THE SOUNDS OF SPEECH 591 



made a very careful study of the whole matter. According to this 

 theory the obvious procedure is to apply the classical Fourier analysis 

 to determine the characteristic components of the vowel sounds. 



Turninj; now to the other (and earlier) view, the so-called "Inhar- 

 monic Theory" of Willis (182*.)) later developed by Hermann and 

 rather recently by Scripture (ref. (6)) we are invited to believe that 

 the "characteristic frequencies" of the vowel sounds are the natural 

 vibrations or transients in the oral cavities, when excited impulsively 

 by the (more or less) periodic puffs of air from the glottis. According 

 to this theory no harmonic relations need obtain between the charac- 

 teristic frequencies of the vowels and the fundamental or cord tone 

 accompanying them; and the classical Fourier analysis is not con- 

 sidered applicable in resolving the vowel sound into simpler compo- 

 nents. According to this "inharmonic" or "transient" theory we 

 must treat the natural \ibrations of the oral cavities as damped 

 vibrations and find the frequencies and damping constants of their 

 components, as best we can from the record of the complete sound 

 vibration. 



In favor of the Heimhoitz or "Harmonic" theory we have the careful 

 studies by Heimhoitz and his successors of the relations between the 

 cord or fundamental tone, its harmonics as reenforced by the oral 

 cavities or other resonators, and the observed characteristic frequen- 

 cies of the vowel sounds. The oral cavities constitute a vibrating 

 system of two or three degrees of freedom, the theory of which has 

 been fully developed by Raylcigh and others, and it is to be expected 

 that, with the speaking mechanism in normal adjustment the vowel 

 qualities can be well accounted for by postulating harmonic forced 

 vibrations in these cavities. This expectation has been realized in 

 the numerous successful attempts which have been made to produce 

 vowels artificially by using a harmonic series of tones, and reenforcing 

 certain harmonics by suitable resonators. Miller's experiments with 

 organ pipes (ref. 3, pp. 246-250), in which he successfully reproduced 

 certain vowel sounds, are well known. 



The Willis-Hermann theory has also suggested much notable experi- 

 mental work. Scripture (ref. 6, p. 114) constructed a "vowel-organ" 

 in which a reed pipe was used to excite the natural vibrations in 

 resonators designed to imitate the conditions in the oral cavities, and 

 attained some success in reproducing vowels. More recently J. Q. 

 Stewart (ref. 8i) has produced an "Electrical Analogue" of the vocal 

 organs with which remarkable results in reproducing vowel sounds 

 and even some of the consonant sounds have been obtained. In this 

 electrical arrangement transients excited by an interrupter in oscilla- 



