 
  comma, 
  as 
  respects 
  the 
  tones 
  they 
  

   replace. 
  "We 
  also 
  see 
  that 
  each 
  tone 
  prevails 
  through 
  4 
  consecutive 
  

   duodenes, 
  and 
  that 
  there 
  are 
  4, 
  and 
  only 
  4, 
  varieties 
  of 
  t, 
  t 
  in 
  each 
  

   column. 
  

  

  This 
  completes 
  the 
  theory 
  of 
  the 
  construction 
  of 
  instruments, 
  because 
  

   the 
  rest 
  is 
  properly 
  the 
  work 
  of 
  the 
  mechanician, 
  and 
  consists 
  simply 
  in 
  

   devising 
  a 
  method 
  for 
  bringing 
  each 
  of 
  these 
  29 
  duodenes 
  under 
  the 
  hand 
  

   of 
  the 
  performer, 
  when 
  indicated 
  by 
  the 
  duodenal. 
  It 
  will 
  be 
  sufficient 
  

   here 
  to 
  point 
  out 
  a 
  few 
  experimental 
  instruments, 
  to 
  suggest 
  some 
  prac- 
  

   tical 
  forms, 
  and 
  to 
  show 
  that 
  means 
  of 
  playing 
  in 
  just 
  intonation 
  with 
  

   fixed 
  tones 
  already 
  exist. 
  

  

  F. 
  Justly 
  or 
  Skhistically 
  Intoned 
  Instruments. 
  

  

  1. 
  Just 
  Concertina 
  (exhibited 
  when 
  this 
  paper 
  was 
  read). 
  The 
  C 
  con- 
  

   certina 
  described 
  in 
  my 
  former 
  paper 
  (Proceedings, 
  

   vol. 
  xiii. 
  p. 
  104) 
  contains 
  the 
  portion 
  of 
  a 
  hepta- 
  

   decad 
  shown 
  in 
  the 
  margin 
  — 
  that 
  is, 
  the 
  duodene 
  of 
  

   E 
  with 
  the 
  exception 
  of 
  A 
  J, 
  and 
  the 
  duodene 
  of 
  A 
  

   with 
  the 
  exception 
  of 
  +E#. 
  It 
  has 
  the 
  whole 
  decad 
  

   of 
  E, 
  and 
  the 
  major 
  scales 
  of 
  E, 
  C, 
  G, 
  E. 
  I 
  have 
  

   found 
  it 
  a 
  most 
  useful 
  instrument 
  in 
  all 
  my 
  ex- 
  

   periments. 
  Using 
  capitals 
  for 
  white 
  and 
  small 
  

   letters 
  for 
  black 
  studs, 
  its 
  14 
  notes 
  are 
  tuned 
  thus 
  : 
  — 
  

  

  fA 
  

  

  

  D 
  E# 
  

  

  

  g 
  b 
  

  

  

  C 
  E 
  

  

  

  E 
  A 
  

  

  

  Et> 
  £D 
  

  

  

  C 
  totf, 
  D 
  id, 
  E 
  Jd#, 
  F 
  f#, 
  G 
  igjf, 
  tA 
  a, 
  B 
  b[>. 
  

  

  