548 THE HUMAN BODY. 



tions simple tones; and we, consequently, recognize in music- 

 tones which are simple (such as those of tuning-forks) and 

 those which are compound; these latter are non-pendular 

 in form. 



We find, then, that the form of aerial vibrations deter- 

 mines in our sensations the occurrence or non-occurrence 

 of upper partial tones. It also, as we have seen, deter- 

 mines the quality or timbre of the tone, since vibrational 

 amplitude and rate are otherwise accounted for in sensa- 

 tion by loudness and pitch. 



It can be proved, by the employment of the higher 

 mathematics, that every periodic non-pendular movement 

 can be analyzed (as the dotted curve of Fig. 150 may be) 

 into a given number of pendular vibrations, that is, every 

 compound vibration into a set of simple ones; and that 

 every periodic non-pendular vibration can be made by the- 

 combination of pendular. Moreover, any given compound 

 vibration can be analyzed into but one set of simple ones;- 

 no other combination will produce it. Consequently a vibra- 

 tional movement of the air in the external auditory passage, 

 producing a compound musical tone sensation, can be ex- 

 hibited always, but only in one way, as the sum of a num- 

 ber of simple vibrations, whose rates are multiples of that 

 which determines the pitch of the tone. 



Now when the trained ear listens to a tone with the 

 object of detecting upper partials if present, it hears then? 

 only when the vibrations producing the tone are non-pen- 

 dular, i.e. when upper partials, theoretically, might be ex- 

 pected; and those heard are exactly those demanded by- 

 theory; by the help of instruments their detection is made- 

 easy even to untrained ears. In ordinary circumstances we 

 do not heed secondary partial tones; we hear a note of the 

 pitch of the primary partial and of a certain timbre; and 

 whenever the upper partials present are different, or of 

 different relative intensities, the timbre of the note varies. 

 Hence it becomes probable that, just as the ear can at will 

 follow any instrument in an orchestra, analyzing the aerial 

 movement so as to select and follow the fraction of the 

 whole due to that one, so it can and does analyze compound; 



