PROCEEDINGS of the
23rd International Congress on Acoustics
9 to 13 September 2019 in Aachen, Germany

Pulse coding in the ensemble of peripheral fibres and auditory
discrimination of the tone burst intensity
Liudmila RIMSKAYA-KORSAKOVA
N. N. Andreev Acoustics institute, Russia

ABSTRACTThe intensity discrimination of tone bursts with middle intensity presented either alone or before (after) noise
masker was poorer than the discrimination of the bursts with low or high intensity. We have offered a generalexplanation of the discrimination of the bursts presented in the different conditions. In simulation
experiments, the properties of two complementary distributions of the spike activity of ensemble ofperipheral fibres were studied. They were the distribution of the spike occurrence in time and the inter-spikeinterval distribution. Model input signals were single pulses, or combined sounds composed the test pulsesthat followed or preceded the masking pulses. The distribution peaks kept different information about thepulses or the combined sounds. The peaks were assumed to be neural bases for various subjective features.
Changes in the amplitudes of either single pulse or the test or masking pulses of combined sound causedchanges in the weights of the feature bases and their sensitivities to an amplitude increment. The results ofour simulation and psychoacoustic experiments revealed a qualitative similarity. In particular, the amplitude(or intensity) discrimination of the masked model pulse (or real tone burst) depended on the amplitude’s (orintensity’s) ratio of the test and masking pulses (or bursts) but did not depend on positions and delays of thetest pulse (or burst) relative to the masking pulse (or burst).
Keywords: Auditory nerve fibre, Ensemble, Distributions, Subjective features, Intensity discrimination

1. INTRODUCTION
Auditory intensity discrimination of a tone burst presented alone or under temporal masking
conditions has been shown to reveal specific characteristics, the origin of which is not yet understoodand differentially interpreted by various authors. Intensity discrimination of the single tone burst withmiddle intensity has been shown to be poorer than discrimination of a burst with either a low or highintensity (1-3). Intensity discrimination of a tone burst of middle intensity and presented after orbefore an intense noise masker was also shown to be poorer than discrimination of a burst with either
low or high intensity (4-9).
Deterioration of intensity discrimination has been found in the intensity range of the tone burst,
where a loudness enhancement effect was present. For listeners, tone bursts having middle intensityand presented under temporal masking can be perceived as louder than similar bursts presented insilence (8, 10-12). The loudness enhancement was suggested to cause an increase in the variability of
the representations of intensity; therefore, the intensity discrimination may deteriorate ( 8, 12).
In the present work, we have offered a general explanation of these effects.
The process of converting the receptor potentials of inner hair cells into action potentials (spikes)
of auditory nerve fibres could be crucial for intensity encoding of high frequency sound. According to
the volley theory (13), multiple fibres simultaneously discharge to reproduce the structure of thesesounds. This multiple response could be represented in the form of complementary distributions of
spike activity (14). We assumed (15) that the auditory system is able to use information from at least
two complementary distributions of ensemble activity of the peripheral fibers in the loudness
formation or in the intensity discrimination of high-frequency pulses, presented alone or within a
combined sound. These include the distribution of the spike occurrence in time and the inter-spikeinterval distribution. We assumed that the peaks of the distributions could create neural bases for
subjective features of the test pulse and the combined sound.
In this work, the responses of the ensemble of peripheral fibres to tone pulses were simulated, andthe coding properties of the ensemble, as well as the properties of the two abovementioned
distributions were evaluated. In addition, it was simulated an intensity discrimination task using the704

approach (16) that allow one to compared psychophysical thresholds with the sensitivity index d’ (17),calculated based on the activity of peripheral fibres.
To compare the contributions of different subjective features in pulse intensity discrimination, we
evaluated the weights and the sensitivity indices d’ to incremental change in amplitude for the neuralbases of various features, where the weight was equal to the density of the corresponding peak of the
distributions. The discrimination task simulation will allow us to formulate the goals and objectives ofthe psychoacoustic experiments that we can conduct. The results of psychoacoustic and simulation
experiments will be qualitatively compared. The coincidence of the results can confirm the hypothesis
about participation the various distributions of the ensemble activity of the peripheral fibres inintensity discrimination of tone bursts presented alone or under temporal masking.

2. COMPUTER SIMULATION EXPERIMENTS
2.1 Auditory Nerve Fibre Model
To simulate the ensemble response of the auditory nerve fibres (ANF), we applied aphenomenological model (15, 18). The ANF model includes several transformation stages of an input
signal X(t): (1) the formation of the basilar membrane response Y(t); (2) the formation of the receptor
potential of the inner hair cell R(t), synaptic noise S(t) and the synaptic potential of the spiral ganglion
neuron G(t); (3) the generation of a sequence of action potentials (spikes) by the spiral ganglion neuron
Pi. The receptor potential R(t) was equal the response Y(t). Synaptic noise S(t) was modeled as arandom process with a mean value and a rms deviation that were proportional to Y(t). To reproduce theSA, the rms deviation was increased by a value z. The latter value was chosen so that the SA was lessthan 5 spikes per second in all ANF models in the ensemble. The integration process of S(t) completed
the formation of the potential G(t). The transformation of the synaptic potential into the sequence of
spikes included comparing G(t) with a time-dependent threshold function H(t). If G(t) exceeded H(t),an action potential (or a spike) was generated. Each spike caused a temporal increase in the threshold.
During an interval equal to the sum of the absolute and relative refractoriness periods, the threshold
function H(t) decreased to reach the initial value H0. The function H(t) had fast and slow components.
To simulate the adaptation properties, their initial values of these components after spike generation
were increased by the residual values of the components that existed prior to spike generation.
The parameters of the ANF model were chosen to reproduce the well-known responses of the real
ANF. The characteristic frequency of the basilar membrane filter in the ANF model was 4 kHz.
Nonlinear properties of the BM filter were not considered because we focused on the transformation
peculiarities of the receptor potentials of the inner hair cells into the spike response of the ANF
ensemble. The test and masking pulses were segments of a sinusoid with durations of 5 -15 ms andfrequency equal to 4 kHz. The delays between the onsets of the test and masking pulses were equal to
20 - 90 ms. The calculation step in the ANF model was equal to 1 μs.
A post-stimulus time histogram (PSTH) and inter-spike interval histogram (ISIH) were calculated
based on the ensemble reaction consisting of 100 ANF models. The ensemble reaction was obtained in
response to one presentation of the test pulse or the combined sound. The bin width in histograms wasequal to 0.1 ms. The aggregation periods were equal to 100 μs for PSTH and 100 ms for ISIH.
The PSTH and the ISIH obtained in response to the single test pulse had one peak. The density of
the PSTH peak could be the basis for a loudness component called ‘the basic loudness component,’ andthe density of the ISIH peak - the basis for ‘the complementary loudness component’ (15). The PSTH
and the ISIH obtained in response to the combined sound had a pair of peaks. The PSTH peaks
preserved information about the amplitudes and the relative positions of the test and masking pulses.
They were responsible for the basic loudness components of the test and masking pulses. The ISIH
peaks did not carry information about the temporal position of the tone pulse relative to the masker.
The first ISIH peak corresponded to those inter-spike intervals whose width did not exceed theduration of the test and masking pulses. The peak combined the intervals generated in response to thetest and masking pulses and constituted the complementary loudness component of t he combinedsound. The second peak of the ISIH corresponded to the inter-spike intervals whose width correlatedwith the delay of the tone pulse relative to the masker. A temporal position and density of the peakwere responsible for periodicity pitch and strength of the periodicity pitch of the combined sound.
The test pulse presented alone had basic and complementary loudness components. The test pulse
presented before (after) masking pulses had two basic loudness components of the test and masking
pulses, as well as the complementary loudness component of the combined sound. To compare the705participation of these components in intensity discrimination task, we calculated the weights (equate
to the peak densities) and sensitivity indices d' in accordance with the ratios from (19).
2.2 Responses of the ensemble of the fibre models to a single tone pulse
The complementary PSTH and ISIH were obtained in response to a single pulse with duration of 10
or 90 ms (Figure 1, a, b). The pulse detection threshold evaluated based on the PSTH was PS and thethreshold evaluated based on the ISIH was PI (Figure 1, IY). Considering the thresholds PS and PI, theamplitudes of the pulse with a duration of 10 ms could be divided into three groups ( Figure 1, a). The
first group included low-amplitudes S that were lower than the threshold PI. The sum of spikes (N_S)
obtained in response to pulse presentation was lower than the number of fibres in the ensemble(N_S<<100). The sum of intervals (Max1) was equal to zero. Each fibre could respond not more thanonce, and the pulse was coded by the number of excited fibres. Pulse coding scheme was stochastic.
The second group included middle-amplitudes S. They were higher than the threshold PI (S>PI). Most
fibres in the ensemble were involved in the response to the pulse (N_S<=100), but the sum of intervals
was lower than the number of fibres in the ensemble (0<Max1<100). The fibres responded to the pulse
more than once, and pulse was coded by the number of excited fibres and the number of generated
spikes. The coding scheme was mixed, i.e., stochastic and deterministic. The third group included
high-amplitudes S. They were significantly higher than the threshold PI (S>>PI). The sum of spikes(N_S) exceeded the number of fibres in the ensemble (N_S>100). The pulse was coded by the numberof generated spikes, and the coding scheme was predominantly deterministic.

Figure 1 - Profiles of tone pulses (I), the post-stimulus histograms (II), the inter-spike interval histograms(III), the dependences of the sums of spikes N_S and inter-spike intervals Max1 corresponded to thehistogram peaks on the pulse amplitude S (IY). The duration of the pulse is equal 10 ms (a) or 90 ms (b).
The graphs show the amplitude of the pulse S (I), the sum of spikes N_S (II) or inter-spike intervals Max1
(III). On IY, it is marked the range of the mixed coding scheme. Abscissa: time in ms (I, II), inter-spikeinterval in ms, ISI, (III), the pulse amplitude, S, (IY). Ordinate: the pulse amplitudes (I); number of spikes inbin (II); number of inter-spike intervals in bin (III); sum of spikes N_S and inter-spike intervals Max1 (IY).
The division of the amplitudes into groups was related to the pulse duration (Figure 1). For pulses
with a duration of 90 ms, the thresholds PS and PI were lower than that for a pulse with a duration of
10 ms, i.e., 50 and 150 ms vs 100 and 320 ms. An increase in duration caused both a reduction in therange in which the mixed coding schemes operated and a shift in the range towards the low amplitudes.
Regarding this, the thresholds of PS and PI for long-duration tones would be similar and coding
scheme was predominantly deterministic. However, the coding scheme of clicks was stochastic(PI=∞) and the complementary loudness component was absent.
To estimate participation of these components in intensity discrimination, we calculated thedependences of d’(N_S) and d’(Max1) on dS (Figure 2). There are two horizontal lines on the graph,
where d’ is equal 1 or 3, i.e., the detection probability of dS was 76% and 98.5% (19). The pulse
duration was 10 ms. The pulse amplitude S0 was low, middle and high. Because of significant
fluctuations, the indices were calculated 10 times and averaged. The 90% confidence intervals of themean values of d' are shown on Figure 2.
For low-amplitude pulses S0 (250), the coding scheme was stochastic, and the complementary

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component was absent (Figure 2). The weight of the basic component characterized pulse loudness,and only this component contributed to amplitude discriminations of the pulses. For high -amplitude
pulses S0 (750), the coding scheme was predominantly deterministic, so the two loudness components
were present. They had different weights but the relative difference in their weights had decreased.
The mean values of d’(N_S) and d’(Max1) were similar, and the confidence intervals were the lowest.
Both components equally contributed to loudness assessment and amplitude discrimination of thepulse.

Figure 2 - The dependences of the sensitivity indices d’(N_S) and d’(Max1) on the amplitude increment dS.
The pulse amplitudes S0 are shown on graphs. Abscissa - increment dS. Ordinate - value of d’(N_S) andd’(Max1). Horizontal lines pass through the points d’ =1 and 3.
For middle-amplitude pulses S0 (400), the coding scheme of the pulses was mixed, and the two
loudness components were present. In contrast to the basic component, the complementary one had alower weight, was more sensitive to the amplitude increment, and had wider ranging confidence
intervals for the mean values of d’. Feedback between the weights and the sensitivity indices d’ could
lower the accuracy of loudness assessment and impair the amplitude discrimination of the pulses. Thus,
changes in the coding schemes could affect loudness formation and amplitude discrimination of thepulses.
2.3 Responses of the ensemble of the fibre models to the combined soundThe response of the ANF ensemble was received to a single presentation of the combined soundcomposed of the test pulse (stimulus) and the masker pulse (masker) with durations of 10 ms (Figure 3).
The stimulus amplitudes S were middle and the masker amplitudes M varied from 100 to 800.
The profiles of the PSTH and the ISIH had pairs of peaks (N_S, N_M and Max1, Max2). Variationsin amplitude M influenced the reactions induced by the stimulus. The density of the peak N_S changed
only when the stimulus followed the masker. The densities of the peaks Max1 and Max2 depended on
the ratio of the amplitudes M and S but not on the position and the delay of the stimulus relative to themasker or on their durations. If M<S, then the density of the peak Max1 was held approximately
constant, and the density of the peak Max2 increased with increasing amplitude M. If M>S, then,conversely, the density of the peak Max1 increased, and the density of the peak Max2 remained
constant with increasing amplitude M.
The three loudness components (N_S, N_M and Max1) were involved in the intensity
discrimination task. N_S and N_M were the bases for the basic loudness components of the stimulus
and masker and Max1 was the basis for the complementary component of the combined sound. To
evaluate participation of the three loudness components in amplitude increment detection, it wascompared their weights (that equate to the peak densities) and sensitivity indices d' (Figure 4). The
stimulus amplitude S0 was always considered middle, equal to 400. The masker amplitude M could be
low, middle or high. The weights of the N_M, N_S and Max1 components fluctuated very weakly but
the indices of d'(N_S) and d'(Max1) fluctuated strongly. Thus, the indices were calculated 10 times andaveraged. The 90% confidence intervals of the mean values of d' are shown on Figure 4.
For low-amplitude M (250) and S>M, the masker coding scheme was stochastic, and the stimulus
coding scheme was mixed. The complementary component (Max1) was formed only by the inter-spikeintervals caused by the stimulus. The N_M component did not affect increment detection dS. The
weight of the stimulus basic loudness component (N_S) significantly exceeded the low weight of thecomplementary loudness component (Max1), but sensitivities of the stimulus basic component (N_S)
exceeded the sensitivities of the complementary component (Max1). Thus, the feedback between theweights and sensitivities of the N_S and Max1 components could reduce the accuracy of loudness
assessment and impair amplitude discrimination of the pulses. We could see the same conditions when
the stimulus was presented in silence.
For high-amplitude M (750) and S<<M, the weight of the masker basic component (N_M) had
noticeably exceeded the weight of the stimulus basic component (N_S). Due to the large contribution707

of the N_M, the sensitivity index of d’(Max1) decreased relative to the index of d’(N_S). The weight ofthe stimulus basic component (N_S) was low, and the sensitivity index d’(N_S) was high. By contrast,
the weight of the complementary component (Max1) was high, and the sensitivity index d’(Max1) was
low. Thus, the feedback between the weights and sensitivities of the N_S and Max1 components could
lower the accuracy of loudness assessment and impair amplitude discrimination of the pulses.
abcdFigure 3 - Profiles of the combined sounds (I); the post-stimulus histograms (II) and inter-spike interval
histograms (III); dependences of the sums of spikes (N_S and N_M) and the sum of inter-spike intervals(Max1 and Max2) correspondent to peaks of the histograms on the masker amplitude M (IY). The graphs
show the pulse and masker amplitudes (S and M); the delays, D; the sum of spikes N_S and N_M (II)corresponded to the two peaks of the of post-stimulus histogram arisen by pulse and masker; the sum ofinter-spike intervals Max1 and Max1 corresponded to the two peaks of inter-spike interval histogram arisen
by combined sound. On a and b, it is shown comparison of the responses to the combined sounds withdifferent positions the pulses relative to the maskers; on b and c –with different delays D of the pulses relative
to the maskers; on c and d – with different delays D, the amplitudes S and the pulse durations. Abscissa: timein ms (I, II), inter-spike interval, ISI, in ms (III), amplitude M (IY). Ordinate: the pulse and masker
amplitudes (I); number of spikes in bin (II); number of inter-spike intervals in bin (III); sum of spikes orinter-spike intervals corresponded to histogram peaks (IY).

Figure 4 - The dependences of the sums of spikes N_S, N_M and inter-spike intervals Max1 on the amplitudeof pulse S (I) and the dependences of the sensitivity indices d’(N_S) and d’(Max1) on the increment dS (II).
The tone pulses preceded the pulse maskers. On (I), the graphs show the pulse S0 and masker M amplitudes.
N_S and N_M - the sum of spikes corresponded to the two peaks of post-stimulus histogram arisen by pulse
and masker; Max1 and Max1 - the sum of inter-spike intervals corresponded to the two peaks of inter-spikeinterval histogram arisen by combined sound. Abscissa: amplitude of the pulse (S0+dS) (I); - increment dS(II). Ordinate: the sums of spikes (N_S and N_M) or inter-spike intervals (Max1) corresponded to the peaks ofthe two histograms (I); the mean values of indices d’(N_S) and d’(Max1). Horizontal lines pass throughpoints d’=1 and 3.
For the middle-amplitude M (400) and S~<M, the coding schemes of the stimulus and the masker

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were mixed. The complementary component (Max1) was formed by the stimulus and the masker. The
weights of all loudness components (N_M, N_S and Max1) were comparable. The complementarycomponent (Max1) could enhance one of the two basic components (N_S or N_M). The indicesd’(Max1) and d’(N_S) were equal. The similarity between the coding schemes, between the weights ofthe three loudness components (N_M, N_S and Max1) and the indices d’(Max1) and d’(N_S) could leadto errors in loudness assessment of the stimulus and the masker, as well as to deterioration in amplitude
discrimination of the stimulus. We received a similar result when the stimulus followed the masker (itis not shown). The worst conditions for loudness formation of the test and masking pulses and for
amplitude discrimination of the test pulse occurred when the pulses had middle amplitudes and theircoding schemes were mixed. It is important that the amplitudes the test and masking pulses, but nottheir temporal positions or delays (Figures 3-4) were responsible for the coding schemes and theappearance of the complementary component of the combined sound.

3. PSYCHOACOUSTIC EXPERIMENTS
3.1 Introduction
According to the simulation, loudness assessment and amplitude discrimination of the test pulsesthat followed or preceded the masking pulse depended on the ratio of amplitudes of the test pulse andthe masking pulse rather than the positions and delays of the test pulse relative to the masking pulse. If
similar properties we could find in the auditory perception, it would indicate that the two distributionsof ANF ensemble activity involved in the pulse intensity discrimination.
The auditory deterioration of intensity discrimination and loudness enhancement of the test tone
burst (stimuli) with intensity of 25-, 55- or 85-dB SPL were found when the intensity of the masking
pulses was varied (9). The stimuli followed the maskers. The delay between them was 100 ms. The
profiles of the dependence of the Weber fraction (or the ratio of the smallest noticeable intensity
increment, dI, to the pulse intensity, Is; dI/Is in dB) on masker intensity were related to the ratio of theintensity of the stimuli and maskers. If the masker intensity was lower than stimulus intensity, thevalues of the Weber fraction fluctuated relative to that obtained in quiet. If masker intensity exceeded
stimulus intensity by less than 15-30 dB, the Weber fraction increased proportionally to the increase inmasker intensity. If masker intensity exceeded stimuli intensity by more than 15 -30 dB, then thegrowth of the Weber fraction exhibited a slowdown. For the same listeners, Oberfeld (9) estimated theloudness of stimuli that followed the masker. A significant correlation between the deterioration of
intensity discrimination and loudness enhancement of the stimuli was demonstrat ed. Suggest that thereason for the correlation was the similarity between the stimuli and maskers. Considering date from(8, 9, 12), we designed our experiments. We aimed to obtain the dependences of the Weber fraction onmasker intensity when the tone burst both followed and preceded the masking burst, the timing of thetone burst relative to the masking burst, tone burst intensity and duration varied.
3.2. Method and Results
The auditory experiments were carried out in a soundproof chamber. An adaptive two -interval
procedure with two alternative forced-choices was used. The test sequence consisted of two intervals.
One interval contained the test and the masking bursts, and the other - the standard and masking bursts.
The intervals were generated digitally as files. The files were played in a random order using the EMU
0204 24-bit audio adapter with a sampling frequency of 44.1 kHz. The sounds were presented tolisteners’ right ear using Shennheiser HD-265 headphones. All bursts were Gaussian-shaped sinusoids
with a frequency of 4 kHz and a bandwidth of 460 Hz in the first and second series of measurements
and 200 Hz in the last one. The intensities of the standard tone bursts (Is) were equal to 20, 30, or 40 dB
SL i.e., over the individual absolute threshold for the tone burst. The intensities of the masking bursts(Im) varied in the range of 10-70 dB SL. The tone bursts presented before or after the masking bursts.
The delays, D, between the middle parts of the tone bursts and the masking bursts were equal to 20-180 ms. Three listeners with normal hearing under the age of 35 years participated in the experiment.
The Weber fraction function was the dependence of the intensity discrimination threshold (dI/Is) on
the intensity of the masking bursts (Im). For all tested listeners, the functions obtained were very
similar and, therefore, were averaged. In the first series of experiments the standard tone bursts had
different intensities (Is) and a delay (D) of 50 ms (Figure 5, a). In the following experiment thestandard tone bursts had an intensity of 40 dB SL and the delays of 20, 50 and 80 ms (Figure 5, b). In
the last series of experiments, the bandwidth of the stimuli and the maskers was reduced to 200 Hz and709

the range of masking intensity was increased. The tone burst intensity was equal to 40 dB SL, and thedelays to 80, 130 and 180 ms (Figure 5, c). All Weber fraction functions had an inflection point that
corresponded to the masker intensity being equal to the standard burst intensity. If the intensity of themasker was below the inflection point, then the Weber fraction corresponded to those obtained in quiet.
If the masker intensity exceeded the inflection point, the Weber fraction increased proportionally tothe masker intensity. As the intensity of the standard burst increased, the values of the Weber fraction
obtained in quite decreased. The inflection point moved towards the higher intensities of the masker.
In the masker intensity range of 60-70 dB SL, the Weber fractions could exhibit a slowdown in growth.
The well-known and our Weber fraction functions matched each other. The profiles of the functions
depended on the ratio of amplitudes of the stimuli and maskers rather than their temporal positions anddelays.
abcFigure 5 - The dependence of intensity discrimination thresholds for tone bursts that preceded or followed themasking bursts on the intensity of the latter. The delay has a minus sign if the stimuli preceded the maskers
and a plus sign if the stimuli followed the maskers. On a and b: the bandwidth of both the stimulus andmasker is equal to 460 Hz; on c – 200 Hz. Parameters on a: the intensity of standard burst; the delay between
the burst and the masker; on b and c: intensity of standard burst and delays. The points on the ordinatescorrespond to the intensity discrimination thresholds in quiet. Abscissa: the masker’s intensity in dB SL.
Ordinate: intensity discrimination thresholds in dB.

4. SUMMARY AND CONCLUSIONS
To explain the intensity discrimination of tone bursts presented alone and under temporal masking
it was evaluated the coding schemes for high-frequency pulses with different amplitudes and durationsin an ensemble of peripheral fibers. It was received the two complementary distributions of theensemble activities received in response to the single pulse presented alone or under temporal masking.
The distributions peaks carried different information about the test and masking pulses. The peaks
could create the bases for the basic loudness components for the two pulses and the complementary
loudness component of the combined sound.
It was found that the coding properties (Figure 3) and the amplitude discrimination properties(Figure 4) of the test pulse presented before or after masking pulse depended on the amplitude’s ratioof these pulses but did not depend on their positions and delays between them. The own auditory
experiments (Figure 5) confirmed this conclusions. Considering the simulation results, the intensity
discrimination of tone bursts could be explanted as follows:
1. The deterioration of intensity discrimination of a single mid -intensity tone bursts (1-3) could
appear due to feedback between the weights and the sensitivities of the basic and complementary
loudness components (Figure 1-2). The feedback could lower the accuracy of the loudness estimate
and therefore degrade the amplitude discrimination of the single tone bursts.
2. The mid-intensity tone bursts under temporal masking could be subjectively louder than bursts
presented alone (8, 10-12) because the complementary loudness component of the combined soundcould enhance the loudness of the masked bursts (Figure 3).
3. The deterioration of intensity discrimination of the tone bursts under temporal masking (9)provided that the test and masking bursts have similar intensities could be due to the similarity of thecoding schemes of the test and masking bursts and appearances the complementary loudness710

component of the combined sound. The simulation revealed a relationship between loudness anddiscrimination of the intensity of the test pulse (6, 8, 9, and 12). In particular, for test and masking
pulses with similar amplitudes (but the masker amplitude was some higher), the two loudness
components were similar sensitive to the test pulse amplitude changes and the third loudness
component was insensitive to that changes (Figure 4). The weight of the basic loudness component of
the test pulse was less than the weight of the basic component of the masking pulse, but was more than
the weight of the complementary one. The last component could enhance the loudness of either test or
masking pulse. We believed that confusion in the weights and sensitivities of the three loudness
components could cause deterioration in discrimination of the intensity of the test pulse. The greater
the amplitude of the masking pulse, the greater the weight of the complementary component, thegreater the confusion. However, if differences between amplitudes of the test and masking pulses weresignificant then their loudness differed better in the presence the complementary component of the
combined sound (Figure 4). The feedback between the weights and the sensitivities of the basic
loudness component for the test pulse and the complementary one for the combined sound could lower
the accuracy of the loudness estimate and therefore somewhat degrade the amplitude discrimination of
the test pulse. In this case, the causes of deterioration were similar to those that occurred in theamplitude discrimination of single mid-amplitude pulses.
Thus, our study confirmed the hypothesis (14) that the neural temporal code used by the auditory
system to analysis the high-frequency sound could combine information from the complementary
distributions of the ensemble activity of the peripheral fibres.
Supported by the Russian Foundation for Basic Research (RFBR, grant No. 14-04-00155).

REFERENCES
1. Avakyan RV, Radionova EA. The special features of differential intensity thresholds for a brief soundsignal. Sov Phys-Acoust. 1963. 8. p. 320-323.
2. Raab DH, Taub HB. Click-intensity discrimination with and without a background masking noise. J
Acoust Soc Am. 1969. 46 4B. p. 965-968.
3. Carlyon RP, Moore BCJ. Intensity discrimination: a severe departure from Weber's law. J Acoust Soc
Am. 1984. 76. p. 1369-1376.
4. Zeng FG, Turner CW, Relkin EM. Recovery from prior stimulation. II. Effects upon intensity
discrimination. Hearing Research 1991. 55. p. 223–230.
5. Plack CJ, Viemeister NF. The effects of notched noise on intensity discrimination under forward masking.
J Acoust Soc Am. 1992. 92. p. 1902–1910.
6. Carlyon RP, Beveridge HA. Effects of forward masking on intensity discrimination, frequency
discrimination, and the detection of tones in noise. J Acoust Soc Am. 1993. 93. p. 2886–2895.
7. Plack CJ, Carlyon RP, Viemeister NF. Intensity discrimination under forward and backward masking:Role of referential encoding. J Acoust Soc Am. 1959. 7. p. 1141–1149.
8. Plack CJ. Loudness enhancement and intensity discrimination under forward and backward masking. J
Acoust Soc Am. 1996. 100. p. 1024–1030.
9. Oberfeld D. The mid-difference hump in forward-masked intensity discrimination. J Acoust Soc Am.
2008. 123. p. 1574-1581.
10. Irwin RJ, Zwisklocki JJ. Loudness effects in pairs of tone bursts. Percept Psychophys. 1971.10.189–192.
11. Zwislocki JJ., Sokolich WG. On loudness enhancement of a tone burst by a preceding tone burst by apreceding tone burst. Percept.Psychophys 1974. 16. p. 87–90.
12. Zeng FG. Loudness growth in forward masking: Relation to intensity discrimination. J Acoust Soc Am.
1994. 96. p. 2127–2132.
13. Wever EG. Theory of Hearing. Dover Press, New York. 1949.
14. Cariani PA. Temporal coding of periodicity pitch in auditory system: An Overview. Neural plasticity
1999; 6. p. 147-171.
15. Rimskaya-Korsakova LK. Manifestation of peripheral coding in the effect of the loudness enhancement
and intensity discrimination of tone bursts presented before and after tone burst noise. Acoustical
Physics. 2017. 63. p. 478–489.
16. Viemeister NF. Auditory Function. ed. G. Edelman, W. Gall, W. Cowan. Wiley, N Y. 1988. p. 213–241.
17. Green JA. Signal Detection Theory and Psychophysics. Wiley, New York. 1966.
18. Dubrovskii NA, Rimskaya-Korsakova LK. Model parameters of auditory neurons involved in soundmodulation discrimination: natural impulse periodicity. Acoustical Physics. 1997. 43. p. 421-428.
19. Egan J. Signal Detection Theory and ROC Analysis. Academic Press, N Y. 1975.

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