564 A UDITORY SENSATIONS. [BOOK in. 



recurrence below 30 a second 1 are unable to produce a sensation of 

 sound ; if the waves are powerful enough we may feel them, but 

 we do not hear them if the vibrations are simple, and such as 

 would give rise to a pure tone ; if the fundamental tone is accom- 

 panied by overtones we may hear these, and are thus apt to say we 

 hear the former when in reality we only hear the latter. The note 

 of the 16-feet organ pipe, 33 vibrations a second, gives us the sen- 

 sation of a droning sound. A tone of 40 vibrations is however 

 quite distinct. In the other direction it is possible to hear a note 

 caused by 38,000 vibrations a second, though the limit for most 

 persons is far lower, about 16,000. Some persons hear grave 

 sounds more easily than high ones, and vice versa. This may be so 

 pronounced as to justify the subjects being spoken of as deaf to 

 grave or high tones respectively. The range in different animals 

 is very different. 



The power of distinguishing one note from another varies, as is 

 well known, in different individuals, according as they have or have 

 not a ' musical ear.' A well-trained ear can distinguish the differ- 

 ence of a single or even of a half vibration a second, and that 

 through a long range of notes. The range of an ordinary apprecia- 

 tion of tones lies between 40 and 4000 vibrations a second, i.e. be- 

 tween the lowest bass C (O x 33 vibrations) and the highest treble 

 C (C 5 4224 vibrations) of the piano ; tones above and below these, 

 even when audible, being distinguished from each other with great 

 difficulty. 



When two consecutive sounds follow each other at a sufficiently 

 short interval the sensations are fused into one. In this respect 

 auditory sensations are of shorter duration than ocular sensations. 

 When ocular sensations are repeated ten times in a second they 

 become fused (p. 520), whereas the ticks of a pendulum beating 

 100 in a second are readily audible as distinct sounds. When two 

 tuning-forks not quite in tune are struck together the interference 

 of the vibrations gives rise to an alternating rise and fall of the 

 sound, known as 'beats.' When the beats follow each other as 

 rapidly as 132 in a second they cease to be recognised, that is to 

 say, the sensations which they cause become fused. Before 

 they disappear they give a peculiar disagreeable roughness to the 

 sound. The pleasure given by musical sounds depends largely on 

 the absence of this incomplete fusion of sensations. 



Corresponding to entoptic phenomena there are various entotic 

 phenomena, sensations or modifications of sensations originating in 

 the tympanum or in the labyrinth ; moreover sensations of sound 

 may rise in the auditory nerve or in the brain itself, without any 

 vibration whatever falling on the labyrinth. 



1 By some authors the limit is placed as low as 24 or even 15 a second. 



