622 



THE NERVOUS SYSTEM. 



stretched between two points is set in' vibration, as by drawing 

 the bow of a violin over it, it will vibrate as a whole (Fig. 399, 

 a-b) and emit a tone which, being the lowest that it can emit, is its 

 fundamental or prime tone. If now this string is held at its 

 middle point, c, and either half is bowed, that half of the string 

 will vibrate, and after the finger has been removed the other half 

 will also vibrate, and the tone emitted will be an octave higher ; 

 in a similar manner the string may be held at one-third, one- 

 fourth, etc., of its length, and the string when bowed will divide 



into three or four segments, and the 

 frequency of the emitted tones will 

 be three or four times that emitted 

 by the string when it vibrated as a 

 whole. Such a series of tones is a 

 harmonic series, and all the tones 

 above the fundamental are har- 

 monic overtones , or upper partial 

 tones, or simply partial tones. To 

 demonstrate this more effectively, a 

 sonometer may be used, which con- 

 sists of a wire stretched over a sounding-box (Fig. 400) with a 

 graduated scale, so that the divisions of the wire may be accurately 

 determined. In order to produce these overtones it is not neces- 

 sary to divide the string with the finger, or, in the case of the sonom- 

 eter, the wire with the bridge ; for in the vibration of the string 

 or wire as a whole it divides itself, so that it may vibrate as a whole 

 and also in segments ; and consequently, while the whole vibrat- 

 ing string or wire emits the fundamental tone, the subdivided seg- 

 ments emit each its own partial tone, producing therefore compound 

 tones, the fundamental tone determining the pitch. As a rule, the 



FIG. 399. Vibrating strings. 



FIG. 400. Sonometer. 



sounds of musical instruments are compound tones, and, as Helm- 

 holtz has shown, it is the partial tones which determine their quality 

 by which they are differentiated from one another, there being no 

 difference in the fundamental tones. Thus if a key on a piano, 

 say "middle C," is struck, the string will vibrate^ as a whole 

 1 32 times in a second, producing one fundamental tone, C, and it 

 will also break up into segments which will vibrate respectively 

 264 times, producing the octave C f ; 396 times, producing the fifth 

 above this ; 528 times, producing the second octave C" ; 660 times, 

 producing the third above this, etc. 



