1897-98.] Prof. M £ Kendrick on Theories of Vowel Sounds. 83 
Boy , aged 12, singing aa — 
Pitch. 1 2 3 4 5 6 7 8 9 10 Partials. 
g' 384 v.d., 1 1‘22 2‘67 0*45 0-17 0’06 
e" 640 ,, 1 8 ‘09 1*45 0*53 ... ' ... ss 
Dr Lloyd has examined these figures, and supplied me with the 
following very instructive table : — 
Man’s aa. 
f 170 v.d., 
c' 256 „ 
Boy’s aa. 
g' 384 v.d., 
e" 640 „ 
Partials 
reinforced. 
Evaluated by 
Hermann’s method. 
Me ™, V.D. 
partial. 
Evaluated by 
Pipping’s method 
( = Lloyd’s formula). 
Mean y ^ 
partial. 
4-6 
4*96 
846 
4*90 
836 
3-4 
339 
868 
335 
859 
2-4 
2-82 
1084 
2*75 
1057 
1-3 
2-04 
1307 
1-98 
1267 
A study of these figures will show (1) that the man’s resonance 
rises slightly (J semitone) in ascending 7 semitones in the middle 
of his register ; (2) that the boy’s resonance rises 3 semitones in 
ascending 9 semitones in the upper half of his register ; and in the 
mid-register the boy’s resonance is to the man’s as 5:4. This 
indicates that, as we ascend a scale in singing a vowel, the pitch of 
the oral cavity slightly changes. 
Dr Lloyd holds a view differing from those already described. 
Vowels, according to him, owe their character, not to the resonance 
of a partial or partials of a certain fixed pitch, but to the relative 
pitch of two or more partials. This view accounts for a fact which 
is not explained by the other theories, namely, that the articulation 
of a vowel seems to be the same for a child as for an adult. Thus, 
in the vowel a, as in “ fat,” sung on a note having a pitch of 134 
v.d., Lloyd finds two partials, the lower of which he terms the 
pharyngeal or a-resonance, and the other the oral or /3-resonance. 
Of these the lower for a in “ fat ” has a vibrational number of 
736 v., while the upper has 1121. The ratio of these two partials 
is, therefore, 
1121 
763 
1*47. 
This is termed by Lloyd the radical 
ratio, and it determines the nature of the vowel. Again, the 
radical ratio of the Swedish long a is P35. 
The following instructive curves were sent to me by Dr Boeke, 
