4 DYNAMICAL THEOEY OF SOUND 



by which a note of good musical quality is actually produced, 

 we find that the vibration can be resolved into a series of simple- 

 harmonic components whose frequencies stand to one another 

 in a certain special relation, viz. they are proportional to the 

 numbers 1, 2, 3, .... Individual members of the series may be 

 absent, and there is practically a limit on the ascending side, 

 but no other ratios are admissible. It is evident from the 

 above relation that the resultant vibration-form is necessarily 

 periodic in character, recurring exactly at intervals equal to the 

 period in which the first member of the series goes through its 

 phases. It must be remembered, however, that the ear has no 

 knowledge of the periodic character as such, and it must not be 

 supposed that every periodic vibration will necessarily produce a 

 sensation which is musically tolerable. The superposition of 

 simple-harmonic vibrations to produce periodic vibration-forms 

 is illustrated by some of the diagrams given below in 

 Chapter III. 



One musical note may differ from another in respect of 

 pitch, quality, and loudriess. The pitch is usually estimated 

 as that of the first simple-harmonic vibration in the series, viz. 

 that of lowest frequency, but if the amplitude of this first 

 component be relatively small, and especially if it fall near the 

 lower limit of the audible scale, the estimated pitch may be 

 that of the second component. 



By " quality " is meant that unmistakable character which 

 distinguishes a note on one instrument from the note of the 

 same pitch as given by another. Every musical instrument 

 has as a rule its own specific quality*, which is seldom likely to 

 be confused with that of another. Everyone recognizes for 

 instance the difference in character between the sound of a 

 flute, a violin, a trumpet, and the human voice, respectively. 

 It is obvious that difference of quality, so far as it is not due to 

 adventitious circumstances f, can only be ascribed to difference 

 of vibration-form, and so to differences in the relative amplitudes 

 and phases of the simple-harmonic constituents. According to 



* French timbre ; German Klangfarbe. 



f Such as the manner in which the sound sets in and ceases ; this is different 

 for instance in the violin and the piano. 



