566 PHYSIOLOGY 



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 therefore 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 disagreeable, just as the rapid alterna- 

 tion of illumination produced by a flickering 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 

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

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

 constituent 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 con- 

 cerns 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 : 



Octave 

 . Fifth 



Fourth 



. Major third 

 Minor third 

 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 



