568 THE HUMAN BODY. 



recognized as due to noises or to several simultaneous in- 

 harmonic musical tones; this is commonly the case when 

 musical tones are not united designedly, and the ear thus 

 gets one criterion for distinguishing movements of the air 

 due to several simultaneous musical tones. However, a com- 

 posite set of tones will give rise to periodic vibrations when 

 all are due to vibrations of rates which are multiples of the 

 same whole number. In such cases the movement of the 

 air in the auditory meatus has no property except vibrational 

 form by which the ear could distinguish it from a simple 

 tone; when the two tuning-forks giving the forms of vibra- 

 tion (with rates as 1 to 2), represented in Fig. 169 by con- 

 tinuous lines, are sounded together, we get the new form of 

 vibration represented by the dotted line, and this has the 

 same period as that of the lower-pitched fork; yet the ear 

 can clearly distinguish the resultant sound from that of this 

 fork alone, as a note of the same pitch but of different 

 timbre; and with practice can recognize exactly what simple 

 vibrations go to make it up. 



The Analysis of Non-Pendular Vibrations. If a per- 

 son with a trained ear listens attentively to any ordinary 

 musical tone, such as that of a piano, he hears, not only the 

 note whose vibrational rate determines the pitch of the tone 

 as a whole, but a whole series of higher notes, in harmony 

 with the general or fundamental tone; this latter is the 

 primary partial tone, and the others are secondary partial 

 tones; nearly all tones used in music contain both. If the 

 prime tone be due to 132 vibrations a second (c), its first 

 upper partial is c' (= 264 vibrations per second); the next is 

 the fifth of this octave (g' 396 132 X 3 vibrations per 1'); 

 the next is the second octave, c" (132x4 = 528 vibrations per 

 1'); the next is the major third of the c" ( 132 X 5 = 660 

 vibrations per second = e"), and so on. The only form of 

 vibration which gives no upper partial tones is the pendular; 

 we may call notes due to such vibrations simple tones; and 

 we, consequently, recognize in music tones which are simple 

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

 pound ; 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, determines the 

 quality or timbre of the tone, since vibrational amplitude and 



