6H PHYSIOLOGY 



and the other at 101 times a second, and that they begin vibrating together. 

 At first the waves of compression started by each fork will coincide, so that 

 the total compression of the air at each beat will be the compound effect 

 of the compression produced by the two forks. The two forks will 

 reinforce one another. After the lapse of half a second the tuning-forks will 

 be at different phases of their excursion. The 101 fork will be moving in one 

 direction while the 100 fork is moving in the other, so that the compression 

 produced by one fork coincides with the expansion of the air produced by 

 the moving backwards of the other fork. The sound produced by one fork- 

 is therefore diminished by the sound produced by the other fork, and the 

 total sound is less than either of the two forks. At the end of one second, 

 the phases of the two forks once more corresponding, we shall get the sound 

 increased in loudness ; thus there is an alternate waxing and waning of the 

 sound which recurs once a second and is spoken of as a ' beat/ 



The number of beats per second may be used to determine the differences 

 in the vibration frequencies of two forks. Thus two forks vibrating one at 

 100 and the other at 110 will give ten beats per second. As the number of 

 beats increases the effect produced on the ear becomes more and more dis- 

 agreeable, just as, the rapid alternation of illumination produced by a nicker- 

 ing light is disagreeable to the eye. This objectionable character of the 

 sound is most marked when the beats recur at about thirty-three times per 

 second ; the individual beats are not then distinguished, but we speak of the 

 sound as discordant or dissonant. 



CONSONANCE. The opposite condition of consonance or harmony in- 

 volves therefore, in the first place, an absence of beats, i.e. of rhythmic 

 oscillations of amplitude of sound waves which reach the ear. The con- 

 stituent tones and overtones must be capable of being combined into a 

 compound wave of regular amplitude and rhythm. In the most complete 

 consonance the component notes are identical as concerns at any rate the 

 greater number of their overtones. The most complete consonance is 

 attained when the two notes which are sounded together are identical. 

 Almost as complete is the consonance obtained when a note is sounded 

 together with its octave. The other consonant intervals which are employed 

 in music are as follows : 



1 ; - ..... Octave 



2:3 . ... Fifth 



'*:*. . Fourth 



4:5. .... Major third 



5 : <i . .... Minor third 



s . Minor sixth 



'*:>. ..... Major sixth 



It will be noticed that in all these consonant combinations the vibration 

 frequencies of the notes are in proportion to small whole numbers. If we 

 put down not only the fundamental tones of these notes but also their over- 

 tones, we shall see that tlu-iv is considerable identity as regards the latter. 

 In the case of the octave the two are almost identical, the only difference 



