770 PROFESSOR FLEEMING JENKIN AND J. A. EWING ON THE 
vol, xviii. p. 167, we have given a short account of what we believed to be the 
existing state of the theory of vowel sounds, and we will take advantage of that 
publication to make our reference in this place to previous writers on the subject 
as brief as possible. It is generally recognised that vowel qualities of tone are 
produced by the action of the oral cavities in reinforcing by resonance certain 
partial tones in the composite sound given by the vocal chords. ‘The “ constant 
cavity theory” of vowel sounds, which is taught by Donprrs, and which is 
frequently spoken of as the doctrine of HELMHOLTz (aithough we have found no 
definite and rigid statement of it in his Tonempfindungen), also asserts that for 
a given vowel the resonance cavity of the mouth is unaltered at all pitches on 
which the vowel is sung, and that the cavities for different vowels are distin- 
guished by their “ proper ” or “ characteristic ” tones, or, in other words, by their 
pitches of maximum resonances, which are nearly independent of age and sex, 
and depend solely on the vowels for pronouncing which the mouth has been 
arranged. Then, when the vowel is sung on any subtone of the pitch of maxi- 
mum resonance of the cavity, the overtone corresponding to that pitch will be 
very strongly present. The theory does not give a definite answer to the 
question, what will happen when no partial of the note sung coincides even 
approximately with the pitch of the proper tone, or how the vowel is recognised 
in that case. The pitches of the characteristic tones for various vowels have 
been examined by noticing the pitch of the whispered vowel, and also by 
observing the resonance when tuning forks are held before the mouth, the 
mouth being set for a particular vowel; but they are far from identical, as 
determined by different observers. This, however, may be explained by saying 
that the quality of the vowels experimented on was not the same. HELMHOLTZ 
says that he has detected only one proper tone for the vowels @, 6, a’, and @. 
For 6 he gives 0,’, and for @ b,”, while a occupies an intermediate position, vari- 
able with the quality of the vowel. For a he says it is by no means easy to find 
the pitch of resonance by tuning forks : he gives / as the pitch for this vowel, 
adding, however, in a footnote that there appear to be great personal differences, 
so that small alterations of the pronunciation may drive the pitch up to /’. 
HELMHOLTZ does not say (so far as we have seen) whether the mouth-cavities 
for these vowels, for which he has detected only one proper tone, differ phoneti- 
cally in any other respect than in the pitch of that proper tone. 
Passing now to our own results, it is clear that the quality of a vowel sound 
does not depend either on the absolute pitch of reinforcement of the constituent 
tones alone, or on the simple grouping of relative partials independently of pitch. 
Before the constituents of a vowel can be assigned, the pitch of the prime must 
be given; and, on the other hand, the pitch of the most strongly reinforced 
partial is not alone sufficient to allow us to name the vowel. To do this we 
must also know the relation of the constituent partials to one another. 
