36 BELL SYSTEM TECHNICAL JOURNAL 



these conditions the observer generally corrects one to a value con- 

 sistent with the other except in extreme cases where the correction 

 required for this purpose would be inordinately large. When this 

 occurs he may either assume both to be correct and form two images — 

 one based on the phase difference together with a mentally supplied 

 intensity ratio consistent with it, and the other similarly derived 

 from the observed intensity ratio — or he may fail to have a sense 

 of location at all. 



Before considering the available characteristics of complex sounds 

 in general let us confine our attention for a time to those which are 

 made up of a limited number of sustained pure tones such as an organ 

 note with its series of overtones, or a group of tuning forks. Here the 

 number of characteristics increases rapidly with the number of com- 

 ponent tones. For each component tone there are two quantities: 

 intensity ratio and phase difference. In addition, at either ear alone 

 the relative intensities of any two of the tones changes with the 

 position of the source, owing to the diffraction of the sound waves 

 around the head being different for different frequencies. There are 

 therefore as many of these observable intensity ratios as there are 

 pairs of components. Similarly, for any two tones whose frequencies 

 are commensurable, the relative phases of the two at the same ear 

 depend upon the position of the source. 



Not all of these characteristics are capable of contributing to 

 binaural as distinct from monaural location. In fact, only the phase 

 differences and intensity ratios of the separate components are bi- 

 naural. A man who is deaf in one ear has available all of the rela- 

 tions between the intensities and phases of the various components 

 at his normal ear. That these relations do actually contribute to 

 sound location is supported by experimental evidence. Myers ^ 

 found that, after familiarizing himself with a complex sound, a blind- 

 folded observer could locate its position with considerable accuracy, 

 even when it was moved about in the median plane, but that his 

 accuracy could be destroyed by varying the relative intensities of the 

 components.' It is not surprising then, that for complex sounds the 

 accuracy is about the same whether the location is binaural or mo- 

 naural.* The observed failure of monaural location in the case of a 



» C. S. Myers, Proc. Royal Soc, 1914, B 88,267. 



' It should be noticed that this effect must have been purely psychological since it 

 could be produced without moving the source at all. It therefore lends plausibility 

 to the assumption upon which our theory is based: that when discordant or unusual 

 stimuli are experienced, a mental readjustment of the stimuli is made in order to 

 render them more nearly consistent with every-day experience. 



* As shown by the experiments of Angell and Fite upon persons deaf in one ear. 

 Psychol. Rev., vol. 8, pp. 225-246, 1911. 



