Binaural summation of loudness: Noise and two-tone complexes

A series of six experiments used the method of magnitude estimation to assess how the two ears sum the loudness of stimuli with various spectra. The results showed that the binaural system sums loudnesses by at least two distinct sets of rules, one applicable to narrow-band stimuli (complete loudness summation), another to wide-band noises (partial summation, dependent on level). The main findings were: (1) Narrow-band noise (Vi-octave bands at 1,000 Hz) showed complete binaural loudness summation, like that previously reported for pure tones (Marks, 1978a). At all but low SPL, a monaural stimulus must be 10 dB greater than a binaural stimulus to be equally loud; a stimulus ratio of 10 dB corresponds to a loudness ratio of 2:1 on Stevens’ sone scale. (2) Wide-band noise (300-4,800 Hz) showed only partial summation, the subadditivity being confined largely to levels below about 60 dB SPL. This result obtained both with bands of white noise (flat spectrum) and pink noise (—3 dB/ octave). (3) Binaural summation of two-tone complexes depended slightly on frequency spacing. Narrow spacing (860 and 1,160 Hz) gave summation equal to about 10 dB, like that of narrowband noises and single tones, whereas wider spacing (675 and 1,475 Hz) gave less summation, equal to about 9 dB, and more like wide-band noise; however, a very wide spacing (300 and 4,800 Hz) gave summation like that of narrow-band noises and single pure tones.     

Range and regression, loudness scales, and loudness processing: toward a context-bound psychophysics

How does context affect basic processes of sensory integration and the implicit psychophysical scales that underlie those processes? Five experiments examined how stimulus range and response regression determine characteristics of (a) psychophysical scales for loudness and (b) 3 kinds of intensity summation: binaural loudness summation, summation of loudness between tones widely spaced in frequency, and temporal loudness summation. Context affected the overt loudness scales in that smaller power-function exponents characterized larger versus smaller range of stimulation and characterized magnitude estimation versus magnitude production. More important, however, context simultaneously affected the degree of loudness integration as measured in terms of matching stimulus levels. Thus, stimulus range and scaling procedure influence not only overt response scales, but measures of underlying intensity processing.     

Binaural loudness gain measured by simple reaction time

In order to yield equal loudness, different studies using scaling or matching methods have found binaural level differences between monaural and diotic presentations ranging from less than 2 dB to as much as 10 dB. In the present study, a reaction time methodology was employed to measure the binaural level difference producing equal reaction time (BLDERT). Participants had to respond to the onset of 1-kHz pure tones with sound pressure levels ranging from 45 to 85 dB, and being presented to the right, the left, or both ears. Equal RTs for monaural and diotic presentation (BLDERTs) were obtained with a level difference of approximately 5 dB. A second experiment showed that different results obtained for the left and right ear are largely due to the responding hand, with ipsilateral responses being faster than contralateral ones. A third experiment investigated the BLDERT for dichotic stimuli, tracing the transition between binaural and monaural stimulation. The results of all three RT experiments are consistent with current models of binaural loudness and contradict earlier claims of perfect binaural summation.     

Individual differences in loudness processing and loudness scales

Parameters of the psychophysical function for loudness (a 1000-Hz tone) were assessed for individual subjects in three experiments: (a) binaural loudness summation, (b) temporal loudness summation, and (c) judgments of loudness intervals. The loudness scales that underlay the additive binaural summation closely approximated S. S. Stevens's (1956) sone scale but were nonlinearly related to the scales that underlay the subtractive interval judgments, the latter approximating Garner's (1954) lambda scale. Interindividual differences in temporal summation were unrelated to differences in scaling performance or in binaural summation. Although the exponents of magnitude-estimation functions and the exponents underlying interval judgments varied considerably from subject to subject, exponents computed on the basis of underlying binaural summation varied less. The results suggest that interindividual variation in the exponent of magnitude-estimation functions largely reflects differences in the ways that subjects use numbers to describe loudnesses and that the sensory representations of loudness are fairly uniform, though probably not wholly uniform, among people with normal hearing. The magnitude of individual variation in at least one measure of auditory intensity processing, namely, temporal summation, seems at least as great as the magnitude of the variation in the underlying loudness scale.     

Binaural summation after learning psychophysical functions for loudness

Do response-related processes affect perceptual processes? Sometimes they may: Algom and Marks (1990) produced different loudness exponents by manipulating stimulus range, and thereby also modified the rules of loudness summation determined by magnitude scaling. The present study manipulated exponents by having a dozen subjects learn prescribed power functions with exponents of 0.3, 0.6, or 1.2 (re sound pressure). Subjects gave magnitude estimates of the loudness of binaural signals during training, and of monaural and binaural signals after training. During training, subjects’ responses followed the nominal functions reasonably well. Immediately following training, subjects applied the numeric response scales uniformly to binaural and monaural signals alike; the implicit monaural-binaural loudness matches, and thus the basic rules underlying binaural summation, were unaffected by the exponent learned. Comparison of these results with those of Algom and Marks leads us to conclude that changing stimulus range likely influences underlying perceptual events, whereas “calibrating” a loudness scale through pretraining leaves the perceptual processes unaffected.     

Brightness and loudness as functions of stimulus duration

The brightness of white light and the loudness of white noise were measured by magnitude estimation for sets of stimuli that varied in intensity and duration. Brightness and loudness both grow as power functions of duration up to a critical duration, beyond which apparent magnitude is essentially independent of duration. For brightness, the critical duration decreases with increasing intensity, but for loudness the critical duration is nearly constant at about 150 msec. Loudness and brightness also grow as power functions of intensity. The loudness exponent is the same for all durations, but the brightness exponent is about half again as large for short durations as for long. The psychophysical power functions were used to generate equal-loudness and equal-brightness functions, which specify the combinations of intensity E and duration T that produce the same apparent magnitude. Below the critical duration ET equals k for equal brightness, and ET^a equa Is k for equal loudness. The value a is about 0.7 for threshold and about 1.25 for supraliminal loudness.     

Brightness and loudness as functions of stimulus duration

The brightness of white light and the loudness of white noise were measured by magnitude estimation for sets of stimuli that varied in intensity and duration. Brightness and loudness both grow as power functions of duration up to a critical duration, beyond which apparent magnitude is essentially independent of duration. For brightness, the critical duration decreases with increasing intensity, but for loudness the critical duration is nearly constant at about 150 msec. Loudness and brightness also grow as power functions of intensity. The loudness exponent is the same for all durations, but the brightness exponent is about half again as large for short durations as for long. The psychophysical power functions were used to generate equal-loudness and equal-brightness functions, which specify the combinations of intensity E and duration T that produce the same apparent magnitude. Below the critical duration ET equals k for equal brightness, and ET^a equals k for equal loudness. The value a is about 0.7 for threshold and about 1.25 for supraliminal loudness.     

Nomnetric scaling of loudness and pitch using similarity and difference estimates

In Experiment 1, nonmetric analyses of estimates of similarity and difference were used to generate a scale of loudness for 1,200-Hz tones varying in intensity. For both similarity and difference estimates, loudness was found to grow approximately as the 0.26 power of sound pressure. In Experiment 2, nomnetric analyses of estimates of similarity and difference were used to generate a scale of pitch for 83.3-dB pure tones varying in frequency. For both similarity and difference estimates, pitch was found to vary with frequency in accordance with the mel scale.     

Monaural and binaural temporal integration of noise bursts

Summary A comparison was made between monaural and binaural temporal integration of noise bursts at threshold. The data indicate partial integration, with approximately a 6 dB decrease in threshold per decade increase in noise burst duration for both conditions of stimulation (i.e., parallel functions) for durations ranging from 4 to 256 msec. When thresholds in dB are plotted as a function of log duration, the linear component accounts for 99% of the data indicating no essential change in the partial integration functions up to at least 256 msec. The intercept difference between the monaural and binaural integration functions is 2.5 dB.     

Loudness effects in pairs of tone bursts

The loudness of dichotic and monotic pairs of short tone bursts was investigated as a function of the interburst time interval. For short intervals, the loudness was increased relative ty the loudness of a single burst. However, the loudness of a burst pair was equal to the loudness of the second burst in the pair and, therefore, no loudness summation but only a loudness enhancement took place. In dichotic bursts, the loudness enhancement decayed monotonically as the time interval increased, and the rate of decay increased with sound intensity. In monotic bursts, the loudness enhancement decayed to a minimum at about 40 msec, independent of sound intensity. It had a tendency to rebound at longer time intervals and go through a relative maximum in the vicinity of 200 msec. The results are interpreted in terms of an interaction of peripheral and central poststimulatory inhibition with temporal summation.     

Auditory temporal summation in infants and adults: Effects of stimulus bandwidth and masking noise

A visually reinforced operant procedure was employed to determine the behavioral thresholds of 6- to 7-month-old infants and adults for stimuli of various bandwidths and durations. Experiment 1 compared absolute thresholds for broadband and 1/3-octavefiltered clicks and 300-msec noise bursts. For adult subjects, the difference in threshold for clicks and noise bursts was -quite comparable in the two bandwidth conditions, but infants’ click-noise threshold differences were significantly larger for broadband than for 1/3-octave stimuli. In Experiment 2, 2-point threshold-duration functions were compared for 4-kHz tones and octave-band noise bursts presented in backgrounds of quiet and continuous noise. Infants’ threshold-duration function for octave-band noise bursts was significantly steeper than the comparable adult function in quiet, but not in masking noise. These results suggest that young infants may have particular difficulty detecting low intensity broadband sounds when durations are very short.     

Sensory and cognitive factors in judgments of loudness

One thousand Hertz tones were presented at equal or unequal intensities to the two ears. In a binaural-summation experiment, the presentation of components was simultaneous, the auditory system integrated the components automatically, and the subjects judged the loudness of the unitary sensation. In two cognitive-summation experiments, the presentation of components was successive, and the subjects had to integrate the two sensations consciously to judge their "total loudness." Results of all three experiments are consistent with models of linear summation of "loudness," but the loudness scales differ in the two tasks: The scales that underlie binaural summation and cognitive summation are nonlinearly related. This outcome suggests two nested processes: First, the auditory system transduces stimulus energy to loudness sensations by means of a nonlinear function; second, tasks that require subjects to judge combinational relations between sensations may impose additional nonlinear transformations on the sensations before the latter are combined.     

The startle response and auditory temporal summation in neonates

The present study assessed temporal summation of transient and sustained stimuli in the startle eyeblink response system in neonates during quiet sleep. Subjects received 100-dB(A), fast-rising broadband noise bursts of two types: (a) single stimuli varying in duration from 20 to 100 ms and (b) pairs of 3-ms bursts presented at interpulse intervals corresponding to the single-stimulus durations. In addition, a single 3-ms pulse was used as an anchor point for both stimulus types. For startle amplitude, single stimuli were more effective than were paired stimuli, but the temporal summation functions were similar for the two types of stimuli. Response amplitude increased as stimulus duration/interval increased to 50 ms, but not beyond. For startle probability, temporal summation was similar for single and paired stimuli at 20 ms. Pairs of pulses were equally effective at 20, 35, and 50 ms, beyond which the second pulse was not effective. Increasing the duration of single stimuli from 20 to 35 ms resulted in increased probability, illustrating a contribution of sustained summation beyond that of transient summation. Response latency was generally greater for paired than for single stimuli. The results suggest that temporal summation of brief stimuli is deficient in the neonate. These data were compared to adult data from an analogous study, and suggest that the transient system is immature in infants, and that this immaturity is expressed differently by startle amplitude, probability, and latency.     

Temporal summation related to the nature of the proximal stimulus for the warmth sense

Magnitude estimations of the warmth aroused by radiant stimulation of the forehead showed that warmth obeys the psychophysical power law when the’ duration of the stimulus is relatively long (3 or 6 sec). When duration is short (0.25, 0.5. or 1 sec), however, warmth grows as a more complex function of irradiation. The family of psychophysical functions measured for the various durations can be used to generate the rules by which radiant intensity and duration trade to preserve constant warmth. These rules vary systematically from complete temporal summation (i.e., complete reciprocity) near threshold to less and less complete summation as warmth level increases. When, however, the stimulus is expressed as an equivalent change of temperature in the skin, there is no summation, only adaptation. It can be shown that temporal summation observed psychophysically must result from the heat-transfer properties of skin tissue.     

A constant error in the perception of brief temporal intervals

Ss were presented two stimuli of equal duration separated in time. The parrs of stimuli were vibrotactile, auditory, or visual. The Ss adjusted the time between the two stimuli to be equal to the duration of the first stimulus. The results show that for stimulus durations ranging from 100 to 1,200 msec, Ss set the tune between the two stimuli too long and by a constant amount. For vibrotactfle stimuli, the constant was 596 msec; for auditory stimuli, 657 msec; and for visual stimuli, 436 msec. Changing the intensity of the vibrotactile stimuli did not change the size of the constant error. When Ss were presented two tones with a burst of white noise between the tones and adjusted the duration of the white noise to be equal to the duration of the first tone, the white noise was not adjusted too long by a constant amount. The results suggest that there is a constant error in the perception of unfilled relative to filled temporal intervals.     

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

Weber functions (ΔI/I 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 perceptual basis of loudness ratio judgments

In Experiment 1, subjects were required to estimateloudness ratios for 45 pairs of tones. Ten 1,200-Hz tones, differing only in intensity, were used to generate the 45 distinct tone pairs. In Experiment 2, subjects were required to directly compare two pairs of tones (chosen from among the set of 45) and indicate which pair of tones had the greaterloudness ratio. In both Experiments 1 and 2, the subjects’ judgments were used to rank order the tone pairs with respect to their judged loudness ratios. Nonmetric analyses of these rank orders indicated that both magnitude estimates of loudness ratios and direct comparisons of loudness ratios were based on loudnessintervals ordifferences where loudness was a power function of sound pressure. These experiments, along with those on loudness difference judgments (Parker & Schneider, 1974; Schneider, Parker, & Stein, 1974), support Torgerson’s (1961) conjecture that there is but one comparative perceptual relationship for ioudnesses, and that differences in numerical estimates for loudness ratios as opposed to loudness intervals simply reflect different reporting strategies generated by the two sets of instructions.     

The long and the short of it: On the nature and origin of functional overlap between representations of space and time

When we describe time, we often use the language of space (The movie was long; The deadline is approaching). Experiments 1–3 asked whether—as patterns in language suggest—a structural similarity between representations of spatial length and temporal duration is easier to access than one between length and other dimensions of experience, such as loudness. Adult participants were shown pairings of lines of different length with tones of different duration (Experiment 1) or tones of different loudness (Experiment 2). The length of the lines and duration or loudness of the tones was either positively or negatively correlated. Participants were better able to bind particular lengths and durations when they were positively correlated than when they were not, a pattern not observed for pairings of lengths and tone amplitudes, even after controlling for the presence of visual cues to duration in Experiment 1 (Experiment 3). This suggests that representations of length and duration may functionally overlap to a greater extent than representations of length and loudness. Experiments 4 and 5 asked whether experience with and mastery of words like long and short—which can flexibly refer to both space and time—itself creates this privileged relationship. Nine-month-old infants, like adults, were better able to bind representations of particular lengths and durations when these were positively correlated (Experiment 4), and failed to show this pattern for pairings of lengths and tone amplitudes (Experiment 5). We conclude that the functional overlap between representations of length and duration does not result from a metaphoric construction processes mediated by learning to flexibly use words such as long and short. We suggest instead that it may reflect an evolutionary recycling of spatial representations for more general purposes.     

Dichotic, diotic, and monaural summation of loudness: a comprehensive analysis of composition and psychophysical functions

In a series of six experiments, the method of magnitude estimation, constrained by a multivariate model, was used to assess the rules that govern the summation of the loudness of two-tone complexes. This methodology enabled us to specify the amounts of summation and simultaneously to construct the corresponding loudness scales. The components had different frequency separations and in the different experiments were presented (1) dichotically, a different frequency to each ear; (2) diotically, to both ears; and (3) monaurally. Results replicated and in some conditions extended known features of multiple signal processing by the auditory system. Thus, qualitatively different rules of loudness integration appeared. For monaural and diotic modes of stimulation, overall loudness depended on total sound energy within the critical band, but on the simple sum of component loudnesses beyond the critical band. For dichotic presentations, a fully additive rule of loudness summation appeared, regardless of frequency spacing. For the latter (but not the former), loudness summation was perfect, with the underlying loudness scales closely approximating Stevens's sone scale.