394 



THE SPECIAL SENSES. 



parts, as is represented in Fig. 176, illustrating the vibrations of a 

 string. When the string is plucked, it vibrates as a whole (a), giv- 

 ing large waves which produce what is called the fundamental tone, 

 but at the same time each half (6), third (c), fourth (d), etc., may 

 vibrate, giving each its own simple tone. The combination of all 

 of these simple waves forms a compound wave whose form or, at 

 least, whose composition, determines the quality of the tone heard. 

 As many as ten or sixteen of these overtones may be detected from 

 the vibrating strings of a violin or guitar. When the period of 

 vibration of these overtones bears a simple ratio to that of the 

 fundamental, a ratio that can be expressed by the simple num- 



FiE. 176. — To illustrate the mechanism of the formation of overtones. — (Helmholtz.) 

 In a the string vibrates as a whole, giving ita fundamental tone; in b, c, and d, its halves, 

 thirds, and fourths are vibrating independently. When a string is struck, plucked, or bowed 

 these movements may happen simultaneously and the fundamental note due to the vibra- 

 tions of the whole string is combined with the notes due to the vibrations of aliquot parts, 

 the overtones. The combination gives a compound wave whose form and musical quality 

 vary with the number and relative strength of the overtones. 



bers 1, 2, 3, 4, 5, they harmonize with it and form the harmonic 

 overtones. It should be borne in mind that, so far as the tympanic 

 membrane is concerned, it does not respond separately to the single 

 tones which constitute the compound wave, but swings in unison 

 with the movement of the compound wave. Nevertheless, the in- 

 ternal ear, according to the law of Ohm, is capable of analyzing the 

 compound wave form into the series of simple or pendular wave 

 forms of which it is composed, and of distinguishing the series of 

 corresponding tones. While this analysis cannot be made con- 

 sciously except by the trained musician, it is made unconsciously, 

 as it were, by every normal ear, and in consequence of this analysis 



