38 BELL SYSTEM TECHNICAL JOURNAL 



on both tones to make them consistent and arrived at an image of 

 the chord between the other two. 



Similar results were obtained with forks of 256 and 384 cycles 

 per second, except that in general the lower tone was completely 

 blotted out. The higher tone was usually quite distinct and defin- 

 itely located. The image of the chord was nearer to the image formed 

 when the higher component was sounded by itself than to the image 

 formed from the lower one alone. With settings for which the direc- 

 tions of the tones separately were the same, whether right, left, or 

 middle, the upper tone disappeared leaving only the chord. In 

 experiments with forks of 256 and 512 cycles it was difificult to dis- f 

 tinguish the separate notes. With settings for which the two separ- 

 ately were on opposite sides the combination was on the side of the 

 lower fork. This can be interpreted as meaning that the octave 

 relationship is inherently difficult to resolve, or else that tones an 

 octave apart so generally come from a common source that the ob- 

 server was unwilling to make any other assumption. 



Although the explanation of these results is not yet thoroughly 

 understood, they show very definitely that in locating complex sounds 

 made up of pure tones the observer does within limits locate the 

 components separately. If they agree, a single image is formed; if 

 they do not, he may either locate the tones separately or form a single 

 compromise image or do both. 



It is in this way that the theory developed for pure tones is ap- | 

 plied to complex sounds made up of pure tones. The next step is to 

 extend it so as to include complex sounds in general. To do this we 

 must picture the observer as resolving each sound into sinusoidal 

 components locating the components separately and forming one or 

 more images based on a combination of the apparent sources as in- 

 dicated by the separate components. While it is fairly easy to effect 

 such a resolution mathematically it is somewhat less easy to interpret 

 the result in a manner satisfactory to our intuitive conceptions of the 

 phenomena involved; also, granted the theoretical possibility of the 

 resolution, there remains the question of what physical or psycho- 

 logical limitations there may be to its application. 



In view of the fact that a really pure component tone has no begin- 

 ning or end, and no fluctuations in its amplitude, it is not at once 

 apparent how a single discrete sound such as the bark of a dog can be 

 resolved into components of that nature. However, if enough com- 

 ponents are available it has been established beyond question that 

 by properly choosing their frequencies, amplitudes, and phases, a 



