1897-98.] Dr Lloyd on Analysis of Tracings of Vowels. 103 
rather than strong. Compare this with what happens to the partials 
of each of these vowels in their phonograms. In the a phonograms 
we have a richly harmonic set of strong partials from the 4th to 
the 8th (fig. 2) ; in the o phonograms it is the lower and softer 
harmonics which come strongly into evidence, from the 2nd to the 
4th ; whilst in the i phonograms of this pitch (fig. 4 is not an 
exact illustration, because it is sung at a much higher pitch, and, 
as the resonance remains unchanged, the reinforcements naturally 
appear on much lower partials) there is strong reinforcement of 
the 2nd partial, and again of the 13th and 14th, or 16th and 17th, 
— high partials of a penetrating dissonance, but all the richer and 
higher harmonics are only feebly present. If the reinforcements 
were not to a large extent true partials, — not merely concomitant 
inharmonic resonances, — these effects could scarcely follow\ 
The evaluation of the pitch of any resonance which only reinforces 
a single partial is exceedingly simple. It is expressed by the 
equation 
n = Np. 
Where N is the pitch-number of the fundamental tone, p is the 
number of the partial, and n is the pitch-number of the required 
resonance. In fig. 4, for example, the isolated reinforcement of 
the 10th partial in a vowel sung at 293 v.d. proves the existence 
of a resonance of 293x 10 = 2930 v.d. The case in which two 
partials are equally reinforced is not quite so simple. We may say 
approximately that 
e.g., in fig. 4 the resonance which reinforces the 7th and 8th 
15 
partials is about 293 x-^- = 2198 v.d. But even here there are 
minor considerations involved, w T hich can only be seen clearly after 
examining one or two more general and more complex cases. 
Let us first take an instance of German long a, sung and 
analysed by Hermann ( Pfl . Arch ., xlvii. 355). The pitch is 
98 v.d., and the analysis is only carried to ten partials, so that it 
does not display the higher resonance of this vowel, except slightly 
on the 10th partial, which is all the better for the present purpose. 
