250 BELL SYSTEM TECHNICAL JOURNAL 



and upon the observe-'s familiarity with the acoustic conditions sur- 

 rounding the reproduction. Since the depth locaHzation is inaccurate 

 even when Hstening directly, it is difficult to obtain sufficiently accurate 

 data to be of much use in a quantitative way. Because of this inac- 

 curacy, good auditory perspective may be obtained with reproduced 

 sounds even though the properties controlling depth localization depart 

 materially from those of the original sound. 



Angular Localization 



Fortunately, the properties entering into lateral or angular local- 

 ization permit more quantitative treatment. In dealing with angular 

 localization, it has been found convenient to neglect entirely the 

 effects of reverberant sound and to deal only with the properties of the 

 sound waves reaching the observer's ears without reflections. The 

 reflected waves or reverberant sounds do appear to have a small 

 effect on angular localization, but it has not been found possible to 

 deal with such sound in a quantitative way. One of the difficulties 

 is that, because of differences in the build-up times of the direct and 

 reflected sound waves, the amount of direct sound relative to rever- 

 berant sound reaching the observer's ears for impulsive sounds such 

 as speech and music is much greater than would be expected from 

 steady state methods of dealing with reverberant sound. 



For the case of a plane progressive wave from a single sound source, 

 and where the observer's head is held in a fixed position, there are 

 apparently only three factors that can assist in angular localization: 

 namely, phase difference, loudness difference, and quality difference 

 between the sounds received by the two ears. 



In applying these factors to the localization of sounds from more 

 than one source, as in the present case, the effects of phase differences 

 have been neglected. It is difficult to see how phase differences in 

 this case can assist in localization in the ordinary way. The two re- 

 maining factors, loudness and quality differences, both arise from the 

 directivity of hearing. This directivity probably is due in part to the 

 shadow and diffraction effects of the head and to the differences in the 

 angle subtended by the ear openings. Measurements of the directivity 

 with a source of pure tone located in various positions around the 

 head in a horizontal plane have been reported by Sivian and White.^ 

 From these measurements, the loudness level differences between near 

 and far ears have been determined for various frequencies. These 

 differences are shown in Fig. 2 from which, using the pure tone data 

 given, similar loudness level differences for complex tones may be 

 calculated. Such calculated differences for speech are shown in Fig. 3. 



