1006 BEATS. [BOOK in. 



the matter is one which has been much disputed, the evidence 

 seems to shew that the continuous sensation thus produced is a 

 musical sound, a tone, which has been called a " beat-tone," 

 whose pitch is determined by the number of beats repeated in a 

 second. 



The rapidity however with which beats must be repeated in 

 order to give rise to a continuous sensation, is different from 

 that with which single vibrations must be repeated in order to 

 give rise to a musical sound. Beats repeated 30 or 40 times a 

 second are readily distinguished as such; it is not until they 

 reach a rapidity of repetition of about 132 a second that they 

 cease to be distinctly recognized. Before they disappear or as 

 they disappear, at the time when they can no longer be recog- 

 nized as separate beats, but have not as yet become fused into 

 a completely continuous sensation, they give to the sound 

 which they accompany a peculiar quality, a particular rough- 

 ness and harshness. This quality if excessive is disagreeable 

 to the ear ; we speak of it as dissonance. 



From what has been said it is obvious that when a piece of 

 music is played on an instrument and still more when it is 

 played, as in a concert, on several instruments of different 

 kinds, the disturbance in the air, and the consequent vibrations 

 of the tympanic membrane and of the perilymph, are in the 

 highest degree complex. If the disturbance has certain 

 characters, the sound gives us pleasure, if other characters, 

 we regard the sound as disagreeable ; and it is found that the 

 disagreeable features of music are associated with the presence 

 of beats, and still more with the presence of that ill-defined 

 roughness which, as we said just now, is the characteristic of 

 beats when, through rapidity of repetition, they are about to 

 disappear. At the same time there are reasons for thinking 

 that it is the prominence rather than the mere presence of this 

 element which offends the ear, that the element is a necessary 

 ingredient of effective music, and that even the very quality 

 of a musical sound is dependent in part on a certain minute 

 admixture of vibrations disagreeing in period with the funda- 

 mental tone and with the regular partial tones. But this is a 

 matter into which we cannot enter here ; we have referred to 

 it because it illustrates the extreme complexity of the processes 

 which underlie our sensations of sound. 



