102 Proceedings of Royal Society of Edinburgh. [sess. 
eiently strong to be recognised separately by the ear, as they 
certainly are in whisper, and that it is thus we arrive at the cogni- 
tion of the vowel, as distinguished from that of the musical tone. 
We need not doubt the power of the ear to make this separate 
cognition ; it is a much simpler matter than the separate cognition 
of two voices heard simultaneously ; and the fact that the reson- 
ances are not, except by accident, harmonic to the glottal tone, or 
to any of its partials, may reasonably be thought to afford to the 
ear a criterion of distinction ; though the auditory mechanism for 
such a distinction may not yet have been made clear. But if the 
phonogram contains inharmonic elements, how is it possible that it 
can be completely analysed into harmonic elements h Simply 
because the inharmonic elements, that is to say the resonances, 
arise and fall within the limits of each wave of the phonogram ; 
they take a fresh start at each opening of the glottis. Hermann 
has illustrated this very fully (op, cit.). They are thus periodic, 
though not harmonic ; and anything periodic can be analysed 
approximately into harmonic partials of a tone of that period. 
As a matter of fact the inharmonic elements come out in the 
analysis mainly as apparent reinforcements of those harmonic 
elements which they most closely resemble, i.e., of those very 
partials which they really reinforce. Hence, for the purpose of 
locating and evaluating the proper pitch of a resonance, it is prac- 
tically immaterial whether we adopt Hensen’s view or Hermann’s, 
or an intermediate one. In any case, the locality of any reinforce- 
ment of the partials indicates in a general way the pitch of the 
resonance which has caused it. We may proceed, in fact, to use 
the data of the reinforcements to calculate the independent pitch 
of the resonance. But on doing so, certain preliminary questions 
present themselves for solution. 
Before trying to deal with these, a class of facts may be noted 
which go to show that the reinforcements seen in vowel-phonograms 
are also, in some considerable measure, real partials of the glottal 
note. Let a good male voice sing o, a, i in their Italian values, at 
a pitch about 165 v.d. — the middle e of a bass voice. Hot only 
does the vowel change, but the musical quality of the tone changes 
also. The brightest vowel is a ; the o is agreeable, but softer and 
duller ; the i is much thinner in quality, and sometimes incisive 
