34 BELL SYSTEM TECHNICAL JOURNAL 



in one ear can locate familiar complex sounds almost as well as those 

 with normal hearing. 



Practically all theories of sound location start from the assumption 

 that the listener subconsciously observes certain sound characteris- 

 tics which depend upon the position of the source and forms a judg- 

 ment of where the source must be by comparing these characteristics 

 with information which he has stored up as a result of his past ex- 

 perience with cases in which the position of the source was known. 

 In order to fix the position of the source he must assign to it three 

 coordinates such as its distance and some two angles which define 

 its direction. To do this he must be able to observe at least three 

 independent properties of the sound which are functions of the posi- 

 tion of the source. If fewer than three are available some difficulty 

 in location is certain to arise. If more than three are available there 

 is the possibility of a number of simultaneous independent determina- 

 tions of the three coordinates. 



If the sounds of every-day life were never distorted in transmission 

 all of these determinations would yield the same set of coordinates 

 and the only advantage which the listener would gain from the addi- 

 tional information available would lie in the fact that some one set 

 might be peculiarly sensitive to slight differences in the position 

 of the source, and therefore might lead to increased certainty on the 

 part of the observer. Owing to reflection from the walls of buildings 

 and the like, the sounds of every-day life seldom arrive undistorted, 

 so that the observer must always be somewhat uncertain as to whether 

 or not the coordinates of the sound source are actually those which 

 he deduces from the properties of the sound wave as it reaches his 

 ears. If enough properties are available to permit him to make 

 two independent determinations he may use one of them to check the 

 other, and if they agree he is justified in a feeling of increased cer- 

 tainty as to the accuracy of his judgment. The more independent 

 determinations he can make the more checks he will be able to apply 

 and consequently the more confident he will be.^ 



It should not be inferred, however, that it is only the sounds of 

 the street which reach the observer in a distorted form. In a great 

 many laboratory experiments the characteristics of the sounds have 



^ It is interesting to note in this connection that it is not surprising that an observer 

 locates a complex tone with much greater certainty than a pure tone when we con- 

 sider how rapidly the number of independent sets of data increases with increase 

 in complexity of sound. We have already said that three indepsndent pro jerties 

 are needed for the determination of the three coordinates of the source. Hence 

 if only three are available, only one determination can be made and no checks are 

 possible. On the other hand, if four are available, four groups of three each can 

 be formed and therefore four separate determinations can be made. Similarly, 

 10 determinations can be made from 5 properties, 20 from 6, and 120 from 10. 



