Introduction

Many models of time perception presuppose the existence of an underlying mechanism maintaining a constant rhythm. The internal clock model1,2,3, for instance, comprises a pacemaker and an accumulator. The pacemaker emits pulses at regular intervals, while the accumulator collects these pulses. The number of accumulated pulses is then compared to a reference stored in memory to estimate the passage of time. Another example is the oscillator-based model4, which postulates the presence of a set of neural oscillators, each running at a distinct rate, allowing unique expressions of different intervals based on the lowest common multiple of specific subsets of these oscillators5,6 have proposed a plausible neurobiological mechanism to realize this concept, suggesting that cortical neurons serve as oscillators, with dopamine release from the ventral tegmental area resetting the phases of these oscillators at the onset of timed intervals. Whether considering neural pulses or oscillatory phases, these models posit the existence of internal pacemakers underlying time perception. Indeed, the presence of intrinsic pacemakers has been implicated in various studies across behavioral, physiological, and neuroscience domains7,8,9.

At the behavioral level, it is well-established that individuals exhibit their own distinct and preferred pace when performing regular, repetitive movements such as walking or swimming, with this pace varying from person to person. This inherent, natural pace is referred to as SMT. In laboratory settings, SMT is primarily assessed through free tapping tasks, where participants are instructed to tap their fingers or hands at their most comfortable and natural tempo. Fraisse12 conducted a comprehensive review of prior research, revealing considerable interindividual variability in SMT, spanning a range from 200 to 1400 ms. In contrast, within-individual variability remained low. Fraisse12 also cited earlier studies indicating that the correlation of SMT between two different trials typically falls within the range of 0.75–0.95. Similarly, we previously showed that the correlation of SMT between several testing sessions ranged between 0.74 and 0.9810. Furthermore, it is noteworthy that SMT does not significantly differ when assessed through finger-tapping, toe-tapping, or stepping on the spot11. This high level of reliability underscores the assertion that SMT is a distinctive trait of each individual10,11,12.

A related concept, known as Preferred Perceptual Tempo (PPT), deserves mention. PPT represents the tempo at which a series of sounds or lights feels most natural, that is, neither too slow nor too fast. Importantly, there is a strong correlation between SMT and PPT13,14. Notably, McAuley et al.13 conducted a study encompassing participants aged 4–94 years and reported that both SMT and PPT tend to slow with advancing age. These findings imply that both SMT and PPT are indicative of the pace set by a hypothetical endogenous oscillator13,14.

Numerous physiological indicators have also been documented as being associated with the pacemaker’s tempo. Changes in body temperature10,15,16, skin conductance levels17, and dopamine activity18 have been reported to exhibit correlations with variations in the pacemaker’s rate. Additionally, some have proposed that the heartbeat itself may serve as a pacemaker19,20,21.

In the quest to uncover the neural foundations of internal clock mechanisms, it may be tempting to draw parallels between the ticking of clocks and the oscillations within neural networks. Electroencephalogram (EEG) power exhibits a prominent peak within the alpha band (8–13 Hz). This peak is termed the IAF, and it varies among individuals. Notably, the modulation of IAF through transcranial alternating current stimulation (tACS) has been observed to alter the temporal window within which multiple successive stimuli are processed as a single event22. Moreover, the manipulation of IAF has been shown to impact subjective duration23. These findings suggest that IAF serves as a reflection of the brain’s temporal resolution, akin to an intrinsic tempo (see also Wiener and Kanai24).

As delineated above, the concept of intrinsic tempo, which underpins time perception, has been substantiated in behavioral, physiological, and neuroscience research. However, to date, no studies have explored the interrelations among these domains. If the “pacemaker” serves as a central mechanism, it may be conceivable to elucidate whether SMT, an outcome of this pacemaker, can be explained by variables such as IAF and heart rate, which could potentially reflect the pacemaker’s activity.

The aim of this study was to systematically measure SMT, IAF, and heart rate for each participant and to explore correlations among these variables. During the experiment, both EEG and heart rate were recorded while participants remained seated in a relaxed state with closed eyes for 5 min. Subsequently, participants were instructed to tap the space key with their index finger at a regular tempo representing their most comfortable pace, with the interval between taps defined as SMT. Furthermore, participants completed a questionnaire that solicited demographic information, including age, chronotype, and musical experience, as potential factors that might influence SMT13,25,26,27,28,29. We then employed correlation and regression analyses to investigate relationships between SMT, IAF, and heart rate. The present study was designed to investigate the concept of a pacemaker-like system, which is believed to play a crucial role in how we perceive time. Although SMT, IAF, and heart rate are each associated with intrinsic tempo, we did not have specific hypotheses about how these variables might correlate with one another. Instead, we focused on systematically measuring these variables within individual participants and evaluating the correlations among them. By analyzing the interactions between these behavioral, physiological, and neuroscientific measures, we aimed to gain insights into the underlying mechanisms of temporal perception.

In the realm of experimental psychology, a study sometimes fails to yield statistically significant results even when the hypothesis appears theoretically plausible. In such scenarios, not to report the findings due to the absence of significant differences can introduce publication bias, hindering the advancement of scientific knowledge. Consequently, we have chosen to present our results, retaining transparency and validity of the analysis by pre-registering all hypotheses, experimental methods, and analysis scripts at Open Science Framework (OSF) Preregistration (https://osf.io/xp9hv) prior to data collection. To comprehensively evaluate the evidence, we employed both Bayes factors and frequentist statistics, examining not only the presence or absence of statistical differences but also the strength of the evidence.

Method

Participants

We recruited 39 university students (19 male and 20 female), aged between 18 and 21 (mean age = 19.08 years, SD = 0.81). They were confirmed on a written questionnaire to exhibit no signs of major psychological disorders, had no history of traumatic brain injury, were not taking medication for anxiety, depression, or schizophrenia, and did not have motor or visual impairments. All subjects gave written informed consent in accordance with the Declaration of Helsinki. The protocol was approved by the institutional review boards of the University of Tokyo.

An a priori power analysis was used to determine the sample size. We conducted a pilot study with six participants (one participant was excluded due to massive body movement during recording), employing the same design as we planned for the main experiment. We opted to calculate correlation coefficients, as this method requires a smaller sample size compared to estimating regression coefficients in a linear model. The observed correlation coefficients were ρ = 0.63 between Inter-Response Interval (IRI) and Inter-Beat Interval (IBI) and ρ = 0.77 between IRI and IAF. Considering the possibility that our pilot study overestimated the effect size due to the small sample size, we adopted a conservative effect size of 0.5, which is still conventionally considered large. G*Power (Version 3.1.9.630) analysis using an effect size of 0.5 revealed that a sample size of 29 would afford 80% power to detect the effect.

We announced the experiment via email to those who have subscribed to our mailing list for psychological experiment recruitment. Assuming that some participants could not be included in the analysis due to poor data quality, we recruited 39 subjects who responded in the first 48 h after the recruitment announcement was sent out to the mailing list.

Seven participants made substantial movements during the electrocardiographic (ECG)/EEG recording, and heartbeats or alpha oscillations were not detectable. After the rejection of the seven participants, we had 32 participants (15 male and 17 female), aged between 18 and 21 (mean age = 19.0 years, SD = 0.80).

General procedure

First, we measured participants’ IAF and heartbeat by attaching electrodes and allowing them to rest alone in the experiment room for five minutes. They underwent one or two EEG/ECG recordings depending on the cleanliness of the data for analysis. Following this, the electrodes were removed, and participants undertook a spontaneous finger-tapping task twice consecutively. Finally, participants completed self-report questionnaires regarding their musical experience and circadian rhythms. The comprehensive data acquisition and pre-processing methods for each procedure are described in the sections below.

EEG and ECG

We utilized The Human SpikerBox (Backyard Brains, US) to concurrently collect EEG and ECG data at a sampling rate of 5000 Hz. To record EEG data, two electrodes were positioned at PO3 and PO4, according to the 10–20 system, with the reference point placed at the right mastoid. Heartbeats were recorded using ECG electrodes attached to the right and left palms, with the back of the left hand serving as a reference. With these electrodes in place, participants were asked to sit back in a chair, relax, and rest their hands comfortably on their laps. They then partook in a 5-min eyes-closed resting-state EEG and ECG session. To ensure participants feel safe and comfortable with their eyes closed, the experimenter left the room during the recording. After the recording was completed, the data was visually inspected. If any obvious large body movements were observed, the 5-min recording was repeated. After the second recording, the data were not checked on the spot, and no more than two measurements were taken regardless of the quality of the data, due to time constraint. If there were two recordings, the higher-quality data was selected for later analysis.

EEG data was analyzed offline using EEGLAB31. A Fourier transform was performed on the two electrodes (PO3 and PO4) using the EEGLAB function spectopo. We employed the Hamming window as the window function, with the window length equal to the sampling rate (5000 Hz) with no overlaps. The frequency resolution was set at 0.001 Hz for power calculatiton. The IAF was then extracted by detecting the maximum power value in the frequency spectrum range between 8 and 13 Hz.

ECG data were subjected to a bandpass filter between 3 and 45 Hz (default setting) to detect R-peaks using the Python toolbox, BioSPPy32. Then, we used the Python toolbox pyHRV33 to calculate RR-intervals (i.e., the interval between two R-peaks)33. The IBI is defined as the mean of RR-intervals, and its coefficient of variation (CV) is computed by dividing the standard deviation of RR-intervals by the IBI.

Finger tapping task

In the finger-tapping tasks, participants were instructed to tap the spacebar of a laptop as regularly as possible at their preferred pace, using the index finger of their dominant hand. To avoid influencing the participants’ preferred tempo, the experimenter did not provide any example tapping demonstrations, instead relying solely on verbal instructions. The beginning and end of a tapping session were marked by a white cross displayed at the center of the computer screen. Participants began tapping when the cross first appeared and continued until the cross disappeared after 45 taps. The participants were not informed of the number of taps. The participants performed the tapping session twice.

The first tap was excluded from subsequent analysis, resulting in 44 taps for each session. The IRI was defined as the average interval between taps and its CV was calculated as a measure of variability (CV = SD/IRI). The participants performed the tapping session twice, and the IRI and its CV were calculated from a total of 86 intervals ((43 intervals between 44 taps) * 2 sessions).

Self-report questionnaires

We recorded the time when the experiment took place and the ages of the participants. To assess circadian preferences, we utilized a shortened version (5 items) of the morningness-eveningness questionnaire34. Based on responses the questionnaire, the participants were categorized into five groups: Definitely Morning Type, Moderately Morning Type, Neither Type, Moderately Evening Type, and Definitely Evening Type. Since musical experience might impact SMT, participants were asked to indicate whether they engaged in musical activities, such as practicing at a music club or taking musical instrument lessons, at least once a week on average. Their response options were ‘yes’ or ‘no.’

Data analysis

The following metrics were calculated or computed for each participant using the method detailed above: IAF, Inter-Beat Interval (IBI) and its Coefficient of Variation (CV), Inter-Response Interval (IRI) and its CV, along with control variables like musical experience and chronotype, which were gathered via a questionnaire.

Since the main goal of the current study was to explore the relationships between these variables, we initially calculated the correlation coefficients for each pair of observed variables. Bayes factors against a null model (presuming no correlation) were also calculated using the free online JASP software (version 0.16.1.0), incorporating default priors.

Next, we delved deeper using separate multiple regression analyses. The IRI was modeled through a generalized linear regression, employing the glm function in R35, with IBI and IAF serving as independent variables. In a similar vein, the CV of the IRI was modeled through a generalized linear regression with the CV of the IBI and IAF as independent variables.

We contemplated including control variables in the model to examine their potential confounding effects further. The model initially incorporated all observed variables (IRI, the CV of IRI, IBI, the CV of IBI, IAF) and control variables primarily obtained through questionnaires (time of day, age, musical experience, self-reported chronotype). Subsequently, the best model was chosen through a stepwise method using the step function in R. Bayes factors were also computed using the JASP to compare the models.

These regression analyses aimed to examine the joint contribution of all physiological traits to the behavioral data while controlling potential confounding factors. Standardized regression coefficients (standardized betas) were compared across variables to determine how changes in physiological traits correlate with changes in behavioral tapping intervals.

Results

We measured the following metrics for each participant: IAF, the mean and CV of IBI, the mean and CV of inter-response interval (IRI), and control variables such as musical experience and chronotype obtained through a questionnaire. Descriptive statistics are summarized in Table 1.

Table 1 Descriptive statistics of observed variables: the mean and the CV of the Inter-Response Interval (IRI_mean, IRI_cv) for the tapping, the mean and the CV of the Inter-Beat Interval (IBI_mean, IBI_cv) for the heart rate, Individual Alpha Frequency (IAF), the age of the participants (age), and time at which the experiment was conducted (time).
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Correlation

Figure 1 shows the relationship among IRI, IBI, and IAF and Fig. 2 shows the relationship among the CV of IRI, the CV of IBI, and IAF.

Fig. 1
figure 1

The relationship between Inter-Response Interval (IRI) and Inter-Beat Interval (IBI) (left), and IRI and Individual Alpha Frequency (IAF) (right). In both panels, each dot represents an individual. The dots are colored according to IAF: red for higher IAF and blue for lower IAF. No systematic relationships were observed among IRI, IBI, and IAF.

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Fig. 2
figure 2

The relationship between the CV of Inter-Response Interval (IRI) and the CV of Inter-Beat Interval (IBI) (left), and the CV of IRI and Individual Alpha Frequency (IAF) (right). In both panels, each dot represents an individual. The dots are colored according to IAF: red for higher IAF and blue for lower IAF. No systematic relationships were observed among the CV of IRI, the CV of IBI, and the CV of IAF.

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We calculated correlation coefficients for each pair of observed variables (Fig. 3). We calculated Spearman’s rho when at least one of the variables of a pair was ordinal variables (age, time of the day, music_experience, and chronotype), otherwise calculated Pearson’s r. The metrics of were highly correlated with each other as expected. No significant correlation was found involving the mean and CV of IBI, the mean and CV of IRI, and IAF (See Table 2 and Supplementary Table 2 for statistics). Bayes factors against a null model (presuming no correlation) also showed anecdotal evidence for no correlations (Supplementary Tables 3 and 4).

Fig. 3
figure 3

The correlation coefficients between each pair of the observed variables. Cells with positive correlations are colored in red and cells with negative correlations are colored in blue. No significant correlation was found involving the mean and CV of IBI, the mean and CV of IRI, and IAF. IRI: Inter-Response Interval for tapping; IBI: inter-beat interval for heart rate; IAF: Individual Alpha Frequency, age: the ages of the participants’, time: the time when the experiment took place, music_experience: whether the participants engaged in musical activities at least once a week on average (yes or no), chronotype_rmeq: a categorical variable classified into 5 levels from Definitely Morning Type to Definitely Evening Type.

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Table 2 The Pearson’s correlation coefficients and p-values between each pair of the observed variables.
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Regression models

In the regression analysis, the IRI was modeled through a generalized linear regression with IBI and IAF serving as independent variables. In a similar vein, the CV of the IRI was modeled through a generalized linear regression with the CV of the IBI and IAF as independent variables. In both models, none of the independent variables exhibited significant regression coefficients (Table 3).

Table 3 The regression coefficients (Estimate), their standard errors (Std. Error), t-values, and p-values, obtained from the generalized linear regression analyses.
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Next, we created a full model that incorporated all observed variables (IRI, the CV of IRI, IBI, the CV of IBI, IAF) and control variables primarily obtained through questionnaires (time of day, age, musical experience, self-reported chronotype). In both models that explain the mean and CV of the IRI respectively, none of the independent variables exhibited significant regression coefficients (Supplementary Table 5).

The best model was chosen through a stepwise method using the step function in R. In the model that explains the mean of the IRI, the selected variable was only the CV of IRI though its coefficient was not significant. In the model that explains the CV of the IRI, the selected variables were the mean of IRI and the CV of the IBI, though their coefficient was not significant, either (Table 4). Bayes factors also indicated that no model was strongly preferred over the null model (Supplementary Tables 6 and 7).

Table 4 The best models chosen through the stepwise regression analysis.
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Discussion

The current study aimed to examine the relationship between SMT, IAF, and heart rate. Our hypothesis posited that if a central internal pacemaker exists, then SMT, as a product of this pacemaker, should be explicable by IAF and HR, both of which have been proposed to reflect the activity of the pacemaker13,14,19,20,21,24. However, we found no significant correlation between either the mean or CV of SMT and IAF, or heart rate.

Timing is a critical aspect of various everyday activities, and researchers have developed multiple models of time perception. The concept of an internal clock serves as a fundamental foundation, from which numerous intricate computational models have evolved7,36. A key question that remains unresolved pertains to the extent to which the mechanism for timing is centralized or distributed. The central time clock theory (intrinsic models) posits the existence of a single master clock, while the distributed time clock theory (dedicated models) suggests the presence of multiple clocks, each dedicated to distinct tasks or modalities8.

Additionally, it is well-documented that temporal processing varies depending on the duration of time being perceived. The perception of time intervals shorter than 1 s tends to be more automatic, whereas durations longer than 1 s often necessitate the allocation of additional cognitive resources37,38. From a neuroanatomical perspective, the cerebellum and basal ganglia appear to function akin to a fundamental internal clock mechanism39,40, while the prefrontal area is responsible for overseeing supplementary cognitive functions such as attention and working memory41,42, which are integral to time perception.

Therefore, even if we accept the hypothesis that SMT, heart rate, and IAF are all linked to an internal clock, it does not automatically imply that they are governed by a single master clock. This may explain why we did not find a direct correlation between SMT, heart rate, and IAF, despite earlier studies indicating their association with internal clocks. In the subsequent sections, we will explore the distinctive ways in which SMT, heart rate, and IAF are connected to time perception.

SMT represents an individual’s most natural pace and is primarily assessed through a free-tapping task, where participants are instructed to tap their fingers at their preferred rhythm. Schwartze et al.43 compared SMT between patients with basal ganglia lesions and healthy controls. While the mean SMT remained consistent in both groups, the patient group exhibited a more diverse distribution of SMT compared to the control group. Additionally, the CV of SMT was notably higher in the patient group. These findings suggest the involvement of the basal ganglia in the process that determines SMT. It is important to note that temporal processing of sub-second durations is closely associated with automatic motor control and implicates the cerebellum and basal ganglia, whereas processing durations longer than a second is of a more cognitive nature and involve the prefrontal areas37,38. Given that SMT is based on finger tapping, a motor action, its inherent connection to the fundamental internal clock system, in which the basal ganglia play a role, is entirely plausible.

Researchers have suggested that bodily signals, such as heart rate, may play a significant role in time perception. Notably, activity within the insula cortex demonstrates a linear increase during the encoding and reproduction of time intervals44,45. Given that the insula cortex serves as the primary sensory region responsible for processing bodily sensations, this accumulator-like activity suggests the integration of bodily signals during encoding, contributing to the representation of duration44. In alignment with the concept that subjective time is embodied, numerous studies have aimed to establish connections between various physiological parameters and the accuracy of temporal processing, although definitive conclusions remain elusive. Some studies have failed to identify relationships between average heart rate or respiration rate and temporal estimation accuracy46,47. In contrast, Jamin et al.48 instructed participants to hold their breath during a time estimation task and observed that a slower heart rate during apnea led to an overestimation of 20-s intervals. However, it is important to recognize that an increase in heart rate indicates heightened physiological arousal, which could potentially serve as a confounding factor affecting time perception. As a result, clear-cut conclusions in this regard have not yet been reached.

Heart rate variability (HRV) serves as an indicator of the extent to which the prefrontal cortex modulates the autonomic nervous system49,50. Given the prefrontal cortex’s involvement in attentional regulation and executive functions, a potential link between HRV and these processes is suggested. In a study by Hansen et al.51, participants were stratified into two groups based on their HRV levels recorded during a 5-min resting state. These groups were then subjected to a battery of cognitive tasks, including a continuous performance test (CPT) and a two-back task, aimed at assessing sustained attention and working memory, respectively. The results demonstrated superior performance in the high-HRV group, characterized by faster reaction times and fewer false-positive responses when compared to the low-HRV group. Furthermore, Cellini et al.52 established that heart rate variability accounted for 41% of the absolute error in 1-s finger-tapping tasks. Considering the correlation between HRV and attentional regulation, as discussed earlier, these findings suggest that higher HRV may enhance the allocation of attentional resources required for precise time estimation. In essence, HRV’s relation to time perception can be attributed to its impact on the prefrontal cortex’s functioning.

The internal clock model was initially conceptual when first introduced by Treisman3. However, with the subsequent discovery of endogenous oscillatory activity in the brain, studies have been undertaken based on the hypothesis that these oscillations may represent an implementation of the internal pacemaker24. The peak in the alpha range (8–13 Hz) evident in EEG power is designated as the IAF due to its inter-individual variability. Samaha and Postle53 reported that the phase of alpha oscillations determines whether two temporally proximate visual stimuli are perceived as simultaneous or distinct events. Additionally, Cecere et al.22 demonstrated that the temporal window for integrating visual-auditory stimuli occurring in close temporal proximity is altered when transcranial alternating current stimulation (tACS) is applied near the IAF. These studies collectively signify that the IAF represents the minimum temporal resolution for visual processing, akin to an inherent tempo.

Many studies have directly explored the relationship between duration estimation and alpha oscillations. Mioni et al.23 demonstrated that changes in IAF induced by tACS led to alterations in time perception, as subjects engaged in a time generalization task while exposed to tACS stimuli at IAF + -2Hz. In a study by Ross54 participants were instructed to complete a temporal production task of 10 s under four distinct conditions, including the presentation of a visual flicker stimulus synchronized with each participant’s respective IAF. This study revealed that perceived time was extended under conditions conducive to heightened synchronization. Hashimoto and Yotsumoto55 conducted an EEG-based investigation, showing that temporal reproduction was lengthened when the amplitude of entrained alpha oscillations was increased.

Consequently, it seems evident that alpha oscillations are associated with temporal perception, encompassing both their frequency and amplitude. However, it is worth noting that the studies described above predominantly employed visual stimuli and button press responses. In other words, while it is certain that alpha oscillations play a pivotal role in visuo-temporal processing, it remains uncertain whether this internal clock mechanism is shared across different sensory modalities and tasks.

In summary, SMT, heart rate, and IAF are all linked to timing mechanisms, albeit in distinct ways. SMT, being grounded in motor actions, is more closely associated with the fundamental internal clock system, which prominently involves the basal ganglia. Although heart rate is connected to the activity of the insula cortex and prefrontal cortex, its direct relationship with temporal perception remains unclear. While IAF is recognized for its role in temporal processing and duration estimation, most studies have been confined to the realm of visual perception. Consequently, despite the interconnectedness of SMT, HR, and IAF with internal clocks, identifying a direct correlation among them has proven challenging. Our study did not reveal evidence of a single master clock or direct relationships among these clocks. Nevertheless, the degree of centralization or distribution of internal clock mechanisms, as well as the specificity of each clock to sensory modalities and tasks, continue to be topics of active debate. Our study adds to this ongoing discussion by measuring SMT, heart rate, and IAF simultaneously within the same experimental context for the first time.

This study has several limitations. Firstly, it was conducted with a specific group of healthy university students aged 18–21. Therefore, it is uncertain whether the findings can be generalized to other demographic groups, such as older adults or individuals with cardiac conditions. Notably, previous research has indicated that SMT, heart rate, and IAF tend to decrease with age 13,56. Thus, the impact of aging on the correlations among these variables merits further investigation in future studies. Second, while we assumed contributions from multiple brain regions, such as the frontal areas and basal ganglia, we did not directly measure localized neural activities. Further studies are needed to examine the interplay between spontaneous motor tempo, heart rate, and oscillatory neural activities in the context of time perception.