PHYSICS NINETEENTH CENT. SOUND. 



543 



FIG. 258. PROFESSOR HELMHOLTZ. 



Now, Helmholtz has demonstrated by various ingenious experi- 

 mental contrivances that whenever we hear a musical note sounding 

 on any instrument, there are present not only the principal set of 

 vibrations which gives the pitch of the note, but other sets determined 

 by properties of the sounding body. Thus, for example, a stretched 

 string will not vibrate simply as a whole, but will also divide itself into 

 segments, each of which vibrates independently. The result is that 

 accompanying the note due to the vibration of the string as a whole, 

 there are sounds corresponding with a string of half the length, of 

 one-third, one-fourth, one-fifth, etc., of that length. The vibration 

 rates of these secondary tones, which, are called by Helmholtz partial 

 tones, would therefore be twice, three times, four times, etc., as great 

 as that of the fundamental tone. If we represent the vibration rate 

 of the latter by the number 24, the figures representing the vibration 

 rates of the several partial tones would be as follows : 



ist partial (the prime or fundamental tone) 24 



2nd upper partial tone 48 



3rd , 72 



4th , 96 



5th , 120 



6th 

 7th 

 etc. 



144 

 168 

 etc. 



