1897-98.] Prof. M‘Kendrick on Theories of Vowel Sounds. 73 
uphold the theory of relative as opposed to those who contend for 
the theory of fixed pitch. Assuming that a vowel is always a 
compound tone, composed of a fundamental and partials, those 
who uphold the relative pitch theory state that if the pitch of the 
fundamental tone is changed, the pitch of the partials must undergo 
a relative change, while their opponents contend that whatever 
may be the pitch of the tone produced by the larynx, the pitch of 
the partial that gives quality or character to a vowel is always the 
same, or, in other words, vowel-tones have a fixed pitch. 
There are many methods of investigating this problem, but 
these may be grouped in two divisions : — ls£, Experimental 
methods by which the pitch of the oral cavity, in the position 
suitable for the production of any given vowel, may be deter- 
mined; and 2 nd, mathematical methods by which the curve, or 
wave-form, representing a certain quality of vowel-tone, may be 
analysed into its components, in accordance with Fourier’s 
theorem. 
One of the early experiments of Willis* favoured the fixed 
pitch theory. A piece of watch spring was held by forceps against 
a revolving toothed wheel. A compound tone was produced which, 
of course, retained the same pitch so long as the wheel revolved 
uniformly. Now, by keeping the wheel steadily revolving at a 
uniform rate, and at the same time changing the length of the 
portion of the spring which was allowed to vibrate, Willis found 
that the qualities of various vowels were obtained with consider- 
able distinctness. The objection to this experiment obviously is 
that it had nothing to do with resonating cavities. 
Willis also used reed pipes attached to cylindrical chambers of 
variable length, and altered the quality of tone by increasing or 
diminishing the length of the resonant chamber. The shortest 
tubes gave i, then e, a, o, to u. In this way he determined the 
pitch of the vowels, as they sound in words. + 
As already stated, DondersJ was the first to show that the cavity 
* Willis, op. cit ., p. 231. 
t Ellis, see footnote in Sensations of Tone by Helmholtz, p. 170 ; also 
“ Sound,” in Encyc. Metropol ., p. 375, by Sir John Herschell. 
£ Donders, op. cit.; also Archiv. fur die hollandischen Beitrage , vol. i. ; 
see also references to older observers in Helmholtz’s Sensations of Tone , 
p. 162 (footnote). 
