﻿14 
  

  

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

  

  The 
  Harmonic 
  Heptadecad, 
  or 
  Unit 
  of 
  Modulation 
  (or 
  Decadation), 
  

  

  trlb 
  

  

  +f 
  

   1 
  L 
  

  

  

  

  

  

  fo 
  

  

  le 
  

  

  

  

  teb 
  

  

  tBb 
  

  

  D 
  

  

  Hr 
  

  

  

  Sll 
  

  

  To 
  

  

  Re 
  

  

  

  

  to|j 
  

  

  

  a 
  

  

  B 
  

  

  tat 
  

  

  du 
  

  

  Mo 
  

  

  So 
  

  

  Ti 
  

  

  ri 
  

  

  

  tAb 
  

  

  c 
  

  

  E 
  

  

  

  or 
  - 
  

  

  Lo 
  

  

  Do 
  

  

  Mi 
  

  

  se 
  

  

  

  

  F 
  

  

  A 
  

  

  

  

  ro 
  

  

  Fa 
  

  

  La 
  

  

  de 
  

  

  

  

  

  id 
  

  

  

  

  

  ta 
  

  

  ra 
  

  

  

  consists 
  of 
  seven 
  interwoven 
  decads, 
  which 
  are 
  constructed 
  on 
  the 
  

   seven 
  tones 
  of 
  a 
  heptad 
  as 
  tonics, 
  and 
  contains 
  24 
  tones. 
  On 
  the 
  left 
  is 
  

   the 
  heptadecad 
  of 
  0, 
  in 
  which 
  the 
  decad 
  of 
  C 
  is 
  printed 
  in 
  capitals, 
  and 
  

   the 
  added 
  tones 
  necessary 
  to 
  complete 
  the 
  heptadecad 
  in 
  small 
  letters. 
  

   On 
  the 
  right 
  solfeggio 
  names 
  are 
  proposed 
  as 
  substitutes, 
  to 
  be 
  pronounced 
  

   with 
  Italian 
  vowels. 
  These 
  names 
  are 
  founded 
  on 
  those 
  used 
  by 
  the 
  

   Tonic 
  Solfaists, 
  and 
  are 
  suitable 
  to 
  any 
  original 
  tonic 
  Do 
  ; 
  and 
  they 
  are 
  

   introduced 
  because 
  singers 
  in 
  just 
  intonation 
  should 
  become 
  accustomed 
  

   to 
  the 
  " 
  mental 
  effect 
  " 
  of 
  each 
  of 
  these 
  tones 
  in 
  relation 
  to 
  the 
  Do 
  selected. 
  

   The 
  decads 
  are 
  named 
  from 
  the 
  names 
  of 
  the 
  tones 
  in 
  the 
  original 
  decad. 
  

   The 
  G- 
  decad 
  is 
  the 
  dominant 
  or 
  So 
  decad 
  ; 
  the 
  F 
  the 
  subdominant 
  or 
  Fa 
  

   decad 
  ; 
  the 
  A 
  the 
  right 
  relative, 
  or 
  major 
  Sixth, 
  or 
  La 
  decad 
  ; 
  the 
  tE[? 
  is 
  

   the 
  left 
  relative 
  or 
  minor 
  Third 
  or 
  Mo 
  decad 
  ; 
  the 
  E 
  is 
  the 
  right 
  cor- 
  

   relative 
  or 
  major 
  Third, 
  or 
  Mi 
  decad 
  ; 
  and 
  the 
  tA[? 
  is 
  the 
  left 
  correlative 
  

   or 
  minor 
  Sixth 
  or 
  Lo 
  decad 
  — 
  all 
  with 
  reference 
  to 
  the 
  C 
  or 
  tonic 
  or 
  Do 
  

   decad. 
  These 
  six 
  decads 
  are 
  related 
  to 
  the 
  original 
  decad 
  in 
  the 
  first 
  

   degree. 
  The 
  dominant 
  and 
  subdominant 
  decads 
  have 
  each 
  seven 
  tones, 
  

   the 
  relative 
  and 
  correlative 
  decads 
  have 
  each 
  six 
  tones, 
  in 
  common 
  with 
  

   the 
  original 
  decad. 
  The 
  dominant 
  decad 
  raises 
  two 
  tones, 
  F 
  and 
  A, 
  by 
  a 
  

  

  comma, 
  to 
  tf 
  and 
  ta, 
  and 
  one, 
  F, 
  by 
  a 
  sharp, 
  to 
  f 
  J. 
  The 
  subdo- 
  

   minant 
  depresses 
  two 
  tones, 
  tB|? 
  and 
  D, 
  by 
  a 
  comma, 
  to 
  b\} 
  and 
  id, 
  and 
  

   one, 
  D, 
  by 
  a 
  sharp, 
  to 
  dj?. 
  These 
  two 
  decads 
  are 
  therefore 
  equally 
  related 
  

   to 
  the 
  original. 
  The 
  right 
  relative 
  decad 
  depresses 
  one 
  tone, 
  D, 
  by 
  a 
  

  

  comma, 
  to 
  id, 
  and 
  raises 
  three 
  tones, 
  F, 
  C, 
  Gr, 
  by 
  a 
  low 
  sharp, 
  to 
  

  

  ±f#, 
  tcjf, 
  Jgjf. 
  The 
  right 
  correlative 
  decad 
  raises 
  one 
  tone, 
  F, 
  by 
  a 
  sharp, 
  

   to 
  f 
  J, 
  and 
  three 
  tones, 
  C, 
  Gr, 
  D, 
  by 
  a 
  low 
  sharp, 
  to 
  Jc#, 
  ig(, 
  +3$. 
  Hence 
  

   the 
  right 
  relative 
  is 
  more 
  nearly 
  related 
  to 
  the 
  original 
  than 
  the 
  right 
  

   correlative. 
  Similarly- 
  the 
  left 
  relative, 
  changing 
  F 
  in 
  tf, 
  and 
  C, 
  Gr, 
  D 
  

   into 
  te|}, 
  tgj?, 
  td[>, 
  is 
  more 
  nearly 
  related 
  than 
  the 
  left 
  correlative, 
  which 
  

   changes 
  D 
  into 
  d\), 
  and 
  F, 
  C, 
  Gr 
  into 
  tfp, 
  tc[>, 
  tgt>. 
  In 
  commatic 
  tem- 
  

   peraments, 
  where 
  id, 
  tf 
  are 
  not 
  distinguished 
  from 
  D, 
  F, 
  the 
  relative 
  

   decads 
  seem, 
  like 
  the 
  just 
  dominant 
  and 
  subdominant, 
  to 
  have 
  7 
  tones 
  in 
  

   common 
  with 
  the 
  original, 
  and 
  similarly 
  the 
  dominaut 
  and 
  subdominant 
  

   decads 
  appear 
  to 
  have 
  9 
  tones 
  in 
  common 
  with 
  the 
  original. 
  Hence 
  

   various 
  important 
  confusions 
  have 
  arisen, 
  of 
  which 
  it 
  must 
  suffice 
  to 
  have 
  

   indicated 
  the 
  source. 
  Since 
  the 
  most 
  natural 
  and 
  easy 
  harmonic 
  tri- 
  

  

  