THE PHYSICAL I5ASIS OF MUSICAL HARMONY. 349 



holes of varying" size, but spaced out so as to correspond to a ditfereuce 

 of half a wave between the sets. AYith this disk, beats are distinctly 

 produced with slow rotation, and a beat-tone when the rotation is 

 more rapid. 



Finding this result from the spacing out of apertures to correspond 

 in position and magnitude to the individual wavelets of a complex train 

 of waves, it occurred to Dr. Kicnig that the phenomena of beats and 

 of beat-tones might be still more fully re-produced if the edge of the disk 

 were cut away into a wave-form corresponding precisely to the case of 

 the resultant wave produced by the composition of two interfering 

 waves. Accordingly he calculated the wave-forms for the cases of sev- 

 eral intervals, and having set out these curves around the periphery 

 of a brass plate, cut away the edge of the plate to the form of the de- 

 sired wave. Two such wave-disks, looking rather like circular saws 

 with in egnlar teeth, arc depicted in Figs. 3 and 4. These correspond to 



120 

 '64' 



JC 



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h 



I] f 



rio. 3. Fig. 4. 



the respective intervals 8 : 15 and 8 : 23. A number of such wave- 

 disks corresponding to other intervals lie upon the table; these two 

 will however suffice. In the first of these the curve is that which 

 would be obtained by setting out around the i)eriphery a series of 120 

 simple sinusoidal waves, and a second set of (54 waves, and then com- 

 l)0uuding them into one resultant wave. In order to permit of a com- 

 parison being made with the simple component sounds, two concentric 

 rings of holes have been also pierced with 120 and 04 holes respectively. 

 Regarding these two numbers as the frequency of two i)rimary tones, 

 there ought to result beats of fre(iuency 8 (being the negative re- 

 mainder corresponding to the superior beat). An interior set of 8 holes 

 is also pierced, to enable a comparison to be made. To experiment 

 with such wave disks they are mounted upon a smoothly running 

 whirling-table, and wind from a suitable wind-chest is blown against 

 the wave edge from behind through a narrow slit set radially. In 

 this way the air-pressures in front of the wave-edge are varied by the 

 rush of air between the teeth. It is a question not yet decided how 



