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...

Results of Wilbanks and Whitmore on the binaural detection of monaurally presented tones in broad-band noise for interaural noise correlation ranging from 0 to +1 and signal frequency ranging from 150 to 4000 Hz are reexamined. The appropriate equations and corresponding curves based on the equalization–cancellation and correlation models are compared to each other and to the equation and curves presented by Wilbanks and Whitmore. The Wilbanks and Whitmore ’’empirical ’’ equation is shown to be a special case of the correlation model equation. Subject Classification: 65.62, 65.60, 65.58.

Sets of psychometric functions for the detection of tone in noise are reexamined for several interaural listening conditions. Best-fit sets of functions are determined for a "correlation" model of binaural masking level differences (MLDs). Based on only three parameters, this model predicts both the forms and relative positions of all such functions. The finding that MLDs are relatively independent of the detection level chosen for their determination is predicted by the model, and the sets of theoretical functions describe the data nearly as well as a previously determined empirical relation which requires M + 1 parameters for M curves.

This paper compares performance in tone-on-tone coherent binaural masking for conditions with and without listener knowledge concerning the phase angle of addition of the signal to the masker. Uncertainty was introduced by randomizing the four phase angles: 0,45,90, and 135 deg. Stimuli were 125-msec tone bursts at 250 Hz. The results showed a clear decrement in detection performance under the uncertainty condition at 135 deg, with weaker evidence for decrements at other phase angle values. This supports the assumption that the decision process was a function of the phase angle in previous studies of binaural tone-on-tone masking.One major class of published research on binaural detection concerns coherent binaural masking, in which binaural signals and maskers originate from the same source and have identical spectra during the appropriate presentation interval. Tonal, narrowband noise and broad-band noise waveforms have been studied. Masker waveforms were interaurally identical (condition MO), while the signal was presented with an interaural phase shift of either 0 deg (condition SO) or 180 deg (condition Sn), independently of frequency. The signal is added to the masker after a phase shift, which, for convenience, is designated a (alpha) at one ear (and, consequently, 180 deg -a at the other ear for the Sn condition). 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. However, those results are heavily dependent on practice effects and show large individual differences, in which the variability for MO-Sn of the dependency of threshold on a is great across subjects, as well as across signal frequencies for a given listener. Below 1,000 Hz, the results are generally highly asymmetrical about a = 90 deg, and even for a < 90 deg (where interaural time and intensive differences are consonant), the thresholds for different listeners may increase as well as decrease with increasing a. Our concern in this paper is with the shape of the function relating detection performance (threshold) to a in the antiphasic (MOSn) condition for 0 deg~a~135 deg.(Above a =90 deg, interaural time and intensive differences are dissonant.) The form of the results for the homophasic (MOSO) condition generally conforms to what would be expected if detection were based on the energy increment's resulting from the addition of the signal to the masker at either ear. In the MOSn conditions, however, the addition of the signal to the masker creates an interaural intensive difference as well as an interaural phase shift, and d...