1897-98.] Prof. M‘Kendrick on Theories of Vowel Sounds. 75 
illustration will show how Helmholtz, following out the theory 
applicable to all musical instruments, endeavoured to explain the 
quality of different voices. His theory as to vowel-tone is summed 
up in the following sentence “ Vowel qualities of tone conse- 
quently are essentially distinguished from the tones of most other 
musical instruments by the fact that the loudness of their partial 
tones does not depend upon the numerical order but upon the abso- 
lute pitch of those partials. Thus, when I sing the vowel a to the 
note Eb> the reinforced tone b"\ ? is the 12 th partial tone of the 
compound ; and when I sing the same vowel a to the note V b> the 
reinforced tone is still b" b> but is now the 2 nd partial of the com- 
pound tone sung.” * 
Further, Helmholtz endeavoured to demonstrate the correctness 
of his view by synthetically combining the tones of certain tuning- 
forks in his well-known vowel- tone apparatus.! He in early 
experiments used eight forks, the first being the fundamental tone 
sqbj and the others the first seven partials. Thus 
si 4 b si 2 b fa 3 si 3 b re 4 fa 4 la 4 b si 4 b- 
The vowel o is well sounded with this apparatus when we sound 
sigb (characteristic of o) strongly, more feebly si 2 b> fa 3 , re 3 , and the 
fundamental softly, ou is good with ei x b strong, and the partials 
feeble. Using, in another apparatus, 
si 2 b si 3 b fa 4 si 4 b re 5 fa 6 la 5 b si 5 b> 
ou was given with si 2 b (the fundamental) alone, o was sounded 
by fundamental si 2 b moderate, si 3 b strong, and fa 4 weak. If we 
sound si 2 b (fundamental) along with si 3 b> and fa moderate, and 
si 4 b and re 5 strongly, we obtain a. This vowel is characterised by 
si 4 b> along with the partials si 3 b and si 2 b* To obtain e, give 
si 2 b and si 3 b moderate, and fa 3 , la 3 b> and si 3 b as strong as possible. 
The characteristic partial of this vowel is si 3 b* I have performed 
many experiments with this apparatus, and find the results obtained 
by Helmholtz to be consistent with experience. Much depends, in 
the appreciation of this experiment, on careful attention, practice, 
and a good ear. 
* Helmholtz, Sensations of Tone, p. 172. 
t For figure and description of this famous apparatus, see M‘Kendrick’s 
Physiology , vol. ii. p. 691. 
