252 PHYSIOLOGY CHAP. 



we say that the ratio of the fifth is 3 : 2, this means that to every 

 two vibrations in the fundamental tone there are three in the 

 other tone, and that all these vibrations are necessary to make 

 up the period of the interval. The two groups of vibrations, by 

 fusing into a single period, arouse the complex sensation of the 

 interval, whenever the duration of the new period differs from 

 that of the periods of the two component tones, and is short 

 enough to be comprised within the Limits of tone-perception. 



The special periodicity of the intervals at once becomes 

 perceptible if we substitute a corresponding optical for the 

 acoustic phenomenon. The optic image of the intervals can be 

 obtained both with parallel and with vertical combination of the 

 vibrations of the two component tones. The second case is 

 represented by Lissajou's figures. 



Lissajou's sound - images are geometrical forms which, result from the 

 rectangular combination of the vibratory movements of two simultaneous 

 tones, produced by a beam of light. 



In order to obtain optic figures of musical intervals Zambiasi used two 

 tuning-forks, the tones of which formed definite intervals. To the end of 

 one prong of the deep fork he attached a small aluminium plate with a hole 

 in it, balancing the other prong by an equivalent weight ; to the end of the 

 high fork he attached the lens of a microscope. With the illuminating 

 apparatus of the microscope he concentrated an intense beam of light upon 

 the little hole of the first fork, and projected the image of the hole upon a 

 screen with the lens of the second fork. 



The two forks were so placed one vertical, the other horizontal that 

 they vibrated in planes perpendicular to the direction of the beam of light. 

 The first fork in vibrating gave the image of a horizontal band of light upon 

 the stationary screen, the second that of a vertical band. When both forks 

 vibrated simultaneously Lissajou's figure, corresponding with the vertical 

 coincidence of their vibratory movements, was produced. In order to 

 photograph these figures Zambiasi substituted a sensitive plate for the 

 screen, and placed it in a camera without a lens, using the lens of the second 

 tuning-fork as the objective. In order to regulate the exposure as desired, 

 a rotatory shutter is introduced which can be turned at the required speed. 



To make Lissajou's figures mobile, so that instead of coinciding they fall 

 one after another in successive phases upon a plane, Zambiasi substituted a 

 frame for the screen, with a plane vertical to the direction of the beam of 

 light, and allowed the carrier with the sensitive plate to pass at a uniform 

 rate across the frame, so that the beam of light traced Lissajou's figure 

 upon it. 



Just as, on observing Lissajou's figures fixed on a stationary 

 plate traced on a parallelogram, the number of vibrations of the 

 two component tones can be recognised by the points of contact 

 with two adjacent sides of the parallelogram, so on studying the 

 tracings of these figures, as photographed by Zambiasi on his 

 moving plate, the periods of the intervals can be seen at a glance 

 and their duration measured. 



The curves of Fig. 102 represent the optic images of five 

 intervals arranged in the order of decreasing consonance : unison, 

 fifth, fourth, seventh, augmented fourth. On comparing the dura- 



