ANALYSIS OP VIBRATIONS. 547 



.-and in one direction of movement, this being the resultant 

 of all the forces acting upon it; all clashing, and some push- 

 ing one way and others another. If the resultant move- 

 ment be not periodic it will be recognized as due to noises 

 or to several simultaneous inharmonic musical tones; this 

 is commonly the case when musical tones are not united 

 designedly, and the ear thus gets one criterion for distin- 

 guishing movements of the air due to several simultaneous 

 musical tones. However, a composite 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 vibration (with rates as 

 1 to 2), represented in Fig. 150 by continuous lines, are 

 sounded together, we get the new form of vibration repre- 

 sented by the dotted line, and this has the same period as 

 that of the lower-pitched fork; yet the ear can clearly dis- 

 tinguish 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 1 = 396 = 132 X 3 

 vibrations per 1'); the next is the second octave, c" (132 X 

 4 = 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 vibra- 



