1897-98.] Dr Lloyd on Analysis of Tracings of Vowels. 
113 
of 500 to 800 v.d. between the resonances, much more does it arise 
in one where the difference is only 230 to 360 v.d. Such a vowel 
is o. But before passing from aa, two or three minor points may 
he noticed. Observe in Herr von Duinen’s first vowel that the 
same superposition of resonances is at work as in fig. 10, though 
it fortunately does not obscure the analysis. The “common 
partial” is the 7th, — equally removed from the 5th, on which 
culminates the a-resonance, and from the 9th, on which the 
other culminates. There is concurrent reinforcement in this 
case also ; for there is a numerical culmination on the common 
partial. But this culmination is due to no independent reson- 
ance ; for no such resonance shows any trace of existence in the 
other analyses. 
Note how much less variable is the ratio between the resonances 
than are the resonances themselves. The highest resonances are 
seen in the 5th, 6th, and 8th of Boeke’s spoken vowels, and it is 
important to notice that these (and the 7th) are just those which 
were spoken in the middle of a word, as long vowels between two 
closed consonants. For explanation of this coincidence, and also 
of the observable slight general tendency of Herr von Duinen’s 
resonances to rise in pitch as he ascended the scale, see Journ. of 
Anat. and Phys., vol. xxxi. pp. 235-7. Soon after that article was 
published, Dr Boeke favoured me with analyses of two phonograms 
of Dutch aa, sung by his son, aged 12. I was able in both cases 
to evaluate the a-resonance, and found it to be four semitones higher 
than Dr Boeke’s. This is quite favourable, so far as it goes, to the 
views of vowel composition put forward in that article. But more 
such analyses are needed : the smaller the child, the more valuable 
would be the analysis. 
Observations of the articulation of o have led me to believe that 
it has two resonances, differing by about an octave. An experi- 
ment of Helmholtz (Sens. Tone , p. 60) points strongly in the 
same direction. Yet no phonographic observer has noticed more 
than one resonance in his analysis. But the considerations con- 
tained in this paper readily explain why that is the case. In a 
vowel having two resonances differing only by about 300 v.d., it is 
useless to look for any sign of doubleness in the reinforcements 
evidenced by the Fourierian analysis, unless the vowel is sung 
YOL. XXII. 26/3/98. 
H 
