728 SPECIAL SENSES 



phenomena here observed have their analogies in nearly all varieties of 

 musical sounds. If a stretched string is made to vibrate, the secondary 

 tones, which qualify the fundamental, are called harmonics, or overtones. 



While it is difficult at all times to distinguish by the ear the individ- 

 ual overtones of vibrating strings, their existence can be demonstrated 

 by certain simple experiments. Take, for example, a string, the funda- 

 mental tone of which is C. If this string is damped with a feather at 

 one-fourth of its length and a violin-bow is drawn across the shorter 

 section, not only the fourth part of the string across which the bow is 

 drawn is made to vibrate, but the remaining three-fourths ; and if little 

 riders of paper are placed on the longer section at distances equal to 

 one-fourth of the entire string, they will remain undisturbed, while riders 

 placed at any other points on the string will be thrown off. This ex- 

 periment shows that the three-fourths of the string have been divided. 

 This may be illustrated by connecting one end of the string with a tun- 

 ing-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 in- 

 creased tension, into three, four and so on. By damping a string with 

 the light touch of a feather, it is possible to suppress the fundamental 

 tone and bring out the overtones, which exist in all vibrating strings but 

 usually are overpowered by the fundamental. The points that mark 

 the subdivisions of the string into segments of secondary vibrations are 

 called nodes. When the string is damped at its centre, the fundamental 

 tone is quenched and there are overtones an octave above ; damping it 

 at a distance of one-fourth, there is the second octave above, and so on. 

 When the string is damped at a distance of one-fifth from the end, the 

 four-fifths sound the 3d of the fundamental, with the second octave of 

 the 3d. If it is damped at a distance of two-thirds, there is the 5th of 

 the fundamental, with the octave of the 5th. Every vibrating string 

 thus possesses a fundamental tone and overtones. Qualifying the 

 fundamental, there is 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 they form the 

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

 the greater intensity of the fundamental that they can not easily be 

 distinguished by the unaided ear, unless the fundamental has been 

 quenched in some way. In the same way the harmonic 5ths and 3ds 

 overpower other overtones; for the string is subdivided -again and again 

 into overtones, which are not harmonious like the notes of the common 

 chord of the fundamental. 



The presence of overtones, resultant tones and additional tones. 



