Weber’s law, the “near miss,” and binaural detection

Abstract

Weber functions (AliI in dB) for gated 250-Hz tones were studied for monaural and several binaural stimulus configurations (homophasic, and antiphasic with varying phase angle for addition of signal to masker). The various cues for discrimination of signal plus masker from masker alone are functions of intensity increments at one or both ears, an intensity increment at one ear coupled with a decrement at the other, or the introduction of a phase difference between the ears. The decline of the Weber fraction with increasing masker level (the "near miss" to Weber's law) was confirmed for monaural discrimination over the entire 40-dB range, and a similar rate of decline was found for various binaural stimuli over the lower half of that range. The data also confirm the individual differences found in other studies for sensitivity favoring either interaural amplitude or interaural phase shifts. The Weber function for monaural intensity discrimination of tone bursts provides an interesting and important deviation from Weber's law. McGill and Goldberg (1968a, 1968b) have highlighted the problem, calling it the "near miss" to Weber's law, and have shown how it may reflect the compression role of the transduction of stimulus energy (E) to neural counts (fi) by the transform n: == aEP. Using I for stimulus intensity and M for the magnitude of its just discriminable (energy) increment, the fact that empirical plots of AI in dB against I in dB are well fitted by linear functions with slopes of about .90 (the near miss), rather than 1.00 (Weber's law), means that the exponent of the power transform (p) is about .20 rather than unity. Given our understanding of monaural and bin-aural processes, Schacknow and Raab (1973), reporting confirmation of the monaural near miss for several test frequencies, and Yost (1972), reporting confirmation of Weber's law for hornophasic and anti phasic binaural tones, appear to contradict each other. With homophasic tones, the listener receives identical inputs at the two ears, and it is commonly assumed that detection or discrimination mechanisms for that configuration are the same as for monaural listening. Indeed, careful examination of the two papers shows that they did use stimulus parameters that were almost identical, except for duration and range of I. Schack now and Raab include data for 250-Hz tones of 250 msec duration with lO-msec rise/fall times. The Weber function slope of about .90 was confirmed for a 40-dB range of I. Yost studied 250-Hz tones of 128 msec duration with lO-msec rise/fall times. Weber's law was apparently confirmed for a 12-dB range of I. (Yost did not raise the question of the near miss.) The results of Schacknow and Raab were presented as AI/I in dB SL, while Yost's results were presented as (I + M)/I in dB SPL. Adjusting for absolute threshold would place the Yost data well within the intensity range studied by Schacknow and Raab. Yost may have missed the near miss because his range for I was too small. (Indeed, for one of the two subjects of Schacknow and Raab...

Binaural masking of tones by tones: Effects of uncertainty regarding the phase angle of addition of signal to masker

“…For other values of a, the large changes are of the order of .10.] There is no doubt that uncertainty regarding a produces a large decrement in performance at a = 135 deg, and this is com- they compare favorably with the values obtained from other studies (as summarized in Table 7 of Osman et al, 1980). Examination of the graphs shows some small improvements in performance over time that are scattered over listeners and values of a.…”

“…In relation to the general functioning of the auditory system for sound localization, the dissonance condition is a most unnatural task, and therefore may be most subject to the effects of uncertainty. Evidence in support of the large individual differences in the' data for nondissonance conditions of Figure 3 (a~90 deg) exists throughout the literature in that subjects have been categorized in terms of the tendency to be differentially sensitive to interaural phase and interaural amplitude (Grantham & Robinson, 1977;Hafter & Carrier, 1972;McFadden et al, 1971;McFadden et al, 1972;Osman et al, 1980). Thus, we shall limit our summary interpretation of this study to the following.…”

“…We chose to use MR/I R (as defined in Figure 1) for the ordinate of Figure 2, as in Osman, Tzuo, and Tzuo (1980) (which also shows data of Listener H.T.) and Yost (1972).…”

“…The results are reported in some form representing the signal-to-masker ratios required for a constant level of detectability as a function of a. The relevant papers include Grantham and Robinson (1977), Hafter and Carrier (1970), Jeffress and McFadden (1971), McFadden, Jeffress, and Ermey (1971), Lakey (1972), Osman, Tzuo, andTzuo (1980), Robinson, Langford, and Yost (1974), Wightman (1971), and Yost (1972. We are interested in evaluating how well various binaural processing models can be used to describe quantitatively the results of such coherent masking experiments.…”

“…The recent paper of Osman et al (1980) reports an experimental study of binaural coherent masking with varying levels of masker intensity in the conceptual framework of intensity discrimination. It includes a detailed review and discussion of the most relevant data from earlier a experiments.…”