A NEW THEOEY OF HEABING. 347 



ponding phase at c', —, ~, G —., etc. The second series 

 A o 4 



pass in the same way at g', -L, ^ , %-, etc. These 



points expressed in the simplified form are c', c, F, C and 

 g' ', g, c, G, (notation of Helmholtz, Lord Eayleigh and 

 others) and it will be seen that the point c, is common to 

 both series. This means that the simultaneous sounding 

 of a tone and its fifth will produce a disturbance at a 

 point corresponding to an octave below the lower tone 

 and corresponding also to a twelfth below the upper tone. 

 Each of these tones alone produces a small disturbance at 

 this point and we have already seen that whether that 

 disturbance is or is not sufficient to produce stimulation 

 at this point depends upon the intensity of the sound. It 

 will also depend upon the intensity in this case, but if the 

 intensity of each be alone insufficient to produce this 

 effect when sounded alone, the two combined may still be 

 sufficient to produce this effect — an effect well-known to 

 musicians. 



Similarly, any other two tones of sufficient intensity 

 may by their combined effects produce stimulation in the 

 organ of Corti at a point corresponding to a tone below 

 these two which is due to vibrations whose number is the 

 the greatest common measure of the vibration-numbers of 

 the two tones sounded. This is also true even when the 

 two tones are not in harmony with each other, that is 

 when this resultant tone is more than an interval of a 

 seventeenth lower than the lower of the two tones. (The 

 ratio of numbers of vibrations of two tones separated by 

 an interval of a seventeenth is 1 : 5, e.g., A flat : c'.) And 

 this leads to the next problem. 



Problem V. Intra-cochlear effects of discords^ consisting 



of two tones. 



