THEORIES OF VO WEL TONES. 1217 



are ranged in two camps those who uphold the theory of relative as 

 opposed to those who contend for the theory of fixed pitch. Assuming 

 that a vowel is always a compound tone, composed of a fundamental and 

 partials, those who uphold the relative pitch theory state that, if the 

 pitch of the fundamental tone is changed, the pitch of the partials 

 must undergo a relative change ; while their opponents contend that 

 whatever may be the pitch of the tone produced by the larynx, the 

 pitch of the partial that gives quality or character to a vowel is always 

 the same, or, in other words, vowel-tones have a fixed pitch. 



There are many methods of investigating this problem, but these 

 may be grouped in two divisions first, experimental methods, by which 

 the pitch of the oral cavity, in the position suitable for the production 

 of any given vowel, may be determined ; and, second, mathematical 

 methods, by which the curve or wave-form, representing a certain quality 

 of vowel-tone, may be analysed into its components, in accordance with 

 Fourier's theorem. 



One of the early experiments of Willis l favoured the fixed-pitch 

 theory. A piece of watch-spring was held by forceps against a revolv- 

 ing toothed wheel. A compound tone was produced, which of course 

 retained the same pitch so long as the wheel revolved uniformly. Now, 

 by keeping the wheel revolving at a uniform rate, and at the same time 

 changing the length of the portion of the spring which was allowed 

 to vibrate, Willis found that the qualities of various vowels were 

 obtained with considerable distinctness. 



Willis also used reed pipes attached to cylindrical chambers of 

 variable length, and altered the quality of tone by increasing or 

 diminishing the length of the resonant chamber. The shortest tubes 

 gave /, then E, A, 0, to U. In this way he determined the pitch of the 

 vowel as it sounds in words. 2 



As already stated, Bonders 3 was the first to show that the cavity of 

 the mouth, as arranged for the giving forth of a vowel, was tuned as 

 a resonator for a tone of a certain pitch, and that different pitches 

 corresponded to the forms of the cavity for the different vowels. This 

 he discovered, not by the use of tuning-forks, but by the peculiar noise 

 produced in the mouth when the different vowels are whispered. The 

 cavity of the mouth is then blown like an organ-pipe, and by its 

 resonance reinforces the corresponding partials in the rushing wind- 

 like noise. The question was then taken up by Helmholtz, 4 and 

 treated in his usual masterly fashion. To determine the pitch of the 

 cavity of the mouth, considered as a resonance cavity ,he struck tuning- 

 forks of different pitches, and held them before the opening of the 

 mouth, say widely opened. Then, the louder the proper tone of the 

 fork was heard, the nearer " it corresponded with one of the proper tones 

 of the included mass of air." As the shape of the mouth could be altered 

 at pleasure, according to the vowel to be emitted, it was easy to 



1 Op. tit., p. 231. 



2 Ellis. See footnote in "Sensations of Tone," by Helmholtz, p. 170; also article 

 'Sound" in Encyc. MetropoL, par. 375, by Sir John Herschell. 



3 Op. cit.; also Arch. /. d. holldnd. Beitr. z. Nat- u. Heilk., Utrecht, 1857, Bd. i. S. 

 157 ; see also references to older observers in Helrnholtz's " Sensations of Tone," p. 162 

 (footnote). 



4 "Ueber die Vokale," Arch. f. d. holldnd. Beitr. z. Nat- u. Heilk., Utrecht, 1857, Bd. 

 i. S. 354-355 ; also "Ueber die Klangfarbe der Vocale," Gel. Anz. d. k. bayr. Akad. d. 

 (fissensch., 1879, S. 537-541 ; Ann. d. Phys. u. Chem., Leipzig, Bd. cviii. S. 280 ; also in 

 Wissensch. Abhandlungen, Bd. i. S. 395-397 : also "Sensations of Tone," chap. v. p. 153. 



VOL. II. 77 



