S28 AN AMERICAN TEXT-BOOK OF PHYSIOLOGY. 



represented graphically by depicting under one another a series of waves having 

 two, three, four, etc. times the rate of succession of the curve indicating the 

 fundamental tone. If a vertical line be drawn across the series representing 

 the vibration-rates of the various tones, and an algebraic addition be made of 

 the distance of each point of intersection above or below the line of rest, the 

 result will determine the position of the composite curve on the same vertical 

 (Fig. 283). It is evident that the form of the composite wave must change 

 with every change in the number and relative prominence of musical overtones, 

 and the movement imparted by it to the tympanic membrane and the wave 



FIG. 283. The curve B represents twfce the vibration-rate of A. When the two curves are combined 

 by the algebraic addition of their ordinates, the result is the periodic curve c (solid line), having a dif- 

 ferent form ; the dotted line of c is a reproduction of A. If B is displaced to the right until e falls under 

 d in A (change of phase), the combination of A and B will give the curve D, the dotted line in D repre- 

 senting A as before. 



generated in the perilymph must have corresponding differences. Notes of 

 different quality are produced by composite air- waves of different forms. But 

 waves differing in form may still produce notes of the same quality ; for if, 

 in the graphical figure, one or more of the curves representing simple tones 

 be slid to the right or the left, the form of the composite wave will thereby be 

 changed, but not the quality of the sound produced by it. In other words, 

 change of phase of the partial tones does not alter the quality of the note. 1 

 The quality of any complex note may be reproduced by sounding together 

 a series of tuning-forks which have, respectively, the vibration-rate of the 

 fundamental tone and that of one of the overtones of the complex note. 



Analysis of Composite Tones by the Ear. According to the theory 

 outlined on page 824, the composite wave, beating against the sensitive organ 

 of the cochlea, is again analyzed into the elements composing it, one part of 

 the basilar membrane vibrating sympathetically with one partial tone, another 

 with another. The isolated irritation of each nerve-element arouses in the 

 mind the idea of a tone of a certain pitch and loudness ; but when a number 



1 Helmholtz, op. cit., pp. 30-34. 



