of Edinburgh, Session 1877-78. 
715 
second partial might vary greatly at any one pitch, although the sounds 
were all sung or spoken as o, and received by the ear as (generically) 
that vowel. For example, on b one voice gave the ratio of prime 
to second as 1 to 0’87, while another voice on the same note gave 
the ratio 1 to 1*8. In any one voice there is not very much change in 
the ratio in passing from note to note. When the pitch is as high 
as d' or higher, the ratio of prime to second is decidedly greater 
than on the lower notes of this range. It is probable that the ratio 
is a minimum for any one voice about the pitch 5b, but this is a 
point requiring further investigation. We have not yet got any 
satisfactory o’s above /'. 
When, however, the investigation was carried lower in the scale 
by help of voices of a wider range, several much less simple pheno- 
mena presented themselves. Voices capable of singing bass, when 
singing u down the scale gave the usual simple harmonic from above 
a ; but, at or near that note a remarkable change suddenly took 
place in the wave-form given by the vowel sound u. At that point 
it became a duplex wave, with a very small prime, which corre- 
sponded to the pitch, and an immensely strong second partial, the 
ratio of amplitudes being somewhere about 1 to 4. This form 
continued as the voice went down the scale ; but in addition to the 
very strong second partial a weak third appeared, which became 
pretty strong on c. We cannot say that we have got true and 
articulate w’s at any lower pitch. 
The voice of small range mentioned at the beginning of this paper 
continued to give the single simple harmonic form for u down to 
/, below which it could not go. Two other voices experimented 
with agreed in making the change at or near a. 
The excessive weakness of the prime in the lower, or what we 
call the duplex, form of u shows how weak a prime tone may be 
as compared with its upper partials, and yet fix the musical pitch. 
It also shows how small even the prime may be when not reinforced 
by oral resonance. The primes of the duplex ?As, even when 
loudly uttered, were absolutely as well as relatively much weaker 
than those of the o’s already described. 
The experiments with u seem to point to the conclusion that so 
long as the simple form is given the mouth cavity is adjusted so as 
to reinforce the prime exclusively, whatever be the pitch. When 
