PREFACE. / 



arbitrary procedure which gives no idea of the real composition until some 

 physical hypothesis is introduced, later investigators have not hesitated 

 to assume that the analysis proves the components of vowels to be rein- 

 forced overtones from the glottis. The unsatisfactory results of many 

 hundreds of analyses made it evident that the simple harmonic analysis 

 was not directly appHcable to vowel curves. In fact, the vowel vibrations 

 are not composed of simple sinusoids, but of sinusoids affected by factors 

 of friction (logarithmic decrement). An analysis that does not provide 

 for this gives incorrect results, as can be readily shown by analyzing fric- 

 tional sinusoids whose equations are known. In Chapter VII, I have 

 explained a method of analysis that provides for the introduction of a 

 single factor of friction. I hope that some mathematician or physicist will 

 devise a way to introduce two factors of friction, one of moderate size to 

 represent the friction in the vocal cavities and one that may vary from 

 to very great values to represent the suddenness of the glottal vibrations. 

 Chapter VIII discusses the theories of vowel production. Professor 

 Hermann (Konigsberg) has given final proof of the incorrectness of the 

 overtone theory (Wheatstone, Grassmann, Helmholtz). The two essen- 

 tials of the theory of Willis and Hermann, namely, that the glottis emits 

 puffs of greater or less sharpness and that the vowel tones are generally 

 inharmonic to the glottal tone, can be considered as definitely estab- 

 Ushed. The reason for the puff-character of the glottal action has been 

 found by Professor Ewald (Strassburg) in the fact that the^ glottal lips 

 are masses of muscle which yield by compression and do not vibrate like 

 membranes. These facts have remained largely unknown, and we still 

 find in the text-books the totally false theory that the vowels are produced 

 by membrane-Uke vibrations in the larynx. I have adopted the WilHs- 

 liermann theory and have taken into consideration some further elements 

 also; namely, friction in the vocal cavities and associative formation of 

 the vowel at the glottis. It is strange that the friction in the vocal cavities 

 should have been so long overlooked; they have for the most part soft 

 walls covered by a moist membrane and their laws of resonance must 

 differ from those of brass or glass cavities. As I have shown with water 

 resonators, the phenomena of resonance in soft cavities are quite different 

 from those with resonators of metal. The other new element was sug- 

 gested by experiments in making artificial vowels which led me to believe 

 that the action of the glottal Hps differs not only for each emotion but 

 also for each vowel; I assume that the nervous impulses to the various 

 portions of these muscles differ for the different vowels, with the result 

 that the glottal lips contract differently for each typical vowel. 



