THE SENSE OF HEARING. ■>■> 



of such elements are simultaneously stimulated, the mind takes note, not of the 

 individual sensations thereby aroused, but of a resultant sensation formed by 

 the fusion of these. 



That apparently simple tones are actually made up of a number of partials, 

 having rates of vibration which form simple multiples of the fundamental 

 tone, may easily be demonstrated at the open piano. If any note, as c in the 

 bass clef, be struck while the key of its octave c is depressed, and then the 

 struck string be damped, it will be found that the octave c rings out with its 

 proper note. So in turn the g above that, the second octave and the e above 

 that, may be made to sound when the lower c is struck, because each of these 

 strings is so tuned that its fundamental note has the same vibration-rate as 

 one of the overtones of the lower c. A note sung near the piano may in 

 the same way be analyzed more or less completely into its component tones. 

 The organ of hearing certainly has some such power of musical analysis, for 

 some cultivated ears can not only follow any special instrument in a play- 

 ing orchestra, but can even distinguish the overtones in a single musical 

 note. 



The ear has little or no power of distinguishing difference of pitch in tones 

 of less than 40 or more than 4000 vibrations per second ; but in the upper 

 median parts of the musical scale the sensitiveness to change of pitch is very 

 acute. Thus, according to Preyer, 1 in the double-accented octave a difference 

 of pitch of one-half vibration in a second can be detected ; that is, in the 

 octave included between 500 and 1000 vibrations per second, 1000 degrees of 

 pitch can be perceived. 



Every elastic body is capable of sympathetic vibration ; that is, air- waves 

 beating upon it at its own natural rate of vibration set it into corresponding 

 motion. In the same manner a heavy pendulum may be forced into violent 

 movement by exceedingly light taps with the finger, the only necessary condi- 

 tion being that the impulses imparted by the finger be exactly timed to the 

 periodic motion of the pendulum or to some multiple of it. A bodv capable 

 of sympathetic vibration with some particular tone is set into vibration by that 

 tone, and reinforces or magnifies it, whether the tone exists alone or as the 

 fundamental of a complex note, or is contained in the latter simply as an 

 upper partial. 



The analysis of musical sounds is usually carried out by the use of resona- 

 tors, which are hollow cylinders or spheres of glass or of* metal, rather widely 

 open at one pole, and narrow-pointed at the opposite end for insertion into 

 the ear. The mass of enclosed air vibrates, according to its size and shape, 

 at some particular rate, and it is very readily set into sympathetic vibration 

 whenever its fundamental tone is contained in any sound reaching it. By this 

 means it is possible strongly to magnify, and thus select, the individual over- 

 tones contained in a note. The vowel sounds of human speech owe their 

 difference of quality to the adjustment in size and shape of the resonant air- 

 chambers above the vocal cords. 



1 Veber die Grenzen der Tbnwahrnehmung, June, 1876. 

 Vol. II.— 25 



