6o 



UNIVERSITY OF MISSOURI STUDIES 



A second class of ratios which is of particular interest, 



is that of the ratios whose numbers differ by one. In each 



of these cases the difference tone 1 is audi- 



Second law of ble, but often quite a number of additional 



difference tones difference tones can be perceived. If the 



numbers of the ratio are rather small, 



as in the case of 5:4, all the tones from the 



highest, that is, 5, down to 1 are without any great difficulty 



noticeable. As we study ratios of increasing numbers, the 



tones following directly upon 1 (in a rising direction) seem 



to have a tendency to drop out. And if we go on in the same 



Objective tones 



Difference tones easily audible 



2, I 



3, 2) I 



4, 3, ?, 



5, 4, ?, 



6, 5, ?, 



7, 6, s, 



way, we soon find only one difference tone left, the tone 1. We 

 have then simply reached a case in which the difference tone 

 is determined by the first law above. The accompanying table 

 represents this class of ratios with their difference tones. 



A third class of ratios are the ratios made up of com- 

 paratively small numbers, representing intervals less than an 



