1897-98.] Prof. M‘Kendrick on Theories of Vowel Sounds. 77 
constant, must be due to the super-position of a tone developed in 
the mouth, characteristic of the vowel, upon the tone emitted by 
the larynx.* 
According to Koenig, in man, ou is always easily emitted with 
si 2 b> and the neighbouring tones la 2 , sol 2 with the lower partials sib> 
and mijj ; o is emitted with si 3 b> the partials la 3 , sol 3 , and the lower 
partials si 2 b> mi 2 b> sib ; a comes with si 4 b> with la 4 , with sol 4 , along 
with the lower partials si 3 b> mi 3 b> si 2 b ; e and i are not easily sounded 
on low tones, as their characteristic partials are very high. On 
tones lower than ut 3 , the female voice turns involuntarily to o or 
ou, which have si 3 b and si 2 b as their characteristic partials. Above 
fa 4 it is a, of which si 4 b is characteristic, which is most readily 
given. Above si 4 the voice passes into e and i. These observa- 
tions of Koenig are harmonious with the conclusions of Helmholtz, 
and favour the fixed pitch theory. 
Hallockf has recently employed a device founded on that of 
Koenig. Eight resonators in harmonic series were each con- 
nected with a manometric capsule, and photographs were taken of 
the eight bands of flame pictures, reflected in a mirror, when the 
vowels were sung before the resonators. J From these photo- 
graphs the partials present in any vowel-tone within the range of 
the resonators could be determined. Of course the higher partials, 
on which, as pointed out by Helmholtz, much depends, were not 
detected. 
Wave forms of Voivel-tones . — We must now turn to the evidence 
adduced by an analysis of the wave forms of vowel-tones. To 
appreciate this evidence the following statements must be kept in 
view : — 
1. Pitch depends on the length of time in which each single 
vibration is executed, or, in other words, on the vibrational num- 
ber of the tone. 
2. Musical tones are higher the greater their vibrational number 
that is to say, the shorter the vibrational period. 
3. The sensation excited by a periodic vibration is a musical 
* Gavarett, Phenomenes Physique de la Phonation et de V Audition, 
Paris, 1877, p. 394. 
t Hallock, American Annual of Photography, 1896, p. 21. 
X For a figure of such an analyser, see M ‘Kendrick’s Physiology , vol. ii. fig. 
418, p. 686. 
