2.1 Participants

Seventeen right-handed healthy participants (7 male and 10 female), with an average age of 23.3 ± 2.6 years (mean ± SD), engaged in the study. Exclusion criteria were: a skin disease affecting the skin on the head; epilepsy; a brain surgery in the past; a psychiatric or neurological disease in the past year; the use of drugs affecting the central nervous system (e.g., antidepressants, antipsychotics); or substance abuse in the past year. The data collection of the current study was combined with one of the experimental sessions of another EEG study, using the same EEG equipment (Heijs et al. 2021). Therefore, 13 out of 17 participants performed another experimental protocol of approximately 40 min before the start of the current study (Heijs et al. 2021). Although three additional left-handed participants performed both experiments, their data were excluded from this study due to the significant hemispheric lateralization of motor control mechanisms (Mutha et al. 2012). Thus, only data from right-handed participants (N = 17) were included in this study.

All participants signed written informed consent before the start of the experiments. The experiments were approved by the Research Ethics Committee of the Faculty of Social Sciences of Radboud University, Nijmegen (ECSW2016-2208-413).

2.2 Experimental Protocol

The experiments were performed in a quiet room with dimmed lights. Participants were asked to take a seat behind a standard laptop (distance to screen approximately 65 cm) with their dominant hand resting on the table while fixating their eyes on the black screen during the experiment. They were instructed to tap with the index finger of their dominant hand following the rhythm of an external, sensory cue. The auditory cues were presented via insert earphones (Etymotic ER1, Etymotic Research Inc., Elk Grove Village, IL, USA), and the visual cues were presented on the laptop's screen (14 in., 60-Hz refresh rate). A short instruction video was shown to introduce the different cue conditions. Eight different cue conditions were tested in a 2 × 2 × 2 design (Figure 1), each condition characterized by a unique combination of cue frequency, cue modality and cue rhythmicity.

The effect of cue frequency was evaluated by presenting cues at either 1 Hz (i.e., inter–stimulus interval [ISI] of 1 s between consecutive cues) or 3.2 Hz (i.e., ISI of 0.3125 s between consecutive cues). The frequencies were selected below and above the expected cut-off frequency (around 2 Hz) for either discrete or continuous movement processing (Stegemöller et al. 2016; Toma et al. 2002). Conditions of 1 and 3.2 Hz will be referred to as ‘1Hz’ and ‘3Hz’, respectively.

The effect of cue modality was evaluated by presenting either auditory or visual cues. The auditory cue consisted of a tone of 0.15 s (pitch A5, i.e., 880 Hz), with fade-in and fade-out slopes of 0.05 ms to prevent artefacts like spectral splatter or abrupt changes that might distort the auditory perception. The visual cues consisted of a flashing white circle, presented at the centre of the black background screen for half the ISI duration (i.e., 0.5 and 0.156 s for cues presented at 1 and 3.2 Hz, respectively). Note that cue duration was different between cue modalities. Auditory and visual conditions will be referred to as ‘AUD’ and ‘VIS’, respectively.

The effect of cue rhythmicity was evaluated by presenting either isorhythmic or polyrhythmic cues. Isorhythmic cues consisted of a single, main rhythm, while polyrhythmic cues consisted of two rhythms: the main rhythm and a simultaneously presented faster secondary rhythm in a [2:3] frequency relationship, respectively. Participants were instructed to tap at the main rhythm only. In auditory-polyrhythmic conditions, the main tone (A5, i.e., 880 Hz) was accompanied by a secondary tone presented at a lower pitch (pitch D3, i.e., 146 Hz). In visual-isorhythmic conditions, a single white flashing circle was presented in the centre of the screen (visual angle of 5.7°) without a fixation point. In visual-polyrhythmic conditions, two white, flashing circles were presented left and right of a central, red fixation point (visual angle of 2.8°, distance between two circles 5.7°). Participants were instructed to tap at the rhythm of the left circle (i.e., the main rhythm) while fixating their eyes on the red fixation point in between the two flashing circles. Isorhythmic and polyrhythmic conditions will be referred to as ‘ISO’ and ‘POLY’, respectively.

Due to a minor error in the experimental code, the cue frequency for the condition with fast auditory polyrhythmic cues (i.e., ‘AUD-POLY-3Hz’) was set to 3.0 Hz instead of the intended 3.2 Hz for all participants. We do not expect that this influenced the results.

Each cue condition started with a 15-s resting-state baseline period, followed by five sequences of finger tapping, of approximately 16 s each, with a short break of 5 s in between sequences. During the baseline period, participants were asked to sit quietly and fixate their eyes on the black screen. Within one sequence of finger tapping, the condition-specific cue was presented either 16 or 51 times for 1- and 3-Hz conditions, respectively. Participants tapped with their index finger following the rhythm of the main beat. The order of cue conditions was randomized between participants. The MATLAB toolbox, Psychtoolbox-3 (Brainard 1997), was used for the presentation of cues.

2.3 Data Acquisition

Electrical brain activity was measured using an EEG system (waveguard original, ANT Neuro b.v., Hengelo, the Netherlands) with 32 silver/silver chloride (Ag/AgCl) electrodes, positioned according to the 10–10 international system. The ground and reference electrodes were located at the positions AFz and CPz, respectively. By application of conductive gel, the electrode-skin impedance was aimed to be below 20 kΩ. The finger taps were recorded using a three-dimensional accelerometer (XS-354, ANT Neuro b.v., Hengelo, the Netherlands), positioned at the dorsum of the dominant hand, underneath the head of the metacarpal bone of the index finger. Both data from the EEG system and the accelerometer were recorded synchronously at a sampling frequency of 1024 Hz, using the eego amplifier (EE-225, ANT Neuro b.v., Hengelo, the Netherlands) and the software (eego software v1.9.1., ANT Neuro b.v., Hengelo, the Netherlands).

2.4 Data Analysis

Finger taps were recorded using an accelerometer and were used (1) to eliminate sequences that were not performed correctly by comparing the number of finger taps relative to the number of cues (i.e., the intended number of finger taps); (2) to assess the performance of SMS within the different cue conditions; and (3) to segment the EEG data into epochs centred around the occurrences of the taps. The EEG data were used to discern differences in the cortical oscillatory activity of the beta band (12–30 Hz) during finger tapping. The data were analysed with hierarchical Bayesian models to estimate the differences between cue conditions in movement-related cortical activity and the performance of SMS. Data preprocessing and analysis were executed using MATLAB (version R2023a). The open-source toolbox EEGLAB was used for the preprocessing and visualization of the data (Delorme and Makeig 2004).

2.5 Accelerometer Data

The magnitude of the three-dimensional acceleration data was calculated by taking the L2 norm. The accelerometer signal was filtered with a zero-phase, second-order Butterworth bandpass filter with cut-off frequencies set at 0.5–70 Hz and down-sampled to 256 Hz. Finger taps were detected using a sliding window with a size equal to one ISI. Within this window, the highest peak was identified as a finger tap, and the time of the finger tap was extracted (Figure 2A, bottom). The first window was centred around the first cue of the tap sequence (window [cue − 0.5 × ISI : cue + 0.5 × ISI]). If no peak was detected within this window, the subsequent window was centred around the next cue. However, when a finger tap was detected, consecutive windows were positioned relative to the last detected tap, with a shift of half a window length (window [tap + 0.5 × ISI : tap + 1.5 × ISI]). Occasional misidentifications or failures to detect taps, arising from irregular or inaccurate tapping speeds, were corrected through visual inspection. The acceleration data, measured in millivolts, was converted to metres per square second using the calibration points provided by the eego recording software.

2.6 EEG Data

The EEG data were filtered using a zero-phase, second-order Butterworth bandpass filter with cut-off frequencies set at 1–35 Hz. No artefactual channels, caused by poor electrode-skin contact, were identified in any of the participants, as the channels' absolute amplitude did not exceed the threshold (> 50 or < 1 μV). Thereafter, independent component analysis was applied to eliminate artefacts attributable to eye blinks or horizontal eye movements (Chaumon et al. 2015). Visual inspection of the independent components was performed to search for the characteristic frontal topographical distribution and the characteristic patterns in the time series, i.e., large deviations in amplitude and step-like events over time, for eye blinks and horizontal eye movements, respectively. After removal of artefactual independent components, the data were down-sampled to 256 Hz, and noisy channels were identified through visual inspection of their time series and power spectral density. On average, 1.9 ± 1.0 channels (mean ± SD) out of the 32 per participant were rejected and interpolated using spherical spline interpolation.

Subsequently, the data were re-referenced using two distinct reference schemes. The average reference (V) was applied for the identification of artefactual epochs. The Laplacian reference (V/m²), which acts as a spatial filter and improves the spatial specificity (Kayser and Tenke 2015), was preferred for evaluating changes in power at the electrode level (Pfurtscheller and Lopes da Silva 1999). After the removal of the mastoid electrodes, the data with the average reference and Laplacian reference were stored as two separate datasets.

Time-frequency analysis was conducted on both datasets using the complex Morlet wavelet convolution, implemented through the spectral multiplication of the EEG data and the complex Morlet wavelets (Cohen 2014). The frequency of the wavelets ranged from 12 to 32 Hz and the number of cycles of the wavelets ranged from 3 to 5 cycles, in 11 logarithmically spaced steps. Power was calculated by taking the square of the absolute wavelet coefficients.

The time series and time-frequency maps of both datasets were segmented into baseline and condition data. Baseline periods were subdivided into 0.5-s epochs after excluding the first and last seconds of each 15-s period. For the cue conditions, epochs with a duration of twice the ISI, centred around the finger tap, were created and grouped according to the specific cue condition.

Artefactual time-frequency epochs were removed from the baseline and condition data using predefined channel-specific thresholds. Artefactual epochs were identified based on the dataset with the average reference and later removed from the dataset with the Laplacian reference. An epoch with a potential artefact was detected if (1) the average absolute amplitude (threshold: mean + 2 × SD of the average absolute amplitude), (2) the maximum absolute amplitude (threshold: mean + 10 × SD of the average absolute amplitude), or (3) the maximum power (threshold: mean + 20 × SD of the average power) of one of the channels exceeded the threshold. Next, a visual inspection of the time series was conducted to manually remove any missed artefacts and to check the detection of the potential artefactual epochs.

2.7 Data Exclusion Criteria

Some participants struggled to adhere to the rhythm of the cues, especially during the first sequences of a cue condition, likely because of the lack of a practice block before the start of the experiment. To address this, we compared the number of finger taps to the number of cues, reflecting the intended number of taps for that sequence. Sequences were excluded from the analysis if the number of finger taps deviated by more than 30% from the number of cues (i.e., the intended number of finger taps; 12–20 taps for the 1-Hz condition and 36–66 for the 3.2-Hz condition) as this indicated inattentiveness or non-adherence to the task. Additionally, if four out of five sequences within a given cue condition were inaccurately performed, the entire cue condition was excluded from subsequent analyses due to the limited amount of available data. Furthermore, the first two taps of each sequence were removed to eliminate potential start-up effects. Consequently, the percentage of excluded tap sequences across participants was 0% for AUD-ISO-1Hz, 4.7% for AUD-POLY-1Hz (five sequences from one participant), 0% for AUD-ISO-3Hz, 1.2% for AUD-POLY-3Hz (one sequence from one participant), 0% for VIS-ISO-1Hz, 5.9% for VIS-POLY-1Hz (five sequences from one participant), 1.2% for VIS-ISO-3Hz and 7.1% for VIS-POLY-3Hz (three sequences from two participants). For the remaining sequences, an average of 3.6% ± 1.4% (mean ± SD) artefactual EEG epochs was removed per cue or baseline condition.

2.8 Statistical Analysis

3.1 SMS Performance

3.1.1 Tap Accuracy and Consistency

In auditory conditions, participants accurately tapped at the intended speed (ITI-D = 1; Figure 3A and Table 1). Neither the frequency nor the rhythmicity affected their ability to maintain the correct speed. However, tapping variability significantly increased with 3-Hz compared to 1-Hz auditory cues (ITI-CV: 1–3 Hz; Figure 3B and Table 2).

TABLE 1. Descriptive of the performance measures for each cue condition.

	ITI-D		ITI-CV (%)		Phase (°)
AUD-ISO-1Hz	1	[0.99 1.01]	5.40%	[4.4 6.4]	330°	(310–352)
AUD-POLY-1Hz	1	[0.99 1.01]	6.40%	[5.3 7.5]	134°	(122–173)
AUD-ISO-3Hz	1	[0.99 1.00]	8.30%	[7.3 9.3]	222°	(191–239)
AUD-POLY-3Hz	1	[0.99 1.00]	8.10%	[7.0 9.1]	13°	(4–36)
VIS-ISO-1Hz	1	[0.99 1.00]	6.80%	[5.7 7.8]	35°	(7–85)
VIS-POLY-1Hz	1	[0.98 1.01]	7.00%	[5.9 8.2]	55°	(34–113)
VIS-ISO-3Hz	1.04	[1.03 1.04]	7.90%	[6.9 9.0]	49°	(96–350)
VIS-POLY-3Hz	1.11	[1.11 1.12]	9.90%	[8.8 11.0]	60°	(7–76)

• Note: Values represent the mean (99% highest density interval [99%-HDI]) of the posterior distribution of the inter–tap interval discrepancy (ITI-D) and coefficient of variations (ITI-CV) and the median (interquartile range [IQR]) of the phase (in degrees).

TABLE 2. Posterior difference distribution of the performance measures for each comparison of interest.

	ITI-D		ITI-CV
Frequency: 1–3 Hz
AUD-ISO	0	[0.00 0.01]	−2.90%	[−4.3 −1.4]a
AUD-POLY	0	[−0.01 0.02]	−1.70%	[−3.2 −0.1]a
VIS-ISO	−0.04	[−0.05 −0.03]a	−1.20%	[−2.6 0.3]
VIS-POLY	−0.12	[−0.13 −0.10]a	−2.90%	[−4.5 −1.3]a
Modality: AUD–VIS
ISO-1Hz	0	[−0.01 0.01]	−1.40%	[−2.9 0.1]
POLY-1Hz	0	[−0.02 0.02]	−0.60%	[−2.2 1.0]
ISO-3Hz	−0.04	[−0.05 −0.03]a	0.30%	[−1.1 1.8]
POLY-3Hz	−0.12	[−0.12 −0.11]a	−1.80%	[−3.4 −0.3]a
Rhythmicity: ISO–POLY
AUD-1Hz	0	[−0.01 0.02]	−1.00%	[−2.5 0.5]
AUD-3Hz	0	[−0.01 0.01]	0.20%	[−1.2 1.7]
VIS-1Hz	0	[−0.02 0.02]	−0.20%	[−1.8 1.3]
VIS-3Hz	−0.08	[−0.08 −0.07]a	−2.00%	[−3.5 −0.5]a

• Note: Values represent the mean (99% highest density interval [99%-HDI]) of the posterior difference distribution. Inter-tap-interval discrepancy (ITI-D); Inter-tap-interval coefficient of variation (ITI-CV).
• ^a Significant comparisons of interest for which the 99%-HDI of the posterior difference distribution excludes zero.

In visual conditions, participants tapped at the intended speed with 1-Hz cues but tapped too slowly with 3-Hz cues (ITI-D: 1–3 Hz; Figure 3A and Table 2). This significant reduction in tap accuracy with 3-Hz cues was evident for both isorhythmic and polyrhythmic cues but was more pronounced with polyrhythmic cues (ITI-D: ISO–POLY; Figure 3A and Table 2). Maintaining a consistent tapping speed was particularly challenging with visual, polyrhythmic cues presented at 3 Hz, resulting in a significantly increased tapping variability across modality, rhythmicity and frequency conditions (ITI-CV: AUD–VIS; Figure 3B and Table 2).

In summary, in auditory conditions, participants accurately synchronized with the speed of both slow and fast cues, although tap variability was greater with 3-Hz compared to 1-Hz cues. In visual conditions, participants tapped too slowly with 3-Hz cues and struggled to maintain a consistent tapping speed with fast, polyrhythmic cues.

3.2 Beta Oscillations

Time-frequency maps were calculated for each cue condition to represent changes in the beta power, time-locked to the finger tap (expressed in decibels; Figure 4), allowing for valid comparisons across conditions regardless of SMS performance. Additionally, scalp distributions of the average beta band are shown for the two time windows: around the finger tap and after the finger tap. The topographical distribution of the data estimated by the hierarchical Bayesian model (Model) closely mirrored the distribution of the measured data (EEG), demonstrating a good model performance (Figure 4; see Data S1 for further details and visualizations on the sampling performance).

Across cue conditions, the beta oscillations, time-locked to the finger taps, showed a consistent topographical distribution. This distribution was characterized by beta enhancement in midline electrodes over frontal and parietal cortices and beta suppression in lateral central electrodes (C3/C4) extending towards frontocentral and centroparietal electrodes (FC5/FC6, CP5/CP6), covering the sensorimotor, premotor and lateral parietal cortices. We observed differences in the strength and spread of the beta power across the scalp depending on the characteristics of the cue.

Subsequent sections present the scalp topographies of the posterior distributions for each cue condition (red/blue) and the posterior difference distribution (green/purple) of comparisons of interest (Figure 5). Differences in beta power between two cue conditions were significant if the 99%-HDI of the electrode's posterior difference distribution excluded zero and its absolute mean exceeded 0.4 dB. Significant electrode positions are marked with asterisks in the scalp distributions and are described in the text by their mean and [99%-HDI]. For regions with multiple significant electrodes, the electrode with the largest effect size is reported in the text.

First, we describe differences in beta band modulations over time in response to cue characteristics. Next, we focus on changes in the scalp distribution of the beta band, in response to cue frequency, cue modality and cue rhythmicity. As statistical results were consistent for the time windows around and after the tap for comparisons regarding cue modality and cue rhythmicity, we report only the results observed around the tap. Complete tables of the results for all electrodes, comparisons and both time windows are provided in Data S2.

4.1 Discrete Movement Processing With Slow Cues Facilitates More Consistent Synchronization Than Continuous Movement Processing With Fast Cues

Participants performed better with 1-Hz cues compared to 3-Hz cues, particularly in visual conditions. With auditory cues, they accurately synchronized their tapping speed with both cue frequencies, although tapping variability increased with faster cues. With visual cues, participants accurately synchronized with the frequency of 1-Hz cues, whereas they tapped too slowly and with greater variability with 3-Hz cues. Notably, none of the participants synchronized their tapping rhythm with fast visual cues at 3.2 Hz but tapped too slowly at 3.1 Hz (ITI-D of 1.03) or 2.9 Hz (ITI-D of 1.11) with visual isorhythmic and polyrhythmic cues, respectively. This finding emphasizes the challenges associated with synchronizing finger tapping to fast visual cues and supports earlier research suggesting a threshold of approximately 2.2 Hz for successful synchronization to visual cues (Hove et al. 2010; Kolers and Brewster 1985; Repp 2003b). The inability to synchronize with fast visual cues implies that participants may have relied on their own internal rhythm rather than adhering to the stimulus-driven pace.

Consistent with previous literature on slow and fast movements (Boonstra et al. 2006; Seeber et al. 2016; Stegemöller et al. 2016; Toma et al. 2002), we found that the beta oscillations in the contralateral sensorimotor cortex were modulated by cue frequency and, consequently, movement speed. Specifically, with 1-Hz cues, beta suppression before and during the execution of a finger tap was followed by a strong beta rebound approximately 200 ms after the tap, indicating the preparation and execution of discrete, individually timed movements (Toma et al. 2002). In contrast, with 3-Hz cues, a sustained beta suppression was observed, which implies continuous rather than discrete movement processing (Toma et al. 2002). Previous EEG studies have identified a cut-off point between discrete and continuous movement processing at around 2 Hz (Stegemöller et al. 2016; Toma et al. 2002). This threshold corresponds to the behavioural study of Huys et al. (2008) showing that repetitive, discrete movements are typically feasible up to velocities of 2 Hz, whereas higher speeds result in the execution of continuous movements (Huys et al. 2008). While finger taps were consistently executed as discrete movements across cue conditions, including a stationary phase at the table surface, we propose that at higher cue frequencies, the timing of individual movements was no longer processed distinctly. Instead, the general rhythm of tapping was prioritized. This continuous movement processing may explain the increased tap variability with 3-Hz cues, as taps are no longer aligned individually with the timing of cues. These differences in beta modulation over time may directly drive the observed variations in tap velocity and performance between 1- and 3-Hz cues, or alternatively, the neural activity could be shaped by the variations in tapping behaviour.

Furthermore, our results revealed that the distribution of beta oscillations varied across the scalp depending on cue frequency. With 1-Hz cues, we observed stronger beta suppression above the left sensorimotor cortex around the tap that extended further into the premotor and parietal cortices, compared to more localized activity with 3-Hz cues. The increased activation of the premotor cortex, related to sensory guidance and timing of movements (Chen et al. 2008, 2009; Pollok et al. 2009; Pollok, Rothkegel, et al. 2008), likely facilitated accurate synchronization to slow cues, as positive correlations between activity in the dorsal premotor cortex and tapping accuracy have been reported (Miyata et al. 2022). The increased activation of the parietal cortex likely aided in aligning individual taps with the timing of cues, considering its role in sensorimotor integration and anticipatory motor control by comparing actual movements with the intended motor plan (Krause et al. 2014; Pollok, Gross, et al. 2008; Pollok et al. 2005). For example, beta suppression of the parietal cortex has been observed during gait adaptations in response to cue-induced changes in step tempo (Wagner et al. 2016). Thus, the allocation of sensorimotor, premotor and parietal areas around the tap, along with more accurate tapping performance with 1-Hz cues, suggests that temporal information was more easily extracted from slow cues, facilitating more effective sensorimotor integration and error correction, resulting in more accurate alignment of each finger tap to the timing of the cue.

In contrast, with 3-Hz cues, we observed a stronger beta enhancement around the tap in the frontal cortex. This suggests greater engagement of the frontoparietal network, which is involved in endogenous, top-down attention and control of behaviour (Buschman and Miller 2007, 2014; Engel and Fries 2010). The frontal cortex plays a critical role in integrating sensory information into internal models via its connections with secondary motor areas, particularly during more complex tasks (Miller and Cohen 2001). For example, enhanced frontal beta power has been observed during fast compared to slow movements (Miller and Cohen 2001; Seeber et al. 2016) and during gait adaptations following cue-induced changes in step tempo (Wagner et al. 2016). Therefore, the stronger beta enhancement around the tap in the frontal cortex suggests increased cognitive demands to synchronize with fast cues.

In summary, our findings suggest distinct neural mechanisms underlying SMS with slow versus fast cues. The differences in the beta activity in the contralateral sensorimotor cortex over time may reflect discrete and continuous processing of movement timing with 1- and 3-Hz cues, respectively. However, it remains to be determined whether these differences in neural dynamics directly drive differences in motor behaviour, i.e., tapping speed, or are the consequence of it. Additionally, we expect that the allocation of the left motor, premotor and parietal areas with 1-Hz cues around the execution of the finger tap, facilitated sensorimotor integration and error correction, aligning individual finger taps to the timing of cues. This discrete processing of the timing of finger taps resulted in a consistent and stable tap rhythm when tapping to 1-Hz cues. With 3-Hz cues, stronger beta enhancement in frontal areas and increased tap variability may reflect greater endogenous, top-down control of movement, in which the rhythm instead of the specific timing of the cues is more important. The timing of movements may be processed continuously, resulting in greater tap variability when tapping to 3-Hz cues.

4.2 Enhanced Sensory Guidance With Auditory Cues Leads to More Accurate Synchronization Compared to Visual Cues

Our results showed that finger tapping with auditory cues allows for higher cue frequencies as compared to visual cues, in line with the literature (Hove et al. 2010; Repp 2003b). Participants were unable to synchronize their tapping speed to the rhythm of fast visual cues, whereas tapping to auditory cues was performed accurately for both cue frequencies. Tapping too slowly or too fast naturally resulted in a highly variable phase for the fast visual cues. Consistent with our results, Repp (2003b) reported that differences between auditory and visual cues were not observed in terms of the variability of ITI, but rather in the variability of the phase relative to the cue, and noticed during the experiments that ‘participants rarely attempted to correct their tapping but simply continued to tap “blindly” at a steady state, hoping that the taps would coincide with the sequence events’ (Repp 2003b). Therefore, we expect that participants aligned their finger taps to an internally generated rhythm, rather than the occurrences of the fast visual cues. (Repp 2003b).

Beta band oscillations did not show time-dependent modulation based on cue modality; similar significant results were found around and after the tap. Therefore, we focus our discussion on differences in scalp distribution of beta activity between auditory and visual cues around the tap. Above the left premotor cortex (electrode FC5), beta suppression was stronger for auditory cues, especially in 3-Hz conditions. Given the superior tapping performance with fast auditory cues, this suggests that temporal auditory information was more easily integrated into the motor plan and that auditory cues provided better sensory guidance during finger tapping.

In other brain areas, we did not observe a distinct and consistent effect of cue modality across multiple comparisons of interest. We propose that observed differences may be introduced by other cue characteristics, potentially overshadowing any modality-dependent beta oscillatory networks for SMS, as reported in the literature. A previous EEG study examined predictive beta activity using an omission paradigm with auditory and visual rhythms (Comstock et al. 2021). They found common activations in parietal and frontal cortices but modality-specific activations in temporoparietal, midline and occipital areas for visual cues and sensorimotor areas for auditory cues. Additionally, MEG and fMRI studies on finger tapping reported conflicting results regarding the role of the dorsal and ventral premotor cortices with auditory and visual cues (Jäncke et al. 2000; Jantzen et al. 2005; Pollok et al. 2009). The present study cannot further elucidate contradicting findings in the literature. The low spatial resolution of EEG and limited electrode coverage on the primary auditory and visual cortices may have contributed to the lack of clear modality-specific differences in beta band activity in this study.

In summary, our results showed that participants were unable to synchronize with fast visual cues, whereas tapping to auditory cues was performed accurately. The enhanced beta suppression around the left premotor area observed for auditory cues suggests more sensory guidance of movements with auditory compared to visual cues.

4.3 Bottom–Up Processing and Subdivision Benefit of Polyrhythms Results in Similar Tap Accuracy Compared to Top-Down Processing of Isorhythmic Cues

In auditory conditions, cue rhythmicity influenced the phase of tapping relative to the cues, with approximately half a cycle. Our results align with previous studies, showing that distractor tones can strongly affect the timing of tapping relative to the target stimuli (Repp 2003a, 2004). In polyrhythmic tapping tasks without specific instructions, individuals tend to synchronize with the fastest or the lowest pitched rhythm (Handel and Oshinsky 1981), as synchronization to lower pitched tones is more accurate and requires less listening effort (Shivhare and Sanjram 2021; Varlet et al. 2020). Despite instructions in the present study to tap into the slowest, high-pitched rhythm, the natural tendency to synchronize with the fastest or lowest pitched rhythm (Handel and Oshinsky 1981; Repp 2003a) likely contributed to the phase shift towards the secondary beat with auditory polyrhythmic cues.

Although the secondary rhythm caused a phase delay between isorhythmic and polyrhythmic cues, tapping speed accuracy and variability with auditory polyrhythmic cues remained unaffected by cue rhythmicity. This may be explained by the so-called subdivision benefit, introduced by the secondary beat (Repp 2003b). Tapping every second event of a faster sequence (1:2 tapping) reduces phase variability compared to tapping every event (1:1 tapping) of a sequence. This benefit has been observed for auditory and visual sequences with inter–beat intervals above 250–200 and 470 ms, respectively (Repp 2003b). We propose that auditory polyrhythms shifted the tapping phase towards the secondary beat due to its rhythm and pitch, while the subdivision benefit of polyrhythms simultaneously facilitated synchronization, resulting in an accurate and consistent tapping rhythm.

With visual cues, the subdivision benefit likely facilitated synchronization to slow polyrhythmic cues, but not too fast visual polyrhythmic cues. The short inter–beat interval for fast polyrhythms may have limited this benefit, reducing tapping accuracy and consistency. Alternatively, the increased tap variability may be due to differences in stimuli presentation, with foveal presentation of isorhythmic cues and peripheral presentation of polyrhythmic cues, potentially causing differences in visual processing time (Staugaard et al. 2016). Therefore, the effect of rhythmicity with visual cues needs further investigation by using either foveal or peripheral cue presentation.

Beta band oscillations did not show time-dependent modulation based on cue rhythmicity; similar significant results were found around and after the tap. Therefore, we focus our discussion on differences in scalp distribution of beta activity between isorhythmic and polyrhythmic cues around the tap. Our results revealed distinct differences in the distribution of beta oscillations between isorhythmic and polyrhythmic cues. Given that tapping accuracy and variability were comparable for isorhythmic and polyrhythmic cues, we suggest that these differences in beta band activity reflect distinct control strategies or compensatory processes to maintain consistent tap performance.

In general, isorhythmic cues demonstrated a stronger beta enhancement in the frontal and parietal regions, indicating more endogenous, top-down control of movement. In contrast, polyrhythmic cues, especially at 1 Hz, were characterized by reduced beta enhancement or even beta suppression in these areas, accompanied by strong beta suppression in the right hemisphere extending into the (pre)motor, lateral frontal and parietal regions.

The pronounced beta suppression in the right hemisphere with slow polyrhythms aligns with previous fMRI studies, showing increased activations in the right premotor, prefrontal and inferior parietal cortices, as well as bilateral supplementary motor areas and cerebellum, in response to greater rhythmic complexity (Chen et al. 2008; Thaut et al. 2008). Since motor performance remained unaffected by rhythmic complexity, it has been suggested that the observed differences reflect compensatory processes that adapt to variations in internal processing demands for sensorimotor integration, ensuring a consistent motor output (Thaut et al. 2008).

The right hemisphere plays a crucial role in both timing and visuomotor information processing. Studies on timing processing highlighted the crucial role of the right hemisphere, especially the right dorsolateral prefrontal cortex and the right inferior parietal cortex (Koch et al. 2009; Macar et al. 2002). Similarly, the right hemisphere is more important in visuomotor information processing than the left hemisphere and is considered more ‘visually intelligent’ in a spatial search task (Corballis 2003; Farnè et al. 2003). Therefore, we propose that the enhanced beta suppression in the right hemisphere reflects increased demands on temporal processing and sensorimotor integration posed by the slow polyrhythmic cues to achieve similar tap accuracy as with slow isorhythmic cues.

We further propose that polyrhythmic cues elicit more exogenous, bottom-up attention and control of movements as suggested by several observations: (1) The reduced or absent beta enhancement in the frontal cortex suggests limited top-down control of movement. (2) The strong involvement of the right hemisphere may point towards engagement of the ventral attention network, which is associated with exogenous, stimulus-driven attention (i.e., bottom-up) in visual tasks, as opposed to the dorsal attention network, which is related to endogenous, goal-directed attention (i.e., top-down) (Tang et al. 2016). Although the spatial resolution of the EEG data is insufficient to conclusively differentiate between the dorsal (frontal eye fields, inferior and superior parietal cortices) and ventral areas (temporal–parietal junction, ventral frontal cortex), the scalp distribution of the beta oscillations points more towards the role of the ventral than the dorsal attention network. (3) The half-cycle phase shift observed with auditory polyrhythmic cues further supports stimulus-driven, bottom-up attention and control of movement, as the natural tendency to align taps with the faster, low-pitched secondary beat (i.e., bottom-up) prevailed over the internal goal to tap to the primary beat (i.e., top-down).

In summary, tap accuracy and consistency were comparable between isorhythmic and polyrhythmic cues, likely as a result of the subdivision benefit introduced by the secondary beat of the polyrhythmic cues. Beta enhancement in frontal and parietal areas suggests greater endogenous, top-down control of movement with isorhythmic cues. In contrast, the widespread beta suppression with polyrhythmic cues (especially 1 Hz) and the phase delay with auditory polyrhythmic cues suggest more stimulus-driven, bottom-up control of movement with polyrhythmic cues.

4.4 Limitations and Recommendations

Future research should explore the role and direction of beta band modulation in relation to SMS, particularly in regions beyond the commonly studied motor areas. Additionally, methodological limitations in the experimental design should be considered in future studies. First, to obtain a better understanding of the variability between participants, we propose the inclusion of questionnaires that assess participants' musicality (Chen et al. 2009; Repp 2003b; Whitton and Jiang 2023) and their preferences and experiences regarding the various cue conditions. These questionnaires may provide valuable insights into the variability between participants observed in performance measures or cortical activity in certain cue conditions.

Second, additional experimental conditions should be considered to gain insights into the distinct cortical dynamics induced solely by the cues or the motor task. The beta oscillations demonstrated in our results represent a summation, or possibly interaction, of the cortical activity related to both motor processing and sensory processing of the cues. It remains unclear which electrophysiological changes can be attributed to cue-related motor control. To disentangle these effects, future studies may measure additional conditions with cue presentation during rest and continuation of tapping after the elimination of the sensory cue, as previously done (Boonstra et al. 2006; Jäncke et al. 2000; Jantzen et al. 2005; Konoike et al. 2012; Lewis et al. 2004; Meijer et al. 2016; Pouthas et al. 2005; Rao et al. 1997; Seeber et al. 2016). Furthermore, the repetitive and cyclic nature of the tapping tasks raises the question of whether beta modulation drives or results from the actual tapping behaviour. Neuromodulation techniques, such as transcranial magnetic stimulation, could help clarify the causal relationship between beta band activity and motor output (Pollok, Rothkegel, et al. 2008). However, considering the already substantial number of conditions and subsequently a large number of statistical comparisons, we made the decision not to include these additional conditions in the present study.

Third, the study did not include a formal practice block at the start of the experiment, but only a brief instructional video to introduce the cue conditions. Consequently, some participants found it challenging to synchronize with the rhythm of the cues, particularly during the first sequences of a cue condition. These sequences effectively served as an unintended ‘practice period’ and were therefore excluded from further analyses if the number of taps deviated by more than 30% from the number of cues. This criterion was subjectively chosen as a practical compromise to balance retaining correct sequences and excluding incorrect, practice-like sequences.

Fourth, differences in the cue presentation must be considered when comparing cue conditions: (1) Auditory (0.15 s) and visual cues (half the ISI) differ in presentation time, with visual cues potentially introducing a binary meter due to their on/off pattern. It is unclear if this introduced a subdivision benefit as discussed above for polyrhythmic cues or how it affects time perception or tapping performance. (2) The foveal presentation of visual isorhythmic cues may differ in visual processing from the peripheral presentation of visual polyrhythmic cues (Staugaard et al. 2016). These differences in stimulus presentation require further investigation. (3) The experimental setup introduced a slight jitter in stimulus presentation, which could be improved in future studies by using specialized screens with higher refresh rates and dedicated audio cards. We do not expect that this minor jitter affected the participant's ability to perceive the rhythms, as none of them reported noticing any irregularities in the stimulus presentation.

Last, the hierarchical Bayesian models used in this study were beneficial because they enabled the implementation of our complex 2 × 2 × 2 study designs and avoided the need for multiple comparisons. The hierarchical Bayesian model could potentially be improved by incorporating prior knowledge of specific locations of the electrodes on the scalp, as suggested by Dimmock et al. (2023). However, introducing another parameter to the already extensive model used in the current study might have made the model too complex and ineffective to estimate the data.