This thesis described work, using both experiments and simulations, designed to assess the relative contributions of across- and within-channel processes to Comodulation Detection Differences. Firstly, a demonstration of CDD under a number of conditions was described. Combination bands were found to affect threshold when only two bands were present, but once this was allowed for the results mainly supported a within-channel mechanism. Secondly, an experiment that manipulated stimulus parameters known to affect grouping was presented. It was found that introducing an onset asynchrony had no effect on the size of CDD which suggests that perceptual grouping of the signal and masker bands plays little role. Next, CDD was tested as a function of masker-signal frequency separation in a paradigm similar to two-tone masking (Zwicker, 1954) which limits off-frequency listening. CDD was found to be highest when the masking bands were placed with a frequency separation from the signal of 30-40% of the signal frequency. At narrow frequency separations, beats possibly reduced the CDD. At the wider frequency separations, the signal threshold in all conditions approached absolute zero and so the CDD inevitably declined. After that, the relative contribution of bands above and below the signal frequency was assessed at a number of masker levels. It was found that the modulation pattern of the lower band was entirely responsible for the CDD at the levels used in the previous experiments. If lower masker levels were used, the two bands became more equal in their contribution. This fits in with the upward spread of masking which is consistent with a within-channel process. Next, a model was presented that was based on a within-channel process only. The model made a number of predictions which were tested experimentally. The predictions included the steepness of the psychometric functions with correlated and uncorrelated signals, the effect of altering the bandwidth of the noises and the effect of introducing a time-delay between the signal and masker bands. The results of the experiments were consistent with the predictions of the model which provided further support for CDD being mainly governed by within-channel processes. The cues for detection present when using a within-channel mechanism were discussed.
In experiment 1, the signal was a narrow band of noise centred at 1500 Hz. There could be up to six masking bands spaced logarithmically around the signal frequency; three lower in frequency and three higher in frequency. Each masking band could be correlated with the signal, uncorrelated with the signal or replaced by a sinusoid of the same overall power. Each band was 20-Hz wide and had the same spectrum level. Two different spectrum levels were used; 50 and 65 dB SPL. There were a large number of conditions each representing a different combination of maskers. The results showed:
Increasing the number of bands gives a larger CDD.
This appears to fit in with an across-channel mechanism as increasing the number of bands increases the number of channels providing information. However, a close look at the results reveals that:
Adding more flanking bands of the same type only increases threshold for correlated bands.
This shows that the larger CDD when more bands are added is mainly due to an increase in the threshold when bands are correlated rather than a decrease in threshold when they are uncorrelated. This does not fit in with an across-channel grouping view as increasing the number of uncorrelated bands should group the masking bands more tightly as a separate source from the signal and so threshold should drop.
Adding bands (even steady sinusoids) more remote in frequency from the signal than correlated inner masking bands increases the threshold irrespective of the modulation pattern of the outer bands.
Adding four more bands increased the long-term level of the maskers by 4.8 dB. However, this gave rise to an extra 5.2 dB of masking which is very high considering that the outer masker bands would be substantially attenuated by the auditory filter. This increase was probably mainly due to combination bands (Greenwood, 1971) being audible when there was only one band below the signal frequency, but being masked when there were more bands.
Adding bands (even steady sinusoids) outside of uncorrelated inner masking bands did not increase the threshold unless the middle bands were correlated with the signal.
As mentioned above, increasing the number of uncorrelated bands from two to six did not alter the threshold. Threshold only increased if the middle bands (masker bands 2 and 5) were correlated. i.e.
This cannot be explained by the combination band explanation above. Combination bands will be lower in average level if the primary bands are uncorrelated as peaks in the envelopes of the signal and masker bands will not always occur at the same time. Also, thresholds were so low for the masker all-uncorrelated conditions that the combination bands would probably have been below absolute threshold. The fact that the outer bands had no effect if correlated is consistent with a within-channel view; these bands would have been much more attenuated by the auditory filter centred on the signal frequency. However, the lack of effect can only be explained by an across-channel view if one supposes that there is a preferred frequency separation of the channels that are monitored. Such a spacing was demonstrated in a CMR experiment by Schooneveldt and Moore (1989b). They showed that there appeared to be a limit of three critical bands over which adding comodulated bands improved performance.
Increasing the level of the masker bands made the modulation characteristics of the innermost bands less important.
The conditions where all masker bands were correlated with the signal and where all except the inner two bands were correlated gave very similar thresholds at the higher masker level; they were very different at the lower masker level. i.e.
This is consistent with a within-channel mechanism as the 'upward spread of masking' would mean that the outer bands would be attenuated less at the higher masker level. There is no obvious reason from an across-channel point of view why this should occur.
In conclusion, experiment 1 demonstrated the concept of CDD. The results were largely explicable by a within-channel process.
It has been postulated that some across-channel processes are linked to the mechanisms responsible for perceptual grouping. Such a grouping mechanism could be seen as being responsible for allocating the output of each peripheral channel to one of a number of sources. Once grouped it would be difficult to hear out the separate components. This would appear neatly to explain the results of CMR and CDD experiments. Comodulated bands would be grouped together and heard as one source. In CMR experiments, correlated flanking bands would be grouped with the on-frequency band, thus making it easier to hear the sinusoidal signal which would be perceived as coming from a separate source. If the flanking bands were not present or were uncorrelated, then the on-frequency band would remain as a separate source and thus the signal would be harder to detect. In CDD experiments, if the signal was correlated (and thus grouped) with the maskers it would be harder to hear than if it was uncorrelated (and thus from a separate source). If CDDs are due to an across-channel grouping mechanism, then it should be possible to alter the pattern of results by manipulating factors known to affect auditory grouping. One such factor is onset asynchrony. It has been reported that simultaneous onset has at least as large an effect as correlated amplitude changes in the perceptual fusion of sounds (Rasch, 1978; Darwin, 1984). Introducing a sufficiently large onset asynchrony should therefore provide a good test of whether perceptual fusion plays a role in the CDD experiments described here. If CDD is governed only by within-channel processes, the magnitude of the CDD should be roughly constant as the onset asynchrony between signal and masker is altered.
In experiment 2, there were three orthogonal stimulus manipulations of which all combinations were tested; two versus six bands, correlated versus uncorrelated signal and masker bands and zero versus 200-ms onset asynchrony. The results showed:
The size of the CDD was the same at both onset asynchronies.
There is no evidence that across-channel grouping has any effect on CDD. This is consistent with a within-channel mechanism.
Moreover, introducing an onset asynchrony has no effect whatsoever on any of the conditions.
Introducing an onset asynchrony might have been expected to lower the signal threshold in the correlated condition (thus decreasing the CDD). This is because the asynchrony would stop the signal band being grouped with the masking bands. If introducing an onset asynchrony had made a difference with only two bands, one might have expected a different pattern of results with six bands as the masker bands would have been more tightly grouped into one source. If grouping was responsible for the CDD, then having more bands would promote the grouping as there would be more channels with a common modulation pattern. Having six correlated bands would increase the contrast when an onset asynchrony was introduced, meaning that the signal would be more detectable.
In conclusion, experiment 2 showed that manipulating onset asynchrony (which is known to be a very powerful cue for grouping) had no effect whatsoever. This indicates that an across-channel mechanism based on perceptual grouping is not responsible for CDD. The results are consistent with the results of one group of subjects in the experiments of McFadden and Wright (1990). It is possible that if more subjects had been used in experiment 2 then some may have shown the pattern of results exhibited by the second group of subjects in the earlier work, i.e. very high masked thresholds overall with a decline in masked threshold as the onset asynchrony increased.
Experiment 1 provided a clear demonstration of CDD. However, it is possible that combination bands produced by the interaction between signal and masker bands affected the results. The results of experiment 1 suggested that the frequency placing of the bands had an effect on the size of CDD, yet because all the bands were fixed in frequency this was difficult to quantify.
Experiment 3 used a paradigm based on two-tone masking (after Zwicker, 1954). The signal was either a band of noise or a signal. Two narrow band noise maskers were used which were linearly spaced on either side of the signal frequency (i.e. at frequencies f±Df where f is the signal frequency). Two maskers were used to try to minimise the effect of off-frequency listening (Johnson-Davis and Patterson, 1979; O'Loughlin and Moore, 1981). A number of spacings (Df) were used ranging from 100 to 1400 Hz. A low-pass noise was used to mask any possible cubic combination bands. There were three signal conditions; Correlated noise band (C), Uncorrelated noise band (U) and Sinusoid of the same overall power (S). The results showed:
The CDD (defined as C-U) was highest at the 429- and 600-Hz spacings (roughly 30 - 40% of the signal frequency or 2 to 3 ERBs). It declined at larger spacings.
This is consistent with an across-channel view if one assumes that across-channel processes are most effective with a 2-3 ERB spacing. i.e. channels to compare across must be reasonably close together. This is consistent with the findings of Schooneveldt and Moore (1989b) for CMR. The thresholds decline as spacing increases; they give a rough indication of the auditory filter shape. The skirts of the auditory filter get less steep as frequency separation from the centre frequency increases. This may be partly due to the dynamic range of the filter being limited by absolute threshold. As the threshold for the uncorrelated condition is lower than the threshold for the correlated condition, the slope for the uncorrelated condition flattens off sooner than that for the correlated condition. This means that CDD declines. Thus the CDD would be expected to decline with increasing masker-signal frequency separation, based a within-channel process which was only using one filter for detection. Therefore the decline at wider separations is consistent with both across-channel and within-channel processes.
The CDD declined at narrow frequency separations.
At very narrow frequency separations (e.g. 100 Hz), the masker and signal bands fall mainly in the same channel. This could be explained by an across-channel mechanism being less effective as there would be fewer channels containing energy to be monitored by such a process and there would be less independence between any such channels. However, the decline is seen at frequency separations of at least 1-2 ERBs or 300-400 Hz. As many harmonic sounds in real life (e.g. speech) have fundamentals in this range (and thus the distance between adjacent harmonics is in the same range), one would expect the auditory system to be efficient at grouping components with such spacings. Moore and Schooneveldt (1990) showed by using a dichotic presentation that an across-channel mechanism gave higher CMRs as the frequency separation decreased.
At first glance, the decline at small spacings would seem to be inconsistent with a within-channel mechanism. However as the masker bands and signal bands become closer in frequency they will give rise to beats which would provide a within-channel cue that would be effective in all signal conditions, but possibly more so in the correlated condition, thus leading to a decline in the CDD. All subjects reported a roughness at the 100- and 200-Hz spacings. One subject actually had much lower thresholds at the narrowest spacing, thus showing that he must have been using a different cue for detection in that condition. Nonetheless, a decline in CDD at small separations has been taken as evidence of an across-channel mechanism (Wright, 1990). There is no reason why this should be so. Therefore the decline at narrow separations is consistent with both across-channel and within-channel processes.
The sinusoidal signal and the uncorrelated signal gave virtually identical thresholds for all values of Df. The thresholds in the correlated condition were much higher.
In summary, the results of experiment 3 can be explained easily in terms of a within-channel mechanism. To an extent, they can also be explained in terms of an across-channel mechanism, but this requires a number of assumptions to be made for which there is no evidence (e.g. a 'sweet-spot' separation over which an across-channel mechanism is more effective). The form of the results (i.e. a decline at narrow and wide frequency separations) is more readily explained by a within-channel mechanism.
Auditory filters are roughly symmetric on a linear frequency scale at moderate levels, but at higher levels the low-frequency skirt tends to be more shallow than the high-frequency skirt. As sound level increases, the lower frequency skirt gets more and more shallow, meaning that maskers at a lower frequency than the signal are attenuated less (Moore and Glasberg, 1987). The so-called phenomenon of the 'upward spread of masking' is well known. It is possible therefore that at the masker levels used in Experiment 3, the lower frequency masking band was responsible for most of the masking. To test this, the envelopes of the two masking bands were individually altered so that, for example, the lower band could be uncorrelated with the signal and the upper band correlated with the signal. If an asymmetry was found, then a within-channel explanation would predict that if the level of both masker bands was decreased, the two masking bands would have a more even contribution (perhaps even swapping over the dominance at low levels). The results of Moore and Schooneveldt (1990) showed that in a dichotic CMR experiment (i.e. across-channel only) with a similar noise bandwidth, the magnitude of the CMR was virtually the same at negative and positive separations (i.e. fDf = f+Df). Therefore, if it is assumed that the across-channel mechanisms in CMR are also responsible for CDD, one would expect that both the upper and lower bands to have similar contributions.
Five conditions were used; All correlated (C), all bands uncorrelated (I), maskers co-uncorrelated (U), upper correlated/lower uncorrelated (UC) and lower correlated/upper uncorrelated (LC). The C and U conditions were the same as used in experiment 3. Three masker spectrum levels were used; 45, 55 and 65 dB SPL. The results showed that:
At the 65 dB SPL spectrum level (the same as used in earlier experiments), the results fall clearly into two groups; the conditions in which the lower band is correlated (C and LC), which give higher thresholds, and the conditions in which the lower band is uncorrelated (U, UC and I) which give lower thresholds. The modulation characteristic of the upper band is unimportant.
The envelope of the lower band is entirely responsible for CDD. This is very strong evidence for upward spread of masking and a within-channel basis to the CDD.
As the masker level decreases, the thresholds for the LC and UC conditions become more equal or swap over.
The upward spread of masking will be much smaller at lower masker levels. This is supported by calculating excitation patterns. The upward spread of masking being responsible for the results is entirely consistent with a within-channel mechanism. It cannot be explained by the across-channel mechanisms used to account for CMR, as in CMR the across-channel processes have been shown to be generally independent of the level of the flanking bands (within limits) (Schooneveldt and Moore, 1987; Moore and Emmerich, 1990; Moore and Shailer, 1991). Across-channel processes have also been shown to be roughly symmetric for separations above and below the signal frequency (Moore and Schooneveldt, 1990).
In conclusion, experiment 4 provides very strong evidence for a within-channel mechanism. The results show a different pattern of results to the literature on across-channel processes in CMR.
A model based on within-channel processes only was presented. The model is based on the calculation of the envelopes of short (300 ms) samples of masker and signal using a sliding window technique. A simulated auditory filter (roex(p)) with the lower slope being dependent upon masker input level was centred on the signal frequency. The signal level and the masker level (after passing through the filter) were compared for the whole sample. If the signal-to-masker ratio exceeded a criterion level at a given point, then that was counted as providing a detection opportunity. The total time during which the signal could be detected was calculated for each set of samples. 1000 sets of samples were calculated in all. It is assumed that a certain total detection time is required for threshold to be reached. The masker and signal conditions could be altered as desired (e.g. correlation, delay, bandwidth and level). The model could also be used to calculate correlation coefficients between masker and signal. It could also be used to determine the average number and level of envelope maxima and minima. The output of the model was generally plotted as detection time as a function of signal level. Assuming that detection time is monotonically related to detectability, then the resulting curves are related to psychometric functions. Threshold corresponds to a certain d' or percentage correct value on the abscissa of the psychometric function (signal level is the ordinate). If the detection times corresponding to the thresholds measured in earlier experiments are determined by using the detection time curve calculated by the model for the same condition, then it is found that the detection times are very similar. Therefore, both the slope and position of the output functions of the model are of interest. The model was used to make a number of predictions which were tested experimentally.
The detection time model predicts that the psychometric function for a correlated signal will be a lot steeper than that for an uncorrelated signal. This was tested experimentally. A straight line was fitted to the graph of detectability (d') as a function of signal level. The results showed:
The slope of the psychometric function for the correlated condition was, on average, almost double that for the uncorrelated condition.
This is entirely consistent with the within-channel detection time model. Is it consistent with an across-channel mechanism? Moore et al. (1990b) measured psychometric functions for CMR and found a small, but significant difference in the slopes between the correlated and uncorrelated conditions (for which no explanation was given). However, the difference in slopes measured for CDD was much greater than that for CMR which suggests that some extra process was involved, probably based on within-channel processes.
The detection time model was presented with a number of conditions in which the masker and signal were always correlated, but where there was a time delay in the envelopes of the signal and masker bands. This has the effect of decorrelating the bands by differing amounts (i.e. partial correlation). Assuming that threshold corresponds to a certain constant detection time, then it is possible to predict thresholds from the model by determining the signal threshold necessary for that constant detection time. When the predicted thresholds derived from such a process were compared, it was predicted that a delay of about 30 ms would be required to make the thresholds drop to the level produced by an uncorrelated signal. This was supported by calculating the correlation between the masker and signal with various delays. The correlation dropped to zero with delays of about 30 ms. The results showed:
A delay of about ±30 ms (there was no significant asymmetry) was sufficient for the thresholds to drop to that for an uncorrelated signal.
This is entirely consistent with the predictions of the within-channel detection time model. This corresponds to a delay of about 40% of an envelope period (Rice, 1954). The results of McFadden (1986) and Moore and Schooneveldt (1990) show that a larger time delay is needed to reduce the CMR to zero. A delay corresponding to approximately one whole period of the envelope of the noise bands is needed. Therefore, one would predict that a larger time delay would be required if an across-channel process similar to that used in CMR was responsible for CDD.
In conclusion, the results of experiment 6 fit in very closely to the prediction of a within-channel model, but are not consistent with the results of previous CMR experiments (in which across-channel processes are known to play a major role).
The within-channel detection time model predicted that a very large increase in bandwidth and hence in fluctuation rate would be required to reduce the size of the CDD. Increasing bandwidth from 20 Hz to 80 Hz was predicted to have virtually no effect. An increase in bandwidth to 320 Hz was required to halve the predicted CDD. Earlier work such as that of Schooneveldt and Moore (1987) showed that both the within- and across-channel contributions to CMR decrease as bandwidth increases and that the within-channel component, if anything, was affected more. However, if only the spacings between the flanking/masker band centre frequency and the signal frequency in the CMR experiment that are comparable to those used in the CDD experiments are considered, then the CMR laries little (certainly the CMR(R-C) measure) over a similarly large range of bandwidths. At such frequency separations, there is little, if any, within-channel component to the CMR as the results for the monaural and dichotic conditions are about the same.
The effect of increasing the bandwidth was tested experimentally by performing analogous CDD and CMR experiments. So that the wider noisebands would not be affected by auditory filtering, it was necessary to use a higher signal frequency, so that the critical band would be wider. A signal frequency of 4 kHz was chosen. The results showed:
Altering the bandwidth of both the signal and masker from 20 Hz to 160 Hz had almost no effect on the CDD.
This is consistent with the predictions of the within-channel detection time model. The within-channel component of earlier CMR work shows a large dependence upon bandwidth but the across-channel component did not. This suggests that the within-channel mechanisms in CDD and CMR may not be the same or perhaps the same across-channel processes that play a role in CMR are also used in CDD
Only one subject showed a large CMR; the other two subjects showed very small CMRs.
This may have been because the subjects had been performing only CDD experiments for a year or so. They would have become highly tuned to the cues for detection in CDD which, as the observation above shows, may be very different to CMR cues. At the high signal frequency used, CMR is found to differ greatly between subjects (Fantini et al., 1993). Fantini et al. (1993) and Moore and Jorasz (1992) have discussed the balance between interference effects, probably related to MDI, and processes giving CMR. Subjects may have differed in their susceptibility to interference and the balance between CMR and interference. Substantial individual differences have been reported in susceptibility to interference/MDI effects (Moore et al., 1990b; Hall and Grose, 1991; Moore and Jorasz, 1992). The present CMR experiment was meant to be as similar to the CDD condition as possible. It is unfortunate that such conditions do not produce a consistent CMR across subjects.
Altering the bandwidth from 20 Hz to 160 Hz had no effect on the CMR.
Given the masker/signal spacing used (masker/flanker centre frequency was 0.6 of the signal frequency), this is consistent with earlier work using the same separations.
In summary, the results of experiment 7 are consistent with the predictions of the within-channel detection time model. The CMR experiment is consistent with other similar experiments, though only a limited number of conditions was used. The large within-channel dependency on bandwidth seen in CMR experiments was not seen in the CDD experiment, which suggests that different cues are used in CDD experiments.
The results of the experiments presented can be explained by a within-channel mechanism. Where the stimuli have been presented to the within-channel detection-time model (which has no across-channel component at all), the output of the model has been broadly consistent with the experimental data. Some of the results are also consistent with an across-channel mechanism and the results of earlier CMR experiments. For example, the decline in CDD at wider frequency separations between signal and masker could be explained by an across-channel process, if it is assumed that such a mechanism is most efficient over a limited range of channel separations. However, no direct evidence was seen in favour of an across-channel mechanism. This is not to say that such a mechanism does not play a role in CDD. The limitations of the CDD paradigm mean that it is very difficult to design conditions that promote the use of an across-channel mechanism in order to directly test the contribution that it might make (unlike, for instance, the ability to use dichotic presentation in CMR experiments).
Some of the experimental results are contrary to the predictions of an across-channel mechanism. Such results provide perhaps the strongest evidence in favour of a within-channel mechanism. Experiment 4 provides particularly clear evidence in favour of a role for the upward spread of masking. It shows a clear difference in the effects of altering the correlation of bands above and below the signal frequency. It also shows a large dependence upon masker level.
The results of the research presented here show that before more complicated explanations are searched for, the vigilant researcher should consider more simple and mundane explanations based on classical models (c.f. Occam's razor). From a psychological point of view, processes which are less computationally demanding are likely to be used unless there is clear advantage is using a more complicated process.
Even if it were proved beyond doubt that a within-channel mechanism was entirely responsible for CDD, one would still need to determine what that mechanism was. Two possible mechanisms were discussed in chapter 9. The firings of the neurones that are attached to the hair cells in the cochlea are phase locked to the stimulating waveform. If a pure tone is presented, firing will tend to occur at the same point in the period on each cycle. If a complex waveform is presented, the neural firings tend to be phase locked to the dominant frequency at the appropriate position on the basilar membrane. If a neurone corresponding to the signal frequency region of the basilar membrane is monitored, it will be phase locked to the lower masker (because of the upward spread of masking) when the signal is not present. When the signal band is present the dominance in phase locking would shift towards the signal frequency at times where the signal was dominant in level. If the signal was correlated with the maskers, as the signal level increased, so would the masker level and so the dominance would not alter greatly. If the signal was uncorrelated, there would be times where the signal was at a high level and the masker was at a low level. This would not have to be true for the whole 300 ms steady state presentation of the signal. Only a small number of detection opportunities would be required in which the dominant phase locking would alter, thus providing a cue.
There appears to be an upper limit to phase locking of 4-5 kHz (Rose et al., 1968). Could phase locking still play a role in experiment 7 where a signal frequency of 4 kHz was used? It was argued in chapter 9 that the lack of phase locking (or smearing of the nerve spikes) could itself be used as a cue if the masker frequency was sufficiently low to allow phase locking (which it was in experiment 7).
Another cue discussed was the rate and depth of envelope fluctuations in the signal channel. If a correlated signal and masker are added together, the rate and depth of the envelope fluctuations will not change. The envelope fluctuations will remain the same with and without the signal present. Only the long-term RMS level will be altered and so the task effectively becomes an intensity discrimination task. However, if a masker and uncorrelated signal are summed in one channel, the envelope statistics alter greatly. The envelope tends to become flatter and the rate of fluctuations increases. This was shown by running a simulation of the summation. For the correlated condition, the ratio of the mean levels of the maxima and minima and also the number of maxima/minima were unaltered when a signal was added. When an uncorrelated signal was added, the number of fluctuations increased by 12% and the envelope was much flatter. The mean maxima/minima ratio for the masker alone was 19.06 dB; for the masker and signal summed it was 7.32 dB. Therefore, both the rate and depth of envelope fluctuations could be effective cues for signal detection.
Given the success of the detection time model in predicting the results of the experiments it was tested with, it would useful to extend the model to deal with more masker bands (at present, only one masker band can be used). Also, the function mapping between detection time and detectability could be quantified. This will probably require a variable taking listener efficiency into account. This is because there are two variables in the detection process. One is the frequency selectivity which is reflected in the detection time measure. The other is the ability of the listener to take advantage of the detection opportunities presented. In other words, how well can the listener use the cues discussed above? Once more masker bands can be used and the mapping between psychometric function and detection time is known, then it should be possible to simulate more accurately the earlier experiments. Ideally, the model should be sufficiently flexible to be able to predict the outcome of experiment 1 (which had 6 masker bands which were altered in a large number of ways).
It would be interesting to use conditions where the maskers and signal were all at frequencies above 4-5 kHz, so that the phase locking cue was abolished. Would this affect the size of the CDD? It is possible that the envelope flattening cue is sufficient to give rise to a large CDD.
It may be possible to use an adapted binaural masking level difference (BMLD) paradigm to look at across-channel mechanisms within CDD. For instance, the signal band could be presented to one ear masked by an unmodulated band of noise wide enough to cover a large number of ERBs in order to raise the detection threshold above absolute threshold. The flanking bands could then presented to either both ears or the other ear alone.
Both the CDD and CMR parts of experiment 7 could be repeated with a number of frequency spacings. The threshold for the CMR reference condition with no flanking bands could also be measured. More work could be done on assessing the effect that the interference due to adding uncorrelated bands has on the CMR. Also, the bandwidth could be increased up to 320 Hz or so. All in all, these changes would make the comparison of CMR and CDD more effective. The model predicts that the higher bandwidths would lead to smaller CDDs.
It may be that no evidence can be found for an across-channel mechanism or rather that the large within-channel effects mean that any across-channel contribution is swamped. If this is the case, then perhaps CDD experiments will have gone as far as they can.