HARMONICS. OR OVERTONES. 183 



suppose, for example, that we have a string, the fundamental 

 note of which is C. We damp this string with a feather 

 at one-fourth of its length and draw a violin-bow across the 

 smaller section. We then sound, not only the fourth part of 

 the string, across which the bow is drawn, but the remaining 

 three-fourths ; but if we have placed little riders of paper 

 upon the longer segment, at distances equal to one-fourth of 

 the entire string, they will remain undisturbed, while riders 

 placed at any other portion of the string will be thrown off. 

 This experiment shows that the three-fourths of the string 

 have been divided, as we have sounded the second octave 

 above the fundamental note. This may be illustrated by 

 connecting one end of the string with a tuning-fork. When 

 this is done, and the string is brought to the proper degree of 

 tension, it will first vibrate as a whole, then, when a little 

 tighter, will spontaneously divide into two equal parts, and, 

 under increased tension, into three, four, and so on. By 

 damping a string with the light touch of a feather, we sup- 

 press the fundamental note and bring out the overtones, 

 which exist in all vibrating strings, but are usually concealed 

 by the fundamental. The points which mark the subdivis- 

 ions of the string into segments of secondary vibrations are 

 called nodes. When we damp the string at*its centre, we 

 quench the fundamental note and have overtones an octave 

 above ; damping it at a distance of one-fourth, we have the 

 second octave above, and so on. When we damp it at a dis- 

 tance of one-fifth from the end, we have the four-fifths sound- 

 ing the 3d of the fundamental, with the second octave of the 

 3d. If we damp it at a distance of two-thirds, we have the 

 5th of the fundamental, w r ith the octave of the 5th. 



Every vibrating string possesses, thus, a fundamental tone 

 and overtones. We have, qualifying the fundamental, first, as 

 the most simple, a series of octaves ; next, a series of 5ths of 

 the fundamental and their octaves ; and next, a series of 3ds. 

 These are the most powerful overtones, and form the common 

 chord of the fundamental ; but they are so far concealed by 



