1222 



ON VOCAL SOUNDS. 



ances is obtained in the narrow tube formed between the tongue and the 

 hard palate. This resonance has a very narrow range, for the tube will 

 not respond to any partial having a pitch much different from its own. 

 A rounded cavity, on the other hand, such as is formed when we articulate 



55-0 



1-6 



1-0 



1-9 



0-8 



3-3 



3'4 



0-2 



1-4 



0-2 0-2 



0-3 



FIG. 435. Diagram showing the amplitude, as indicated by the height of the ordinates, 

 of the partials of the Swedish i, sung at pitch of 293 vibs. 



aa, will have a much greater range of resonance. 1 The valuation of 

 the pitch of any resonance which only reinforces a single partial, is very 

 simple, and is expressed by the equation 



where N is the vibrational number of the fundamental tone, p the 

 number of the partial, and n is the vibrational number of the resonance, 

 or, in other words, its pitch. In the above figure, for example, the 

 isolated reinforcement of the tenth partial in the vowel sung at 29o 

 v. d. shows the existence of a resonance of 293 x 10 = 2930 vibs. Where 

 two partials are equally reinforced by one cavity, the case is not so 

 simple. Approximately, it is expressed by the equation 



Thus the resonance which reinforces the seventh and eighth partials 

 is about 293 x -^ = 2198 v. d. Even here there are minor considera- 



tions involved, which can only be seen clearly after examining one or 

 two more general and more complex cases. 



Let us take first an instance of German long a, sung and analysed by 

 Hermann. 2 The pitch is 98 vibs., and the analysis is only carried to ten 

 partials, so that it does not display the higher resonances of this vowel, 

 except slightly on the tenth partial. 



1 Lloyd, "On the Fourierian Analysis of Phonographic Tracings of Vowels," Proc. 

 Roy. Soc. Edin., 1898. 



2 " Phonophotographisch. Untersuch.," Bd. i.-v. ; Arch. f. d. ges. PhysioL, Bonn, Bd. 

 xlv. S. 582 ; Bd. xlvii. S. 44 ; Bd. xlvii. S. 347 ; Bd. liii. S. 1 ; Bd. Iviii. S. 255, contain 

 many analyses and much controversy about the Fourierian analysis. No. 2 contains an 

 account of a method of lightening the labour of these analyses ; also, " Bemerkungen zur 

 Vocale-frage " (ibid., Bd. xlviii. S. 181); also, "Vocale im Telephon und Microphon " 

 (ibid., Bd. xlviii. S. 543) ; also, "Weitere Untersuch. ueber das Wesen der Vocale" (ibid., 

 Bd. Ix. S. 169) deals chiefly with short (German) vowels. 



