544: THE HUMAN BODY. 



vibrational rate about 40 per second are not well heard, 

 and a little below this become inaudible. The highest 

 note used in orchestras is the d* of the fifth accented 

 octave, produced by the piccolo flute, due to 4752 vibra- 

 tions in a second; and the lowest-pitched is the E l9 of the 

 contra octave, produced by the double bass. Modern grand 

 pianos and organs go down to G l9 in the contra octave (33 

 vibrations per second) or even A u , (27), but the musical 

 quality of such notes is imperfect; they produce rather a 

 "hum" than a true tone sensation, and are only used 

 along with notes of higher octaves to which they give a 

 character of greater depth. 



Pendular Vibrations. Since the loudness of a tone de- 

 pends on the vibrational amplitude of its physical antece- 

 dent, and its pitch on the vibrational rate, we have still 

 o seek the cause of timbre; the quality by which we recog- 

 nize the human voice, the violin, the piano, and the flute, 

 even when all sound the same note and of the same 

 loudness. The only quality of periodic vibrations left to 

 account for this, is what we may call wave-form. Think of 

 the movement of a pendulum; starting slowly from its 

 highest point, it sweeps faster and faster to its lowest, and 

 then slower and slower to its highest point on the opposite 

 side; and then repeats the movements in the reverse direc- 

 tion. Graphically we may represent such vibrations by the 

 outer continuous curved line in Fig. 150. Suppose the 

 lower end of the pendulum to bear a writing point which 

 marked on a sheet of paper traveling down uniformly 

 behind it, and at such a rate as to travel the distance 0-1 

 in two seconds. If the pendulum were at rest the straight 

 vertical line would be drawn. But if the pendulum were 

 swinging we would get a curved line, compounded of the 

 vertical movement of the paper and the to-and-fro move- 

 ment of the pendulum, writing sometimes on one side 

 of the line 0-1-2 and sometimes on the other. Starting 

 at a moment when the pendulum crosses the middle, 0.. we 

 would get described the curve a\ a* az, at first separating 

 fast from the vertical line, then slower., then returning, at first 



