Authors: Cecilie Møller (Center for Music in the Brain, Department of Clinical Medicine, Aarhus University & The Royal Academy of Music Aarhus/Aalborg, Aarhus, Denmark), Alexandre Celma‐Miralles (Center for Music in the Brain, Department of Clinical Medicine, Aarhus University & The Royal Academy of Music Aarhus/Aalborg, Aarhus, Denmark), Heidi Bliddal Borges (Department of Electrical and Computer Engineering, Aarhus University, Aarhus, Denmark), Jan Stupacher (Center for Music in the Brain, Department of Clinical Medicine, Aarhus University & The Royal Academy of Music Aarhus/Aalborg, Aarhus, Denmark), Christian Bech Christensen (Department of Electrical and Computer Engineering, Aarhus University, Aarhus, Denmark), Peter Vuust (Center for Music in the Brain, Department of Clinical Medicine, Aarhus University & The Royal Academy of Music Aarhus/Aalborg, Aarhus, Denmark), Preben Kidmose (Department of Electrical and Computer Engineering, Aarhus University, Aarhus, Denmark)
Categories: Original Article, ambiguous rhythms, beat perception, EEG, frequency tagging, music, priming, sensorimotor synchronization
Source: Annals of the New York Academy of Sciences
Doi: 10.1111/nyas.70290
Polyrhythms in the Brain: Metrical Priming, Acoustic Balance, and Perceptual Biases
Authors: Cecilie Møller, Alexandre Celma‐Miralles, Heidi Bliddal Borges, Jan Stupacher, Christian Bech Christensen, Peter Vuust, Preben Kidmose
Abstract
In polyrhythms, two pulse trains at different rates are presented simultaneously, yet listeners perceive only one as the underlying beat. This makes polyrhythms ideal for studying neural correlates of divergent percepts from identical stimuli. Across two electroencephalographic studies, we distinguished acoustic balance from perceptual ambiguity by designing stimuli that controlled for acoustic imbalances within the power spectrum and perceptual biases in polyrhythm beat perception. Using frequency tagging, we assessed metrical priming effects in 4 (Study perceptual ambiguity) and 3 (Study acoustic balance) polyrhythms under three no priming, fast‐pulse priming, and slow‐pulse priming. In Study 1, priming the 3‐beat slightly increased neural activity at its periodicity. In Study 2, participants tapped the perceived beat after each trial, enabling trial classification by subjective perception. This revealed close correspondence between perceived beat and neural activity, an effect obscured in the priming‐based analysis. Tapping responses revealed differences in priming success across conditions and individuals, highlighting the need for trial‐by‐trial measures of perceived beat in polyrhythm studies assessing endogenous contributions to beat perception. Together, the two studies show that polyrhythm perception is influenced by metrical priming at both behavioral and neural levels, but is also constrained by perceptual biases.
Introduction
One of the most pervasive problems in cognitive neuroscience is dissociating sensory‐driven neural activity from processes linked to conscious perception [1]. Music listening, dancing, and music making depend on the interaction between these two processes [2]. This is because they require the extraction of a stable underlying temporal structure with at least three hierarchically related levels (i.e., subdivision, beat, and meter) [3, 4] from complex sensory inputs [5−7].
Several studies used ambiguous auditory rhythms to study metrical interpretation in brain and behavior, as they provide a way to explore how different perceptual experiences can arise from the same stimulus [8−16]. In ambiguous rhythms, different grouping structures at the subdivision and beat levels can give rise to the perception of mutually exclusive musical meters, for example, the same rhythm with six subdivisions can be interpreted in a 6/8 meter (compound duple meter), or in a 3/4 meter (simple triple meter) (see Box 1 for notes on terminology).
In polyrhythms, a special case of ambigous rhythms, two regular pulse trains at different rates are presented simultaneously, and listeners may at any given time perceive one or the other as the underlying beat [17]. As such, polyrhythms are used to create tension and expression in music across genres and geographic locations. Polyrhythms, including cross‐rhythms and interlocked patterns, appear in many musical idioms, from the metrically ambiguous 12/8 bell patterns in West African traditions [18, 19], to the superimposed textures of the kotekan in Balinese gamelan music [20−22] and the cyclical clapping patterns of tala in South Asian regions [23]. In Western music, polyrhythms are most often used to “spice up” a main meter, for example, with metrically ambigous openings, tension/relief progressions, or the introduction of occasionally occurring countermeters [24−27], whereas in other cultures, for example, African drumming traditions, polyrhythms are an inherent part of the musical fabric itself, and several meters coexist on equal terms [19, 28]. In all cases, polyrhythms offer more than one possible metrical interpretation, which makes them often preferred tools in the study of the cognitive organization of temporal structures and associated perceptual biases—the topic of the present work.
During the past decade, the neural correlates of beat perception have been addressed using a broad range of neuroscientific tools. Perhaps the most direct method involves frequency tagging of electroencephalographic (EEG) recordings [29−31]. This method exploits the strict regularity of musical rhythms by measuring steady‐state evoked potentials (SSEPs) at periodicities related to the beat and meter of auditory rhythms, regardless of its presence in the stimuli [32−35]. Research using frequency tagging has also revealed direct correspondences between neural synchronization to the perceived beat and movement synchronization accuracy [20], which reflect similar categorical representation of rhythms in behavior and the brain [23]. Importantly, frequency tagging not only captures exogenous brain responses to the stimuli, but can also reveal endogenous activity, for example, related to imagery processes, that modulate the neural responses to enhance relevant periodicities in the stimuli [36−39]. These enhancements can reflect voluntary groupings of the beat [8, 40, 41], and also more unconscious/automatic groupings of faster events to generate a comfortable pulse [32], both in weakly periodic single‐tone rhythms [33] and in melodies [42]. Other studies used frequency tagging to show that a perceived beat can be sustained in ambiguous rhythms in children [43] and infants [44], and encoded from early development [45, 46]. Taken together, research confirms that frequency tagging can be a reliable tool to measure neural activity at the periodicities of regular as well as ambiguous rhythms, although a recent multilab replication study suggested that effect sizes might be quite small [41]. In studies using ambigous rhythms, a potentially important contributor to small effect sizes is perceptual misclassification, where condition labels may not reliably reflect participants’ perceived beat or meter. Consequently, neural responses associated with different percepts may be unintentionally mixed, attenuating observed effects when trials are averaged.
Experimental designs that include ambiguous auditory rhythms are often constructed under the assumption that if a musical rhythm is acoustically balanced, that is, if the energy is equally distributed across metrical positions, then it will also be perceptually ambiguous. However, true perceptual ambiguity—where two metrical interpretations are equally salient—rarely follows from perception of acoustically balanced stimuli, as evident from the growing literature on beat perception in polyrhythms [47]. Behavioral studies on polyrhythm perception in Western listeners have shown how perceptual biases can arise from changes in tempo [48] and pitch separation [49], and how listeners consistently avoid synchronizing with pulse trains that admit a ternary subdivision of the beat in favor of pulse trains that admit a binary subdivision [4]. Spontaneous motor tempo, that is, self‐paced finger tapping rates [50], and level of musicianship are examples of individual factors that also influence beat perception in polyrhythms [51]. When strong enough, such perceptual biases can potentially disambiguate seemingly ambiguous polyrhythms.
To study the human capacity for beat and meter perception in different contexts, previous studies have used metrical priming, in which an initial priming stimulus biases the interpretation of a subsequent ambiguous rhythm. Priming can be volitional and cognitive, as in metrical imagery [8], or induced through acoustic accents [52] or physical movements [9, 14−16] at beat‐ and meter‐related frequencies. Metrical priming allows researchers to assess particular metrical interpretations in ambiguous rhythms through neurophysiological and behavioral measures. However, when biases are strong and consistent, as demonstrated in the polyrhythm literature [4, 17], relying on priming paradigms without either accounting for these biases in the stimulus or including a reliable measure of priming success may conflate the data, as some trials may not reflect the primed perceptual experience hypothesized by the researcher. Furthermore, asymmetric behavioral results have led some researchers to propose that greater ease of synchronizing movements to the 3‐beat than to the 2‐beat in the widely used 3 polyrhythm may be explained by a perceptual bias toward the periodicity with the greatest spectral power [9], which is the case for the 3‐beat frequency when the 3 polyrhythm is created with equal intensity at the two frequencies. Yet, this is not the case for 4 polyrhythms in which higher spectral power is in the 4‐beat related frequency, and nonetheless, participants avoid synchronizing with the 4‐beat regardless of stimulus tempo and spontaneous motor tempo [4, 51].
Here, we directly address these issues by examining the effects of metrical priming in perceptually ambiguous and acoustically balanced polyrhythms and their associated neural correlates, without assuming that perceptual ambiguity arises from presentation of intensity‐balanced polyrhythms. We argue that to make firm conclusions about enhancements of neural responses at beat‐related frequencies, it is necessary to control the stimulus design by creating acoustically balanced stimuli, where spectral power, not intensity, is matched at the beat‐related frequencies. Furthermore, because of perceptual biases, particularly the binary subdivision bias, convincing trial‐by‐trial behavioral measures of actually perceived beat rather than expected metrical interpretation based on priming must be included in the analysis of the neural responses. While a trial‐by‐trial approach has been used in relation to ambiguous rhythms [10], it is also important to include behavioral verification in the growing neuroscientific literature on polyrhythms, in order to benefit from the advantages that polyrhythms provide for cognitive neuroscience research.
In two EEG studies, we used polyrhythms, priming, and frequency tagging to study contextual influences on metrical interpretation in the brain while controlling stimulus features. Whereas previous EEG research addressed priming in intensity‐balanced polyrhythms, here we adjusted the intensity level differently for each periodicity to control for perceptual ambiguity (promoting maximal perceptual flexibility in Study 1) and balance in the spectral energy (promoting direct comparisons of neural amplitudes in Study 2). By comparing the neural amplitudes at different beat‐related frequencies, we can study how the brain modulates the incoming signal to selectively enhance specific periodicities in the auditory response, leading to a stable percept that corresponds to one of the two metrical interpretations. In Study 1 (n = 16), participants listened to perceptually ambiguous 4 polyrhythms preceded by the sound of a drum set emphasizing the 3‐beat or the 4‐beat. After the EEG recordings, participants tapped the perceived beat to verify the perceptual ambiguity of the stimulus. We hypothesized that the EEG would show larger amplitudes at 1.5 Hz (the 3‐beat frequency) compared to 2 Hz (the 4‐beat frequency), when presented in the 3‐beat context, and vice versa when presented in the 4‐beat context. In Study 2 (n = 16), we presented acoustically balanced 3 polyrhythms in a context that used speech patterns to strongly reinforce either the 2‐beat or the 3‐beat. Here, participants were asked to tap along to the perceived beat at the end of each single trial, allowing us to assess overall priming success as well as to directly link neural amplitudes to behavioral measures of beat perception. We hypothesized that trials perceived as 2‐beat would show larger amplitudes at 1.5 Hz (the 2‐beat frequency) compared to 2.25 Hz (the 3‐beat frequency), and vice versa for 3‐beat trials. Any amplitude difference between these two frequencies must reflect neural transformations of the auditory response that enhances relevant periodicities—through priming success or the persistence of a perceptual bias—thereby supporting metrical stability.
Methods—Study 1
General Description
For Study 1, we used the 4 polyrhythm and designed a stimulus that was perceptually ambiguous, that is, leading to approximately equal distribution of 3‐beat and 4‐beat percepts in unprimed conditions. To do so, we used intensity modulations to counteract the propensity toward perceiving the 3‐beat as the underlying beat in this particular polyrhythm [4, 51, 53]. This allowed us to assess the effects of priming on neural amplitudes across priming conditions, while avoiding a stimulus‐driven bias that would reduce the effectiveness of 4‐beat priming and make 3‐beat priming redundant.
Participants
Sixteen participants (mean 23.13 years; age 18–32 years; 7 women) with normal hearing and no neurological or psychiatric disorders were recruited through a local online research participation pool (SONA systems). Nine had 2–16 years of musical training, and three had 2–3 years of dance training. The study was approved by the Danish Neuroscience Center IRB (IRB‐2019‐004), took place at the EEG research lab at Aarhus University Hospital, Denmark, and all gave informed consent, in accordance with the Declaration of Helsinki.
Stimuli and Procedure
The auditory stimulus was a natural drum sound presenting a 4 polyrhythm with a cycle frequency (a whole repeating pattern) of 0.5 Hz (2000 ms IOI), a 3‐beat frequency of 1.5 Hz (666 ms IOI/90 BPM), and a 4‐beat frequency of 2 Hz (500 ms IOI/120 BPM). The stimuli were created using an online polyrhythm generator (https://mynoise.net/NoiseMachines/polyrhythmBeatGenerator.php). The intensity of the 3‐beat (1.5 Hz) was attenuated by 8 dB compared to the 4‐beat (2 Hz), based on pilot studies showing that this resulted in a perceptually ambiguous 4 polyrhythm, that is, where 50% of participants perceived the 4‐beat. Stimuli were delivered through Etymotic ER2 in‐ear headphones at a comfortable level. Before the EEG recordings, we explained the importance of sitting still during the session, as body, facial, and eye movements would otherwise create artifacts in the data. Participants listened carefully to the rhythms while EEG was recorded, with additional written instructions to move as little as possible and a fixation cross shown on a screen in front of them. The EEG paradigm (see Figure 1) contained two Block 1 contained seven No Priming trials (16 cycles, 32 s each) (Audio S1). Block 2 contained seven 3‐Beat Priming trials (Audio S2) and seven 4‐Beat Priming trials (Audio S3), presented in pseudo‐random order, where the polyrhythm was preceded by an 8 s drum pattern reinforcing a triple meter (X x x x X x x x X x x x) or a quadruple meter (X x x X x x X x x X x x). After EEG recordings, participants completed a tapping task on three No‐Priming trials using a Makey Makey (https://makeymakey.com/), an Arduino‐based USB controller. For this task, stimuli were presented through on‐ear headphones, and participants were verbally instructed to tap along to the underlying beat. Thorough verbal instructions (see Supplementary Materials) were preferred over providing actual tapping examples so as to avoid inducing one or the other metrical interpretation or a specific tempo. The whole session lasted ∼15 min, including self‐paced breaks.
EEG Recordings
Participants’ EEGs were recorded with a 32‐electrode actiCAP (Brain Products). The active electrodes were placed following the international 10/20 system, using the FCz as reference. Electrodes were placed on the left and right mastoid (LM and RM) for offline re‐referencing and at the infraorbital ridge and the outer canthus (EOG‐V and EOG‐H), allowing removal of eye‐related artifacts. Electrodes’ impedances were kept below 20 kΩ, and the signal was amplified and digitized at a sampling rate of 1000 Hz.
Analyses
Finger Tapping
Intertapping intervals were converted into circular measures following previous work [4] to identify tapping periodicities (i.e., cycle, 2‐beat, 3‐beat, 4‐beat, other). One participant tapped inconsistently across the three trials and was removed from the analysis, which separates participants according to tapping responses.
EEG Preprocessing
The FieldTrip Toolbox for MATLAB [54] was used to preprocess the EEG data. Data were detrended and notch‐filtered at 50, 100, and 150 Hz, high‐pass filtered at 0.3 Hz, and low‐pass filtered at 20 Hz (filter order 4). Signals were segmented into 21 epochs based on the triggers signaling stimulus onset. We checked for bad channels (high amplitude noise or flat signal) during EEG recordings with the intent to replace them using the standard Fieldtrip method for weighted interpolation of neighboring channels, but all channels showed good signal during the short EEG session. We then ran independent component analysis [55, 56], with the Fieldtrip fastica algorithm to identify and remove eye‐related artifacts caused by blinks and horizontal eye movements. This was evident as vertical bumps in the signal and square‐shaped artifacts, respectively, located in the most frontal peripherical regions of the topographies. Data were re‐referenced to the mean of mastoid channels. Epochs were trimmed to exclude the priming section (i.e., 8 s) and first cycle of the polyrhythm (i.e., 2 s), resulting in 21 homogeneous 30 s epochs, seven for each condition (see Figure 1). Frequency analyses were conducted with custom‐made MATLAB scripts (Mathworks, v. 2019b).
Frequency Tagging Analyses
EEG epochs were averaged within each condition for each participant and electrode to enhance phase‐locked neural activity, then transformed with a fast Fourier transform (FFT) to convert time‐domain amplitudes (µV/s) into frequency‐domain amplitudes (µV/Hz), with a frequency resolution of 0.033 Hz. To identify peaks at the polyrhythm periodicities, that is, 1.5 and 2 Hz, each frequency bin was normalized by subtracting the mean of surrounding nonadjacent bins (± 4 to 5 frequency bins) within −0.166 to −0.100 Hz and 0.100 to 0.166 Hz, leaving SSEPs present in the signal as peaks. For statistical analyses, we averaged the activity of eight frontocentral Fz, F3, F4, FC1, FC2, Cz, C3, and C4, based on previous work locating beat‐related SSEPs here [37, 42, 48, 57−59]. Topographies in Figures S1 and S2 confirm that the neural activity related to the two beats of the polyrhythm was mainly picked up in the frontocentral electrodes. For each participant (see Figures S3 and S4), the frequency tagging analysis provided six amplitude values to be compared statistically, that is, two frequencies of interest (1.5 and 2 Hz) in three conditions (No Priming, 3‐Beat Priming, and 4‐Beat Priming).
To control for stimulus intensity imbalance, we normalized neural activity at periodicities present in the stimulus envelope between the polyrhythm cycle (0.5 Hz) and the shared subdivision (6 Hz). Ten peaks appeared beyond our beat‐related frequencies of interest (FOI, 1.5 and 2 Hz): 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, and 6 Hz (see Figure 2). We z‐scored the neural amplitudes at these frequencies and subtracted the z‐scored amplitudes from the stimulus's envelope spectrum [33, 34]. Individual z‐scores were calculated in the following (x − mean across frequencies)/standard deviation across frequencies. We refer to these normalized amplitudes as stimulus‐subtracted neural z‐scores, or subtracted z‐scores for short.
The acoustic properties of the priming periods preceding the polyrhythm and their corresponding neural amplitudes are shown in Figure S5. The plots confirm that the two priming phases elicited neural responses synchronized with the 3‐beat (1.5 Hz) and the 4‐beat (2 Hz), respectively.
Statistical Analyses
We used one‐sample t‐tests against zero to assess peaks at stimulus‐related frequencies across conditions. To test whether priming enhanced beat‐related activity at the two frequencies (1.5 and 2 Hz), amplitudes were compared across conditions (No Priming, 3‐Beat Priming, and 4‐Beat Priming) with a repeated‐measures ANOVA. Then, stimulus‐subtracted neural z‐scores were compared with the same ANOVA. Finally, a mixed‐design ANOVA with Condition, Frequency, and the between‐groups factor Tapping Preference (3‐Beat, 4‐Beat) examined differences in z‐scored amplitudes between participants who synchronized with the 3‐beat versus the 4‐beat after the EEG recordings. This latter analysis was performed to assess possible differences at beat‐related frequencies related to general beat perception bias as measured by tapping preference in a separate task.
Results—Study 1
Behavioral Results
Finger tapping results confirmed the perceptual ambiguity of the 4 polyrhythm. Half of the participants (eight participants) synchronized with either the 4‐beat (six participants) or every other beat of the 4‐beat (two participants), while the remaining participants (eight participants) synchronized with the 3‐beat (six participants), the 3‐beat and the rhythm (one participant) or the 3‐beat and every other beat of the 4‐beat (one participant). All but three participants tapped consistently across the trials (see Figure S6), and only one of them switched between the 3‐beat and the 4‐beat, testifying to the robustness of a metrical interpretation once established in the listener.
EEG Results
Peaks at Stimulus‐Related Frequencies
Amplitudes were greater than zero for all conditions at the frequencies directly related to the 3‐beat (1.5 Hz) and the 4‐beat (2 Hz), with all p < 0.001. This was also the case for most (sub)harmonics of the 1, 3, 4, 4.5, and 6 Hz; except for 0.5 Hz (the cycle frequency) and 1 Hz (the subharmonic of the 4‐beat) in the 3‐beat priming condition. Table S1 reports the corresponding t‐tests.
ANOVA on Neural Amplitudes
There was no significant main effect of Condition (No Priming, 3‐Beat Priming, 4‐Beat Priming), F(2, 30) = 1.19, p = 0.319, partial η ^2^ = 0.07 on beat‐related neural amplitudes. However, there was a significant main effect of Frequency (1.5 and 2 Hz), F(1, 15) = 30.78, p < 0.001, partial η ^2^ = 0.67, indicating a large effect. The Condition*Frequency interaction was not significant, F(2, 30) = 0.28, p = 0.756, partial η ^2^ = 0.02.
Post hoc comparisons using Holm‐adjusted p‐values revealed a significant difference between 1.5 and 2 Hz, t = −5.55, p < 0.001, with smaller amplitudes at 1.5 Hz than at 2 Hz, MD = −0.25, SE = 0.04 (see Figure 3A). This difference, however, reflects the loudness imbalance between the two frequencies in the stimulus, which makes endogenous processes difficult to interpret and tell apart. To support this, we ran a cochlear model [33] (Figure S7) of the first 10 s of the stimulus, which revealed even larger amplitude differences between the two frequencies at the cochlear level, suggesting that the peak we found at 1.5 Hz in the frequency tagging analysis of the EEG was reinforced by higher cortical regions of the brain that enhanced the 3‐beat periodicity, especially after the 3‐beat priming.
ANOVA on Subtracted Z‐Scored Amplitudes
There was no significant main effect of Condition (no Priming, 3‐Beat Priming, 4‐Beat Priming), F(2, 30) = 0.62, p = 0.543, partial η ^2^ = 0.04 on subtracted z‐scored amplitudes (see Figure 3B). However, there was a significant main effect of Frequency (1.5 and 2 Hz), F(1, 15) = 14.95, p = 0.017, partial η ^2^ = 0.32, indicating a large effect. The Condition*Frequency interaction was not significant, F(2, 30) = 0.37, p = 0.498, partial η ^2^ = 0.05. Post hoc comparisons using Holm‐adjusted p‐values revealed a significant difference between 1.5 and 2 Hz, t = 2.67, p = 0.017, with greater amplitudes at 1.5 than at 2 Hz, MD = 0.79, SE = 0.30. The positive, larger z‐scores at 1.5 Hz could reflect a relative enhancement of the less prominent (i.e., acoustically lower in intensity) 3‐beat periodicity in the brain.
To specifically investigate this enhancement, one‐sample t‐tests against zero were conducted to determine whether the sample means at 1.5 Hz were significantly greater than the subtracted stimulus z‐scores. Amplitudes were significantly greater than zero at 1.5 Hz in the 3‐Beat Priming t(15) = 1.97, p = 0.034, d = 0.49; but not in the 4‐Beat Priming t(15) = 1.06, p = 0.154, d = 0.26; nor in the No Priming t(15) = 1.48, p = 0.081, d = 0.37.
ANOVA on Z‐Scored Amplitudes Grouped by Tapping Responses
In the mixed‐design ANOVA, there was no significant main effect of Condition, F(2, 26) = 0.79, p = 0.466, partial η ^2^ = 0.06, nor ConditionTapping Preference interaction, F(2, 26) = 1.16, p = 0.330, partial η ^2^ = 0.08. Similarly, the ConditionFrequency interaction did not reach significance, F(2, 26) = 0.59, p = 0.561, partial η ^2^ = 0.04, nor did the three‐way interaction of ConditionFrequencyTapping Preference, F(2, 26) = 0.77, p = 0.471, partial η ^2^ = 0.06. There was a significant main effect of Frequency, F(1, 13) = 5.96, p < 0.030, partial η ^2^ = 0.31, but the Frequency*Tapping Preference interaction was not significant, F(1, 13) = 0.15, p = 0.703, partial η ^2^ = 0.01. The between‐subjects effect of Tapping Preference was not statistically significant, F(1, 13) = 0.20, p = 0.659, partial η ^2^ = 0.02. Regarding the main effect of Frequency, post hoc comparisons revealed greater amplitudes at 1.5 Hz than at 2 Hz, MD = 0.80, SE = 0.33, t = 2.441, p = 0.030.
Methods—Study 2
General Description
For Study 1, perceptually ambiguous stimuli were created by increasing the intensity of the 4‐beat compared to the 3‐beat by 8 dB. This imbalance in physical energy at the two beat‐related frequencies counteracted the natural tendency to hear the 3‐beat as the underlying beat [4], yet it made the corresponding neural responses difficult to compare. Even with a secondary analysis that aimed to control for this imbalance by subtracting the normalized amplitudes of the stimulus spectrum from that of the EEG, results were limited to showing larger amplitudes at the 3‐beat periodicity after 3‐Beat Priming. This motivated a second experiment.
To make neural responses to the two pulses directly comparable, we designed acoustically balanced rather than perceptually ambiguous polyrhythm stimuli for Study 2. This can be achieved by increasing the intensity of the slower beat of the polyrhythm. The 4 polyrhythm was, therefore, not suitable for this purpose as it would entail increasing the intensity of the 3‐beat, thereby enhancing the already present perceptual bias toward this periodicity [4]. Therefore, a balanced 3 polyrhythm was created by increasing the intensity of the 2‐beat slightly compared to the 3‐beat, resulting in equal power of the two periodicities, with the aim that the exogenous evoked potentials at the two frequencies would be approximately equal. At the same time, this counteracts the bias toward perceiving the 3‐beat as the underlying beat [4]. An additional improvement to the design of Study 2 was the inclusion of a tapping period at the end of each individual trial. This ensured not only assessment of perceived beat at the trial level but also assessment of participants’ susceptibility to priming, both of which were not measured in the first experiment.
Participants
Twenty participants with normal hearing, no neurological or psychiatric history were recruited via SONA systems; data from four were excluded (three technical issues, one poor signal), leaving 16 participants in the sample (mean 27.62 years; age 20–44; 7 women). Five were left‐handed, and all were musicians (four amateur, six serious amateur, three semi‐professional, three professional) with 7–36 years of experience (M = 18.50) and mean onset age 8.06 (range 5–15), playing piano (5), voice (4), drums (2), saxophone (2), guitar (1), clarinet (1), or violin (1). The study was approved by the Danish Neuroscience Center IRB (IRB‐2020‐007) and conducted in a soundproof room at the Department of Electrical and Computer Engineering, Aarhus University, Denmark; all participants gave informed consent in accordance with the Declaration of Helsinki.
Stimuli and Procedure
The auditory stimulus was a 3 polyrhythm with a cycle frequency of 0.75 Hz (1333 ms IOI), a 2‐beat frequency of 1.5 Hz (666 ms IOI), and a 3‐beat frequency of 2.25 Hz (444 ms IOI). It was created using a cowbell sound from the sample library of the software sampler Halion SE in Cubase Pro 8 (version 8.0.30). The stimulus was balanced such that the envelope contained the same power at the frequency of the 2‐beat (1.5 Hz) and the 3‐beat (2.25 Hz), resulting in a subtle increase in intensity of the sound at the 2‐beat periodicity, see Figure 5. The stimulus was presented to each participant through 3A Insert Earphones E‐A‐RTONE GOLD (3 M, US) at 60 dB above individual hearing threshold for the cowbell sound used in the experiment. Hearing thresholds were determined prior to the recordings using an ascending staircase procedure, following ISO 8253‐1.
The paradigm (see Figure 4) contained three blocks, each with 15 trials separated by a 2 s break. The No Priming block (Audio S4) was always presented first, while the order of the 2‐Beat Priming block (Audio S5) and the 3‐Beat Priming block (Audio S6) were counterbalanced across participants. In the No Priming block, each trial comprised a listening phase (13 cycles, 17.33 s) followed by a tapping phase (five cycles, 6.67 s). The trials in the remaining blocks were identical to those in the No Priming block, except that they were preceded by a priming period of nine cycles (12 s), in which speech and drums reinforced either the 2‐Beat (“FEEL the RHY‐thm”; X x x X x x) or the 3‐Beat (“KEEP UP the BEAT”; X x X x X x). The priming stimulus included a 4 s fade in and 4 s fade out. Both sentences used a semantically similar imperative verbal form followed by a determined noun phrase, but adapted the prosodic stress of the syllables to align with the different metrical interpretations of the polyrhythm. Participants were instructed to listen carefully to the rhythm without moving in the listening phase and then to tap along to the perceived beat in the tapping phase, indicated by a bell sound and a hand icon displayed on the computer screen in front of them. They tapped with the index finger of their dominant hand on the Mobita EEG amplifier, which has a built‐in accelerometer and was placed on their lap. The beat was defined as “the steady pulse you feel when listening to music.” To avoid that participants merely imitated the rhythm itself, further examples were given, including “The beat is like a clock's tick” and “Your feet emphasize the beat, when you walk at a constant pace in time with music.” All instructions were provided on the screen. The No Priming block was 6.5 min long, and the others each lasted 9.5 min, that is, the experiment had a total duration of 25.5 min + two self‐paced breaks between blocks.
In a training session preceding the experiment, participants familiarized themselves with the tapping task. The stimulus was identical to that used in the No Priming block, yet the listening period was shortened by 4 s, and the tapping period was prolonged accordingly. The participant repeated the training only if the experimenter, observing through a window, noticed nonisochronous tapping.
EEG and Finger Tapping Recordings
EEG was recorded using a 32‐channel EEG cap (TMSi, Netherlands) with electrode placement according to the international 10–20 system. Signals were sampled at 1000 Hz using two Mobita EEG amplifiers (TMSi): one for the EEG channels and one for the EOG (electrooculography) and mastoid channels. Both amplifiers were connected to a shared electrode at Fpz, allowing to post hoc combine the signals as if they were acquired from a single amplifier. Following data acquisition, recordings from the two amplifiers were re‐referenced to Fpz and merged into a unified dataset within the same domain.
Finger‐tapping responses were recorded as time‐series data of three‐dimensional coordinates using the accelerometer built into the Mobita EEG amplifier.
Analyses
Finger Tapping Analyses
We used an accelerometer to assess the beat periodicity perceived by participants in each trial. The accelerometer was placed on participants’ lap during the whole experiment, which allowed us to also confirm that no periodic movement took place during the listening phase of each trial. Previous research has used electromyography and motion capture to control for this [39]. The tapping signal was derived from the accelerometer by computing the square root of the sum of squares of the three axes, and an FFT was performed on the envelope of the absolute acceleration. Peaks in the frequency spectrum were identified and served to classify the tapping responses into tapping the 2‐Beat (1.5 Hz), tapping the 3‐Beat (2.25 Hz), tapping the Cycle (0.75 Hz), or tapping Other/No tap (peaks at several or no frequencies).
EEG Preprocessing
The preprocessing steps were almost identical to those of Study 1, with the exception that we applied a high‐pass filter at 0.4 Hz and a low‐pass filter at 40 Hz. In this longer EEG recording session, participants had to provide tapping responses for each trial, which resulted in some electrodes becoming noisy or flat over time. Therefore, we removed and interpolated a mean of 1.8 ±1.6 electrodes, within a range of 0−5 bad channels across participants. Epochs were trimmed to exclude the priming section (i.e., 9 s), the first cycle of the listening phase (i.e., 1.33 s), and the tapping period at the end of the trials (i.e., 6.66 s), resulting in 45 homogeneous 16‐s epochs, 15 for each condition (see Figure 4).
Frequency Tagging Analyses of the EEG
First, we applied standard frequency tagging to the preprocessed data, following the procedure described in Study 1, with minor adjustments reflecting the difference in epoch length. In Study 2, the epoch length was 16 s, corresponding to 12 polyrhythm cycles, yielding a frequency resolution of 0.0625 Hz. In the normalization step, we subtracted at each frequency bin the mean of the surrounding nonadjacent amplitudes (±3 to 5 frequency bins) falling between −0.3125 and −0.1875 Hz and between 0.1875 and 0.3125 Hz. We averaged the activity of eight frontocentral Fz, F3, F4, FC1, FC2, Cz, C3, and C4. The peaks in Figure 5 and topographies in Figure S23 show that this cluster captures frontocentral activity related to the processing of the 3 polyrhythm. Its averaged activity is, therefore, used in the statistical analyses. For each participant (see Figures S8 and S9), this frequency tagging analysis resulted in six amplitude values, that is, the two frequencies of interest (1.5 and 2.25 Hz) for the three conditions (No Priming, 2‐Beat Priming, and 3‐Beat Priming).
Then, to be able to take tapping responses after each trial into account, we performed frequency tagging at the single‐trial level. This was done by repeating the steps from the standard frequency tagging analysis, with the exception of applying the FFT to each of the 45 individual epochs, that is, before any averaging took place. For each participant, this single‐trial frequency tagging analysis resulted in 45 amplitude values, that is, 15 values per priming block for each of the two frequencies of interest. Because the single‐trial analysis does not average the data before applying the FFT, the stimulus‐unrelated activity and background noise is not attenuated, and may also include stimulus‐related nonphase locked activity. Figures S10 and S11 illustrate the inherent differences between averaging trials within the priming block before the FFT (standard frequency tagging analysis) and after the FFT (single‐trial frequency tagging), which corresponds to the traditional distinction between evoked and induced neural responses [60].
The acoustic properties of the priming periods preceding the polyrhythm and their corresponding neural amplitudes are shown in Figure S12. The plots confirm that the two priming phases elicited neural responses synchronized with the 2‐beat (1.5 Hz) and the 3‐beat (2.25 Hz), respectively.
Statistical Analyses
To statistically confirm the presence of peaks related to the 3 polyrhythm in the frequency tagging as well as the single‐trial frequency tagging analyses, we selected the amplitudes at two frequencies of 1.5 Hz (corresponding to the 2‐beat) and 2.25 Hz (corresponding to the 3‐beat), and tested whether these amplitudes were greater than zero (see Table S2). The effect of priming on frequency‐tagged EEG amplitudes was evaluated with a repeated measures ANOVA with Primed Beat (No Priming, 2‐Beat Priming, 3‐Beat Priming), Frequency (1.5 and 2.25 Hz), and their interaction as within‐subject effects. The ANOVA and the t‐tests were run in JASP (version 0.19.0.0). Single‐trial analyses included perceived beat as assessed by participants’ tapping responses at the end of each trial. Using a linear mixed effects model allowed us to retain all trials in the analysis and assess the effects of priming and the effect of tapping type in parallel. We used R (v. 2025.05.0) and the lme4 package [61] to fit a linear mixed‐effects model assessing the effect of Tapped Beat (Cycle, 2‐Beat, 3‐Beat), Primed Beat (No Priming, 2‐Beat Priming, 3‐Beat Priming) and Frequency (1.5 and 2.25 Hz) and the interaction between Tapped Beat and Frequency and between Primed Beat and Frequency on EEG amplitudes obtained using single‐trial frequency analyses. The model included random intercepts and random Frequency slopes for Tapped Beat nested within Participant: EEGAmplitude∼TappedBeat∗Frequency+PrimedBeat∗Frequency+1+Frequency|Participant/TappedBeat
The complex structure of the model resulted in overfitting. We chose this model nonetheless, because it best reflected the design of the experiment. Because the distribution of residuals was skewed in the linear mixed effects model, we report analyses using log‐transformed amplitudes, which led to better Q−Q plots. The emmeans package [62] was used for pairwise comparisons.
Results—Study 2
Behavioral Results
Participants tapped the 3‐Beat in most of the trials (Figure 6A): 81.3% after No Priming, 22.1% after 2‐Beat Priming, and 86.7% after 3‐Beat Priming. They tapped the 2‐Beat in fewer 3% after No Priming, 53.3% after 2‐Beat Priming, 2.1% after 3‐Beat Priming. These responses indicate a perceptual bias toward the 3‐Beat, despite the 2‐Beat periodicity being louder (Figure 4). Large individual differences appeared in trials with 2‐Beat Priming (see Figure 6C). The 2‐Beat Tapping was the preferred response in only 8 out of 16 participants (participants 2, 5, 7, 8, 10, 12, 16, and 17). Regardless of the tapped periodicity, the majority of participants synchronized consistently within each block. Exceptions are participants 6 and 11. When asked about tapping strategies in the debriefing, the latter explicitly reported “playing around with different beat patterns.”
Out of the 45 trials presented in the paradigm and regardless of priming condition, the average participant tapped the cycle in 5.75 trials (SD = 10.8, range 0–40), the 2‐beat in 8.75 trials (SD = 6.63, range 0–16), and the 3‐beat in 28.2 trials (SD = 10.9, range = 0–45).
Presentation order influenced susceptibility to 2‐Beat Priming (see Figure 6B). A Pearson Chi‐square test with Yates continuity correction showed that participants who took part in the 2‐Beat Priming block before the 3‐Beat Priming block were significantly more likely to tap in correspondence with the primed 2‐Beat than participants who took part in the 2‐Beat Priming block as the last of the three blocks, χ ^2^(1) = 28.441, p < 0.001.
EEG Results
The one‐sample t‐tests against zero confirmed the presence of significant peaks (all p < 0.003) within each of the three blocks at the two FOI: the 2‐Beat (1.5 Hz) and the 3‐Beat (2.25 Hz). Table S2 reports t‐tests, and Figures S10 and S11 depict frequency spectra for each participant.
ANOVA on Neural Amplitudes
The repeated measures ANOVA revealed no significant main effect of Frequency (F(1, 15) = 2.47, p = 0.137, partial η ^2^ = 0.14) or Primed Beat (F(2, 30) = 1.96, p = 0.159, partial η ^2^ = 0.12), yet the interaction between Frequency and Primed Beat was significant, (F(2, 30) = 8.12, p = 0.002, partial η ^2^ = 0.35). Post hoc pairwise comparisons showed significantly larger amplitudes at 2.25 Hz after No Priming compared to after 2‐Beat Priming (t = 4.01, p = 0.017, MD = 0.11, SE = 0.03) and 3‐Beat Priming (t = 3.75, p = 0.029, MD = 0.08, SE = 0.02). The amplitudes after 2‐Beat Priming were significantly larger at 1.5 Hz than at 2.25 Hz (t = 4.42, p = 0.008, MD = 0.12, SE = 0.03). No other pairwise comparisons were statistically significant after Bonferroni correction (adjusting for 15 comparisons). Figure 7A shows the neural amplitudes averaged across trials depending on Primed Beat. Figure 7B shows the neural amplitudes averaged across trials depending on Tapped Beat. For this analysis, a linear mixed effect model was applied because each Tapped Beat category includes a substantially different number of trials across participants (e.g., missing values), violating the assumption of balanced data pertaining to the repeated measures ANOVA.
Single‐Trial Frequency Tagging
An ANOVA on the linear mixed‐effects model using amplitudes derived from the single‐trial frequency tagging showed a significant interaction between Tapped Beat and Frequency, (F(2, 162.35) = 7.3632, p < 0.001), while there was no significant interaction between Primed Beat and Frequency (F(2, 1045.77) = 0.9371, p = 0.392), indicating that Tapped Beat was a stronger predictor for amplitude variations across frequencies than Primed Beat (see Figures 7C,D for model predictions based on Primed Beat and Tapped Beat, respectively). There were no significant main effects of Tapped Beat (F(2, 46.15) = 2.3736, p = 0.104), Primed Beat (F(2, 577.52) = 0.9391, p = 0.392), or Frequency (F(1, 24.53) = 0.2663, p = 0.610).
Tukey corrected pairwise comparisons were conducted to explore the interaction between Tapped Beat and Frequency (see Figure 7D). As expected, at 1.5 Hz, amplitudes were significantly larger in trials followed by 2‐Beat Tapping than in trials followed by 3‐Beat Tapping (t(56.7) = 2.456, p = 0.045) and Cycle Tapping (t(41.1) = −3.136, p = 0.009). At 2.25 Hz, amplitudes were more evenly distributed across Tapped Beat, and though the hypothesized difference in amplitudes between 2‐Beat and 3‐Beat tapping trials was clearly visible, it did not reach significance (t(47) = −2.256, p = 0.072). Comparisons between frequencies within each level of Tapped Beat showed a similar picture in trials followed by 2‐Beat Tapping. Those trials contained significantly higher amplitudes at 1.5 Hz than at 2.25 Hz (t(90.3) = 2.94, p = 0.004). Amplitudes did not differ significantly between 1.5 and 2.25 Hz frequencies in trials followed by 3‐Beat Tapping (t(26.8) = −1.615, p = 0.118). The discrepancy between 2‐Beat and 3‐Beat trials may be attributed to the inherent propensity toward perceiving the 3‐beat as the underlying beat in the 3 polyrhythm. Maintaining a 2‐beat perception poses a cognitive challenge to the brain, which is reflected in larger amplitude differences between frequencies. All other pairwise comparisons exploring the Tapped Beat by Frequency interaction were not significantly different (all p >0.33). To compare the effect of Primed Beat to the effect of Tapped Beat, exploratory pairwise comparisons between Primed Beat and Frequency were also run, despite the nonsignificant interaction between Frequency and Primed Beat (see Figure 7C). All comparisons were not significantly different (all p >0.26). Note that the full model included both Primed Beat * Frequency and Tapped Beat * Frequency as predictors. Therefore, the estimated marginal means of Primed Beat in Figure 7C do not mirror the amplitudes shown in Figure 7A because their variance is better explained by the Tapped Beat than by the Primed Beat.
Discussion
Our findings show that neural responses to ambiguous polyrhythms depend on listeners’ metrical interpretation, either induced by priming or by perceptual biases. Participants listened to the same physical stimulus, but their synchronized neural amplitudes differed depending on which underlying beat they perceived. This provides evidence for endogenous contributions to beat perception. Our results suggest that capturing this type of neural response is challenging and requires robust measures of subjective beat perception at a trial‐by‐trial level to account for intertrial differences. In Study 2, we accomplished this by using a single‐trial frequency tagging approach based on participants’ tapping responses. Standard condition‐based analyses, as typically used in metrical priming and frequency tagging studies, obscured these correspondences, while recategorizing trials according to the actually perceived beat revealed clearer neural correlates of different metrical interpretations of the polyrhythm. In line with previous studies [4, 51], we found a strong bias toward beats with binary subdivisions, that is, the 3‐beat in both the 3 and in the 4 polyrhythm, which influenced the effect of metrical priming across conditions and participants. Together, these findings highlight that beat perception in ambiguous rhythms emerges from an interplay of stimulus‐driven constraints, contextual influences, and subjective preferences.
The results of both experiments show the presence of a binary subdivision bias at the behavioral level [4, 51]. In Study 1, half of the participants perceived the 4‐beat as the underlying beat of the 4 polyrhythm only because it was amplified by 8 dB. In Study 2, most participants perceived the 3‐beat without priming (see Figures 6A,C), despite the events of the 2‐beat being louder, a stimulus design that was necessary in order to balance spectral power at the two beat‐related frequencies. Additionally, only half of the participants were susceptible to the 2‐beat priming, and we did not find any spontaneous bias toward 2‐beat responses, as shown in Figure 6. In isolation, the strong bias toward the 3‐beat in Study 2 could be caused by a tapping tempo preference for the faster 135 bpm BPM over 90 BPM. However, in Study 1, amplification of the faster 120 BPM pulse was necessary to draw participants away from the 90 BPM pulse. Furthermore, it was previously shown that increasing the tempo of the 3 polyrhythm does not lead to switching from 3‐beat to 2‐beat tapping. Rather, the vast majority of Western listeners avoid tapping the 2‐beat, just as they avoid tapping the 4‐beat in an intensity‐balanced 4 polyrhythm regardless of tempo [4, 51]. In line with the previous studies, we interpret the current behavioral findings as evidence for the binary subdivision bias, that is, a preference for polyrhythm pulses that admit a binary subdivision of the beat. Given the strength of this perceptual bias, one may ask whether beat perception in polyrhythms is susceptible to metrical priming at all. This is a relevant question because several experiments used the 3 polyrhythm as a case of an ambiguous stimulus, assuming that it offers two equally valid metrical interpretations [11−16]. Our findings indicate that priming success in 3 polyrhythms is, in fact, highly asymmetric.
Perhaps the clearest demonstration of this asymmetry is our finding that presentation order affected susceptibility to 2‐beat priming. Study 2 was designed to maximize the probability that participants would tap in accordance with the priming. This included presenting 2‐beat and 3‐beat priming trials in separate blocks rather than pseudorandomly intermixing them within one block, as in Study 1. Participants who were presented with 3‐beat priming before 2‐beat priming were less likely to tap in accordance with the 2‐beat priming, a metrical interpretation that necessitates a ternary rather than binary subdivision of the beat. This indicates that metrical priming success depends not only on perceptual biases related to the rhythm's metrical structure, but also on the strength of rhythmic priors established in the recent temporal context, supporting the notion that a one‐to‐one mapping of sensory input to perception cannot be assumed [29, 33, 63].
We found strong behavioral asymmetries in the No Priming condition despite the fact that we balanced the prominence of the peaks at the two frequencies of the beat in Study 2. This points to a perceptual bias inherent in the listener and not in the stimulus properties. As described in the Introduction, greater prominence of the 3‐beat frequency in the spectrum of the sound envelope has previously been used as an explanation for similar asymmetric results at the neural level. Chemin and colleagues [9] used body movement to induce the two different metrical interpretations in the 3 polyrhythm and reported that most participants felt uncomfortable performing movements related to the binary meter (our 2‐beat). Enhancements of neural amplitudes at frequencies related to the ternary meter (our 3‐beat) were seen only when body movements primed the 3‐beat, suggesting that the 2‐beat priming was indeed less effective in shaping neural activity.1 It is likely that a large proportion of their participants were not susceptible to the 2‐beat priming. In our Study 2, the behavioral data showed that this was only the case for eight participants (50%), and that priming success depended on priming order. Despite this, our condition‐based ANOVA still managed to capture differentiated neural amplitudes between beat‐related frequencies after priming the 2‐beat (Figure 7A).
We found that the modulation of beat‐related amplitudes was better captured in the linear mixed effects model using single‐trial frequency‐tagged neural responses. This model included the fixed effects Primed Beat and Tapped Beat (see Figure 7). Notably, the advantage of this approach lies in the identification of trials in which the priming did not work as expected to establish a more reliable link between brain and behavior. Its success, in turn, depends on the reliability of each trial categorization. One study used such behavioral verification to exclude trials with tapping responses unrelated to the meter frequency specified by the condition [39]. Another recent attempt to directly link frequency‐tagged neural responses to listener‐reported perception of musical beat led to inconclusive results [10], possibly because their perceptual probe tone detection task provided a less reliable basis for trial categorization than the tapping approach we used in Study 2. Nave et al.’s [10] trial categorization was based on a single button press, leaving results vulnerable to distraction, lack of motivation, and other factors discussed by the authors as potential contributors to the high occurrence of incorrect responses, which had to be discarded from the main analysis. Our thoroughly instructed tapping task ensured that only a negligible proportion of trials could not be categorized as either cycle, 2‐beat, or 3‐beat tapping trials (5%). In addition, because our Tapped Beat recategorization took every trial into account, regardless of which priming condition it came from, we were able to retain almost all trials in the single‐trial analysis, providing greater statistical power to detect the hypothesized relation between perception and neural activity. This approach also compensates for the significantly smaller neural amplitudes inherent in single‐trial analyses, which result from reduced signal‐to‐noise ratio (see Figures S10 and S11). Unlike standard frequency tagging [16], single‐trial frequency tagging does not involve averaging of trials over time to cancel out background noise and enhance stimulus‐related activity, but the clearer correspondence between neural amplitudes and actually perceived beat counteracted this methodological limitation.
With identical acoustically balanced stimuli across trials, the amplitude differences across Tapped Beat categories in Study 2 can be attributed to endogenous neural processes that either sustained the primed beat from the priming period (Figure 7A) or reflected the extraction of an alternative preferred beat (Figure 7D). This neural enhancement was less clear in the acoustically imbalanced 4 polyrhythm of Study 1, though the normalized amplitudes at the 3‐beat periodicity increased slightly after the 3‐Beat Priming (Figure 3B). We interpret the modulation of the amplitudes as a reflection of endogenous processes that represent listeners’ conscious perception of the beat, thereby contributing to the debate on whether beat perception measured with frequency tagging reflects stimulus‐driven or endogenous mechanisms [41, 64−68]. Our findings suggest that single‐trial analyses provide a more sensitive and straightforward approach in priming paradigms to capture the modulations of endogenous processes than the commonly used condition‐based analyses.
The lack of conclusive findings in Study 1 may also be partly rooted in some key differences between Study 1 and Study 2. Paying attention to auditory stimuli increases the neural responses to beat‐related periodicities [36]^.^ In Study 2, the constant engagement of participants in a sensorimotor task may have increased those responses even more [69, 70] by awakening their attention from the repetitive continuous stimuli to consciously select a periodicity to tap to. At the behavioral level, body movement like foot tapping or head nodding during beat extraction leads to greater beat stabilization [71]. As such, the inclusion of an engaging finger tapping task may have contributed to the highly consistent responses within blocks found in most of our participants. This could have been further enhanced, possibly, by encouraging tapping in the priming period, but we had not tried it here.
The priming phase also differed substantially between studies, as Study 2 was designed specifically to maximize the effect of priming. We presented each priming condition in a separate block, increased the number of cycles in the priming phase, and presented the polyrhythm along with drum beats as well as speech. We used speech for enhancing metrical priming because metrically organized rhythms enhance speech comprehension and production [72−74] by engaging mechanisms that organize stress patterns, prosody, and syntax [75, 76]. The syllables and stress patterns of our sentences aligned with the polyrhythm pattern and the relevant metrical structure, which may have helped the listener sustain each induced metrical interpretation once the priming phase faded out. In line with this, EEG activity during the priming phase shows clear amplitude peaks at both frequencies composing the polyrhythm (see Figure S12), even though the nonprimed frequency was less prominent in the spectrum of the stimuli envelope. Neural enhancement of the nonprimed beat frequency did not occur in Study 1, in which the musical sounds only elicited neural activity for the primed beat (Figure S5). This could indicate that the use of speech facilitated the synchronization of neural populations to the full rhythmic structure of the polyrhythm, supporting a more stable percept, which, in turn, may have allowed for a smoother transition between the priming phase and the polyrhythm stimulus and facilitated the maintenance of the induced metrical interpretation. Although they were not explicitly instructed to do so, it is possible that some participants silently rehearsed the sentences during the listening phase. Even if this occurred, such inner speech would be expected to affect both priming conditions in a similar way, owing to the within‐subject experimental design. Moreover, amplitudes in the priming conditions do not appear to be substantially greater than in the control condition (see Figure 7), suggesting that any sporadic involvement of inner speech did not change neural response amplitudes dramatically.
Another difference between our two studies is the level of musical expertise of participants. While Study 1 included a mix of musicians and nonmusicians, in Study 2, musicianship was a recruitment criterion. We previously found that musicians show greater metrical flexibility than nonmusicians when they tap to the 3 polyrhythm. While musicians synchronized with many metrical layers, nonmusicians almost exclusively synchronized with either the 3‐beat or the full cycle of the polyrhythm [51]. It is possible that a lack of metrical flexibility in participants in Study 1 made it harder for us to induce different metrical interpretations, not least because the 4 polyrhythm used in Study 1 is more complex than the 3 polyrhythm used in Study 2. In fact, the metrical flexibility of the musically trained participants of Study 2 varied substantially (see, e.g., participant 4 vs. 6 and 11 in Figure 6C).
A crucial difference between the studies also highlights an important limitation. In Study 1, we enhanced the ternarized 4‐beat to create a perceptually ambiguous stimulus, which resulted in less comparable amplitudes in the neural data (Figure 2), even after normalizing them as z‐scores (Figure 3). This was circumvented in Study 2, since the 3‐beat corresponded to the faster periodicity (with more events) in the 3 polyrhythm, which allowed us to increase the intensity of the less prominent 2‐beat until reaching a balanced acoustic power in the frequency spectrum of the sound envelope (Figure 5). This allowed for direct comparisons of the neural modulations (i.e., enhancement or suppression) of stimulus‐driven responses between frequencies. An unavoidable methodological limitation of polyrhythm research in general is the intrinsic integer ratio nature of polyrhythms, which leads to the issue that harmonics of the two frequencies of interest are shared and, therefore, cannot be assigned to either one or the other of the polyrhythms’ constituent beats. We acknowledge that some part of the neural responses to the beat may be missing by not including activity at harmonics of the beats [58, 77]. But the advantage of our approach is that it ensures balanced statistical comparisons between the two beat‐related frequencies. Otherwise, adding harmonics would introduce an imbalance, always favoring the slowest beat frequency within a determined frequency range. For example, in the 3 polyrhythm, more harmonics uniquely relate to the 2‐beat than to the 3‐beat. Similarly, in the 4 polyrhythm, more harmonics uniquely relate to the 3‐beat than to the 4‐beat. To overcome this particular issue of polyrhythms, future research could complement frequency analyses with autocorrelation‐based methods over the time‐varying EEG signal [31].
Finally, while the unbalanced intensity of the perceptually ambiguous 4 polyrhythm may have played a role in masking some of the effect, lack of statistical power could also explain why effect sizes related to the condition‐based analysis were quite small in Study 1 (partial η ^2^ < 0.1). Although this constitutes a potential limitation to Study 1, it directly motivated the design of Study 2, which allowed for recategorization of trials based on Tapped Beat rather than Primed Beat. This design reduced the risk of obscuring true effects in the data due to trial misclassification, an actual risk given the difficulty of inducing ternarized beat percepts compared with binarized beat percepts. The more successful testing of hypotheses in Study 2 suggests that the improved approach increased sensitivity to the true effect, notably without increasing the sample size and despite the additional stimulus‐unrelated noise resulting from performing the FFT before averaging across trials.
Conclusion
Our two studies used polyrhythms and priming as a framework for investigating how exogenous and endogenous processes shape beat perception. The results of both studies show that perceptual biases, such as the preference for binary subdivision grouping, can limit the effectiveness of metrical priming in polyrhythms and obscure their neural correlates. However, by comparing analyses with and without behavioral verification, we demonstrate that incorporating behavioral responses into single‐trial frequency tagging can mitigate that issue and reveal clearer links between actual perceived beat and neural activity. Future research on metrical priming should control for perceptual biases, such as binary subdivision preferences, the tendency to perceive the beat in lower‐pitched streams, and spontaneous motor tempo, to better understand how low‐level sensory processes give rise to high‐level conscious perception of musical rhythms. This could ultimately help explain the complex and individually diverse experiences of music.
Author Contributions
**Study 1—**Conceptualization, J.S., C.M., A.C.‐M., and P.V.; Investigation: J.S., A.C.‐M., and C.M.; Data curation and formal A.C.‐M.; Funding J.S. and C.M.; Visualization, writing—original C.M. and A.C.‐M.; Writing—review and All authors.
Study 2—Conceptualization, H.B.B., C.M., C.B.C., and P.K.; Investigation: H.B.B.; Data H.B.B., C.B.C., P.K., A.C.‐M., and C.M.; Formal A.C.‐M., C.M., and J.S.; Supervision: C.B.C., C.M., and P.K.; Visualization, writing—original C.M. and A.C.‐M.; Writing—review and All authors.
Conflicts of Interest
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
Funding
Study 1 has been supported by seed funding 2019 (Project 24794) from the Interacting Minds Centre, Aarhus University. Center for Music in the Brain was funded by the Danish National Research Foundation (DNRF117), the Lundbeck Foundation (R469‐2024‐1573), and Købmand Herman Sallings Fond.