Bauhaus-Universität Weimar

Researches in experimental phonetics. 
87 
time. It is merely one case of a more general method1 of interpolation 
by a periodic series ; it is thus considered in works on the adjustment of 
measurements.2 
Such an interpolation formula remains simply a mathematical tool un¬ 
less it is found to express the actual nature of the phenomenon measured. 
It has been assumed by practically all writers, that all musical sounds are 
really combinations of a series of sinusoidal partial tones : for example, 
it can be readily demonstrated that a violin string vibrates not only as a 
whole, but also in halves, thirds, quarters, etc. It is also presumably 
true that each of these parts produces a sinusoidal vibration of the air. 
Thus, the peculiar tone of the violin is presumably really the sum of a 
series of approximately sinusoidal tones. The Fourier analysis in such 
a case undoubtedly expresses the nature of the tone. 
In the case of sung vowels the assumption that the vocal cords vi¬ 
brate like reeds, and the further assumption that the mouth acts as a res¬ 
onator reinforcing one or more of the partial tones of the cord would 
justify the use of the Fourier analysis for finding the partial tones of 
the voice-tone and also the tones reinforced by the mouth, provided these 
assumptions were proved to be correct. 
The vocal cords are certainly to be treated as membranous reeds. In 
the main their vibrations can be supposed to follow the usual laws. 
The other assumption, that the mouth acts also as a resonator to rein¬ 
force some of the partial tones of the cord vibration, is certainly not 
justified (p. 73). The main effect of the mouth is to impose a vibra¬ 
tion of its own upon the vibration coming from the cord. The rein¬ 
forcement of partial tones may possibly be present, but it is certainly not 
prominent. The Fourier analysis would be applicable only if the 
mouth tone were coincident with one of the partial tones of the voice 
tone ; this is, at least generally, not the case in song, as has been indi¬ 
cated by Willis, Donders and Hermann, and is certainly not the case 
in speech as is proven by my curves for a. With a mouth tone not coin¬ 
cident with a partial tone the Fourier analysis may, in a vowel of con¬ 
stant pitch, indicate a reinforcement of the nearest partial vibration, or 
it may show reinforcement of the two nearest partials above or below. 
The analysis can thus be used to indicate the approximate pitch of the 
mouth tone in such a case, although it may not coincide with a partial of 
the voice tone.3 
'Gauss, Theoria interpolationis methodo nova tractata, Werke III 265, 1876. 
2 Weinstein, Physikalische Maassbestimmungen, I 486, Berlin 1886. 
3Hermann, Phonophotog'aphische Untersuchungen, Archiv f. d. ges. Physiol. 
(Pflüger), 1894 LVIII 276.
        

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