Gap detection and masking in hearing-impaired and normal-hearing subjects

Subjects with cochlear impairments often show reduced temporal resolution as measured in gap-detection tasks. The primary goals of these experiments were: to assess the extent to which the enlarged gap thresholds can be explained by elevations in absolute threshold; and to determine whether the large gap thresholds can be explained by the same processes that lead to a slower-than-normal recovery from forward masking. In experiment I gap thresholds were measured for nine unilaterally and eight bilaterally impaired subjects, using bandlimited noise stimuli centered at 0.5, 1.0, and 2.0 kHz. Gap thresholds were usually larger for the impaired ears, even when the comparisons were made at equal sensation levels (SLs). Gap thresholds tended to increase with increasing absolute threshold, but the scatter of gap thresholds was large for a given degree of hearing loss. In experiment II threshold was measured as a function of the delay between the onset of a 210-ms masker and the onset of a 10-ms signal in both simultaneous- and forward-masking conditions. The signal frequency was equal to the center frequency of the bandlimited noise masker, which was 0.5, 1.0, or 2.0 kHz. Five subjects with unilateral cochlear impairments, two subjects with bilateral impairments, and two normal subjects were tested. The rate of recovery from forward masking, particularly the initial rate, was usually slower for the impaired ears, even when the maskers were presented at equal SLs. Large gap thresholds tended to be associated with slow rates of recovery from forward masking.     

Auditory filter shapes in subjects with unilateral and bilateral cochlear impairments

The shape of the auditory filter was estimated at three center frequencies, 0.5, 1.0, and 2.0 kHz, for five subjects with unilateral cochlear impairments. Additional measurements were made at 1.0 kHz using one subject with a unilateral impairment and six subjects with bilateral impairments. Subjects were chosen who had thresholds in the impaired ears which were relatively flat as a function of frequency and ranged from 15 to 70 dB HL. The filter shapes were estimated by measuring thresholds for sinusoidal signals (frequency f) in the presence of two bands of noise, 0.4 f wide, one above and one below f. The spectrum level of the noise was 50 dB (re: 20 mu Pa) and the noise bands were placed both symmetrically and asymmetrically about the signal frequency. The deviation of the nearer edge of each noise band from f varied from 0.0 to 0.8 f. For the normal ears, the filters were markedly asymmetric for center frequencies of 1.0 and 2.0 kHz, the high-frequency branch being steeper. At 0.5 kHz, the filters were more symmetric. For the impaired ears, the filter shapes varied considerably from one subject to another. For most subjects, the lower branch of the filter was much less steep than normal. The upper branch was often less steep than normal, but a few subjects showed a near normal upper branch. For the subjects with unilateral impairments, the equivalent rectangular bandwidth of the filter was always greater for the impaired ear than for the normal ear at each center frequency. For three subjects at 0.5 kHz and one subject at 1.0 kHz, the filter had too little selectivity for its shape to be determined.     

Detection of temporal gaps in sinusoids by normally hearing and hearing-impaired subjects

A two-alternative forced-choice task was used to measure psychometric functions for the detection of temporal gaps in a 1-kHz, 400-ms sinusoidal signal. The signal always started and finished at a positive-going zero crossing, and the gap duration was varied from 0.5 to 6.0 ms in 0.5-ms steps. The signal level was 80 dB SPL, and a spectrally shaped noise was used to mask splatter associated with the abrupt onset and offset of the signal. Two subjects with normal hearing, two subjects with unilateral cochlear hearing loss, and two subjects with bilateral cochlear hearing loss were tested. The impaired ears had confirmed reductions in frequency selectivity at 1 kHz. For the normal ears, the psychometric functions were nonmonotonic, showing minima for gap durations corresponding to integer multiples of the signal period (n ms, where n is a positive integer) and maxima for durations corresponding to (n - 0.5) ms. For the impaired ears, the psychometric functions showed only small (nonsignificant) nonmonotonicities. Performance overall was slightly worse for the impaired than for the normal ears. The main features of the results could be accounted for using a model consisting of a bandpass filter (the auditory filter), a square-law device, and a sliding temporal integrator. Consistent with the data, the model demonstrates that, although a broader auditory filter has a faster transient response, this does not necessarily lead to improved performance in a gap detection task. The model also indicates that gap thresholds do not provide a direct measure of temporal resolution, since they depend at least partly on intensity resolution.     

Temporal gap resolution in narrow-band noises with center frequencies from 6000-14000 Hz

Temporal resolution was examined in normal-hearing subjects using a broadband noise and five narrow-band noises with center frequencies (fc) spaced 2 kHz apart between 6 and 14 kHz. Bandwidths of the narrow-band signals were equal to 0.16 fc, and broadband noise maskers with spectral notches were used to restrict the listening bands. Subjects used a Békésy procedure to track the minimum signal level required to keep a periodic temporal gap of fixed duration at threshold. Gap durations from 25 ms to the smallest trackable value were tested with each signal to generate performance curves, which showed the relationship between gap resolution and signal level in the low-to-moderate intensity range. Results showed that gap resolution improved progressively with increased signal level to about 35 dB SL, where minimum gap thresholds of about 3 ms were observed for all signals. These results, when combined with previous low-frequency data, indicate that gap threshold decreases systematically with increased signal frequency to about 5 kHz, and asymptotes at 2-3 ms for higher frequencies. In the context of functional models, the frequency effect is qualitatively consistent with the notion that both the auditory filter and a sensory integrator operate in series to govern temporal resolution in audition.     

The effect of temporal placement on gap detectability

The detectability of a masked sinusoid increases as its onset approaches the temporal center of a masker. This study was designed to determine whether a similar change in detectability would occur for a silent gap as it was parametrically displaced from the onset of a noise burst. Gap thresholds were obtained for 13 subjects who completed five replications of each condition in 3 to 13 days. Six subjects were inexperienced listeners who ranged in age from 18 to 25 years; seven subjects were highly experienced and ranged in age from 20 to 78 years. The gaps were placed in 150-ms, 6-kHz, low-passed noise bursts presented at an overall level of 75 dB SPL; the bursts were digitally shaped at onset and offset with 10-ms cosine-squared rise-fall envelopes. The gated noise bursts were presented in a continuous, unfiltered, white noise floor attenuated to an overall level of 45 dB SPL. Gap onsets were parametrically delayed from the onset of the noise burst (defined as the first nonzero point on the waveform envelope) by 10, 11, 13, 15, 20, 40, 60, 110, 120, and 130 ms. Results of ANOVAs indicated that the mean gap thresholds were longer when the gaps were proximal to signal onset or offset and shorter when the gaps approached the temporal center of the noise burst. Also, the thresholds of the younger, highly experienced subjects were significantly shorter than those of the younger, inexperienced subjects, especially at placements close to signal onset or offset. The effect of replication (short-term practice) was not significant nor was the interaction between gap placement and replication. Post hoc comparisons indicated that the effect of gap placement resulted from significant decreases in gap detectability when the gap was placed close to stimulus onset and offset.     

Decrement detection in normal and impaired ears.

The smallest detectable duration of a brief decrement in the intensity of wideband noise was measured as a function of the depth of the decrement. In the first experiment, conditions were tested in which the noise before the decrement was more intense than the noise after the decrement, and vice-versa. These data were used to estimate the shape of an intensity-weighting function, or temporal window, describing the temporal resolution of the ear. The equivalent rectangular durations (ERDs) of the temporal windows measured in this way had values of about 5.5, 4.6, and 6.6 ms for noise spectrum levels of 10, 30, and 50 dB, respectively. In a second experiment, decrement detection was measured in subjects with unilateral sensorineural hearing loss. One set of thresholds was measured in the impaired ear, and two sets of thresholds were measured in the normal ear; one with the noise level at equal SPL to the level in the impaired ear, and one with the noise at equal SL. Temporal window shapes were also estimated from these data. Only one of the subjects showed reduced temporal resolution in the impaired ear, the other two subjects having similar ERD values for all three conditions.     

Distortion product otoacoustic emission suppression tuning curves in normal-hearing and hearing-impaired human ears

Distortion product otoacoustic emission (DPOAE) suppression measurements were made in 20 subjects with normal hearing and 21 subjects with mild-to-moderate hearing loss. The probe consisted of two primary tones (f2, f1), with f2 held constant at 4 kHz and f2/f1 = 1.22. Primary levels (L1, L2) were set according to the equation L1 = 0.4 L2 + 39 dB [Kummer et al., J. Acoust. Soc. Am. 103, 3431-3444 (1998)], with L2 ranging from 20 to 70 dB SPL (normal-hearing subjects) and 50-70 dB SPL (subjects with hearing loss). Responses elicited by the probe were suppressed by a third tone (f3), varying in frequency from 1 octave below to 1/2 octave above f2. Suppressor level (L3) varied from 5 to 85 dB SPL. Responses in the presence of the suppressor were subtracted from the unsuppressed condition in order to convert the data into decrements (amount of suppression). The slopes of the decrement versus L3 functions were less steep for lower frequency suppressors and more steep for higher frequency suppressors in impaired ears. Suppression tuning curves, constructed by selecting the L3 that resulted in 3 dB of suppression as a function of f3, resulted in tuning curves that were similar in appearance for normal and impaired ears. Although variable, Q10 and Q(ERB) were slightly larger in impaired ears regardless of whether the comparisons were made at equivalent SPL or equivalent sensation levels (SL). Larger tip-to-tail differences were observed in ears with normal hearing when compared at either the same SPL or the same SL, with a much larger effect at similar SL. These results are consistent with the view that subjects with normal hearing and mild-to-moderate hearing loss have similar tuning around a frequency for which the hearing loss exists, but reduced cochlear-amplifier gain.     

Detection of a temporal gap in low-frequency narrow-band signals by normal-hearing and hearing-impaired listeners

Temporal processing ability in the hearing impaired was investigated in a 2IFC gap-detection paradigm. The stimuli were digitally constructed 50-Hz-wide bands of noise centered at 250, 500, and 1000 Hz. On each trial, two 400-ms noise samples were paired, shaped at onset and offset, filtered, and presented in the quiet with and without a temporal gap. A modified up-down procedure with trial-by-trial feedback was used to establish threshold of detection of the gap. Approximately 4 h of practice preceded data collection; final estimate of threshold was the average of six listening blocks. There were 10 listeners, 19-25 years old. Five had normal hearing; five had a moderate congenital sensorineural hearing loss with relatively flat audiometric configuration. Near threshold (5 dB SL), all listeners performed similarly. At 15 and 25 dB SL, the normal-hearing group performed better than the hearing-impaired group. At 78 dB SPL, equal to the average intensity of the 5-dB SL condition for the hearing impaired, the normal-hearing group continued to improve and demonstrated a frequency effect not seen in the other conditions. Substantial individual differences were found in both groups, though intralistener variability was as small as expected for these narrow-bandwidth signals.     

Temporal integration in normal hearing, cochlear impairment, and impairment simulated by masking

To assess temporal integration in normal hearing, cochlear impairment, and impairment simulated by masking, absolute thresholds for tones were measured as a function of duration. Durations ranged from 500 ms down to 15 ms at 0.25 kHz, 8 ms at 1 kHz, and 2 ms at 4 and 14 kHz. An adaptive 2I, 2AFC procedure with feedback was used. On each trial, two 500-ms observation intervals, marked by lights, were presented with an interstimulus interval of 250 ms. The monaural signal was presented in the temporal center of one observation interval. The results for five normal and six impaired listeners show: (1) normal listeners' thresholds decrease by about 8 to 10 dB per decade of duration, as expected; (2) listeners with cochlear impairments generally show less temporal integration than normal listeners; and (3) listeners with impairments simulated using masking noise generally show the same amount of temporal integration as normal listeners tested in the quiet. The difference between real and simulated impairments indicates that the reduced temporal integration observed in impaired listeners probably is not due to splatter of energy to frequency regions where thresholds are low, but reflects reduced temporal integration per se.     

Discrimination of interaural temporal disparities by normal-hearing listeners and listeners with high-frequency sensorineural hearing loss

Thresholds of ongoing interaural time difference (ITD) were obtained from normal-hearing and hearing-impaired listeners who had high-frequency, sensorineural hearing loss. Several stimuli (a 500-Hz sinusoid, a narrow-band noise centered at 500 Hz, a sinusoidally amplitude-modulated 4000-Hz tone, and a narrow-band noise centered at 4000 Hz) and two criteria [equal sound-pressure level (Eq SPL) and equal sensation level (Eq SL)] for determining the level of stimuli presented to each listener were employed. The ITD thresholds and slopes of the psychometric functions were elevated for hearing-impaired listeners for the two high-frequency stimuli in comparison to: the listener's own low-frequency thresholds; and data obtained from normal-hearing listeners for stimuli presented with Eq SPL interaurally. The two groups of listeners required similar ITDs to reach threshold when stimuli were presented at Eq SLs to each ear. For low-frequency stimuli, the ITD thresholds of the hearing-impaired listener were generally slightly greater than those obtained from the normal-hearing listeners. Whether these stimuli were presented at either Eq SPL or Eq SL did not differentially affect the ITD thresholds across groups.     

Acoustic distortion in the ear canal. I. Cubic difference tones: effects of acute noise injury

Acoustic emissions in the form of cubic difference tones (CDT's), 2f1-f2, were measured in the ear canals of gerbils and cats. The state of the cochlea was manipulated by means of acute exposure to noise and was monitored with the aid of the whole-nerve response to tone pips. The resulting shifts in the levels of emissions generated by pairs of primary tones of equal intensity were then compared to the corresponding threshold shifts of the whole-nerve response across frequency. Data obtained from normal ears before injury indicate that the absolute thresholds of the whole-nerve responses across frequency are not necessarily good predictors of the absolute levels of CDT emissions generated by 70- and 80-dB SPL primaries. While high emission levels were often linked to low whole-nerve thresholds in pre-exposed ears, instances of animals with sensitive whole-nerve thresholds coupled with very weak emissions were also found. Conversely, animals with poor whole-nerve thresholds (shifted by up to 30 dB) could occasionally have high levels of emissions. After acute noise injury, however, the shifts of emission levels as a function of the center frequency of the primary-tone pair largely corresponded to the threshold shifts seen in the whole-nerve response. In other words, the temporary level shift of an acoustic emission largely reflected the acute change to a specific cochlear region associated with the primary frequencies.     

Temporal gaps in noise and sinusoids

The ability of human observers to detect partially filled or completely silent intervals (gaps) was measured using a variety of different waveforms. The slopes of the psychometric functions for gap detection using broadband noise are dependent upon the amount of noise remaining during the gap. For completely silent intervals, the psychometric function covers a range of only 2 ms, but the psychometric functions for partially filled intervals are less steep. The detection of gaps in narrow-band noise (surrounded by complementary band-reject maskers) is strongly influenced by the signal-to-noise ratio. The signal bandwidth and center frequency also influence detectability. Gap detection improved as signal bandwidth increased, and detection improved when signal bands containing gaps were centered at higher frequencies. Detection of gaps in single components of a 21-component, equal-amplitude complex also showed lower thresholds as the frequency of the component containing the gap increased. Increasing the number of components in the complex that contained the gap improved the detectability of the gap, more so when the gaps were all presented at the same time (synchronous condition). Uncertainty about the temporal position of the gap within the observation interval made the gap more difficult to detect. This temporal uncertainty effect occurred for gaps in broadband noise, in narrow-band noise, and in sinusoidal waveforms.     

Temporal gap resolution in listeners with high-frequency sensorineural hearing loss

Temporal gap resolution was measured in five normal-hearing listeners and five cochlear-impaired listeners, whose sensitivity losses were restricted to the frequency regions above 1000 Hz. The stimuli included a broadband noise and three octave band noises centered at 0.5, 1.0, and 4.0 kHz. Results for the normal-hearing subjects agree with previous findings and reveal that gap resolution improves progressively with an increase in signal frequency. Gap resolution in the impaired listeners was significantly poorer than normal for all signals including those that stimulated frequency regions with normal pure-tone sensitivity. Smallest gap thresholds for the impaired listeners were observed with the broadband signal at high levels. This result agrees with data from other experiments and confirms the importance of high-frequency signal audibility in gap detection. The octave band data reveal that resolution deficits can be quite large within restricted frequency regions, even those with minimal sensitivity loss.     

Detection of silent temporal gaps in sinusoidal markers

Gap detection thresholds were measured by forced-choice procedure for conditions where the duration of a silent gap was varied adaptively between pairs of sinusoidal markers of the same or different frequency. Frequencies of the first sinusoid in a pair of markers ranged from F1 = 500 to 4000 Hz. Second-sinusoid marker frequencies F2 included F1 = F2, and usually frequencies 2%, 5%, 24%, and 50% higher than F1. In preliminary studies the role of presentation level (E/N0) on gap detection was considered. Preliminary data revealed confounding extraneous factors arising from gating transients and from overall stimulus (i.e., markers + gap) and/or masker duration cues. In the main experiments, the contributions of these extraneous cues were evaluated with experimental designs aimed at identifying and minimizing the confounding roles of these cues in gap detection. For conditions where extraneous gating transient cues were minimized (by presenting the sinusoidal markers in a continuous noise masker with random onset phase for the second sinusoid in every pair of markers) and overall stimulus duration cues were diminished (by randomizing the duration of each marker independently), gap detection thresholds increased from 5 to 90 ms as the frequency separation between F1 and F2 was increased by half an octave. When the gap detection thresholds were treated as filter attenuation values by normalizing and converting the data into decibels, the data were closely fit by the roex filter model. On average, the listeners' performances were modeled well by a constant-percentage (7%) bandwidth filter centered on F1.     

Distortion product otoacoustic emission input/output functions in normal-hearing and hearing-impaired human ears.

DPOAE input/output (I/O) functions were measured at 7f2 frequencies (1 to 8 kHz; f2/f1 = 1.22) over a range of levels (-5 to 95 dB SPL) in normal-hearing and hearing-impaired human ears. L1-L2 was level dependent in order to produce the largest 2f1-f2 responses in normal ears. System distortion was determined by collecting DP data in six different acoustic cavities. These data were used to derive a multiple linear regression model to predict system distortion levels. The model was tested on cochlear-implant users and used to estimate system distortion in all other ears. At most but not all f2's, measurements in cochlear implant ears were consistent with model predictions. At all f2 frequencies, the ears with normal auditory thresholds produced I/O functions characterized by compressive nonlinear regions at moderate levels, with more rapid growth at low and high stimulus levels. As auditory threshold increased, DPOAE threshold increased, accompanied by DPOAE amplitude reductions, notably over the range of levels where normal ears showed compression. The slope of the I/O function was steeper in impaired ears. The data from normal-hearing ears resembled direct measurements of basilar membrane displacement in lower animals. Data from ears with hearing loss showed that the compressive region was affected by cochlear damage; however, responses at high levels of stimulation resembled those observed in normal ears.     

Overshoot in normal-hearing and hearing-impaired subjects.

Overshoot was measured in both ears of four subjects with normal hearing and in five subjects with permanent, sensorineural hearing loss (two with a unilateral loss). The masker was a 400-ms broadband noise presented at a spectrum level of 20, 30, or 40 dB SPL. The signal was a 10-ms sinusoid presented 1 or 195 ms after the onset of the masker. Signal frequency was 1.0 or 4.0 kHz, which placed the signal in a region of normal (1.0 kHz) or impaired (4.0 kHz) absolute sensitivity for the impaired ears. For the normal-hearing subjects, the effects of signal frequency and masker level were similar to those published previously. In particular, overshoot was larger at 4.0 than at 1.0 kHz, and overshoot at 4.0 kHz tended to decrease with increasing masker level. At 4.0 kHz, overshoot values were significantly larger in the normal ears: Maximum values ranged from about 7-26 dB in the normal ears, but were always less than 5 dB in the impaired ears. The smaller overshoot values resulted from the fact that thresholds in the short-delay condition were considerably better in the hearing-impaired subjects than in the normal-hearing subjects. At 1.0 kHz, overshoot values for the two groups of subjects more or less overlapped. The results suggest that permanent, sensorineural hearing loss disrupts the mechanisms responsible for a large overshoot effect.     

Difference limens for phase in normal and hearing-impaired subjects

These experiments measure the ability to detect a change in the relative phase of a single component in a harmonic complex tone. Complex tones containing the first 20 harmonics of 50, 100, or 200 Hz, all at equal amplitude, were used. All of the harmonics except one started in cosine phase. The remaining harmonic started in cosine phase, but was shifted in phase half-way through either the first or the second of the two stimuli comprising a trial. The subject had to identify the stimulus containing the phase-shifted component. For normally hearing subjects tested at a level of 70 dB SPL per component, thresholds for detecting the phase shift [i.e., phase difference limens (DLs)] were smallest (2 degrees-4 degrees) for harmonics above the eighth and for the lowest fundamental frequency (F0). Changes in phase were not detectable for harmonic numbers below three or four at the lowest F0 and below 5-13 at the highest F0. The DLs increased slightly for the highest harmonics in the complexes. The DLs increased markedly with decreasing level, except for the highest harmonic, where only a small effect of level was found. Subjects reported that the phase-shifted harmonic appeared to "pop out" and was heard with a pure-tone quality. A pitch-matching experiment demonstrated that the pitch of this tone corresponded to the frequency of the phase-shifted component. For the highest harmonic, the phase shift was associated with a downward shift of the edge pitch heard in the reference (all cosine phase) stimulus. When the phases of the components in the reference stimulus were randomized, phase DLs were much higher (and often impossible to measure), the pop-out phenomenon was not observed, and no edge pitch was heard. Subjects with unilateral cochlear hearing impairment generally showed poorer phase sensitivity in their impaired than in their normal ears, when the two ears were compared at equal sound-pressure levels. However, at comparable sensation levels, the impaired ears sometimes showed lower phase DLs. The results are explained by considering the waveforms that would occur at the outputs of the auditory filters in response to these stimuli.     

Detection of tones in noise and the "severe departure" from Weber's law

Thresholds were measured for the detection of 20-ms sinusoids, with frequencies 500, 4000, or 6500 Hz, presented in bursts of bandpass noise of the same duration and centered around the signal frequency. A range of noise levels from 35 to 80 dB SPL was used. Noise at different center frequencies was equated in terms of the total noise power in an assumed auditory filter centered on the signal frequency. Thresholds were expressed as the signal levels, relative to these noise levels, necessary for subjects to achieve 71% correct. For 500-Hz signals, thresholds were about 5 dB regardless of noise level. For 6500-Hz signals, thresholds reached a maximum of 14 dB at intermediate noise levels of 55-65 dB SPL. For 4000-Hz signals, a maximum threshold of 10 dB was observed for noise levels of 45-55 dB SPL. When the bandpass noises were presented continuously, however, thresholds for 6500-Hz, 20-ms signals remained low (about 1 dB) and constant across level. These results are similar to those obtained for the intensity discrimination of brief tones in bandstop noise [R. P. Carlyon and B. C. J. Moore, J. Acoust. Soc. Am. 76, 1369-1376 (1984); R. P. Carlyon and B. C. J. Moore, J. Acoust. Soc. Am. 79, 453-460 (1986)].     

Detection of gaps in sinusoids and pulse trains by patients with cochlear implants

Gap detection thresholds were measured in patients with the Nucleus and Symbion cochlear implants as a function of several current waveform parameters. Detection of gaps in an electrical sinusoidal stimulus or in a train of biphasic pulses by implanted patients was similar to detection of gaps in comparable acoustic stimuli by normal listeners. Threshold gaps were 20-50 ms for low-level stimuli and improved with stimulus level to 2-5 ms for high-level stimuli. Gap detection performance was not affected by the electrode position in the cochlea or by the distance between stimulating electrodes. The data from most patients were well fitted by a trading relation between the duration of the gap and the square of stimulus intensity, indicating energy detection. The similarity of gap thresholds for normal subjects and implant patients suggests that many details of the peripheral neural activity are probably not important for this task, and that there is no retrocochlear loss of auditory temporal resolution with sensorineural hearing loss.     

Within- and across-channel gap detection in cochlear implant listeners

This study examined within- and across-electrode-channel processing of temporal gaps in successful users of MED-EL COMBI 40+ cochlear implants. The first experiment tested across-ear gap duration discrimination (GDD) in four listeners with bilateral implants. The results demonstrated that across-ear GDD thresholds are elevated relative to monaural, within-electrode-channel thresholds; the size of the threshold shift was approximately the same as for monaural, across-electrode-channel configurations. Experiment 1 also demonstrated a decline in GDD performance for channel-asymmetric markers. The second experiment tested the effect of envelope fluctuation on gap detection (GD) for monaural markers carried on a single electrode channel. Results from five cochlear implant listeners indicated that envelopes associated with 50-Hz wide bands of noise resulted in poorer GD thresholds than envelopes associated with 300-Hz wide bands of noise. In both cases GD thresholds improved when envelope fluctuations were compressed by an exponent of 0.2. The results of both experiments parallel those found for acoustic hearing, therefore suggesting that temporal processing of gaps is largely limited by factors central to the cochlea.