Experimental design and rationale.

A. Rhythmicity in behavioural data could have several origins. One the one extreme are rhythmic processes in monaural auditory processes that operate at different frequencies for sounds in each ear (left scheme). As a result, one would observe signatures of rhythmicity in behavioural data for monaural targets at different time scales, and a yet different pattern when presenting binaural stimuli (orange). On the other extreme are high-level processes possibility more tied to cognition than sensation, that operate in the same manner on any sound and which gives to the same rhythmicity in behavioural data following monaural or binaural stimuli (right scheme). B. Genera design of the four experiments. In each experiment independent white noise was presented to each ear over a period of 1.8 s. The task-relevant sounds were presented monaurally and at random time points between 0.3 and 1.5 s following the noise onset. Experiments 1,2,4 featured a tone discrimination task with a decision criterion fixed across trials (tones categorized as ‘low’ or ‘high’). Experiment 3 featured a within trial discrimination of two subsequent tones. Experiment 1 and 2 different in that sound presentation was automatically paced or required manual initialization by the participant. Experiment 1 and 4 differed in that the latter also required participants to perform a dual-task on in the visual fixation This was intended to divert attention across sensory modalities.

Calibration of analysis approaches on simulated data.

We simulated data with and without rhythmicity to calibrate the statistical specificity (false positive rate) of each approach. The approaches are based on the spectra derived from delay-binned data (‘Spectra’), the vector strength of a rhythmic component in linear models applied to delay-binned data (‘Binned’) and the vector strength of a rhythmic component in linear models applied to single trial data (‘Trials’). For each we determined the respective first-level threshold (i.e. method specific p-value) that results in a false-positive rate of about 0.05 when probing for rhythmicity at any frequency. A. Sensitivity of each approach in detecting a rhythmic effect for data generated with a rhythmic effect and different signal to noise ratios (SNR). B. Specificity, shown here as false positive rate in detecting a rhythmic effect in data generated without such an effect (calibrated to about 0.05). C. Illustration of the (log-transformed) first-level p-values for simulated data with an effect at 4Hz and different SNRs, showing the frequency specificity of each approach in detecting an effect.

Illustration of the data for experiments 1-3.

A. Sensitivity (d-prime), bias and reaction times (rt) regardless of target delay. These metrics are shown separately for each ear (R, L) and reaction times (in seconds) are shown separately for each stimulus condition (f1, f2; corresponding to the two target frequencies in experiments 1&2 or the two orders of pitch in experiment 3). B. The same metrics for trials with targets presented at specific delays within the 1.2 s range of target uncertainty. Grey dots and lines denote the individual participant data, thick dots and error-bars denote the group average and standard deviation.

Significance of rhythmicity in the behavioural data.

The individual panels show the group-level (first-level) p-values for each approach (panels A-C) and experiment together with the statistical cut-off used to determine significance (thick grey line; corresponding to p<0.05 corrected for multiple tests across frequencies, calibrating false-positive rate across analyses). For comparison the dashed grey line also shows the cut-off at p<0.01. The coloured shadings indicate significant effects to facilitate their comparison across panels. The precise frequencies with significant effects were: Exp1: Binned/d-prime: 1.8-2.0 Hz; Exp 2: Binned/bias 6.4-6.6Hz; Exp3: Binned/d-prime 2.4-2.8 Hz.

Prevalence of significant effects across random variations in the participant sample.

Using bootstrapping we determined the percentage of participant samples that yield a significant effect when repeating the analysis. For each simulated participant sample, we determined significant effects at p<0.05 (as in Fig. 4) and then counted the number of simulations with effects at each frequency. A value of above e.g. 50% (dashed line) indicates that when randomly sampling from within the collected participants more than 50% of such simulated experiments yield a significant effect. The coloured shadings highlight the same effects as shown in Figure 4.

Averaged prevalence across experiments 1-3.

We focus on the two approaches and metrics yielding the strongest effects in the data for individual experiments. To allow better visibility of the differences between individual ears, the combined-ear data are shown dashed.

Influence of dual task and eye metrics on rhythmicity in experiment 4.

Evidence for rhythmicity was obtained as the group-average vector strength in the model-based analysis of delay-binned data. This evidence was compared between conditions, with the graphs showing the difference (mean, s.e.m.). A. Comparison of blocks with minus dual task those without (n=36). B. Comparison of trials with large pupil diameter minus trials with small diameter (n=24). C. Comparison of trials with less fixation stability (more eye mobility) minus trials with more stability (less eye mobility, n=24). The left panels show the group-level difference (mean, s.e.m.) across the collected participant sample for the combined-ear data. Dots indicate significant effects (paired t-tests, corrected for multiple tests across frequencies at p<0.05; for d-prime in panel C these are 3.4-3.5 Hz). The right panels show the prevalence of effects across random variations in the participant sample for both the combined-ear and individual data.

Illustration of eye tracking data for experiment 4.

A. Trial averaged eye position for horizontal (X) and vertical (Y) dimensions. B. Standard deviation of eye position for each dimension. C. Trial averaged pupil size. D. Average number of saccades per trial and time bin. Thick black lines indicate the participant average (n=30 with good eye tracking data), dashed lines individual data. Note that the figure only shows the data for those trials in which the target appeared with a delay of more than 0.6 s (hence later than 0.9s in the trial) in order to avoid contamination with response periods on this display. This corresponds to half the trials in the experiment. Time 0 s corresponds the onset of the background noise.