52 UNIVERSITY OF MISSOURI STUDIES 



the successive positions of the partition corresponding to this 

 curve. The interpretation of the figure is so simple that the 

 reader will easily read off, without any aid, what tones are to 

 be heard; namely the tones. 3, 2, and 1 with the relative intensi- 

 ties six, thirteen, and eleven. This is exactly the same result 

 as that of our analysis of the curve in figure 11. 



The interval studied above is in musical terminology that 

 of a fifth. Let us now study an interval which is even small- 

 er than a semitone. The compound curve 

 in figure 20 is made up of twenty-four 

 . \'^^^ com- vibrations originating from one source and 



, rtc twenty-five from another. Figure SI 



shows the successive positions of the parti- 

 tion corresponding thereto. The initial 

 section of the partition moves up and down twenty-five times 

 during the period. We may, therefore, conclude that 

 the nerve ends located here will transmit to the brain 

 a process resulting in the sensation of the tone 25. 

 In order to discuss this matter with more accuracy, 

 I have not relied only upon the draftsman's skill in con- 

 structing the compound curve, but computed the ordinate 

 values of some of the maxima and minima. Such a compu- 

 tation is exceedingly tiresome work, since for each pair of val- 

 ues in the table it is necessary to compute twenty or more 

 values in order to select from them what appears as the maxi- 

 mum or minimum. But the accuracy of this method can be 

 carried to any decimal desired. We learn from the table of 

 these values that the relative intensity (when determined in 

 the same way as above) of the tone 25 would be nine (that is, 

 200—191). 



