EXPERIMENTAL PHOKETICS. 255 



depend on the overtones reinforced ))v the oral cavities being" simple 

 multiples of the fundamental tone, and Helmholtz's first theor}' had 

 to be abandoned. 



This led Helmholtz to advance a second theory, as follows: P^ach 

 vowel is characterized by a certain harmonic or partial tone, of con- 

 stant pitch, whatever may be the pitch of the note on which the vowel 

 is sung or spoken. Attempts were then made, notably by Hemholtz 

 and Konig, to fix the pitch of the characteristic partial tone or vocable, 

 and there appeared to be considerable ditt'erences in the results of the 

 two distinguished observers, differences amounting to as much, in 

 some cases, as three semitones. 



The next step was, as has already been explained, to transcribe the 

 marks on the wax cylinder of the phonograph, made on singing or 

 speaking a vowel, into simious curves and to subject these to harmonic 

 analy^^is. It is not difficult, in comparativel}' simple cases, to obtain 

 a curve which is the algebraic sum of the ordinates of several sinus- 

 soidal curves, but it is not so easy to do the reverse operation, namely, 

 to analyze the curves. Fleeming Jenkin, and Ewing, afterwards 

 Schneel)eli, Hensen, Pipping, and Hermann, have done this in accord- 

 ance with the theorem of Fourier and the law of Ohm. In particular, 

 Hermann, b}^ a beautiful and ingenious method, has analyzed the 

 curves obtained l)v his photographic device, and has modified the 

 theory of Helmholtz. His statement is that the oral cavity produces 

 independently a harmonic or partial tone which has no definite relation 

 to the fundamental tone emitted by the larynx. A vowel, according 

 to him, is a special acoustic phenomenon, depending on the intermittent 

 production of a special partial, or '"''formant," or "characteristique." 

 The pitch of the "formant" ma} vary a little without altering the 

 character of the vowel. For a, for example, the '"formant" may var}^ 

 irom fa^ to hf^, even in the same person. He has also attempted, but 

 not with complete success, to reproduce the vowel tones by synthesis. 



There are thus three theories: (1) The first of Helmholtz, now aban- 

 doned, that the pitch of the partials is represented by simple nudtiples 

 of the vi])ration periods of the fundamental; (2) the second of Helm- 

 holtz, that the pitch of the characteristic partial is always fixed, but 

 has a definite relation to the pitch of the fundamental; and (3) that of 

 Hermann, that the pitch of the characteristic ])artial or ''formant" is 

 not absolutely fixed. 



The difficulty of harmonizing these theories has stinudated the zeal 

 of many workers, and in particular Dr. Marage" has ])een remarkably 

 successful in his researches into the nature of vowels. He first of all 

 criticizes the second theory of Helmholtz, pointing out that the failure 

 to reproduce the vowels by synthesis is strongly against it. Thus while, 



« Marage: Tlieorie de la Formation des Voyelles, op. cit. 



