Brian C. J. Moore Department of Experimental Psychology, University of Cambridge, Downing Street, Cambridge CB2 3EB, England

Transcription

1 Asymmetry of masking between complex tones and noise: Partial loudness Hedwig Gockel a) CNBH, Department of Physiology, University of Cambridge, Downing Street, Cambridge CB2 3EG, England Brian C. J. Moore Department of Experimental Psychology, University of Cambridge, Downing Street, Cambridge CB2 3EB, England Roy D. Patterson CNBH, Department of Physiology, University of Cambridge, Downing Street, Cambridge CB2 3EG, England Received 29 July 2002; revised 27 January 2003; accepted 25 April 2003 This experiment examined the partial masking of periodic complex tones by a background of noise, and vice versa. The tones had a fundamental frequency F0 of 62.5 or 250 Hz, and components were added in either cosine phase CPH or random phase RPH. The tones and the noise were bandpass filtered into the same frequency region, from the tenth harmonic up to 5 khz. The target alone was alternated with the target and the background; for the mixture, the background and target were either gated together, or the background was turned on 400 ms before, and off 200 ms after, the target. Subjects had to adjust the level of either the target alone or the target in the background so as to match the loudness of the target in the two intervals. The overall level of the background was 50 db SPL, and loudness matches were obtained for several fixed levels of the target alone or in the background. The resulting loudness-matching functions showed clear asymmetry of partial masking. For a given target-to-background ratio, the partial loudness of a complex tone in a noise background was lower than the partial loudness of a noise in a complex tone background. Expressed as the target-to-background ratio required to achieve a given loudness, the asymmetry typically amounted to db. When the F0 of the complex tone was 62.5 Hz, the asymmetry of partial masking was greater for CPH than for RPH. When the F0 was 250 Hz, the asymmetry was greater for RPH than for CPH. Masked thresholds showed the same pattern as for partial masking for both F0 s. Onset asynchrony had some effect on the loudness matching data when the target was just above its masked threshold, but did not significantly affect the level at which the target in the background reached its unmasked loudness. The results are interpreted in terms of the temporal structure of the stimuli Acoustical Society of America. DOI: / PACS numbers: Cb, Dc, Nm MRL I. INTRODUCTION Recent detection experiments have demonstrated that there are large asymmetries in the masking produced by broadband Gaussian noise, on the one hand, and tonal sounds with the same excitation patterns, on the other hand. Specifically, Gockel et al. 2002a have demonstrated that noise masks harmonic complex tones much more effectively than the reverse and Krumbholz et al have shown that noise masks iterated rippled noise IRN a stimulus which evokes a pitch sensation more effectively than the reverse. In these experiments, when the target sound is well above threshold, a tone and a noise are perceived separately, despite the fact that both excite the same range of frequency channels, and each of the percepts seems to have its own loudness. In the present paper we report an experiment to assess whether and how the asymmetry of masking observed for a Present address: MRC-Cognition and Brain Sciences Unit, 15 Chaucer Rd., Cambridge CB2 2EF, England. Electronic mail: hedwig.gockel@mrccbu.cam.ac.uk masked thresholds translates to supra-threshold levels; the partial loudness of harmonic complex tones in noise, and vice versa, was determined for targets and maskers with identical bandwidth. Partial loudness or masked loudness refers to the loudness of a target sound when presented together with a background or partial masking sound Scharf, 1964; Zwicker and Fastl, The partial loudness of a target sound can be determined either directly by the use of magnitude estimation or magnitude production procedures, or indirectly using loudness-matching procedures Zwicker, 1958, Ina typical loudness-matching procedure, the target is presented alone in one interval and together with the masker in the other interval; its level is fixed in one interval and variable in the other. The listener adjusts the level in order to achieve equal loudness of the target in the two intervals Zwicker, 1963; Hellman, If this is repeated for various fixed levels of the target, a masked loudness-matching function MLMF results, showing the level of the target alone as a function of the level of the target in the mixture at the point J. Acoust. Soc. Am. 114 (1), July /2003/114(1)/349/12/$ Acoustical Society of America 349

2 of equal loudness. The general shape of such an MLMF can be described as follows: When the target sound is close to its threshold in the masker, the level of the target in the masker is set much higher than the level of the target alone. With increasing level of the target in the masker, the matched level of the target alone also increases, but at a faster rate. At a sufficiently high level, the level of the target in the background equals that of the target alone, and this equality then persists at still higher levels Zwicker and Fastl, Most studies of partial loudness have investigated the MLMF for a pure tone as a function of the frequency of the tone and the bandwidth of the masking noise Zwicker, 1963; Hellman and Zwislocki, 1964; Scharf, 1964; Stevens and Guirao, 1967; Hellman, Only a few studies have investigated the partial loudness of noise when masked by a pure tone Zwicker, 1963; Hellman, 1972; Schroeder et al., Zwicker 1963 measured the level of a narrow-band noise target required to give the same loudness as that target presented in a pure tone background, as a function of the level of the background; the frequency of the background equaled the center frequency of the noise. However, he did not measure MLMFs. Schroeder 1979 measured MLMFs for a critical-band wide noise centered at 1 khz, masked by an 80 db SPL sinusoid with various frequencies. The effect of the masking tone was greatest when it was centered on the noise band. Schroeder estimated the slope of the MLMF for a tone frequency of 1 khz to be 3 db/db level of noise alone plotted against level of noise presented with masker when the level of the noise was below 80 db SPL. Hellman 1972 provided the sole study in which the growth of the masked loudness of a noise in a tone was directly compared with that of a tone in a noise. Note, however, that the data for the latter condition were obtained from different subjects, in an earlier study Hellman, Hellman 1970, 1972 used a 1000-Hz pure tone and noise bands of various widths. In the 1970 paper, she investigated MLMFs for a pure tone masked by noises of various bandwidths and levels. For nearly comparable overall masker SPLs, an octave-band noise produced a steeper MLMF than a wide-band noise, and the MLMF was shifted to the right for the former. Increasing the level of a fixed-bandwidth noise masker also produced steeper, right-shifted MLMFs. Importantly, two noise maskers with different bandwidths but with levels chosen to give equal masked thresholds for the tone, produced very similar MLMFs. In the 1972 paper, Hellman reported MLMFs for noise targets of various bandwidths and various levels of the pure tone masker. The slope of the MLMF for the noise target masked by a pure tone with a frequency centered in the noise band became steeper as the bandwidth of the target noise decreased. Comparison of MLMFs for a critical-band wide noise target from the later paper, with MLMFs for the pure tone target and a criticalband wide noise masker from the earlier paper, showed that the two functions agreed reasonably well in position and slope if the level of the tone masker was about 18 db higher than that of the noise masker, i.e., the noise was the more effective masker. Also, the masked threshold for the tone in noise was about 20 db higher than the masked threshold for the noise in the tone. Hellman 1972 concluded that the partial loudness functions for the noise target and the tone target were surprisingly similar, if the level of the tone masker was increased relative to that of the noise masker by the amount necessary to obtain equal masked thresholds of the noise in the tone and the tone in the noise. The present study measured MLMFs using broadband sounds as targets and maskers; the targets and maskers were complex tones and noises with identical bandwidth and nearidentical excitation patterns see below. There were four main objectives: 1 To measure the growth of partial loudness for complex sounds more like those that are common in speech and music. 2 To assess whether the asymmetry between the MLMFs of tones masked by noises and of noises masked by tones would be observed for complex tones and noise of equal bandwidth, or whether the previously observed asymmetry in partial loudness for tones and noise might have been dependent on some difference in the excitation patterns of the stimuli. 3 To assess the influence of onset and offset asynchrony of the target and masker on the resulting MLMFs. In a variety of paradigms, onset and offset asynchrony have been shown to be powerful cues for perceptual segregation of two concurrent sounds see, e.g., Darwin and Carlyon, Therefore, one might expect the target sound to be heard out more clearly and possibly to be louder if the target and masker start asynchronously than if they start synchronously. In past experiments on partial loudness, asynchronous onsets have generally been used in order to facilitate loudness comparisons between the target in the background and the target alone. However, we are not aware of any study quantifying the effect of onset asynchrony on partial loudness. 4 To investigate the influence of the starting phases of the components of the complex tones, which affects the degree of envelope modulation, on the MLMFs. For component phases giving a highly modulated waveform cosine phase one might expect a clearer and stronger pitch percept than for phases giving a less modulated waveform random phase Moore, 1977; Lundeen and Small, A target with a clearer pitch, and therefore less perceptual similarity with the background noise, might be perceptually segregated from the noise more effectively than a target with a weak pitch. As in the case of onset asynchrony, a higher degree of perceptual segregation between complex tone and noise might cause the target sound to be heard as louder. The degree of envelope modulation in the internal representation of a complex tone, i.e., after basilar-membrane BM filtering, is dependent on the number of components interacting at the output of a given auditory filter; the more components the higher the degree of envelope modulation. Hence, for a fixed center frequency, the lower the fundamental frequency F0, the more modulated is the envelope. To further check the effect of degree of envelope 350 J. Acoust. Soc. Am., Vol. 114, No. 1, July 2003 Gockel et al.: Partial loudness

3 modulation and of duration of the repetition period on the MLMFs, two F0s spaced two octaves apart were employed. The stimuli were identical to those used by Gockel et al. 2002a. The F0 of the complex tones was either 62.5 or 250 Hz, and the components of the complex tones started in either random or cosine phase. Gockel et al. 2002a found that the asymmetry of masking as measured by masked thresholds depended on the starting phases of the components, the F0, and, for the low F0, on the level of the masker. We were also interested in determining whether the same pattern of dependence would be observed for partial loudness. II. METHOD A. Stimuli The sound to be matched in loudness is called the target, throughout the study. We used either a harmonic complextone target masked by a noise, or a noise target masked by a harmonic complex tone. The complex tones had an F0 of 62.5 or 250 Hz. The components were added in either random phase RPH or cosine phase CPH. All tones were bandpass filtered into a frequency region from the tenth harmonic to 5000 Hz at the 3-dB down points. The slope of the filter outside the passband was 100 db/oct. Thus, the passband was from 625 to 5000 Hz for the 62.5-Hz F0, and from 2500 to 5000 Hz for the 250-Hz F0. As a result, the components of the harmonic complexes were unresolved by the peripheral auditory system Plomp, 1964; Moore and Ohgushi, The CPH complex would be expected to produce a waveform whose envelope, at the output of each auditory filter, had a higher degree of modulation than that of the RPH complex. The noise presented with a given complex tone either as target or masker was a Gaussian noise filtered in the same way as the given complex. The root-mean-square rms level of the masker was 50 db SPL. For each F0, the excitation patterns for the tone and noise stimuli were essentially identical, when calculated using the procedure described by Glasberg and Moore 1990 ; see Fig. 1 of Gockel et al. 2002a. Thus, based on the longterm excitation patterns, no partial masking asymmetry would be expected between tone targets with noise maskers and noise targets with tone maskers. The duration of the target was always 700 ms including ramps. The masker was gated either synchronously with the target the synchronous condition, or its duration was 1300 ms, in which case it was gated on 400 ms before and off 200 ms after the target the asynchronous condition. In the synchronous condition, all signals were gated with 40-ms, raised-cosine onset and offset ramps. In the asynchronous condition, the target was gated with 40-ms ramps and the masker was gated with 80-ms ramps. The stimuli were generated digitally in advance using a sampling rate of 25 khz. The tones were generated by adding up sinusoids with frequencies ranging from F0 upto10 khz, while the noise was generated in the temporal domain by sampling from a Gaussian distribution. Bandpass filtering was then performed with a 900-tap digital FIR filter with a linear phase response. Ten different realizations were produced for each RPH complex tone and for the Gaussian noise; one of the ten was picked at random for each presentation. The target and masker were played out through separate channels of a Tucker-Davis Technologies TDT DD1 16-bit digital-to-analog converter, and then lowpass filtered at 10 khz TDT FT6-2. They were separately attenuated using two programmable attenuators TDT PA4 and then added TDT SM3. Stimuli were fed to a headphone buffer TDT HB6 and presented monaurally via headphones with a diffuse-field response AKG K 240 DF. Subjects were seated individually in an IAC double-walled soundattenuating booth. B. Procedure A two-alternative forced-choice task was used. The target alone and the target plus masker were presented monaurally, in regular alternation, with 200-ms silent intervals between successive sounds. The alternating intervals were each marked by a light, and subjects were required to indicate in which of the two intervals they heard the target as louder by pressing the button underneath the corresponding light on a response box. Within a given run, either the target alone or the target within the mixture was fixed in level, and the level of the target in the other interval was varied to determine the level corresponding to equal loudness of the target in the two intervals. The range of levels used for the fixed target and the range of starting levels for the variable target were determined after a preliminary experiment. The levels of the fixed target in the masker were chosen so as to cover the range from just above masked threshold to sounds as loud as target presented alone. The levels of the fixed target alone were chosen so that the highest level was the same as that used for the target in the masker, and the lowest level corresponded to the level matching in loudness the lowest level of the target in the masker. On average, ten fixed target levels were used in each condition. The starting level of each variable target was chosen randomly from a range of levels. This range of levels was different for each type of target and each fixed target level; the range was symmetrical about the matched level obtained in the preliminary experiment for the given fixed target level. When the fixed target was judged to be the louder of the two, the target with the variable level was increased in level. When the variable target was judged to be louder, it was decreased in level. The sound level was changed only between stimuli. When no button was pressed, sound presentation continued without any change. A change in the button pressed defined a turnpoint. Initially, the target level was increased or decreased in 5-dB steps. After two turnpoints the step size was reduced to 3 db, and after four turnpoints to 1 db. Subjects were encouraged to bracket the point of equal loudness several times, by going from target alone is louder to target within the mixture is louder, before making the fine adjustment to achieve equal loudness. When they were satisfied with the match, they pressed a third green button, which stopped the run. This satisfied button press was only accepted after the final step size was reached. If J. Acoust. Soc. Am., Vol. 114, No. 1, July 2003 Gockel et al.: Partial loudness 351

4 subjects pressed it earlier, it was ignored, and sound presentation continued without a change. The level of the variable sound at the point when the run was stopped was taken as the matching level. Subjects were asked only to press the satisfied button if they were able to match the loudness of the target alone and the target heard in the mixture, i.e., when they actually heard a sound in the mixture which resembled the target when heard alone. Given this instruction, subjects did not produce matches in some cases, e.g., when the noise target was presented at a very low fixed level with the tone masker. In such a case, the mixture was perceived as a rough tone, i.e., one sound object. The roughness was perceived as an attribute of the tone and, by itself, had no loudness which could be judged; only the tone had a loudness. Similarly, if the noise target alone was presented at a low fixed level, the subjects sometimes could not adjust the level of the noise target in the tone masker in such a way that they actually heard the noise as a sound object in the mixture with the same soft loudness as the noise alone. By the time the variable level of the noise target in the mixture was high enough to enable the subject to hear the noise as such, it was louder than the noise alone. If a match in loudness was deemed to be impossible, subjects pressed a fourth red button. This impossible button press also was only accepted after the final step size was reached. If subjects pressed it earlier, it was ignored, and sound presentation continued without a change. The total duration of a single session was about 2 h, including rest times. The conditions were presented in a counterbalanced order. Half of the subjects started with the harmonic complex tone as target, and half with the noise as target. In each of these conditions, for half of the subjects the complex tone was presented first in RPH and then in CPH, and for the other half the order was reversed. The two onset conditions were alternated, as was the choice of the target with the fixed level target alone, or target with the masker. The level of the fixed target was selected randomly among the ten or so possible levels one threshold was obtained for each condition in turn, before additional measurements were obtained in any other condition. For each subject and condition four measurements were obtained. This took about 13 sessions. After the main experiment was completed, absolute threshold was measured for each signal, and masked threshold was measured for each target in each background, using a two-interval two-alternative forced-choice task and a threedown one-up adaptive procedure. Four threshold estimates were obtained for each condition and each subject; the mean of the four is reported. Masked thresholds were obtained only in the condition with asynchronous onsets, as we showed previously that masked thresholds for these stimuli were not affected by onset asynchrony Gockel et al., 2002a. C. Subjects Eight subjects participated overall. Half of them were tested using the low F0 and half using the higher F0. Their ages ranged from 20 to 22 years, and their quiet thresholds at audiometric frequencies between 500 and 5000 Hz were better than 15 db HL. Subjects had 8 h of practice before the experiment proper was started. No feedback was given following each trial, but during practice subjects were informed about their performance, i.e., the degree to which their MLMFs were monotonic. III. RESULTS In what follows, we use the following six-letter system of abbreviations. The first letter t orn indicates whether the target was a complex tone or a noise. The second, third, and fourth letters indicate whether the tone had components in cosine phase CPH or random phase RPH, regardless of whether the tone was the target or masker. The fifth and sixth letters indicate the gating condition: synchronous onsets so or asynchronous onsets ao. For example, trphso indicates the tone target in RPH with synchronous onsets of target and masker, while ncphao indicates the noise target with the CPH masker and asynchronous onsets of target and masker. Initially, the data were analyzed individually for each subject. Figure 1 shows an example of individual data for the 62.5-Hz F0. 1 Panels a d show conditions with a tone target and panels e h show conditions with a noise target. Each symbol represents one loudness match between the target alone level on the y axis and the target in the masker level on the x axis. Open triangles indicate matches where the level of the target alone was varied; these matches vary along the y axis. Open circles indicate matches where the level of the target in the masker was changed; these matches vary along the x axis. The asterisk shows the value of masked threshold abscissa and threshold in quiet ordinate for the target. Note that there were some trials in which the level of the fixed target was lower than any level plotted in the graph; trials where the subject deemed a match in loudness to be impossible are not plotted. Also, if, for a given fixed level, a match was obtained in one trial and was deemed to be impossible in the remaining three trials for that condition, then the single successful match was discarded. The dotted diagonal line indicates the expected matching values if the loudness of the target in the masker were unaffected by the masker. To derive a simple description of the MLMFs, the data were fitted with two straight lines. One line was the diagonal with slope 1 the dotted lines in the figures. The other was a line with slope 1, described by two parameters, its slope and its point of intersection with the diagonal. Each data point was assigned either to the variable-slope line or to the diagonal. The fitting procedure worked in the following way. Starting values were chosen for the slope and point of intersection of the variable line. Matches from trials where the fixed level of the target was higher than the intersection point were assigned to the diagonal; remaining matches were assigned to the variable line. The slope and intersection were then adjusted the assignment of points to the two lines changed correspondingly so as to minimize the sum of the squared distances of the matches from the variable line and from the diagonal. For matches from trials where the level of the target alone was varied, the vertical distances were minimized. For matches where the level of the target in the mix- 352 J. Acoust. Soc. 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5 FIG. 1. Results of one subject for F Hz. Each panel shows results for one condition, as indicated in the key. The first letter of the key t orn indicates whether the target was a complex tone or a noise. The second, third, and fourth letters indicate whether the tone had components in cosine phase CPH or random phase RPH, regardless of whether the tone was the target or masker. The fifth and sixth letters indicate synchronous onsets so or asynchronous onsets ao. Each symbol represents one loudness match between the target alone and the target in the masker. Open triangles indicate matches from trials where the level of the target in the masker was fixed. Open circles indicate matches from trials where the level of the target alone was fixed. Note that the number of matches is greater than the number of symbols shown, because some symbols are obscured by others. Also, the number of triangles is greater than appears, since many triangles are covered by circles. The asterisk indicates the masked threshold abscissa and the threshold in quiet ordinate of the target. See text for an explanation of the fitted solid line, and its extension dashed line down to the absolute threshold. ture was varied, the horizontal distances were minimized. The two types of minimization were performed simultaneously. The results for the example subject chosen are shown in Fig. 1 as solid lines. The intersection of each fitted line with the diagonal represents the target level at which the masker ceased to have a partial masking effect. The filled circle on the lower end of each line represents the lowest level at which the subject was able to perform the task on at least two out of four trials for that condition. To determine this level, we considered the lowest level which was matched both when the target alone was fixed and when the target in the masker was fixed. The projection of these two matches onto the fitted line in the y direction for the former and the x direction for the latter was determined, and whichever match gave an intersection at the lower point on the line was taken as the lowest matching level. The dashed line which continues from the fitted line below the lowest matched level projects to a y value which is identical to the measured threshold in quiet of the target. The corresponding x value gives the predicted masked threshold for the target under two assumptions: 1 At masked threshold the target has the same loudness as at absolute threshold Moore et al., If it had been possible to measure MLMFs at lower levels, they would have continued as straight lines. The validity of these assumptions is discussed in Sec. III E. To enable a representative comparison of the MLMFs across conditions, an average fitted line was calculated from the four lines fitted to the individual subject data in a given condition. This average fitted line represents the MLMF of a given condition for all subjects, and it was derived in the following way. First, its slope was set equal to the geometric mean of the slopes of the individually fitted lines. Second, its center of gravity was set to the point Xg, Yg corresponding to the mean of the centers of gravity of the individually fitted lines, where the center of gravity of an individually fitted line Xi, Yi is defined in the following way: Xi corresponds to the mean of the minimum x value on the fitted line i.e., the lowest matched x level and the x value at its intersection with the diagonal, and Yi corresponds to the mean of the minimum y value on the fitted line i.e., the lowest matched y level and the y value at its intersection with the diagonal. Finally, the length of the average fitted line was determined as two times the vector length from its center of gravity Xg, Yg to its intersection with the diagonal. Figure 2 shows the resulting averaged MLMFs for the 62.5-Hz F0 a, top and the 250-Hz F0 b, bottom. The symbols close to the x axis give absolute thresholds y axis and masked thresholds x axis for the corresponding conditions, averaged across subjects. A. Asymmetry of masking For both F0s, an asymmetry of partial masking is clearly apparent; all of the fitted lines for the tone targets open symbols lie to the right of the fitted lines for the noise targets solid symbols. This indicates that the asymmetry of partial masking reported by Hellman 1972 for pure tones and noise also holds for complex tones and noise with identical excitation patterns. To quantify these offsets we used the x-axis values at the center of gravity, Xg, of the fitted lines averaged across all subjects. The value of this parameter is shown for each condition in Fig. 3. There was no consistent effect of onset asynchrony on Xg, so the results were averaged for synchronous and asynchronous onsets. For the 62.5-Hz F0, J. Acoust. Soc. Am., Vol. 114, No. 1, July 2003 Gockel et al.: Partial loudness 353

6 FIG. 2. Panel a shows the fitted lines representing the loudness-matching functions obtained for the 62.5-Hz F0, averaged across subjects. See the text for an explanation of how the averaged fitted lines are derived from the individual fits. The open symbols at the endpoints of the lines indicate conditions where the target was a complex tone. The solid symbols at the endpoints of the lines indicate conditions where the noise was the target. Triangles and circles indicate conditions where the components of the complex tone had cosine and random starting phases, respectively. Solid lines and dashed lines indicate synchronous and asynchronous onsets/offsets of target and masker, respectively. The individual symbols close to the x axis show absolute thresholds y axis and masked thresholds x axis for the corresponding conditions, averaged across subjects for the asynchronous condition only. Panel b shows corresponding results for F0 250 Hz. the effect of type of target tone versus noise was 16.5 db for CPH mean of Xg for conditions tcphso and tcphao minus mean of Xg for conditions ncphso and ncphao and 12.0 db for RPH mean of Xg for conditions trphso and trphao minus mean of Xg for conditions nrphso and nr- PHao, i.e., the noise was a more efficient masker than the tones and this asymmetry of partial masking was greater for CPH than for RPH. These asymmetries were very similar to the corresponding asymmetries for the masked thresholds, shown at the bottom of each panel in Fig. 2. The latter were 15.8 threshold of CPH tone masked by noise minus threshold of noise masked by CPH tone and 12.4 db threshold of RPH tone masked by noise minus threshold of noise masked by RPH tone, respectively. For the 250-Hz F0, the effect of type of target was 12.7 db for CPH and 16.5 db for RPH, i.e., the asymmetry of partial masking was greater for RPH than for CPH, the opposite of what was found for F Hz. Again, the asymmetries were similar to the corresponding asymmetries for the masked thresholds, which were 10.5 and 15.2 db, respectively. The correspondence FIG. 3. Mean values of parameters describing the lines fitted to the individual data: 1 Xmin, which is the lowest level of the partially masked sound for which each subject was able to perform the task; 2 Xg, which is the x-axis value of the center of gravity of the average fitted line; and 3 the intersection point with the diagonal, denoted here X Y, which gives an estimate of the level of the partially masked sound at which it reaches its unmasked loudness. The upper and lower panels show values for the and 250-Hz F0s, respectively. The condition is indicated by the keys in the upper and lower panels. Error bars indicate one standard error SE. between the partial masking effects, quantified as the horizontal shift of the center of gravity, and the masked thresholds is consistent with the findings of Hellman 1972 for the asymmetry of masking between sinusoidal tones and bands of noise, as described in the Introduction. To assess the significance of differences between conditions, several within-subject analyses of variance ANOVAs were performed, based on various features of the lines fitted to the data for the individual subjects. For brevity, in what follows, only significant effects (p 0.05) will be discussed. To investigate the asymmetry of masking, separate ANOVAs were performed for CPH and RPH, using the factors type of target tone or noise and onset asynchrony. The intersection with the diagonal indicates the level of the target in the background required for the background no longer to affect loudness. The mean value of this parameter for each condition is shown in Fig. 3 by X Y. There were clear effects of type of target on the intersection point, for both F0s; the x and y values at the intersection points were larger for the tone targets than for the noise targets. ANOVAs based on the intersection points showed a significant effect of whether the 354 J. Acoust. Soc. Am., Vol. 114, No. 1, July 2003 Gockel et al.: Partial loudness

7 FIG. 4. Geometric mean slopes and corresponding SEs of the lines fitted to the individual data. The upper and lower panels show values for the and 250-Hz F0s, respectively. RPH tone was the target or masker; F(1,3) 767.7, p at F Hz and F(1,3) 259.4, p at F0 250 Hz. ANOVAs also showed a significant effect of whether the CPH tone was the target or masker; F(1,3) 43.2, p at F Hz and F(1,3) 256.0, p at F0 250 Hz. The lowest points on the fitted lines in Fig. 2 indicate the lowest matched levels. The mean x-axis value at the lowest points is shown as Xmin in Fig. 3. The large asymmetry of masking was also reflected in those; ANOVAs based on the Xmin values gave highly significant effects of type of target, Xmin being larger for tone targets than for the noise targets. B. Phase effects To investigate the effects of phase, separate ANOVAs were conducted for the tones as targets with factors target phase and onset asynchrony and for the noise as target with factors background phase and onset asynchrony. ANOVAs based on the logarithms of the slopes of the fitted lines revealed no significant effects for F0 250 Hz, but several significant effects for F Hz. The geometric mean slopes of the fitted lines for each condition are shown in Fig. 4. For the tone targets only, there was a significant effect of phase; F(1,3) 36.7, p The geometric mean slope for RPH 3.89 was greater than for CPH An ANOVA based on the values of the intersection points (X Y in Fig. 3 for the tone targets with F Hz also revealed a significant effect of phase; F(1,3) 13.2, p The intersection point was lower for RPH 61.2 than for CPH Taken together, these findings indicate that the loudness of the tone target in the noise background grew more rapidly with increasing target level for the RPH than for the CPH target. An ANOVA based on the logarithms of the slopes for the noise targets alone for F Hz) gave a significant effect of background phase; F(1,3) 88.7, p The geometric mean slope for the RPH background 4.0 was greater than for the CPH background For relatively low levels of the noise target in the masker, the matching level of the target alone was lower for the RPH background, while for higher levels, the matching level of the target alone was lower for the CPH background. An ANOVA based on the values of the intersection points for the noise targets also for F Hz) revealed a significant effect of background phase; F(1,3) 52.0, p The intersection point was lower for the RPH background 47.9 than for the CPH background For low levels of the noise target in the RPH background, subjects reported that the target was hard to hear as a separate sound from the background; consistent with this, an ANOVA based on the Xmin values for the noise target alone also for F Hz) showed a significant effect of background phase; F(1,3) 10.8, p The Xmin value was larger for RPH 42.6 db than for CPH 35.6 db. For F0 250 Hz and for noise targets only, an ANOVA based on the Xmin values gave a significant effect of phase of the background; F(1,3) 79.2, p The mean Xmin value was 43.4 db for CPH and 39.1 for RPH see Fig. 3. This asymmetry is in the opposite direction to that found for F Hz, but the asymmetries at both frequencies are consistent with those observed for the masked thresholds of noise targets in CPH or RPH maskers. C. Onset effects ANOVAs based on the Xmin values gave several significant effects related to the type of onset. For F Hz, considering the data for CPH only as either target or masker, there was a significant effect of onset asynchrony F(1,3) 10.35,p ; the mean Xmin value was lower for the asynchronous onsets 40.4 db than for the synchronous onsets 45.8 db. There was also a significant interaction of type of target and onset asynchrony; F(1,3) 17.55, p This reflects the fact that there was a relatively large effect of asynchrony for the noise as target, but only a small effect for the CPH tone as target see Fig. 3. For the noise target, the asynchrony seemed to help the subjects in hearing the target as a separate sound from the background, when the target-to-background ratio was relatively low. When the onsets were synchronous, the noise target tended to be heard as a roughness of the background tone rather than as a separate sound. For F0 250 Hz, considering the data for RPH only as either target or masker, an ANOVA based on the Xmin val- J. Acoust. Soc. Am., Vol. 114, No. 1, July 2003 Gockel et al.: Partial loudness 355

8 TABLE I. Results of the chi-square tests used to compare, for a given pair of conditions, the number of matches above and below the single line fitted to the matches for those two conditions. The tests were run for each subject individually. The top half is for the 62.5-Hz F0, the lower half for the 250-Hz F0. The condition before the had a significantly greater proportion of matches above the fitted line than the condition after the. The number of subjects out of four who showed a given significant effect (p 0.05) is indicated. F Hz, comparison of synchronous with asynchronous conditions Effect trph.. tcph.. nrph.. ncph.. A0 S S0 A0 3 F Hz, comparison of RPH with CPH conditions Effect t...ao t...so n...ao n...so RPH CPH CPH RPH 3 F0 250 Hz, comparison of synchronous with asynchronous conditions Effect trph.. tcph.. nrph.. ncph.. A0 S S0 A F0 250 Hz, comparison of RPH with CPH conditions Effect t...ao t...so n...ao n...so RPH CPH CPH RPH 1 ues gave a significant effect of onset asynchrony; F(1,3) 12.2, p 0.04, asynchronous onsets leading to a lower Xmin value 45.6 db than synchronous onsets 47.6 db. However, the effect was small. D. Individual subject data Inspection of the data for individuals showed sizable effects of onset asynchrony and component phase for some subjects but not for others. To assess the significance of effects for individual subjects, pairs of conditions were compared in the following way. The matches for a given pair of conditions were fitted as if they were all from the same population, i.e., fitted with a single sloping line plus the diagonal, using the method described earlier. Chi-square tests were then used to compare the proportion of matches falling above and below the fitted line for each condition. On the null hypothesis that the two conditions do not differ, the proportion should be the same for the two conditions. The significant outcomes of these analyses (p 0.05) are shown in Table I. Generally, the effects which occurred most consistently across subjects were also significant in at least one of the within-subject ANOVAs. For example, for the noise target in the CPH background with F Hz, at a given target-tobackground ratio the matching levels of the target alone were higher for asynchronous than for synchronous onsets. E. Discrepancy between predicted and obtained masked thresholds FIG. 5. The bars show mean masked thresholds predicted by extrapolation to absolute threshold of the lines fitted to the data for individual subjects, with associated SEs. The stars show the mean measured masked thresholds, with associated SEs. The upper and lower panels show values for the and 250-Hz F0s, respectively. Consider now the degree of correspondence between the obtained masked thresholds and the masked thresholds predicted from projection of the fitted lines. Recall that the predicted thresholds are based on two assumptions: 1 At masked threshold the target has the same loudness as at absolute threshold Moore et al., If it had been possible to measure MLMFs at lower levels, they would have continued as straight lines. Figure 5 compares the mean values of the predicted bars and obtained stars thresholds. For F Hz, there were no consistent differences between obtained and predicted thresholds for any condition. For F0 250 Hz, the predicted thresholds for the tone targets both CPH and RPH were consistently below the obtained thresholds, for both synchronous and asynchronous onsets. A chi-square test based on the data for all conditions with tone targets revealed a significant difference between obtained and predicted thresholds (p 0.001, two-tailed. For the noise target, there was no consistent difference between obtained and predicted thresholds. The effect for the tone targets is consistent with what has been observed in some previous studies of partial masking using pure tone targets and noise maskers; the MLMF becomes steeper when the tone level in the noise is very close to masked threshold Zwicker, However, no such effect can be seen in our results, as subjects were not able to make loudness matches when the tone target was less than 6 7 db above its masked threshold in the noise. 356 J. Acoust. Soc. Am., Vol. 114, No. 1, July 2003 Gockel et al.: Partial loudness

9 IV. DISCUSSION A. Asymmetry of masking, F0, and phase effects The largest effect in our results was the asymmetry of partial masking between the tone and noise stimuli; noises partially masked complex tones more effectively than complex tones masked noises. The magnitude of the asymmetry was similar to that found for masked thresholds, as was previously reported to be the case for sinusoidal targets and noise maskers Hellman, It should be noted, however, that the horizontal separation between the MLMFs for conditions involving different targets does not generally indicate the difference in target-to-background ratio needed to achieve equal loudness. This is so because, for a fixed overall level, the CPH target, the RPH target, and the noise target typically differ in loudness Gockel et al., 2002b. It is useful to consider whether the mechanisms that have been proposed to account for the asymmetry of masked threshold, reviewed in Gockel et al. 2002a, can also account for the asymmetry of partial loudness. One explanation for the asymmetry in masked threshold is based on the idea that the target is detected by comparing overall level across the intervals in a forced-choice trial. When the masker is a tone, the masker level does not fluctuate from one interval to the next. This makes it easy to detect a small increment in level produced by adding a noise target to the tone masker. However, when the masker is a noise, the level fluctuates from one interval to the next, and this makes it more difficult to detect the change in level produced by adding a tone to the noise Bos and de Boer, 1966; Hellman, It is difficult to see how this explanation could apply to partial loudness, at least for target levels that are well above masked threshold. In order to perform the loudness-matching task, the target has to be segregated from the background, and the overall level of the stimuli is not directly relevant. It is clear that subjects were not matching the overall loudness of the target plus the background, since the matching level of the target alone was often well below that of the background. It has been proposed that the relative bandwidth of the target and masker is important in determining the asymmetry of masked thresholds. Hall 1997 varied the bandwidth of both the target and the masker, from 0 to 256 Hz; the 0-bandwidth stimulus was a pure tone, while other stimuli were noise-like. For a given masker bandwidth, masked thresholds were highest, and essentially constant, for target bandwidths smaller than or equal to that of the masker. For target bandwidths exceeding that of the masker, thresholds decreased with increasing target bandwidth and with decreasing masker bandwidth. Hall concluded that, for target bandwidths smaller than or equal to the masker bandwidth, the results could be explained by a model based on long-term average energy, and that, for greater target bandwidths, the temporal structure of the target must be used as an additional cue. However, the previous results of Gockel et al. 2002a and Krumbholz et al do not support the idea that relative bandwidth is the critical variable. The present results extend this conclusion from masked thresholds to partial loudness. Another explanation for the asymmetry of masked threshold is that, when a tone masker is used, the detection cue is the within-interval random fluctuation in level introduced by the noise target Moore et al., 1998 ; the masker alone has only regular within-interval fluctuation associated with its periodicity, so this cue is highly salient. A noise masker fluctuates randomly in level within each interval, so the level-fluctuation cue is not available in this case, except to the extent that the tone target reduces the amount of random fluctuation Moore, 1975; Richards, 1992; Richards and Nekrich, This sort of information is reflected in the envelope spectra of the stimuli and is used in models for masked thresholds incorporating a modulation filter bank Derleth and Dau, 2000; Verhey, An explanation similar to this could account for the asymmetry of partial loudness. Presumably, what makes a noise sound noise-like are the random fluctuations in amplitude that for a broadband noise are independent in different frequency regions. When a noise target is presented in a tone background, it introduces audible random fluctuations even when it is at a low level relative to the background. When the fluctuations become sufficiently large, the noise becomes audible as a separate sound. Put another way, the steady nature of the background may make it relatively easy for the auditory system to cancel the effect of the background, the residue being the target noise. In this context, it is noteworthy that the intersection points for the noise targets occurred at or slightly below the level of the background 50 db SPL. A tone signal is characterized by its regular periodic nature, which makes it appear to be steady, rather than fluctuating. In auditory models such as the Auditory Image Model Patterson et al., 1995, periodic sounds produce stable auditory images. The regular periodicity of a tone target is easily disrupted by a background noise. Even when a tone target has a level well above that of the background noise, its periodicity is disturbed to some extent. It may be that a tone target in noise only reaches its unmasked loudness when the target-to-background ratio is so high that the noise produces a negligible disruption of the regular periodicity of the target. Consistent with this, the level of the tone target at the intersection was typically db above the noise background level. For the 62.5-Hz tone targets, the intersection point was higher for CPH than for RPH. This may have happened because the noise introduced audible fluctuations in amplitude during the dips of the target waveforms evoked on the basilar membrane. The relatively long dips in the 62.5-Hz targets may have led to these fluctuations being sufficiently salient to reduce the loudness of the CPH target. Perhaps the CPH target only reached its unmasked loudness when the targetto-background ratio was high enough that the noise had a negligible effect on the dips in the target waveform evoked on the basilar membrane. For the 250-Hz F0, the intersection point was similar for the CPH and RPH tone targets. This may reflect a reduced contribution of information from the dips of the CPH target, due to the limited temporal resolution of the auditory system; the 4-ms period of the 250-Hz target is shorter than the estimated duration of the ear s temporal window Moore et al., 1988; Oxenham and Moore, The difference be- J. Acoust. Soc. Am., Vol. 114, No. 1, July 2003 Gockel et al.: Partial loudness 357

10 tween the two F0s may also reflect the fact that, for the lower F0, four times as many components would fall within the passband of a given auditory filter as for the higher F0. Thus, the envelope of the CPH tone with the lower F0 would exhibit greater modulation after auditory filtering than that of the CPH tone with the higher F0. At the higher F0, the degree of modulation might not have been sufficient for the dips in the CPH waveform to play a strong role. Several other significant effects of the phase of the complex tone were found. For F Hz, the slopes of the MLMFs for the tone targets were steeper for RPH than for CPH. As in the case of the intersection points lower for RPH than for CPH, this also may indicate that the minima in the basilar-membrane waveforms evoked by the stimuli need to be at a relatively high level relative to the noise for the noise to have a negligible effect on loudness. For F Hz, the slopes of the MLMFs for the noise targets were steeper for a RPH background than for a CPH background. In this case, there was a crossover effect. For low target-to-background ratios, the noise target was more reduced in loudness relative to its unmasked value in the RPH background than in the CPH background. At higher ratios, the reverse was true. The effect at low levels may reflect the perceptual similarity of the noise target and the RPH background; the RPH background at the low F0 sounded rather noiselike. This made it difficult to hear the noise target as a separate sound from the background. Presumably, for low target-to-background ratios, some of the neural activity evoked by the noise target was assigned to the background when loudness was judged. The reversed effect at high target-to-background ratios may be related to the relatively large peaks evoked by the CPH background on the basilar membrane. These large peaks might produce a partial masking effect even for relatively high target-to-background ratios. B. Onset effects The largest effect of onset asynchrony occurred for the noise target presented in the 62.5-Hz F0 CPH background. When the target-to-background ratio was relatively low, the loudness of the target was reduced less relative to its unmasked value in the asynchronous condition than in the synchronous condition. Also, the lowest level of the noise target in the CPH background at which subjects were able to perform the matching task was lower for asynchronous than for synchronous onsets. The asynchrony seemed to help the subjects in hearing the target as a separate sound from the background, when the target-to-background ratio was relatively low. When the onsets were synchronous, the noise target tended to be heard as a roughness of the background tone rather than as a separate sound. For the 250-Hz F0, the lowest target-to-background ratio of either the tone or noise target at which subjects could perform the task was lower for asynchronous than for synchronous presentation. However, this effect was significant only in the presence of the RPH complex tone. Again, it appears that asynchronous presentation made it easier to hear the target as a separate sound from the background. It is noteworthy that there were some conditions where, for target levels just above those corresponding to the intersection point, the target alone was consistently matched to a level slightly greater than that of the target in the mixture. It was as if part or all of the energy in the background was assigned to the target. This happened most consistently for the noise target in the RPH background with synchronous onsets, and it occurred for both F0s. Onset asynchrony typically abolished this effect. The effects of onset asynchrony may reflect perceptual grouping processes; onset asynchrony can be a powerful cue for the segregation of one sound from another Darwin and Carlyon, Adaptation in the auditory system may influence the grouping process and may also have a direct effect on the loudness of the target. The neural response to the background presumably declines with time, and this may lead to a relatively strong onset response to the target when it is gated on after the background Smith, 1979; Viemeister, As noted in the Introduction, most previous studies of partial masking have used asynchronous onsets of the target and background, to make it easier for subjects to hear out the target. Our results indicate that asynchronous presentation can lead to results somewhat different from those obtained with synchronous gating. However, for most of the conditions of our experiment, the effects of asynchrony were small. Asynchrony did not have a significant effect at the 0.05 level on the level at which the target in the background reached its unmasked loudness the intersection. C. Model considerations Most models of loudness perception derive loudness from the power spectrum of the sound of interest Fletcher and Munson, 1933; Zwicker, 1958; Zwicker and Scharf, 1965; Stevens, 1972; Moore et al., 1997; Glasberg and Moore, None of these models would be able to predict the asymmetry between complex tones and noise in our partial loudness data, as the tones and noise had identical excitation patterns. As mentioned above, the basic aspects of asymmetry of masked thresholds for pure tones in noise and vice versa, and for noises with different bandwidths, can be explained by models based on the concept of a modulation filter bank Derleth and Dau, 2000; Verhey, Similarly, the Auditory Image Model has been successfully used to predict the asymmetry of masked threshold for IRN in noise and vice versa Krumbholz et al., It might be possible to extend such models, in which temporal information is preserved, to account for the asymmetry in partial loudness of noise and complex tones. To date, these models have mainly been used for predicting threshold or pitch, and not for predicting loudness. However, a decision statistic based on the similarity or difference between the internal model representation resulting from the interval containing the target only and that resulting from the interval containing the target plus masker might be used to predict partial loudness judgements. Gockel et al. 2002a pointed out that, in order to account for the strong level dependence which was apparent in the masked threshold data for the noise target in the CPH 358 J. Acoust. Soc. Am., Vol. 114, No. 1, July 2003 Gockel et al.: Partial loudness