HARMONIC ANALYSIS OF CERTAIN VOWEL SOUNDS. 759 
Fig. 5, PlateX XX VIII. and Table V., give the curves and analyses of four 
very low bass 0’s, sung by voice 6. 
Fig. 6, Plate XX XVIII, gives a series of o’s sung by voice 2. The pitch 
of each utterance was, in this case, determined by measurement of the curves. 
Table VI. gives the analyses of the examples in fig. 6. 
Table VII. has been drawn up to facilitate comparison of the results 
obtained for 6 with different voices; and it brings out clearly the points of 
agreement and difference between them. It will be seen that from g upwards 
all the voices agree in forming 0 essentially of two partial tones—the prime 
and the second ; but the proportions in which these are present are far from 
constant. On é’, for example, the ratio of prime to second in voice 3 is 100 : 34, 
while in voice 5 it is 100:102. The second partial is conspicuously weak in 
voice 3 throughout this part of the scale. On 0 the difference between voice 1 
and voice 5 is even greater than this. All the voices, however, are alike in one 
respect, that the proportion of the prime to the second partial is a mznimum on 
the note 0; that is to say, when the second partial falls on 04’ it is specially 
strong. With voice 1 it is nearly two and a half times as strong as the prime, 
and with voice 4 it is actually more than three times as strong as the prime. 
An examination of Tables I. to V. will show that the reinforcement of the 
partials, whether first, second, third, or fourth, reaches a maximum when that 
partial falls on 65’—in other words, all tones thus falling on that pitch are 
specially conspicuous. 
Below g the third partial comes in more or less rapidly ; it is strong when 
the vowel is sung on jf, ¢, and d. On ¢ the fourth has become strong, the 
second and third remain so, but the prime has become conspicuously weaker. 
On B, B,, and A, the fourth partial is very strong; with voice 6 on A, its 
amplitude is nearly nine times that of the prime. On G the second partial has 
become weak, and the fourth is still the most conspicuous. In the solitary 
example on F the fifth partial is immensely strong. 
Thus we see that at the pitches ordinarily used in speech the vowel sound 
6 consists almost wholly of the two constituents—a prime and its octave—the 
ratio of whose amplitudes may vary widely. But when the range is extended 
so as to reach lower pitches, higher partials successively appear in such a way 
as to allow the highest strongly reinforced partial to remain in the neighbour- 
hood of b,’; and further, we observe that all the tones between the prime and 
the highest strongly reinforced partial continue prominent until the note sung 
descends to Gand A. The second seems to disappear as the fifth comes in. 
Generally, we may say, from an examination of the foregoing table, that 
there is a wide range of reinforcement, extending over about two octaves 
(from f or g tof”), within which all tones are more or less strongly reinforced, 
and that there is a specially strong reinforcement at the pitch b,’. 
