418 THE BODY AT WORK 



between the number of separate pieces of apparatus of which 

 it appears to be composed and the number of different musical 

 sounds which, if it were a series of resonators, it might be called 

 upon to discriminate. 



The squeak given by a bat at each turn in its flight has a 

 pitch of about 11,000 vibrations to the second the sixth E 

 above the middle C (Tyndall). In a group of persons listening 

 for the squeak there are usually some who cannot hear it. 

 Above this the range of hearing is very variable. The sudden- 

 ness of transition from perfect hearing to total want of per- 

 ception makes experiments with small pipes or with a siren 

 somewhat amusing, when a number of persons are tested at the 

 same time. One complains that the note is intolerably loud and 

 shrill, whilst others assert that there is perfect silence. Thirty- 

 three thousand vibrations is usually regarded as the upper 

 limit for the human ear, but certain physiologists place it at 

 40,000, or even higher. The upper limit is of little consequence, 

 since there is very little power of discriminating rapidities 

 above the highest note used in music the piccolo stop of the 

 organ, with a pitch of 4,096. It is possible that a sound with 

 a lower frequence than 27 (the contra-bassoon) may be heard 

 as a tone 16 according to certain writers ; but again our 

 power of discriminating very low notes is small. Over a 

 certain range a skilled musician can tell that a note is out of 

 tune when it is one sixty-fourth of a semitone higher or lower 

 than it ought to be. If we assume that by allowing equal 

 sensitiveness for a range of seven octaves, the excess of the 

 allowance over the actual sensitiveness towards either end of 

 this stretch would compensate for the comparatively few 

 distinctions which the ear can make either below or above it 

 64x12x7 = 5,376. A much higher estimate, based upon 

 observations which seem to show that the ear can distinguish 

 sounds less than one sixty-fourth of a semitone apart, places 

 the total number at 11,000. 



On the assumption that one piece of apparatus is tuned 

 to resonate for every distinguishable sound, between 5,000 

 and 11,000 pieces of apparatus would be required. Taking 

 one of Corti's arches as the centre-piece of the resonator, 

 although the rods are certainly not vibratile structures, we 

 find the number to be 3,848 (the number of the outer rods) ; 



