Intensity discrimination as a function of level and frequency and its relation to high-frequency hearing

This paper examines how intensity discrimination depends on the test frequency, the level, and the subjects's high-frequency hearing. Three experiments were performed. In the first experiment, intensity discrimination of pulsed tones was measured as a function of level at 1 and 14 kHz in five listeners. Results show less deviation from Weber's law at 14 kHz than at 1 kHz. In the second experiment, intensity discrimination was measured for a 1-kHz tone at 90-dB SPL as a function of the cutoff frequency of a high-pass masking noise in two listeners. Results show that the audibility of very high frequencies is important for frequency discrimination at 1 kHz. The DL increased by a factor between 1.5 and 2.0 as the cutoff frequency of the noise was lowered from 19 to 6 kHz. In the third experiment, thresholds from 6 to 20 kHz and intensity discrimination for a 1-kHz tone was measured in 12 listeners. Results show that the DLs at 80-dB SPL are correlated with the ability to hear very high frequencies. Results of all three experiments are consistent with the multiband version of the excitation-pattern model for intensity discrimination [Florentine and Buus, J. Acoust. Soc. Am. 70, 1646-1654 (1981)].     

Suprathreshold effects of adaptation produced by amplitude modulation

This work extends the study of adaptation to amplitude modulation (AM) to the perception of highly detectable modulation. A fixed-level matching procedure was used to find perceptually equivalent modulation depths for 16-Hz modulation imposed on a 1-kHz standard and a 4-kHz comparison. The modulation depths in the two stimuli were compared before and after a 10-min exposure to a 1-kHz tone (adaptor) 100% modulated in amplitude at different rates. For modulation depths of 63% (20 log m = -4) and smaller, the perceived modulation depth was reduced after exposure to the adaptor that was modulated at the same rate as the standard. The size of this reduction expressed as a difference between the post- and pre-exposure AM depths was similar to the increase in AM-detection threshold observed after adaptation. Postexposure suprathreshold modulation depth was not appreciably reduced when the modulation depth of the standard was large (approached 100%). A much smaller or no reduction in the perceived modulation depth was also observed when the modulation rates of the adaptor and the standard tone were different. The tuning of the observed effect of the adaptor appears to be much sharper than the tuning shown by modulation-masking results.     

Effects of forward and simultaneous masking on intensity discrimination

Experiments on intensity discrimination determine the size of the smallest detectable increment added to a fixed pedestal. This paper examines the effects of a masker which either precedes the pedestal (forward masking) or is simultaneous with the pedestal. The increment and pedestal were 1-kHz tones masked in forward masking by pure tones and in simultaneous masking by a broadband noise. Simultaneous masking by the broadband noise eliminates the "near miss" to Weber's law, and thus degrades intensity discrimination at high pedestal levels. Forward masking by the pure tone also degrades intensity discrimination, which may, in part, be explained by the elimination of the near miss. However, the effect on intensity discrimination in some cases is greater in forward than in simultaneous masking, suggesting that some additional process (e.g., adaptation) is involved.     

On the relations of intensity jnd's to loudness and neural noise

It is shown experimentally that, in contradiction of the fundamental concept of Fechner's law, the intensity jnd for auditory sinusoidal signals follows loudness, rather than its derivative with respect to sound intensity. The evidence is obtained by comparing the jnd's of a population with normal hearing to those of a population with hearing loss accompanied by loudness recruitment. Although the recruitment increases the slope of the loudness function, the jnd's of both populations were found to be practically equal when the loudness were equal. The phenomenon is accounted for mathematically by assuming that psychophysically relevant neural noise depends not only on the magnitude of loudness, but also on its derivative with respect to sound intensity. A related derivation accounts for the near miss to Weber's law.     

The effect of narrow-band noise maskers on increment detection

It is often assumed that listeners detect an increment in the intensity of a pure tone by detecting an increase in the energy falling within the critical band centered on the signal frequency. A noise masker can be used to limit the use of signal energy falling outside of the critical band, but facets of the noise may impact increment detection beyond this intended purpose. The current study evaluated the impact of envelope fluctuation in a noise masker on thresholds for detection of an increment. Thresholds were obtained for detection of an increment in the intensity of a 0.25- or 4-kHz pedestal in quiet and in the presence of noise of varying bandwidth. Results indicate that thresholds for detection of an increment in the intensity of a pure tone increase with increasing bandwidth for an on-frequency noise masker, but are unchanged by an off-frequency noise masker. Neither a model that includes a modulation-filter-bank analysis of envelope modulation nor a model based on discrimination of spectral patterns can account for all aspects of the observed data.     

Monaural and interaural intensity discrimination: level effects and the "binaural advantage"

This study examined whether the level effects seen in monaural intensity discrimination (Weber's law and the "near miss") in a two-interval task are also observed in discrimination of interaural intensity differences (IIDs) in a single-interval task. Both tasks were performed for various standard levels of 4-kHz pure tones and broadband noise. The Weber functions (10 log deltaI/I versus I in dB) in the monaural and binaural conditions were parallel. For noise, the Weber functions had slopes close to zero (Weber's law) while the Weber functions for the tones had a mean slope of -0.089 (near miss). The near miss for the monaural and binaural tasks with tones was eliminated when a high-pass masker was gated with the listening intervals. The near-miss was also observed for 250- and 1000-Hz tones in the binaural task despite overall decreased sensitivity to changes in IID at 1000 Hz. The binaural thresholds showed a small (about 2-dB) advantage over monaural thresholds only in the broadband noise conditions. More important, however, is the fact that the level effects seen monaurally are also seen binaurally. This suggests that the basic mechanisms responsible for Weber's law and the near miss are common to monaural and binaural processing.     

Intensity discrimination, increment detection, and magnitude estimation for 1-kHz tones

Intensity difference limens (DLs) were measured over a wide intensity range for 200-ms, 1-kHz gated tones and for 200-ms increments in continuous 1-kHz tones. Magnitude estimates also were obtained for the gated tones over a comparable intensity range. The discrimination data are in general agreement with those from earlier studies but they extend them by showing: (1) good discrimination for gated tones over at least a 115-dB dynamic range; (2) a slight increase in the relative DL (delta I/I) as intensity increases above 95 dB SPL; (3) smaller DLs for increments than for gated tones, with the difference approximately independent of intensity; (4) negligible "negative masking" when thresholds are expressed as intensity differences (delta I). For two of the three subjects, magnitude estimates do not conform to a single-exponent power law for suprathreshold intensities. Over the middle range of intensities where a single exponent is appropriate, the value of the exponent is less than 0.1 for all subjects.     

A test of the binaural equal-loudness-ratio hypothesis for tones

It is well known that a tone presented binaurally is louder than the same tone presented monaurally. It is less clear how this loudness ratio changes as a function of level. The present experiment was designed to directly test the Binaural Equal-Loudness-Ratio hypothesis (BELRH), which states that the loudness ratio between equal-SPL monaural and binaural tones is independent of SPL. If true, the BELRH implies that monaural and binaural loudness functions are parallel when plotted on a log scale. Cross-modality matches between string length and loudness were used to directly measure binaural and monaural loudness functions for nine normal listeners. Stimuli were 1-kHz 200-ms tones ranging in level from 5 dB SL to 100 dB SPL. A two-way ANOVA showed significant effects of level and mode (binaural or monaural) on loudness, but no interaction between the level and mode. Consequently, no significant variations were found in the binaural-to-monaural loudness ratio across the range of levels tested. This finding supports the BELRH. In addition, the present data were found to closely match loudness functions derived from binaural level differences for equal loudness using the model proposed by Whilby et al. [J. Acoust. Soc. Am. 119, 3931-3939 (2006)].     

Vibrotactile intensity discrimination measured by three methods

The difference threshold for the detection of changes in vibration amplitude was measured as a function of the intensity and frequency of stimuli delivered through a 2.9-cm2 contactor to the thenar eminence. Stimuli were either 25- or 250-Hz sinusoids, narrow-band noise centered at 250 Hz, or wideband noise. Thresholds were measured by two-interval, forced-choice tracking under three methods of stimulus presentation. In the gated-pedestal method, subjects had to judge which of two 700-ms bursts of vibration separated by 100 ms was more intense. In the continuous-pedestal method, subjects had to detect a 700-ms increment in the amplitude of an ongoing pedestal of vibration. In the two-burst-continuous-pedestal method with 1500-ms pedestals, the subject had to detect which of two successively presented pedestals contained a 500-ms amplitude increment. Thresholds were consistently lower for detecting increments in the amplitude of a continuous pedestal of vibration than for detecting amplitude differences between briefly presented successive pedestals or amplitude increments in successive pedestals. A "near miss" to Weber's law was found both for sinusoidal and for noise stimuli. The difference threshold was not affected by stimulus frequency condition.     

Factors affecting the loudness of modulated sounds.

Loudness matches were obtained between unmodulated carriers and carriers that were amplitude modulated either periodically (rates between 2 and 32 Hz, modulation sinusoidal either on a linear amplitude scale or on a dB scale; the latter is called dB modulation) or with the envelope of the speech of a single talker. The carrier was a 4-kHz sinusoid, white noise, or speech-shaped noise. Both normally hearing subjects and subjects with cochlear hearing loss were tested. Results were expressed as the root-mean-square (rms) level of the modulated carrier minus the level of the unmodulated carrier at the point of equal loudness. If this difference is positive, this indicates that the modulated carrier has a higher rms level at the point of equal loudness. For normally hearing subjects, the results show: (1) For a 4000-Hz sinusoidal carrier, the difference was slightly positive (averaging about 0.7 dB). There was no significant effect of modulation rate or level over the range 20-80 dB SL. (2) For a speech-shaped noise or white noise carrier, the difference was close to zero, although for large modulation depths it tended to be negative. There was no clear effect of level (over the range 35-75 dB SPL) or modulation rate. For the hearing-impaired subjects, the differences were small, but tended to be slightly negative for both the 4000-Hz carrier and the noise carriers, when the modulation rate was above 2 Hz. Again, there was no clear effect of overall level. However, for dB modulation, the differences became more negative with increasing modulation depth. For modulation rates in the range 4-32 Hz, the results could be fitted reasonably well using the assumption that the loudness of modulated sounds is based on the rms value of the time-varying intensity of the response of the basilar membrane (taking into account the compression that occurs in the normal cochlea). The implications of the results for the fitting of multi-band compression hearing aids and for the design of loudness meters are discussed.     

Binaural versus monaural loudness: supersummation of tone partially masked by noise

A series of three experiments used the method of magnitude estimation to examine binaural summation of the loudness of a 1000-Hz tone heard in the quiet and against various backgrounds of masking noise. In the quiet, binaural loudness as measured in sones, is twice monaural loudness. Two conditions of noise masking acted to increase the ratio of binaural/monaural loudness in sones above 2:1--that is, to produce supersummation. (1) When tone was presented to both ears, but masking noise to just one ear (dichotic stimulation), the loudness of the binaural tone was 30%-35% greater than the sum of the loudness of the monaural components. This increase in summation provides a suprathreshold analog to increases in threshold sensitivity observed with dichotic stimulation (masking-level differences). (2) Supersummation was also evident when tone and noise alike were presented to both ears (diotic stimulation); here, the binaural tone's loudness was 10%-25% greater than the sum of the monaural components. The increase in summation with diotic stimulation may be related to the characteristics of binaural summation of the noise masker itself.     

Critical modulation frequency based on detection of AM versus FM tones

The ratios between the modulation index (eta) for just noticeable FM of a sinusoidally modulated pure tone and the degree of modulation (m) for just noticeable AM at the same carrier and the same modulation frequency were measured at carrier frequencies of 0.125, 0.25, 0.5, 1, 2, 4, and 8 kHz. Signal levels were 20 dB SL and 50 dB SPL or 80 dB SPL. At low modulation frequencies, for example, 8 Hz, AM and FM elicit very different auditory sensations (i.e., a fluctuation in loudness or pitch, respectively). In this case, eta and m show different values for just noticeable modulation. Since both stimuli have almost equal amplitude spectra if eta equals m (m less than 0.3), the difference in detection thresholds reflects differences in the phase relation between carrier and sidebands in AM and FM. With increasing modulation frequency, the eta-m ratio decreases and reaches unity at a modulation frequency called the "critical modulation frequency" (CMF). At modulation frequencies above the CMF, the same modulation thresholds are obtained for AM and FM. Therefore, it can be concluded that the difference in phase between the two types of stimuli is not perceived in this range. At center frequencies below 1 kHz, where phase errors caused by headphones and ear canal presumably are small, the CMF is useful in estimating critical bandwidth.     

Frequency and intensity discrimination in humans and monkeys

Frequency and intensity DLs were compared in humans and monkeys using a repeating standard "yes-no" procedure in which subjects reported frequency increments, frequency decrements, intensity increments, or intensity decrements in an ongoing train of 1.0-kHz tone bursts. There was only one experimental condition (intensity increments) in which monkey DLs (1.5-2.0 dB) overlapped those of humans (1.0-1.8 dB). For discrimination of both increments and decrements in frequency, monkey DLs (16-33 Hz) were approximately seven times larger than those of humans (2.4-4.8 Hz), and for discrimination of intensity decrements, monkey DLs (4.4-7.0 dB) were very unstable and larger than those of humans (1.0-1.8 dB). For intensity increment discrimination, humans and monkeys also exhibited similar DLs as SL was varied. However, for frequency increment discrimination, best DLs for humans occurred at a high (50 dB) SL, whereas best DLs for monkeys occurred at a moderate (30 dB) SL. Results are discussed in terms of various neural mechanisms that might be differentially engaged by humans and monkeys in performing these tasks; for example, different amounts of temporal versus rate coding in frequency discrimination, and different mechanisms for monitoring rate decreases in intensity discrimination. The implications of these data for using monkeys as models of human speech sound discrimination are also discussed.     

On the relation between the growth of loudness and the discrimination of intensity for pure tones

The intensity jnd is often assumed to depend on the slope of the loudness function. One way to test this assumption is to measure the jnd for a sound that falls on distinctly different loudness functions. Two such functions were generated by presenting a 1000-Hz tone in narrow-band noise (925-1080 Hz) set at 70 dB SPL and in wideband noise (75-9600 Hz) set at 80 dB SPL. Over a range from near threshold to about 75 dB SPL, the loudness function for the tone is much steeper in the narrow-band noise than in the wideband noise. At 72 dB SPL, where the two loudness curves cross, the tone's jnd was measured in each noise by a block up-down two-interval forced-choice procedure. Despite the differences in slope (and in sensation level), the jnd (delta I/I) is nearly the same in the two noises, 0.22 in narrow-band noise and 0.20 in wideband noise. The mean value of 0.21 is close to the value of 0.25 interpolated from Jesteadt et al. [J. Acoust. Soc. Am. 61, 169-176 (1977)] for a 1000-Hz tone that had the same loudness in quiet as did our 72-dB tone in noise, but lay on a loudness function with a much lower slope. These and other data demonstrate that intensity discrimination for pure tones is unrelated to the slope of the loudness function.     

Effects of flanking noise bands on the rate of growth of loudness of tones in normal and recruiting ears

Five subjects with unilateral cochlear hearing impairments and three normally hearing subjects made loudness matches between tones presented alternately to two ears, as a function of the intensity of the tone in the impaired ear (or the left ear of the normal subjects). The impaired ears showed recruitment; the rate of growth of loudness with increasing intensity was more rapid in the impaired ear than the normal ear. Presenting the tone in the impaired ear with two noise bands on either side of the tone frequency, at a fixed signal-to-noise ratio, did not abolish the recruitment. This suggests that recruitment is not caused by an abnormally rapid spread of excitation in the peripheral auditory system. At low signal-to-noise ratios, a continuous background noise reduced the loudness of the tone more than a noise gated with the tone, suggesting that the continuous noise induces adaptation to the tone. The noise had a greater effect on the loudness of the tone in normal ears than in impaired ears. It is possible that the loudness reduction of the tone in noise is mediated by suppression; suppression is weak or absent in impaired ears, and so the loudness reduction is smaller.     

Dead regions and pitch perception

The perception of pitch for pure tones with frequencies falling inside low- or high-frequency dead regions (DRs) was examined. Subjects adjusted a variable-frequency tone to match the pitch of a fixed tone. Matches within one ear were often erratic for tones falling in a DR, indicating unclear pitch percepts. Matches across ears of subjects with asymmetric hearing loss, and octave matches within ears, indicated that tones falling within a DR were perceived with an unclear pitch and/or a pitch different from "normal" whenever the tones fell more than 0.5 octave within a low- or high-frequency DR. One unilaterally impaired subject, with only a small surviving region between 3 and 4 kHz, matched a fixed 0.5-kHz tone in his impaired ear with, on average, a 3.75-kHz tone in his better ear. When asked to match the 0.5-kHz tone with an amplitude-modulated tone, he adjusted the carrier and modulation frequencies to about 3.8 and 0.5 kHz, respectively, suggesting that some temporal information was still available. Overall, the results indicate that the pitch of low-frequency tones is not conveyed solely by a temporal code. Possibly, there needs to be a correspondence between place and temporal information for a normal pitch to be perceived.     

A new procedure for measuring peripheral compression in normal-hearing and hearing-impaired listeners.

Forward-masking growth functions for on-frequency (6-kHz) and off-frequency (3-kHz) sinusoidal maskers were measured in quiet and in a high-pass noise just above the 6-kHz probe frequency. The data show that estimates of response-growth rates obtained from those functions in quiet, which have been used to infer cochlear compression, are strongly dependent on the spread of probe excitation toward higher frequency regions. Therefore, an alternative procedure for measuring response-growth rates was proposed, one that employs a fixed low-level probe and avoids level-dependent spread of probe excitation. Fixed-probe-level temporal masking curves (TMCs) were obtained from normal-hearing listeners at a test frequency of 1 kHz, where the short 1-kHz probe was fixed in level at about 10 dB SL. The level of the preceding forward masker was adjusted to obtain masked threshold as a function of the time delay between masker and probe. The TMCs were obtained for an on-frequency masker (1 kHz) and for other maskers with frequencies both below and above the probe frequency. From these measurements, input/output response-growth curves were derived for individual ears. Response-growth slopes varied from >1.0 at low masker levels to <0.2 at mid masker levels. In three subjects, response growth increased again at high masker levels (>80 dB SPL). For the fixed-level probe, the TMC slopes changed very little in the presence of a high-pass noise masking upward spread of probe excitation. A greater effect on the TMCs was observed when a high-frequency cueing tone was used with the masking tone. In both cases, however, the net effects on the estimated rate of response growth were minimal.     

Dependence of loudness growth on skirts of excitation patterns

Over a range of 50 dB, the loudness of a 100-Hz tone was measured in the presence of a broadband noise with a low-frequency cutoff at 200 Hz. The noise was varied in intensity along along with the tone so that the signal-to-noise ratio remained constant at either 0 or--10 dB. Listeners judged the loudness of the tone by loudness matching, magnitude estimation, and magnitude production. The noise markedly decreased the tone's rate of loudness growth but not the range over which loudness grows. The overall decrease in steepness of the 100-Hz loudness function was greater than that previously reported at higher frequencies. It is hypothesized that the decrease was greater because the spread of excitation at 100 Hz was more effectively contained than at higher frequencies. Support for this hypothesis is given by measures of intensity discrimination at 100 Hz.     

Manifestation of peripherial coding in the effect of increasing loudness and enhanced discrimination of the intensity of tone bursts before and after tone burst noise

To find the possible reasons for the midlevel elevation of the Weber fraction in intensity discrimination of a tone burst, a comparison was performed for the complementary distributions of spike activity of an ensemble of space nerves, such as the distribution of time instants when spikes occur, the distribution of interspike intervals, and the autocorrelation function. The distribution properties were detected in a poststimulus histogram, an interspike interval histogram, and an autocorrelation histogram—all obtained from the reaction of an ensemble of model space nerves in response to an auditory noise burst–useful tone burst complex. Two configurations were used: in the first, the peak amplitude of the tone burst was varied and the noise amplitude was fixed; in the other, the tone burst amplitude was fixed and the noise amplitude was varied. Noise could precede or follow the tone burst. The noise and tone burst durations, as well as the interval between them, was 4 kHz and corresponded to the characteristic frequencies of the model space nerves. The profiles of all the mentioned histograms had two maxima. The values and the positions of the maxima in the poststimulus histogram corresponded to the amplitudes and mutual time position of the noise and the tone burst. The maximum that occurred in response to the tone burst action could be a basis for the formation of the loudness of the latter (explicit loudness). However, the positions of the maxima in the other two histograms did not depend on the positions of tone bursts and noise in the combinations. The first maximum fell in short intervals and united intervals corresponding to the noise and tone burst durations. The second maximum fell in intervals corresponding to a tone burst delay with respect to noise, and its value was proportional to the noise amplitude or tone burst amplitude that was smaller in the complex. An increase in tone burst or noise amplitudes was caused by nonlinear variations in the two maxima and the ratio between them. The size of the first maximum in the of interspike interval distribution could be the basis for the formation of the loudness of the masked tone burst (implicit loudness), and the size of the second maximum, for the formation of intensity in the periodicity pitch of the complex. The auditory effect of the midlevel enhancement of tone burst loudness could be the result of variations in the implicit tone burst loudness caused by variations in tone-burst or noise intensity. The reason for the enhancement of the Weber fraction could be competitive interaction between such subjective qualities as explicit and implicit tone-burst loudness and the intensity of the periodicity pitch of the complex.     

Intensity discrimination and increment detection in cochlear-implant users

Intensity difference limens (DLs) were measured in users of the Nucleus 22 and Clarion v1.2 cochlear implants and in normal-hearing listeners to better understand mechanisms of intensity discrimination in electric and acoustic hearing and to evaluate the possible role of neural adaptation. Intensity DLs were measured for three modes of presentation: gated (intensity increments gated synchronously with the pedestal), fringe (intensity increments delayed 250 or 650 ms relative to the onset of the pedestal), and continuous (intensity increments occur in the presence of a pedestal that is played throughout the experimental run). Stimuli for cochlear-implant listeners were trains of biphasic pulses; stimuli for normal-hearing listeners were a 1-kHz tone and a wideband noise. Clarion cochlear-implant listeners showed level-dependent effects of presentation mode. At low pedestal levels, gated thresholds were generally similar to thresholds obtained in the fringe and continuous conditions. At higher pedestal levels, however, the fringe and continuous conditions produced smaller intensity DLs than the gated condition, similar to the gated-continuous difference in intensity DLs observed in acoustic hearing. Nucleus cochlear-implant listeners did not show consistent threshold differences for the gated and fringe conditions, and were not tested in the continuous condition. It is not clear why a difference between gated and fringe thresholds occurred for the Clarion but not the Nucleus subjects. Normal-hearing listeners showed improved thresholds for the continuous condition relative to the gated condition, but the effect was larger for the 1-kHz tonal carrier than for the noise carrier. Findings suggest that adaptation occurring central to the inner hair cell synapse mediates the gated-continuous difference observed in Clarion cochlear-implant listeners and may also contribute to the gated-continuous difference in acoustic hearing.