THE EAR AND HEARING. 565 



octave. The note c on the unaccented octave is due to 132 

 vibrations in a second. The note c', the next higher octave 

 of this, is produced by 264 vibrations in a second; the next 

 lower octave (great octave, 0), by 66; and so on. Sound 

 vibrations may be too rapid or too slow in succession to pro- 

 duce sonorous sensations, just as the ultra-violet and ultra- 

 red rays of the solar spectrum fail to excite the retina. The 

 highest-pitched audible note answers to about 38,016 vibra- 

 tions in a second, but it differs in individuals; many persons 

 cannot hear the cry of a bat nor the chirp of a cricket, which 

 lie near this upper audible limit. On the other hand, sounds 

 of 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 v of the fifth accented octave, pro- 

 duced by the piccolo flute, due to 4752 vibrations in a second; 

 and the lowest-pitched is the JE Jf of the contra octave, pro- 

 duced by the double bass. Modern grand pianos and organs 

 go down to 0, in the contra octave (33 vibrations per second) 

 or even A", (27i), 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 to 

 seek the cause of timbre; the quality by which we recognize 

 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 direction. Graphically 

 we may represent such vibrations by the outer continuous 

 curved line in Fig. 169. Suppose the lower end of the pen- 

 dulum to bear a writing point which marked on a sheet of 

 paper travelling down uniformly behind it, and at such a rate 

 as to travel the distance 0-1 in two seconds. If the pendu- 

 lum 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 



