124 



UNIVERSITY OF MISSOURI STUDIES 



a prevailing intensity of 8 seems to be even less favorable to the 

 difference tones than a prevailing intensity of 5. All these con- 

 clusions have, of course, only a relative value, since taking into 

 account the various provisional assumptions changes the result 

 considerably. 



Let us study one more combination of sinusoidal stirrup 

 movements. We have had only one interval greater than an 

 octave, the combination 4 and 9. But 

 we did not, then, take into account the in- 

 flection points of the curve. Let us do 

 this with the combination 3 and 8, taking 

 the amplitude of 3 twice as great as that 

 of 8. This ratio of the amplitudes is arbi- 

 trarily chosen. But the selection of equal 

 amplitudes would be no less arbitrary. The curve in figure 

 40 represents the function 



f(x) = 3sin3.f + sin8;r. 

 The table below contains the abscissa and ordinate values of 

 the maxima, minima, and inflection points of the curve. 



The combination 

 3 and 8. The 

 amplitude of 3 

 twice that of 8 



Fig. 40. The combination 3 and 8 



The successive positions of the partition corresponding 

 to -the maxima, minima, and inflection points are shown in 

 figure 41. 



The thirteen initial sections of the partition move down 

 from g to B, and up from B to D. Down from D to F, and 



