HARMONY IN MUSIC. 



79 



Now suppose that a string has been excited, and, after its tone has 

 been allowed to continue for a moment, it is touched gently at its middle 

 point /3, Fig. 11 b, or d. 2t Fig. 11 d. The vibrational forms a and c, 

 for which this point is in motion, will be immediately checked and 

 destroyed ; but the vibratio nal forms b and d, for which this point is 

 at rest, will not be disturbed, and the tones due to them will continue 

 to be heard. In this way we can readily discover whether certain 

 members of the series of simple tones are contained in the compound 

 tone of a string when excited in any given way, and the ear can be 

 rendered sensible of their existence. 



Fie. 11. 



When once these simple tones in the sound of a string have been 

 thus rendered audible, the ear will readily be able to observe them in 

 the untouched string after a little accurate attention. 



The series of tones which are thus made to combine with a given 

 fundamental tone is perfectly determinate. They are tones which 

 perform twice, thrice, four times, &c., as many vibrations in a second 

 as the fundamental tone. They are called the upper partials, or 

 harmonic overtones, of the fundamental tone. If this last be c, the 



