1897-98.] Dr Lloyd on Analysis of Tracings of Vowels. 107 
opening and shutting of the vocal chords, and it is very easy to 
conceive that the control of the resonances over vibrations starting 
from massive organic movements of this kind may be imperfect 
and capricious. 
Better than wasting time in discussing the difficulties, theoreti- 
cal and practical, thus seen to arise in connection with the lower 
partials, is to avoid, as far as possible, lower partials altogether. 
This can be done by singing the vowel low enough. The lowest 
vowel resonance yet observed is an a-resonance of o, 216 v.d., 
which I have calculated from analyses laid before the Koyal Society 
of Edinburgh twenty years ago by Professors Fleeming Jenkin 
and Ewing. Next comes the a-resonance of % about 280 v.d., and 
of e, about 352 v.d. But good vowels can be sung by male voices 
at 100 v.d., and sometimes much lower. Then we get a reinforce- 
ment in which the fundamental, and often the 2nd partial also, are 
not involved. 
Another advantage of using phonograms of low pitch is that all 
the resonances, upper as well as lower, are displayed in greater detail. 
Imagine a note of 300 v.d., with its partials, entering an articula- 
tory cavity which had a proper pitch of 400 v.d., but was capable 
of reinforcing any partials between 300 and 500 v.d. The only 
partial reinforced in the phonogram would be the fundamental 
300 v.d. ; and we should conclude, wrongly, that the resonance 
was 300 v.d., instead of 400. Under like circumstances a reson- 
ance, apparently only affecting the 2nd partial (600 v.d.), might 
really be due either to a resonance of 500 v.d. or to one of 700 v.d. 
But if the same vowel were sung at 100 v.d., the reinforcements in 
question would culminate exactly on the 4th, or the 5th, or the 
7th partial (400, or 500, or 700 v.d.), according to the real 
resonance. 
More important, and equally common, is the case of two inde- 
pendent resonances acting simultaneously. If a vowel is sung at 
300 v.d. and has two resonances, differing by 300 v.d., it is never 
possible to discern the existence of two separate resonances in the 
analysis, because the partials reinforced are always consecutive. 
Let the resonances, for example, be 900 and 1200 v.d.; the phono- 
grams will then, of course, show in their analysis great reinforce- 
ments of the 3rd and 4th partials. But there will be nothing to 
