118 THE STUDY OF SPEECH CURVES. 



be said to have received an added impulse at every second vibration. 

 Speech curves are continually found whose alternate vibrations are a trifle 

 stronger; we know at once that the vibrations occur in groups of two, 

 that the frequency of the cavity tone is twice that of the glottal tone, 

 and that the puffs are very sharp; such curves are to be seen for [i] line 

 96, [e] Une 104 of the Depew plate, and [i] hne 3, [i] hne 7, [i] line 16, [9] 

 Hne 18 of the Cock Robin plate. Similar conditions where the vibrations 

 occur in groups of three — the cavity tone having a frequency of three 

 times that of the glottal tone— are seen in [u] hne 102, [i] of [ai] hne 111 

 of the Depew plate and [e] hne 17 of Cock Robin plate. In [i] line 11 of 

 the Cock Robin plate groups of four are found. It is a curious fact that 

 this condition seems to be characteristic of certain vowels and not of others. 

 The speech curves also indicate not only that different sets of the 

 cavity tones are present for each kind of vowel, but also that different 

 types of puff forms are used for different vowels. Thus [u] shows a smooth 

 puff, [i] a very sharp one, etc. The vowel character is therefore found 

 in the puff itself as well as in the cavity tones. 



For the ear the succession of puffs produces the tone of the voice, 

 that is, the pitch of the sound heard depends on the interval at which 

 the puff comes. The form of the wave impresses the ear with the effect 

 of timbre, that is, with its character as more or less musical and also 

 with its vowel character. 



Returning, now, to the question of what method of analysis is to be 

 adopted for vowel curves, we must conclude that a frictional analysis is 

 required by the only theory of vocal action which we can accept. The 

 simple harmonic analysis can lead only to false conclusions. 



The reader who does not wish to go into the follovnng more precise 

 statement of the principles involved in the theory of vocal action may 

 pass to the next chapter. 



A vowel consists physically of a series of impulses from the glottis 

 impressed on a set of resonating systems, namely, the air in the vocal 

 cavities. For simphcity each resonance system may be considered 

 to be of one degree of freedom, with the coefficient of elasticity s and 

 the coefficient of friction b. If the friction is neglected or compensated 

 the equation of motion is 



m^=-sy (1) 



of which the solution is 



y = a. sin (\—-t—q). 



