40 BELL SYSTEM TECHNICAL JOURNAL 



Practically, of course, no such refinement of resolution is possible. 

 The ability to distinguish differences in pitch varies from person to 

 person, but the minimum intervals employed in musical composition 

 probably give a rough measure of the normal resolving power of the 

 ear. Even with this limitation the broad sound spectrum, such as an 

 irregular sound produces, is capable of yielding a very large number of 

 separable components; and hence a large number of individual im- 

 ages. It is this fact — that with a very complex sound the number of 

 independent determinations of the image is limited only by the re- 

 solving power of the observer — which makes his accuracy of binaural 

 location as well as his sense of certainty much greater for such sounds 

 than for pure tones. 



So long as the images of all the components coincide, it is of little 

 importance how fine the resolution is, for further refinement only 

 serves to increase the sense of certainty by adding to the volume of 

 accordant evidence. However, when the images are not in agree- 

 ment the problem is more complicated and the degree of resolution 

 becomes important. Here also purely physical considerations cease 

 to be adequate and psychological factors must be considered similar 

 to those involved in the location of a pure tone for which the intensity 

 ratio and phase difference do not correspond to any actual source. 

 When an observer is faced with discordant results he must make 

 some subconscious judgment. For small discrepancies such as occur 

 in every-day experience, he probably assumes those images which 

 depart most from the rest to be misplaced because of distortion dur- 

 ing transmission and so either corrects or ignores them. If the 

 discrepancies are large he may find it difficult on the ground of ex- 

 perience to believe that so much distortion could occur. In such an 

 event he will most likely form several images from different com- 

 ponents or in extreme cases lose the sense of location altogether. 



Bowlker found separate images to occur experimentally both for 

 band music, which approaches a collection of tones and for the 

 irregular barking of dogs. He placed tubes of unequal length to his 

 two ears thereby upsetting the normal diffraction around the head 

 and interposing a longer path on one side than on the other. Obvi- 

 ously, the distortion produced in this manner is of a type not likely 

 to be met in every-day life and affects different frequencies in widely 

 different fashions. He reports that when listening to "a band of 

 three or four instruments played in the open — the notes will be found 

 to be scattered over a wide range, most being to the side of the short 

 tube, some being in front and some being to the side of the long tube. 

 In listening with such a pair of tubes to two dogs furiously barking 



