THE PHYSICAL BASIS OF MUSICAL HARMONY. 



353 



recourse to the wave-siren, an earlier invention of his own, and of which 

 the wave-disks which have already been showo are examples. 



In the first place, Dr. Keen i^ proceeded synthetically to constructthe 

 wave-forms for tones consisting of the resultant of a set of pure har- 

 monics of g^radnally decreasing intensity. The curves of these, up to 

 the tenth member of the series, were carefully compounded graphically : 

 first with zero difference of phase, then with all the upper members 

 shifted on one quarter, then with a difference of a half- wave, then with 

 a difference of three-quarters. The results are shown in the top line of 

 curves in Fig. 6, wherein it will be noticed that the curve for difference 



Fig. 6. 



of phase = ^ is like that for zero difference, but reversed, left for right; 

 and that the curve for difference of phase = | is like that for difference 

 = ^, but inverted. Now, according to von Helmholtz, the sounds of 

 all these four curves should be precisely alike, in spite of their differ- 

 ences of form and position. To test the matter, these carefully plotted 

 curves were set out upon the circumference of a cylindrical band of thin 

 metal, the edge being then cut away, leaving the unshaded portion, 

 the curve being repeated half a dozen times, and meeting itself after 

 passing round the circumference. For convenience, the four curves to 

 be compared are set out upon the separate rims of two such metallic 

 ^cylindrical hoops, which are mounted upon one axis, to which a rapid 

 motion of rotation can be imparted, as shown in Fig. 7. Against the 

 dentilated edges of these rims, wind can be blown through narrow 

 slits connected to the wind chamber of an organ table. In the appara- 

 tus (Fig. 7) the four curves in question are the four lowest of the set of 

 .six. It will be obvious that as the§e curves pass in front of the slits 

 H. Mis. 129 23 



