760 



THE SENSE OF HEARING 



string. Fourier has proved that every sonorous body, when made to 

 vibrate as a whole, also exhibits vibrations of its different segments. 

 For this reason, every compound wave should really be considered 

 as the product of the fusion of a number of simple waves, i.e., if a 

 sonorous body yields, say, 100 vibrations in a second, it also gives off 

 a series of notes in the ratio of 1, 2, 3, 4, etc. The former give rise 

 to the so-called fundamental tone and the latter to the partial tones, 

 overtones or harmonies. 



Inasmuch as all musical instruments, inclusive of the mechanism 

 set aside for the production of the human voice, send forth funda- 

 mental tones as well as overtones, the sounds emitted by them, 



a^ 



l.^--— 



Fig, 379. — To Illustrate the Mechanism of the Formation of Overtones. 



{Helmholtz.) 

 In a the string vibrates as a whole, giving its fundamental tone; in 6, 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 vibration of the whole string is combined with the notes due to the vibra- 

 tions 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. 



are really compound in their nature and not simple. The trained 

 ear is capable of analyzing these sounds, but naturally, they arrive 

 at the tympanic membrane as compound waves and are not separated 

 into their component wavelets. In other words, the tympanic mem- 

 brane is not activated by individual series of molecules of air vibrating 

 with different frequencies, but by whole waves, the form of which 

 varies in accordance with their component wavelets. 



Reinforcement and Interference of Sound Undulations. — If two 

 stones are thrown into the water at some distance from one another, the 

 two systems of wavelets produced around their points of contact, fre- 



