158 HAEMONIC SOUNDS. [SECT. xvn. 



or pulse, continually doubled back on itself by reflection at 

 the fixed extremities. 



Harmonics generally co-exist 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. According to the law of co-existing 

 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 simul- 

 taneously, 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, 

 they 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, <fec. vibrations in the time the 

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

 vibrations 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 har- 

 mony 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 regu- 

 larity and rapid recurrence of the vibrations. The love of 

 poetry and dancing he conceives to arise, in some degree, 

 from the rhythm of the one, and the regularity of the mo- 

 tions in the other. 



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



