1897-98.] Prof. M‘Kendrick on Theories of Vowel Sounds. 79 
produced by the sounds of vowels. In 1870, Pleeming Jenkin 
and Ewing* succeeded in obtaining tracings of the records of vowel 
sounds on the tinfoil phonograph, and the curves were submitted 
to harmonic analysis. This was the beginning of the present dis- 
cussion. These two observers obtained good curves, even with the 
imperfect instrument, and the curves were submitted to analysis, so 
as to determine the amplitude of their constituents up to the 
sixth partial, and the process of measurement and calculation was 
applied to more than 100 curves. The sixth partial was not a 
high limit to reach, but the phonograph at that date did not record 
the higher partials. Eor example, it could not reproduce the 
sound of i in machine nor the Erench or German u. Twelve 
values for y (the lengths of the co-ordinates for one period chosen) 
gave the data for calculating the amplitude and phases of the first 
six partials. Professor Tait supplied the authors with the solu- 
tions of the simultaneous equations for twelve values of y , and the 
results are given in a series of tables, in which the predominance 
of certain partials is unmistakable. In this way each vowel was 
examined. The conclusions arrived at were, on the whole, favour- 
able to the constant pitch theory, and were thus summed up — 
“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 inde- 
pendently of pitch. Before the constituents for 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.” f 
Again, “ the ear is guided by two factors, one depending on the 
harmony or group of relative partials, and the other on the abso- 
lute pitch of the reinforced constituents.” The ear recognises, as 
it were, when it hears a vowel sung at any pitch, the kind of oral 
cavity causing the reinforcement. As to the question, “ is the 
resonance cavity for a vowel sound constant at all pitches ” ? the 
authors are cautious, and their opinion appears to be that, whilst 
* Fleeming Jenkin and Ewing, “ On the Harmonic Analysis of certain 
Vowel Sounds,” Trans. Roy. Soc Edin . , vol. xxviii. p. 745. 
f Jenkin and Ewing, op. cit . , p, 770. 
