For an abruptly gated sound, perceived lateralization is determined primarily by binaural cues at onset. Relatively less is known about the temporal weighing of binaural cues—such as interaural time difference (ITD)—during more naturalistic modulation profiles. Here, an experiment measured the lateralization of a tonal binaural beat modulated by a diotic, 8-Hz sinusoidal amplitude modulation. Binaural beat lateralization (left/right, two alternatives) was compared to that for tones with static ITDs. Across three mean carrier frequencies (200, 500, and 800 Hz), ITDs occurring during early rising amplitude (e.g., 20–25 ms after onset) predicted the perceived lateralization of the binaural beat signals well.

Sensitivity to interaural timing differences (ITDs) contributes to the ability to localize sound sources perceptually. Reverberation poses a unique challenge to localization, as acoustic reflections convey binaural cues pertaining to the location of the reflecting surface. To this end, greater influence is given to cues present during, or near, sound onsets (“the precedence effect”), as the signal received at the ear is most likely free from reflections during a short time window after onset [Wallach et al. (1949) and Haas (1972); see Litovsky (1999) for review].

Dietz et al. (2013) used binaural beats to assess the perceptual weighting of carrier ITD information in an amplitude-modulated signal. A binaural beat is evoked when low-frequency tones of slightly different frequency are presented to either ear over headphones (Licklider et al., 1950; Perrott and Musicant, 1977; Grose et al., 2012). Dietz et al. (2013) presented a signal in which the rate of the binaural beat and the diotic sinusoidal amplitude-modulation (SAM) rate were matched—such that one single rotation (360°) of carrier interaural phase difference (IPD) occurred within one SAM cycle. The common beat and SAM rate were referred to as the amplitude-modulated binaural beat (AMBB) frequency. AMBB frequencies of 4–64 Hz were tested, with a mean carrier frequency of 500 Hz in all cases. In a behavioural task, listeners adjusted the static (non-beating) IPD of a reference tone to match the intracranial image of the AMBB. The authors calculated the time-point within the AMBB where carrier IPD equaled that of the perceptually matched reference tone. This time point occurred during early rising-slope segments of the stimuli; at 37° (26 ms), 40° (14 ms), 62° (11 ms), 83° (7 ms), and 115° (5 ms) of the AMMB cycle for AMBB frequencies of 4, 8, 16, 32, and 64 Hz, respectively (values in parenthesis indicate the corresponding time after AMBB onset/modulation minimum).

These behavioural observations were supported by a range of physiological measures; single-unit neural recordings from the inferior colliculus and the medial superior olive of small mammals (Dietz et al., 2014), as well as magnetoencephalographic (MEG) recordings of cortical responses in humans (Dietz et al., 2013). All data indicated that ITD cues early in the modulation cycle (after onset or modulation minima) were afforded greater weight over cues present during peak amplitude. Dietz et al. (2013) and Dietz et al. (2014) proposed that as late-arriving reverberant sound can be higher in energy than direct sound, so binaural cues present at peak amplitudes are not necessarily informative of source location, and are consequently afforded less neural and perceptual weight.

Matching a reference tone to the perceived intracranial image of a binaural beat requires sufficient time and a degree of listening skill—Dietz et al. (2013) required listeners to best-match the reference tone to both the “centre of gravity” (e.g., lateralization) and the “compactness” (e.g., 0° vs 180° IPD) of the AMBB. Likely reflecting this task difficulty, Dietz et al. (2013) tested experienced binaural listeners, and the experiment required three separate sessions to complete. Here, a simplified, expedited procedure is demonstrated—a 2AFC task that is shown to be suitable for inexperienced binaural listeners. The time-point where carrier IPD during the AMBB cycle best corresponded to overall reported AMBB lateralization, the “point of equivalent lateralization,” was estimated with reference to the lateralization of tones with static IPDs. Mean carrier frequencies of 200, 500, and 800 Hz were tested. The point of equivalent lateralization was estimated at 25, 21, and 20 ms after after modulation onset for these frequencies, respectively.

12 listeners who identified as normal hearing contributed to the study (average age = 25.4 years, ranging from 19 to 33 years). Seven listeners had no previous experience of listening experiments, five had contributed previously to one or more listening experiments. Two listeners completed the AMBB task but not the static-IPD task, so two additional inexperienced listeners were recruited for the static-IPD task. All listeners provided informed consent, and the study was approved by the Ethics Board of Macquarie University.

For the AMBB task, a 4-Hz binaural beat was created from dichotic presentation of tone pairs of either 198 and 202 Hz, 498 and 502 Hz, or 798 and 802 Hz (hereafter referred to by their mean frequencies of 200, 500, and 800 Hz). Tone duration was set to 125 ms (half a cycle of the binaural beat), and a single, diotic 8-Hz SAM cycle was imposed on the signal. A sequence, as heard by listeners, comprised four identical AMBBs, each separated by 50-ms silence [Fig. 1(A)]. All stimuli were presented at 70 dB sound pressure level (SPL).

Fig. 1.

(Color online) Schematic representation of AMBB stimuli and experimental results. (A) An example AMBB cycle. Top: The red/blue traces indicate the signals presented to the right/left ears; here, a “rightward” 4 Hz binaural beat is generated from 498 Hz (left ear) and 502 Hz (right ear) tones. The IPD at onset is −90°. The diotic SAM rate is set to 8 Hz (a period of 125 ms). The three topmost panels each show a single carrier cycle. As denoted by the black symbols, these individual cycles are centred on either the quarter, half, and three-quarter point of the AMBB (from left to right, centred on 31.25, 62.5, and 93.75 ms after onset). The second-topmost panel shows the entire AMBB waveform, and corresponding time-point markers. Lower: The entire AMBB is replotted, but for visual clarity, a gradient is used to represent the carrier IPD throughout the cycle (see legend). Bottom: The complete stimulus, as presented to the listener comprised four identical AMBB cycles, each separated by a 50-ms silence. (B) Illustrative AMBB cycles for each of the ten unique IPD conditions tested. Note that two “paired” conditions were tested for each magnitude of onset IPD. “Paired” conditions were symmetrical in their IPD profile (see main text). (C) AMBB experiment results. Mean lateralization responses (n = 12). Separate traces indicate means for different carrier frequencies (legend). Error bars indicate ±1 standard error. The “lateralization congruent with onset IPD” metric reflects the mean lateralization percept for each “pair” of IPD conditions [Fig. 1(B)]: The metric is direction non-specific; listener's left/right responses were coded as either congruent or incongruent with the direction of the IPD at AMBB onset (see main text for further details).

Fig. 1.

(Color online) Schematic representation of AMBB stimuli and experimental results. (A) An example AMBB cycle. Top: The red/blue traces indicate the signals presented to the right/left ears; here, a “rightward” 4 Hz binaural beat is generated from 498 Hz (left ear) and 502 Hz (right ear) tones. The IPD at onset is −90°. The diotic SAM rate is set to 8 Hz (a period of 125 ms). The three topmost panels each show a single carrier cycle. As denoted by the black symbols, these individual cycles are centred on either the quarter, half, and three-quarter point of the AMBB (from left to right, centred on 31.25, 62.5, and 93.75 ms after onset). The second-topmost panel shows the entire AMBB waveform, and corresponding time-point markers. Lower: The entire AMBB is replotted, but for visual clarity, a gradient is used to represent the carrier IPD throughout the cycle (see legend). Bottom: The complete stimulus, as presented to the listener comprised four identical AMBB cycles, each separated by a 50-ms silence. (B) Illustrative AMBB cycles for each of the ten unique IPD conditions tested. Note that two “paired” conditions were tested for each magnitude of onset IPD. “Paired” conditions were symmetrical in their IPD profile (see main text). (C) AMBB experiment results. Mean lateralization responses (n = 12). Separate traces indicate means for different carrier frequencies (legend). Error bars indicate ±1 standard error. The “lateralization congruent with onset IPD” metric reflects the mean lateralization percept for each “pair” of IPD conditions [Fig. 1(B)]: The metric is direction non-specific; listener's left/right responses were coded as either congruent or incongruent with the direction of the IPD at AMBB onset (see main text for further details).

Close modal

The experiment measured 10 unique IPD conditions, arranged as five “pairs.” Each pair comprised two conditions—one with a right-leading onset IPD and one with an equal-magnitude, left-leading onset IPD [see Fig. 1(B)]—corresponding to onset IPDs of ±0°, ±22.5°, ±45°, ±67.5°, and ±90° [Fig. 1(B)]. Within a “pair” of conditions, the direction of the binaural beat was alternated, such that for a right-leading onset IPD (e.g., +90°) the right-ear carrier frequency was −2 Hz relative to the mean frequency, and the left-ear carrier was +2 Hz; evoking a “leftward” direction of rotation from onset. The paired, left-leading sequence (e.g., “−90°”) was the opposite configuration, creating a “rightward” direction of rotation, generating paired conditions that comprised symmetric IPD profiles. Note that whilst no IPD existed at onset for the “±0°” stimuli pair, naming convention was preserved. The 10 IPD conditions (five pairs) were tested at each of the three carrier frequencies, yielding a total of 30 unique experimental conditions.

For the static-IPD task, stimuli comprised a 125-ms binaural sinusoidal signal (200, 500, or 800 Hz), for which the IPD was set to one of 16 possible values; ranging from 0° to 337.5°, in increments of 22.5°. A diotic 8-Hz SAM envelope was imposed on the signal (70 dB SPL).

Stimuli were created and presented in matlab (R2016b), and sounds were presented via a MOTU Audio Express soundcard over Seinheisser HD 380 Pro headphones (16-bit, 44 100 Hz sampling rate). Testing was conducted on a laptop PC in an audiometric testing booth. Sound levels were calibrated using a model 2250 sound level meter (Brüel & Kjær), and a RA0045 microphone (G.R.A.S) coupled with a Type 43AG ear simulator (G.R.A.S).

On each trial, listeners heard a single condition once, and reported whether the tones were heard towards the “left” or “right” side of the head (2AFC). A 1.2-s silent pause occurred between the keyed response and the start of the next trial. For the AMBB task, trials were organized into blocks comprising a single presentation of each unique condition (i.e., 30 trials per block), presented in shuffled order. Listeners completed two blocks as a training session, for which response data were discarded. The main experiment comprised 20 blocks (i.e., 600 trials). The static-IPD task also comprised 20 blocks/repetitions per condition (320 trials per carrier frequency). Listeners completed three sessions sequentially, each for one of three carrier frequencies (200, 500, or 800 Hz). The presentation order of these sessions was randomized. The AMBB and static-IPD tasks each required under 30 min to complete.

For each carrier frequency separately, AMBB data were averaged across paired conditions to yield a direction-nonspecific measure of lateralization. For example, at 500 Hz, the “+90°” condition was heard right on 92.5% of trials, and the “−90°” condition was heard left on 95% of trials. These results are averaged as 93.75% responses “congruent with onset IPD.” These data, for all paired conditions tested, are shown in Fig. 1(C). The proportion of responses congruent with onset IPD increased with the magnitude of the onset IPD; a two-way, repeated-measures analysis of variance (3 × carrier frequency, 5 × onset IPD) revealed a significant main effect of onset IPD [F(4,44) = 90.58, p < 0.0001], but not of carrier frequency [F(4,22) = 2.94, p > 0.05 (p = 0.074)], but the interaction between factors was significant [F(8,88) = 8.93, p < 0.0001]. The reduced range of lateralization for the 800-Hz conditions is a potential source of this interaction. This is accounted for in the next stage of analysis, where the point of equivalent lateralization is estimated for each carrier frequency separately, by comparing to lateralization of tones with a static IPD.

An AMBB has an instantaneous IPD profile—that is, a discrete carrier IPD at any given time-point during the AMBB cycle. Each discrete IPD can be associated with a corresponding lateralization percept [i.e., Fig. 2(A)]. As such, the time course of the binaural beat can be represented by instantaneous IPD, but also by “instantaneous lateralization.”

Fig. 2.

(Color online) Results from a static IPD lateralization task. (A) Lateralization of tones containing static IPDs (n = 12). The mean number of trials heard towards the right side of the head are plotted for each condition. Separate traces indicate means for different carrier frequencies (legend). Error bars display ±1 standard error. To reflect cyclical IPD, responses for the 180° IPD condition are plotted in two locations. (B) Top: “Instantaneous lateralization” for the −90° onset IPD condition. The thick black trace shows instantaneous IPD during the AMBB cycle (right axis). The coloured traces and symbols show corresponding IPD lateralization (left axis), as extracted directly from (A). This time-lateralization estimate is referred to as “estimated instantaneous lateralization.” Bottom: As for top, except for the +90° onset condition. (C) Estimated instantaneous lateralization for the five “pairs” of onset IPD conditions tested [see Fig. 1(B)]. Within each pair, estimated instantaneous lateralization was averaged in a direction-nonspecific manner (congruence with onset IPD). For the −90° onset IPD example, this metric would essentially “flip” the response curve plotted in Fig. 2(B), as a “right” response would be incongruent with the left-leading onset IPD. This averaging allowed for the comparison between estimated instantaneous lateralization and the results of the AMBB experiment. Estimated instantaneous lateralization for each pair of conditions is shown.

Fig. 2.

(Color online) Results from a static IPD lateralization task. (A) Lateralization of tones containing static IPDs (n = 12). The mean number of trials heard towards the right side of the head are plotted for each condition. Separate traces indicate means for different carrier frequencies (legend). Error bars display ±1 standard error. To reflect cyclical IPD, responses for the 180° IPD condition are plotted in two locations. (B) Top: “Instantaneous lateralization” for the −90° onset IPD condition. The thick black trace shows instantaneous IPD during the AMBB cycle (right axis). The coloured traces and symbols show corresponding IPD lateralization (left axis), as extracted directly from (A). This time-lateralization estimate is referred to as “estimated instantaneous lateralization.” Bottom: As for top, except for the +90° onset condition. (C) Estimated instantaneous lateralization for the five “pairs” of onset IPD conditions tested [see Fig. 1(B)]. Within each pair, estimated instantaneous lateralization was averaged in a direction-nonspecific manner (congruence with onset IPD). For the −90° onset IPD example, this metric would essentially “flip” the response curve plotted in Fig. 2(B), as a “right” response would be incongruent with the left-leading onset IPD. This averaging allowed for the comparison between estimated instantaneous lateralization and the results of the AMBB experiment. Estimated instantaneous lateralization for each pair of conditions is shown.

Close modal

The lateralization of static IPDs —employed to estimate instantaneous lateralization for each AMBB stimulus [Fig. 2(A)]—was consistent with previous reports [e.g., Yost (1981)]. As static IPD lateralization was assessed with a 22.5° resolution, and each AMBB spanned 180° of IPD, so there were eight time-points within each AMBB where instantaneous IPD matched a static IPD tested directly [Fig. 2(B)]. To estimate instantaneous lateralization with a finer temporal resolution, instantaneous IPD was calculated for each millisecond of each AMBB (0, 1,…, 125 ms). For each value of instantaneous IPD calculated, a corresponding lateralization percept was estimated from linear interpolation between observed values in the static IPD dataset. Predicted instantaneous lateralization for paired AMBB stimuli [e.g., +90° and −90°, Fig. 2(B)] was averaged to yield a direction non-specific measure of instantaneous lateralization: congruence with onset IPD [Fig. 2(C)].

For a given carrier frequency, mean responses for all five pairs of onset IPDs [Fig. 1(C)] were compared to five corresponding estimates of instantaneous lateralization, each taken from the same time-point within the AMBB cycle (e.g., 0, 1 ms, etc., Fig. 3). For each comparison, the mean value of the square of the error [minimum mean-square error (MMSE)] was calculated to quantify the goodness-of-fit between the five observed data points from the AMBB lateralization task and the five estimates of instantaneous lateralization. In this manner, the observed AMBB data were compared to predicted instantaneous lateralization at each millisecond of the AMBB stimuli (i.e., 0–125 ms; 126 comparisons). Figure 3 illustrates these comparisons for each carrier frequency. For carriers of 200, 500, and 800 Hz, the lowest MMSE values were observed at 25 ms (MMSE = 14.66), 21 ms (8.81), and 20 ms (8.54) following modulation onset, respectively [Fig. 3(G)]. In each case, estimated instantaneous lateralization at these time points proved a remarkably close match to observed AMBB lateralization [Fig. 3(B), 3(D), and 3(F)].

Fig. 3.

Estimates of the point of equivalent lateralization for AMBBs at each carrier frequency tested. (A) Estimated instantaneous lateralization at 200 Hz is plotted for each of the five onset IPD conditions, each indicated by a different trace [i.e., data are replotted from Fig. 2(C) as a single plot, traces here are labelled by onset IPD]. Observed AMBB lateralization at this frequency is replotted from Fig. 1(C), with a collapsed abscissa, in the narrow leftmost panel. For each millisecond of the AMBB stimuli, the MMSE between estimated instantaneous lateralization and the experimental data is calculated. This is shown in the narrow lower panel. The best fit occurred 25 ms after modulation onset (i.e., the lowest MMSE: 14.66), and these values of estimated instantaneous lateralization are indicated in the main panel by open symbols. (B) The data from (A) are replotted in a manner consistent with Fig. 1(C): Onset IPD is plotted along the abscissa. Filled symbols indicate the experimental data, and open symbols indicate the best estimate from estimated instantaneous lateralization (25 ms). Error bars indicate ±1 standard error. (C), (D) As for A and B, except for 500 Hz. The best fit at this frequency occurred 21 ms after modulation onset. (E), (F) As for A and B, except for 800 Hz. The best fit at this frequency occurred 20 ms after modulation onset. (G) For clarity, and for comparison across frequency, the MMSE plots in the lower panels of (A), (C), and (E) are enlarged and shown together. A schematic of the modulation cycle is shown in the lower subpanel for reference.

Fig. 3.

Estimates of the point of equivalent lateralization for AMBBs at each carrier frequency tested. (A) Estimated instantaneous lateralization at 200 Hz is plotted for each of the five onset IPD conditions, each indicated by a different trace [i.e., data are replotted from Fig. 2(C) as a single plot, traces here are labelled by onset IPD]. Observed AMBB lateralization at this frequency is replotted from Fig. 1(C), with a collapsed abscissa, in the narrow leftmost panel. For each millisecond of the AMBB stimuli, the MMSE between estimated instantaneous lateralization and the experimental data is calculated. This is shown in the narrow lower panel. The best fit occurred 25 ms after modulation onset (i.e., the lowest MMSE: 14.66), and these values of estimated instantaneous lateralization are indicated in the main panel by open symbols. (B) The data from (A) are replotted in a manner consistent with Fig. 1(C): Onset IPD is plotted along the abscissa. Filled symbols indicate the experimental data, and open symbols indicate the best estimate from estimated instantaneous lateralization (25 ms). Error bars indicate ±1 standard error. (C), (D) As for A and B, except for 500 Hz. The best fit at this frequency occurred 21 ms after modulation onset. (E), (F) As for A and B, except for 800 Hz. The best fit at this frequency occurred 20 ms after modulation onset. (G) For clarity, and for comparison across frequency, the MMSE plots in the lower panels of (A), (C), and (E) are enlarged and shown together. A schematic of the modulation cycle is shown in the lower subpanel for reference.

Close modal

The point of equivalent lateralization was estimated to occur 25, 21, and 20 ms after modulation onset, for carrier frequencies centred on 200, 500, and 800 Hz, respectively. The expedited procedure proved suitable for inexperienced binaural listeners, who successfully completed the experiment in around one hour. For a 500-Hz carrier, Dietz et al. (2013) estimated this point to occur 14 ms after onset/modulation minimum for an 8-Hz AMBB, and at 26 ms for a 4-Hz AMBB. The overall agreement between experiments exists despite methodological differences, and that Dietz et al. (2013) presented a continuously amplitude-modulated signal at either 70 or 75 dB SPL, compared to the truncated modulation cycle presented at 70 dB SPL here. The current experiment also tested a unique combination of beat rate (4 Hz) and SAM rate (8 Hz).

The current data suggest the point of equivalent lateralization remains relatively constant across carrier frequency. In a related study, Hu et al. (2017) assessed the effect of carrier frequency on the temporal weighting of carrier ITD, employing low-frequency, sinusoidal-like stimuli generated by narrow-band filtering a train of broadband clicks. This allowed an ITD to be imposed briefly on an otherwise diotic signal with minimal artefact. For a 600-Hz carrier (8- or 20-Hz SAM), listeners were most sensitive to ITDs present at onset, with poorer sensitivity when the ITD occurred at peak, or towards offset. However, performance was comparable between SAM onset and peak for a 200-Hz carrier. From this, one might expect the point of equivalent lateralization to have occurred considerably later in AMBB cycle in the current lowest-frequency condition (200 Hz). A plausible explanation for this apparent difference is that listeners may be sensitive to ITDs during a longer portion, or “read-out window,” of the rising slope of SAM at lower carrier frequencies (e.g., 200 Hz). Whilst the estimated point of equivalent lateralization appears similar across the three frequencies tested here, AMBB lateralization may have been derived from read-out windows of differing length. Indeed, it remains unclear if AMBB lateralization judgments are driven exclusively by the first salient portion of the signal following onset or modulation minimum, or if some sensitivity to IPD is retained throughout the (audible) rising amplitude of the modulation cycle. It is possible to estimate the output of IPD read-out windows by averaging estimates of instantaneous lateralization from a spread of time-points. Whilst such analysis is possible for the current dataset, many permutations of read-out window, and indeed, predicted instantaneous lateralization from a single time-point only, all accurately estimate observed AMBB lateralization. Instead, testing a broader range of AMBB parameters—such as systematic variations in beat rate in an AMBB with a fixed SAM rate—might allow for a more robust test for the duration of IPD sensitivity during rising amplitude. Alternatively, manipulating sound level or even depth of modulation may provide a means of assessing the extent to which the first salient IPD after onset/modulation minimum dominates the lateralization of AMBBs.

This study was supported by an Australian Research Council Laureate Fellowship (No. FL160100108) awarded to David McAlpine.

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