AUDITORY SENSATIONS 509 



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 : 



Octavo 

 . 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 numbers. If we 

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

 tones, we shall see that there is considerable identity as regards the latter. 

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

 being the ground tone of the lower note, and the identity diminishes as we 

 pass from the octave through the thirds to the sixths. The overtones which 

 are identical are shown by black type : 



Fundamental tone Overtone 



(1. 2. 3. 4. 5. 6. 7. 8. 9. 10 

 \ 2 4 6 8 10 



Fifth2:3 . .| j g g ' 12 15 18 



f 3 . 6 . 9 . 12 . 15 . 18 . 21 . 24 . 27 . 30 

 Fourth 3:4. 48 12 16 20 24 28 



f 4 8 12 . 16 . 20 . 24 . 28 . 32 . 

 Major third 4; 6 { 5 10 15 20 25 30 "35 



