108 THE STUDY OF SPEECH CURVES. 



("first overtone") is heard; it is weaker than the tone of the whole string. 

 When it is touched at one-third of its length instead of half, it vibrates 

 in thirds and the "third partial" ("second overtone") appears. The 

 fourth, fifth, and higher partials can be likewise obtained. The tone 

 of the string when vibrating freely is thus proved to consist of a series of 

 partials. That the series is a harmonic one can be proved by determining 

 the pitch of each partial by comparison with tones of known pitch. The 

 sound curve of such a string would be the sum of the curves for each 

 partial, that for the first partial being the predominant one because— as 

 even the eye can see and the ear can hear— that vibration is strongest 

 in the string. It would naturally be treated by harmonic analysis to 

 obtain the partials and their amphtudes. The harmonic analysis would 

 here be not only a mathematical operation but also a true physical 

 analysis. In this case the analysis would not have to be a frictional one, 

 because the sound dies away so slowly in stringed instruments that the 

 factor of friction would hardly show itself within a single wave. In the 

 case of a maintained tone, as from a violin, the bow keeps the string in 

 continual vibration and the tone registered by the curve would also be 

 subjected to a harmonic analysis into simple sinusoids. 



Suppose, now, a glass or metal resonator to be set up close to a string. 

 When the string is plucked it produces its usual complex tone, consisting 

 of a series of partials of which the first is the loudest. If the natural 

 period of the resonator happens to coincide with that of any one of the 

 partials, that partial will be "reinforced" and will appear louder than 

 otherwise. To reinforce a partial the natural period of the resonator 

 must therefore be harmonic to the fundamental tone of the string. If the 

 resonator is inharmonic to the string, no partial will be reinforced. The 

 sound curve in the case of a string with a harmonic resonator will con- 

 tain the sum of the curves of each of the partials of the string; the curve 

 of the fundamental may be strong and predominating as before (because 

 that element of the tone may still be the loudest), but the curve for the 

 reinforced partial will be stronger than in the case of the string without 

 a resonator. If the resonator is inharmonic to the string, no partial is 

 reinforced; the tone remains the same as without a resonator, and the sound 

 curve will also be the same. In either of these cases the method of har- 

 monic analysis into simple sinusoids will be appropriate because such 

 an analysis corresponds to the way in which the sound is built up. 

 The character of the tone produced will depend on what size of resonator 

 is used, that is, on which partial is reinforced. By reinforcing several 

 partials in different degrees of intensity a large number of different sounds 

 can be made. 



