WAVE ANALYSIS IN REFERENCE TO VOCAL ACTION. 123 



If this theory of the vowels is valid, it is the object of the analysis 

 of a vowel curve to pick out the elements indicated by this equation. 

 With the present methods it is impossil)le to do so completely, but some of 

 them may be approximated. 



When the puff is very sharp the forced vil^ration will vanish quickly, 

 leaving only the second element which expresses the free vibrations of 

 the cavities. The curve in such a case is mainly a " cavity curve," because 

 its components are the vibrations of the cavities. Since the differences 

 in combining the cavity vibrations furnish the distinctions between the 

 vowels of the language, the second element of equation (13) may be termed 

 the "vowel component." When the puff is moderately smooth (ff of 

 the same grade as e), the two elements will be nearly evenly balanced. 

 A perfectly smooth puff ^ = gives the result previously considered 

 where the acting force was a.sin pt (p. 120); both elements must be con- 

 sidered at the start, afterwards only the first is present. This last con- 

 dition never occurs in speech, because it never happens that a constant 

 series of smooth puffs acts upon a fixed set of cavities. In song, however, 

 it does sometimes happen that the glottis emits such a series of vibrations 

 and that the cavities are fixed for a time. In such cases, where the first 

 element is the more prominent, the sound acquires less a vowel character 

 than a personal one, that is, the vowels of a person differ less from one 

 another than the sounds of different persons for the same vowel. Since 

 the first member of equation (13) is determined mainly by the character 

 of the action at the glottis, it may be termed the "glottal component," 

 or — since this is the governing factor in the musicalness of the voice — 

 the " musical component. " 



In speech curves both the vowel and the musical components are 

 present at each vibration. No method exists that will perform the analysis 

 completely. 



When the glottal puffs are not sharp, the curve contains all the ele- 

 ments indicated by (13). The expression can be simpHfied by writing 

 the two sums as 



y==A^.e-"'.sm(^^t-q,)+ A,.e -'"-'. sm(^ J- q,) + . . . 



+ R^.e-".sm(^^J-q\)+R,.e—.8{n(~^-q\) + • • • (14) 



All that our methods of analysis can do is to represent such a curve 

 by the harmonic series: 



y^c,.e-".sm(^p-q'\) + c.e-' .sin(^t- q",)+ . . . (15) 



