
HARMONIC ANALYSIS OF CERTAIN VOWEL SOUNDS. 775 
We should describe the a° and a cavities as differing from the 6 cavity 
chiefly in having a higher pitch of resonance. Their range of reinforcement 
appear even more extensive than that of the 6 cavity. 
It is very satisfactory to find that the o’s given by the human voices which 
we have experimented with are marked by the strong resonance on ),’, 
which Hretmuo.tz has noticed by quite different methods of observation. It 
tends to show that our 6 was essentially the same vowel sound as his, and to 
give us confidence in the mode of experiment which we have adopted. This 
resonance is much less noticeable in voice 3 than in the other voices he has 
tried, and it does not appear to exist at all in the artificial o’s given by Dr 
Crum Brown’s bottle. From this we may, perhaps, conclude that it is a 
peculiarity of the human voice rather than a really essential feature of an 6 
cavity. 
Since the experiments were concluded, our attention has been drawn to a 
paper by Ferix Aversacn* (“ Pogg. Ann. Erginzung,” viii. 2), describing an 
investigation of vowel sounds conducted by him in the physical laboratory at 
Berlin, under the guidance of Professor HetmuHoitz. He endeavoured to esti- 
mate, by means of resonators, the comparative strength of the several partial 
tones where given vowels were sung, and from the figures so obtained he has 
deduced what is in many respects a novel theory of vowel sounds. He con- 
ceives the number expressing the intensity of each tone to be capable of being 
split up into two factors, one of which is a function of the absolute pitch, and 
the other of the number of the partial. The second function is of course discon- 
tinuous ; but the first, he states, may be expressed by an equation of the third 
order, giving a curve whose maximum occurs at a pitch which he calls the 
reduced characteristic tone, but with very extended perceptible reinforcement 
on both sides of that pitch. The expression, characteristic tone, appears to be 
used by AUERBACH in a sense very different from that of HELMHoLTz. It will be 
observed that our results are so far in agreement with those of AUERBACH, that 
we recognise the relative and absolute factors as both entering into the com- 
position of a vowel, but we cannot say that our figures agree at all with his 
estimates, or support any conclusions which he has drawn from them, except 
that the two elements of absolute pitch and relation between partials must 
both be taken into account. We have been unable to discover any constant 
multiplier resembling AUERBACH’s factors, and, indeed, the existence of any 
constant multipliers, such as he employs, is inconsistent with the great variation 
in proportion between the constituent tones which we observed with different 
voices and even the same voices. 
In conclusion, we may notice one or two minor points brought out during 
* AUERBACH uses the word ‘‘ factor” to denote a constant multiplier, which is not the sense in which 
the word has been employed on page 772. 
