136 HARMONIC SOUNDS. SECT. XVII. 



interfering, so as to produce nodes ; so that the motion 

 of a string fastened at both ends consists of a wave or 

 pulse, continually doubled back on itself by reflection at 

 the fixed extremities. 



Harmonics generally coexist with the fundamental 

 sound in the same vibrating body. If one of the lowest 

 strings of the piano-forte be struck, an attentive ear 

 will not only hear the fundamental note, but will detect 

 all the others sounding along with it, though "with less 

 and less intensity as their pitch becomes higher. Ac- 

 cording to the law of coexisting undulations, the whole 

 string and each of its aliquot parts are in different and 

 independent states of vibration at the same time ; and 

 as all the resulting notes are heard simultaneously, not 

 only the air but the ear also vibrates in unison with 

 each at the same instant (N. 176). 



Harmony consists in an agreeable combination of 

 sounds. When two chords perform their vibrations in 

 the same time, ttjey are in unison. But when their 

 vibrations are so related as to have a common period 

 after a few oscillations they produce concord. Thus 

 when the vibrations of two strings bear a very simple 

 relation to each other, as where one of them makes 

 two, three, four, &c. vibrations in the time the other 

 makes one ; or if it accomplishes three, four, &c. vibra- 

 tions while the other makes two, the result is a concord 

 which is the more perfect the shorter the common 

 period. In discords, on the contrary, the beats are 

 distinctly audible, which produces a disagreeable and 

 harsh effect, because the vibrations do not bear a simple 

 relation to one another, as where one of two strings 

 makes eight vibrations while the other accomplishes 

 fifteen. The pleasure afforded by harmony is attributed 

 by Dr. Young to the love of order, and to a predilection 

 for a regular repetition of sensations natural to the 

 human mind, which is gratified by the perfect regularity 

 and rapid recurrence of the vibrations. The love of 

 poetry and dancing he conceives to aris,e in some degree 

 from the rhythm of the one and the regularity of the 

 motions in the other. 



A blast of air passing over the open end of a tube, as 

 over the reeds in Pan's pipes ; over a hole in one side, 



