Midlevel Hump Research Articles

A Unified Theory of Psychophysical Laws in Auditory Intensity Perception

Psychophysical laws quantitatively relate perceptual magnitude to stimulus intensity. While most people have accepted Stevens’s power function as the psychophysical law, few believe in Fechner’s original idea using just-noticeable-differences (jnd) as a constant perceptual unit to educe psychophysical laws. Here I present a unified theory in hearing, starting with a general form of Zwislocki’s loudness function (1965) to derive a general form of Brentano’s law. I will arrive at a general form of the loudness-jnd relationship that unifies previous loudness-jnd theories. Specifically, the “slope,” “proportional-jnd,” and “equal-loudness, equal-jnd” theories, are three additive terms in the new unified theory. I will also show that the unified theory is consistent with empirical data in both acoustic and electric hearing. Without any free parameters, the unified theory uses loudness balance functions to successfully predict the jnd function in a wide range of hearing situations. The situations include loudness recruitment and its jnd functions in sensorineural hearing loss and simultaneous masking, loudness enhancement and the midlevel hump in forward and backward masking, abnormal loudness and jnd functions in cochlear implant subjects. Predictions of these loudness-jnd functions were thought to be questionable at best in simultaneous masking or not possible at all in forward masking. The unified theory and its successful applications suggest that although the specific form of Fechner’s law needs to be revised, his original idea is valid in the wide range of hearing situations discussed here.

Notched-noise precursors improve detection of low-frequency amplitude modulation.

Amplitude modulation (AM) detection was measured with a short (50 ms), high-frequency carrier as a function of carrier level (Experiment I) and modulation frequency (Experiment II) for conditions with or without a notched-noise precursor. A longer carrier (500 ms) was also included in Experiment I. When the carrier was preceded by silence (no precursor condition) AM detection thresholds worsened for moderate-level carriers compared to lower- or higher-level carriers, resulting in a "mid-level hump." AM detection thresholds with a precursor were better than those without a precursor, primarily for moderate-to-high level carriers, thus eliminating the mid-level hump in AM detection. When the carrier was 500 ms, AM thresholds improved by a constant (across all levels) relative to AM thresholds with a precursor, consistent with the longer carrier providing more "looks" to detect the AM signal. Experiment II revealed that improved AM detection with compared to without a precursor is limited to low-modulation frequencies (<60 Hz). These results are consistent with (1) a reduction in cochlear gain over the course of the precursor perhaps via the medial olivocochlear reflex or (2) a form of perceptual enhancement which may be mediated by adaptation of inhibition.

Evaluating whether increment detection at mid-to-high pedestal frequencies is consistent with cochlear compression

The ability of the auditory system to encode the amplitude fluctuations of a signal is important for processing complex stimuli, such as speech. A study by Florentine [Florentine et al., J. Acoust. Soc. Am. 81, 1528–1541 (1987)] measured intensity discrimination for multiple frequencies as a function of stimulus level. They observed that, for high frequency stimuli, difference limens were poorer at mid levels than at higher or lower levels. This mid-level “hump” is consistent with cochlear compression and suggests that compression may limit the intensity resolution of the auditory system under certain circumstances. To test the generalizability of this interpretation, the current study measured increment detection for conditions associated with the mid-level hump, based on the assumption that increment detection and intensity discrimination are determined by similar physiological processes. This study is part of a larger series of experiments in our laboratory that test whether intensity perception is con...

The effects of ipsilateral, contralateral, and bilateral broadband noise on the mid-level hump in intensity discrimination.

Previous psychoacoustical and physiological studies indicate that the medial olivocochlear reflex (MOCR), a bilateral, sound-evoked reflex, may lead to improved sound intensity discrimination in background noise. The MOCR can decrease the range of basilar-membrane compression and can counteract effects of neural adaptation from background noise. However, the contribution of these processes to intensity discrimination is not well understood. This study examined the effect of ipsilateral, contralateral, and bilateral noise on the "mid-level hump." The mid-level hump refers to intensity discrimination Weber fractions (WFs) measured for short-duration, high-frequency tones which are poorer at mid levels than at lower or higher levels. The mid-level hump WFs may reflect a limitation due to basilar-membrane compression, and thus may be decreased by the MOCR. The noise was either short (50 ms) or long (150 ms), with the long noise intended to elicit the sluggish MOCR. For a tone in quiet, mid-level hump WFs improved with ipsilateral noise for most listeners, but not with contralateral noise. For a tone in ipsilateral noise, WFs improved with contralateral noise for most listeners, but only when both noises were long. These results are consistent with MOCR-induced WF improvements, possibly via decreases in effects of compression and neural adaptation.

Exploring the source of the mid-level hump for intensity discrimination in quiet and the effects of noise.

Intensity discrimination Weber fractions (WFs) measured for short, high-frequency tones in quiet are larger at mid levels than at lower or higher levels. The source of this "mid-level hump" is a matter of debate. One theory is that the mid-level hump reflects basilar-membrane compression, and that WFs decrease at higher levels due to spread-of-excitation cues. To test this theory, Experiment 1 measured the mid-level hump and growth-of-masking functions to estimate the basilar membrane input/output (I/O) function in the same listeners. Results showed the initial rise in WFs could be accounted for by the change in I/O function slope, but there was additional unexplained variability in WFs. Previously, Plack [(1998). J. Acoust. Soc. Am. 103(5), 2530-2538] showed that long-duration notched noise (NN) presented with the tone reduced the mid-level hump even with a temporal gap in the NN. Plack concluded the results were consistent with central profile analysis. However, simultaneous, forward, and backward NN were not examined separately, which may independently test peripheral and central mechanisms of the NN. Experiment 2 measured WFs at the mid-level hump in the presence of NN and narrowband noise of different durations and temporal positions relative to the tone. Results varied across subjects, but were consistent with more peripheral mechanisms.

Examining the influence of forward, backward, and simultaneous notched noise on the mid-level hump in intensity discrimination

Psychoacoustical intensity discrimination limens (IDLs) for high frequency, short duration pedestals are poorer at mid levels than at lower and higher levels. It has been theorized that this so-called midlevel hump (MLH) may reflect mid-level cochlear compression, whereas the improvement at higher levels may be due to spread of excitation cues. To characterize intensity discrimination within a single frequency channel, researchers (e.g., Plack, 1998) have used simultaneous notched noise (NN) to limit cues from the spread of excitation to other channels. However, additional effects of the NN on the pedestal remain a matter of debate. The NN may provide a reference against which intensity judgments are made. Additionally, the NN may produce excitatory masking in the pedestal frequency channel, suppress the pedestal, and evoke cochlear gain reduction via the medial olivocochlear reflex. These latter two mechanisms change the basilar membrane compression slope, but operate over different time courses. In the present study, we examine the MLH with different durations of forward, backward, and simultaneous NN and pure tone maskers to isolate these potential mechanisms. Results will be interpreted using a computational model of the auditory system. [Research support provided by grants from NIH (NIDCD): R01-DC008327 and the Purdue Research Foundation.]

Auditory intensity discrimination as a function of level-rove and tone duration in normal-hearing and impaired subjects: The “mid-level hump” revisited

The just-noticeable difference (ΔI) in the intensity (I) of sound is typically reported to be a constant or a slightly decreasing ratio of the baseline intensity (known as Weber’s law, and the “near-miss to Weber’s law”, respectively). However, in the relatively few studies on the intensity discrimination of very brief sounds, ΔI/I is usually found to be non-monotonic, with poorest discrimination in the middle of the auditory dynamic range. Here, it is demonstrated that this “severe departure from Weber’s law” or “mid-level hump” is not merely a phenomenon of short-duration sounds. In normal-hearing subjects ( n = 8), the near-miss to Weber’s law that is observed with the discrimination of 300 ms-long, 4 kHz tones, gives way to a significant mid-level hump if tone intensities are not fixed over a great many trials (as is standard practice) but are instead randomly roved, trial-to-trial, over a wide intensity range. This was not the case in subjects with mild to moderate hearing impairment ( n = 4). Furthermore, in the discrimination of widely-roved, 4 ms-long, 4 kHz tone bursts, the performance of normal-hearing subjects did not significantly worsen at mid-levels compared to the unroved condition, unlike what was found with the 300 ms-long tones. It is suggested that mid-level humps could simply be the product of the well-known mid-level compressive nonlinearity in cochlear mechanics. We further suggest that the hump is eliminated, and the near-miss to Weber’s law is produced, by a more central mechanism such as the recently reported “adaptation to sound-level statistics”, which is bypassed during wide-range roving and possibly when sound durations are brief.

The mid-difference hump in forward-masked intensity discrimination

Forward-masked intensity-difference limens (DLs) for pure-tone standards presented at low, medium, and high levels were obtained for a wide range of masker-standard level differences. At a standard level of 25 dB SPL, the masker had a significant effect on intensity resolution, and the data showed a mid-difference hump: The DL elevation was greater at intermediate than at large masker-standard level differences. These results support the hypothesis that the effect of a forward masker on intensity resolution is modulated by the similarity between the masker and the standard. For a given masker-standard level difference, the effect of the masker on the DL was larger for a 55-dB SPL than for the 25-dB SPL standard, providing new support for a midlevel hump. To examine whether the masker-induced DL elevations are related to masker-induced loudness changes [R. P. Carlyon and H. A. Beveridge, J. Acoust. Soc. Am. 93, 2886-2895 (1993)], the effect of the masker on target loudness was measured for the same listeners. Loudness enhancement followed a mid-difference hump pattern at both the low and the intermediate target level. The correlation between loudness changes and DL elevations was significant, but several aspects of the data are incompatible with the predicted one-on-one relation between the two effects.

The intensity-difference limen for 6.5 kHz: An even more severe departure from Weber's law

Intensity-difference limens (DLs) were obtained for tones of 6.5 kHz over levels of 30-90 dB SPL. The tones had Gaussian-shaped envelopes whose duration was expressed as equivalent rectangular duration D, that of a rectangle enclosing the same area as the envelope. D ranged from 0.314 to 30 msec. DL behaviors such as the "severe departure from Weber's law," the "midlevel hump," or the "midduration hump"--that is, a rise in the DL over a range of short durations--were identified using trend analysis. The DL versus level followed a "severe departure" that increased as duration dropped to D approximately 1-2 msec. That midlevel hump then fell with further shortening of the tone pip, producing a mid-duration hump. Materials for this article may be accessed through the Psychonomic Society's Norms, Stimuli, and Data archive, at www.psychonomic.org/archive.

Intensity-difference limens predicted from the click-evoked peripheral N1: The mid-level hump and its implications for intensity encoding

The intensity-difference limen (DL) for an acoustic click rises at moderate click levels, a feature called the ‘mid-level hump’. It has long been hypothesized that, because a click does not evoke sustained firing in any primary afferent, the DL must therefore originate from the initial burst of synchronized spikes in the eighth nerve. That burst causes the N 1 component of the peripheral compound action potential (CAP). It should therefore be possible to predict click DLs from N 1 potentials. Here, a Signal Detection model, using a series expansion, was used to derive equations in N 1 for the level-dependence of the DL. The first-order equation predicts a dependence on the standard deviation of N 1, and an inverse dependence on the rate-of-growth of the mean N 1. The second-order equation is more complicated. Both approximations were applied to N 1s from the cat. Both produced a mid-level hump; at its peak, the DLs from the second-order approximation were the smaller ones, and were of the same order of magnitude as the empirical DLs. Overall, the computations show that the rate-of-growth of the mean N 1, not the standard deviation of N 1, determines the hump in the empirical DL.

The mid-level hump at 2 kHz.

Shortening the duration of a Gaussian-shaped 2-kHz tone-pip causes the intensity-difference limen (DL) to depart from the "near-miss to Weber's law" and swell into a mid-level hump [Nizami et al., J. Acoust. Soc. Am. 110, 2505-2515 (2001)]. For some subjects the size of this hump approaches or exceeds the size reported for longer tones under forward masking, suggesting that forward masking might make little difference to the DL for very brief probes. To test this hypothesis, DLs were determined over 30 to 90 dB SPL for a brief Gaussian-shaped 2-kHz tone-pip. DLs were obtained first without forward masking, then with the pip placed 10 or 100 ms after a 200-ms 2-kHz tone of 50 dB SPL, or 100 ms after a 200-ms 2-kHz tone of 70 dB SPL. DLs inflated significantly under all forward-masking conditions. DLs also enlarged under an 80 dB SPL forward masker at pip delays of 4, 10, 40, and 100 ms. The peaks of the humps obtained under forward masking clustered around a sensation level (SL) that was significantly lower than the average SL for the peaks of the humps obtained without forward masking. Overall, the results do not support the neuronal-recovery-rate model of Zeng et al. [Hear. Res. 55, 223-230 (1991)], but are not incompatible with the Carlyon and Beveridge hypothesis [J. Acoust. Soc. Am. 93, 2886-2895 (1993)] that nonsimultaneous maskers corrupt the memory trace evoked by the probe.

Intensity-difference limens for very brief Gaussian-shaped tones at 500 Hz and 6.5 kHz

The curve of intensity-difference limen (DL) versus level shows a midlevel hump for 6.5-kHz tones having 5-ms cosine-squared ramps and a 26-ms plateau [Carlyon and Moore, J. Acoust. Soc. Am. 76, 1369–1376 (1984)]. DLs were presently obtained for that tone, as well as for 6.5-kHz tones having Gaussian envelopes, for five subjects. Pedestal levels covered 30- to 90-dB SPL and equivalent rectangular durations D were 0.314, 0.627, 1.25, 2.51, 10.03, and 20.1 ms, where D is the Gaussian-envelope duration divided by 3.19. The DLs for the tone of Carlyon and Moore (D∼30) show a midlevel hump smaller than found earlier. The hump grows noticeably with smaller D (i.e., the Gaussian-shaped tones), reaching 7 dB for D=0.627. The peak drops, however, for D=0.314, causing the curve of DL versus duration to peak for D=0.627 for tone levels of 40–60 dB SPL. DLs were also obtained from seven subjects for 500-Hz tones of 30–90 dB SPL for D’s of 1.25, 2.51, 5.02, and 10.03 ms. A midlevel hump at D’s of 1.25 and 2.51 gives way to a near-miss at D’s of 5.02 and 10.03. A mid-duration peak is seen at D=5.02 for levels of 30–60 dB SPL.

The intensity-difference limen for Gaussian-enveloped stimuli as a function of level: tones and broadband noise.

Van Schijndel et al. [J. Acoust. Soc. Am. 105, 3425-3435 (1999)] have proposed that the internal excitation evoked by an auditory stimulus is segmented into "windows" according to the stimulus spectrum and stimulus length. This "multiple looks" model accounts for the mid-duration hump they observed in plots of intensity-difference limens (DLs) versus pip duration for Gaussian-shaped 1- and 4-kHz tones, an effect replicated by Baer et al. [J. Acoust. Soc. Am. 106, 1907-1916 (1999)]. However, van Schijndel et al. and Baer et al. used few levels. A greater number of levels were used by Nizami (1999) for Gaussian-shaped 2-kHz tone-pips whose equivalent rectangular duration (D) was 1.25 ms. The DLs show the mid-level hump known for clicks [Raab and Taub, J. Acoust. Soc. Am. 46, 965-968 (1969)]. At some duration this pattern must become the "near-miss to Weber's law." To determine this duration, as well as the level-dependence of the mid-duration hump, DLs were established for Gaussian-shaped 2-kHz tone-pips of D = 1.25, 2.51, and 10.03 ms at levels of 30-90 dB SPL. The across-subject average DLs for the tone-pips rise up at mid-levels for D= 1.25 and D = 2.51 ms. The DLs for D=2.51 ms are larger, creating the mid-duration hump. At all durations, the new DLs are smaller at high levels than at low levels, consistent with the near-miss to Weber's law. DLs were also obtained here for Gaussian-shaped broadband-noise pips of D=0.63, 1.25, 2.51, 5.02, and 10.03 ms. The DLs for the noise-pip show a mid-level hump for all pip durations. The noise-pip DLs decrease as the pip lengthens, such that the plot of DL versus log duration shows a linear decline, with no mid-duration hump. Analysis of variance reveals that the mid-level hump coexists with the classical patterns of level-dependence, perhaps reflecting the existence of two level-encoding mechanisms, one that depends on firing-rates counted over single neurons and which is responsible for the classical patterns, and one that depends on the initial coordinated burst of neuronal spikes caused by rapid ramping, and which presumably causes the mid-level hump.

Auditory perception in vestibular neurectomy subjects

The auditory efferent nerve is a feedback pathway that originates in the brainstem and projects to the inner ear. Although the anatomy and physiology of efferents have been rather thoroughly described, their functional roles in auditory perception are still not clear. Here, we report data in six human subjects who had undergone vestibular neurectomy, during which their efferent nerves were also presumably severed. The surgery had alleviated these subjects’ vertigo but also resulted in mild to moderate hearing loss. We designed our experiments with a focus on the possible role of efferents in anti-masking. Consistent with previous studies, we found little effects of vestibular neurectomy on pure-tone detection and discrimination in quiet. However, we noted several new findings in all subjects tested. Efferent section increased loudness sensation (one subject), reduced overshoot effect (five subjects), accentuated ‘the midlevel hump’ in forward masking (two subjects), and worsened intensity discrimination in noise (four subjects). Poorer speech in noise recognition was also observed in the surgery ear than the non-surgery ear in three out of four subjects tested, but this finding was confounded by hearing loss. The present results suggest an active role of efferents in auditory perception in noise.

Interactions of forward and simultaneous masking in intensity discrimination.

Intensity coding mechanisms are explored in a paradigm involving both forward and simultaneous masking. For intensity discrimination of 1000-Hz pure tone in quiet, a near-miss to Weber's law is observed. However, as more stimulus components are added to this relatively simple experiment, interactions among components produce a more complex pattern of results. An intense forward masker, while not causing any threshold shift for the test tone, produces a nonmonotonic intensity discrimination function ["the midlevel hump," Zeng et al., Hearing Res. 55, 223-230 (1991)]. The midlevel hump can be removed by the presence of additional notched noise [Plack and Viemeister, J. Acoust. Soc. Am. 92, 1902-1910 (1992)] or narrow-band noise whose level is increased along with the test tone's standard level. The same midlevel hump can also be enhanced by a fixed-low-level notched noise or a high-level, high-pass noise which causes minimal masking at the test frequency. Interactions of forward masking and simultaneous masking present a serious problem for a clear interpretation of these results. For example, the notched noise was originally intended to restrict off-frequency listening, but on-frequency masking compromised this original purpose and confounded the interpretation of the notched noise effects. By measuring systematically the growth-of-masking functions, the present study identified various interactions of forward and simultaneous masking and clarified the role of off-frequency listening in forward-masked intensity discrimination. Both peripheral and central mechanisms may have contributed to the occurrence, reduction and enhancement of the midlevel hump under these masking conditions.

Dual effects of notched noise on forward-masked intensity discrimination

A notched noise simultaneously presented with a standard tone reduces the midlevel hump in forward-masked intensity discrimination [Plack and Viemeister, J. Acoust. Soc. Am. 92, 1902–1910 (1992)]. This reduction is difficult to explain based on the assumption that the notched noise would force the listener to use high-threshold neurons within the on-frequency band and thus should produce an increase in the midlevel hump. However, a problem in the Plack and Viemeister study was that the notched noise level was increased as a function of the standard level. In the present study, thresholds of a 25-ms, 1-kHz tone were measured in a 125-ms notched noise and shown to grow nonlinearly as a function of the noise level. The slope of the masking function was less than 1 at low noise levels and was greater than 1 at high noise levels. Compared with data in the absence of notched noise, the notched noise produced a greater midlevel hump at low noise levels and reduced or removed the midlevel hump at high noise levels. These data suggest dual effects of the notched noise on intensity discrimination: (1) restriction of off-frequency listening at low levels, and (2) masking the on-frequency listening through two-tone suppression at high levels.

Relative contributions of two neural population responses to intensity coding

Two neural population responses have been proposed to encode the 120-dB intensity range: the spread of excitation along the entire basilar membrane and neurons of different thresholds within a narrow region of the basilar membrane. This study tests relative contributions of the two population codes by measuring forward-masked intensity discrimination of a broadband noise (14 kHz) and pure tones from 125 to 8000 Hz in octave steps. The hypothesis is that the broadband noise and low-frequency tones rely more on the spread of the excitation code, whereas high-frequency tones rely more on the high-threshold neuron code. To obtain appropriate forward masker levels, three normal-hearing listeners balanced loudness of the broadband noise and tones to a 100-ms, 90-dB SPL, 1000-Hz standard. Intensity discrimination was measured for a 25-ms probe which had the same spectral characteristic as the masker and occurred after a 100-ms delay from the masker’s offset. The discrimination data showed that the midlevel hump systematically increases from the broadband noise and the low-frequency tone to the high-frequency tone conditions, indicating a greater contribution of high-threshold neurons to intensity coding [Zeng et al., Hear. Res.55 , 223–230 (1991)]. Backward-masked intensity discrimination was also measured and will be discussed.

Deriving the Weber fraction from loudness functions.

In a previous paper [W. S. Hellman and R. P. Hellman, J. Acoust. Soc. Am. 91, 2380(A) (1992)], Weber fractions for intensity discrimination were derived from their concomitant pure tone loudness functions in normal hearing. The calculational procedure employed a generalized McGill–Goldberg model. This work extends these findings to more frequencies, to broadband noise, to tones masked by high‐pass noise, and to forward masking. Weber functions generated by the model are compared to empirical data for the various experimental conditions and stimuli. In all cases, the calculated Weber functions capture the overall shape of the measured intensity‐jnd data over a wide stimulus range. Not only does the model produce the near‐miss relation for pure tones in quiet, it also predicts Weber’s law for broadband noise, a rising characteristic in the Weber function above 60 dB SPL for a tone in high‐pass noise, and the midlevel hump observed in forward masking. These results show that there is sufficient information i...

Mechanisms underlying nonmonotonic Weber functions in forward‐masked intensity discrimination

Nonmonotonic growth in threshold for intensity discrimination has been noted for pure tones preceded by intense sinusoidal maskers; thresholds are highest for 40–60 dB SPL standards, producing what has often been described as a ‘‘midlevel hump.’’ Both physiologic and cognitive factors have ben suggested as mechanisms underlying this phenomenon. Three subjects received four conditions designed to examine this issue. A 2IFC paradigm assessed intensity discrimination of 1000‐Hz, 100‐ms sinusoids. A no‐masker condition provided a baseline. Three forward‐masked conditions were implemented: An ipsilateral condition that typically produces a mid‐level hump; a contralateral condition in which the hump is typically absent or greatly reduced; and a binaural condition presenting these two maskers simultaneously (contralateral stimulation was 13 dB greater than ipsilateral stimulation; listeners perceived only the contralateral masker). It was argued that if this condition produced a hump despite a perceptually absen...

Possible origins of the non-monotonic intensity discrimination function in forward masking

A non-monotonic intensity discrimination function in forward masking has been recently reported [Zeng et al. (1991) Hear. Res. 55, 223–230; Zeng and Turner (1992) J. Acoust Soc. Am. 92, 782–787] in which just-noticeable-differences (jnds) in intensity are largest for midlevel tones and smaller for soft and loud tones following an intense narrow-band noise. One hypothesis was that this midlevel hump reflects the contribution of low-spontaneous rate (SR) neurons to intensity coding, based on the differential recovery from forward masking of low-SR and high-SR neurons [Relkin and Doucet (1991) Hear. Res. 55, 215–222]. The present study conducted three experiments stimulating different stages of the auditory system in an attempt to determine the peripheral and central origins of the midlevel hump. First, in two cochlear implant (CI) listeners, the forward masker produced a midlevel hump on the intensity discrimination function, suggesting that the synapses between the hair cell and the eighth nerve are probably not responsible for the hump, as they are bypassed and the eighth nerve is stimulated directly. Second, in auditory brainstem implant (ABI) listeners, the forward masker produced no midlevel hump, but the masked jnds were larger than those without a masker. The absence of the midlevel hump in the ABI listeners suggests that the occurrence of the hump requires physiological mechanisms in the auditory nerve transmission, or the intrinsic processing circuits of the cochlear nuclei, or both. Third, in normal-hearing listeners, an ipsilateral, 90 dB SPL, pure-tone forward masker produced a midlevel hump, which is similar to that using a narrow-band noise masker; whereas a contralateral forward masker produced essentially no midlevel hump, suggesting that binaural interactions at superior olivary complex and more central sites are probably not responsible.