Unlike the traditional view of a clock, some researchers believe that there might be no clock at all. Such a ‘no-clock’ model is known as a state-dependent timing system or intrinsic model (Ivry & Schlerf, 2008). The ‘state’ here describes the specific circumstances generated by a neural network in response to external changes. Timing is seen as an implicit function of each neural network that is activated for a given sensory modality and is sensitive to pre- and post-interval changes. It is postulated that activity-elicited changes in neural networks directly reflect the inherent temporal structures and therefore serve as references for timing in sub-second intervals (e.g., Karmarkar & Buonomano, 2007). The process is also referred to as “a temporal-to-spatial transformation” (Karmarkar & Buonomano, 2007, p. 3), or the “intrinsic model”, as researchers hypothesize that timing is an integral function of neural activity (Ivry & Schlerf, 2008).

The model essentially suggests that timing as a function is distributed to a variety of neural structures in which oscillatory patterns stay consistent, known as the recurrent neural network (Buonomano & Laje, 2011). Ramping, or climbing activities in neural oscillations ranging from primarily low frequency gamma band to higher frequency such as beta and alpha band (e.g., Wittmann, 2013) have been revealed as the physiological basis for the model, in addition to neural spikes across a wide range of brain regions such as the striatum (Gu et al., 2015). The time stamps, or accumulated states, are hypothesized to be expressed on both micro (individual neurons) as well as macro (populatory neuron excitation/inhibition) levels (Buonomano & Laje, 2011).

The intrinsic model proposes the possibility that timing is an inherent function of multiple dynamic neural networks. The flexibility allows the network to take into account calibrations towards previous durations and to judge the duration of the current event on this basis. Furthermore, by hypothesizing the implicity of timing, there is no need for external triggers even when an event is absent. However, the state-dependent network also has its shortcomings. Studies suggested that the model is only applicable to the subsecond range. That is to say, the cumulative effects of previous events, either enhancing or reducing one’s temporal sensitivity, diminished within up to 300 milliseconds (Buonomano et al., 2009). On the other hand, it does not offer a clear explanation of cross-modal temporal information integration. This is where the central clock model provides a useful alternative perspective.

The central timing mechanism, also known as the dedicated clock model (e.g., Allman et al., 2014), stemmed from Treisman’s (1963) work. Decades of research into the human timing mechanism were based on this model and have assumed that timing is a specific cognitive module, hypothetically located across the global neural network (e.g., Allman & Meck, 2012).

Where is the ‘clock’ in our brain? Neurological studies supporting the timing mechanism as an independent cognitive module that is dedicated solely to this function, however, do not necessarily assume one single structure in the brain for it. Research rather supports the roles of a wide range of brain regions working collaboratively in order to process time (e.g., Buhusi & Meck, 2005). The cerebellum, for example, is involved in short duration judgments, arguably from a few hundred milliseconds to 30 seconds (Allman & Meck, 2012). Disruptions to other cortical and subcortical structures including the basal ganglia can lead to timing deficits also in larger time frames. In Schwartze and colleagues’ (2011) study, participants with basal ganglia lesion failed to detect tempo acceleration and deceleration of tones and could not entrain tapping movements with the signals. The evidence implicates a global network where multiple brain regions are involved; impairments at any part of the chain could possibly lead to malfunctions of the timing mechanism. There are two prominent theories with consequences for time processing in music that will be explained below.

Multisensory inputs often interact with one another in our daily life. A vase dropping to the ground is usually followed by a shattering sound. A knock on the door leads to a knocking sound. To a broader extent, signals from vision, hearing, touch, smell and taste constitute the intangible framework of timing references together. Hence it is critical to understand the specificity of each sensory modality and their joint effects in temporal perception.

The dominant role of audition in temporal processing has been evidenced by a series of studies (e.g., Boltz, 2017; Chen et al., 2018; Repp & Penel, 2002). A number of studies supported higher precision in temporal discrimination in audition compared to vision (e.g., Large, 2008; Phillips & Hall, 2002). Furthermore, auditory temporal processing is capable of interfering with visual timing. In this case, participants’ performances in identifying the correct rhythmic visual patterns were most heavily compromised when the task was accompanied by a new string of isochronous sounds rather than visual display (Guttman et al., 2005). One may assume that temporal information derived from auditory events weighs more than that of visual inputs. The auditory dominance view is, however, not without dispute. van Wassenhove and colleagues (2008) found that incongruent visual displays could distort temporal perception of auditory information in both directions. A recent finding, in addition, suggests that temporal perception was biased towards the visually perceived tempo of natural human movements rather than that of the drumbeats when the two sensory modalities were incongruent (Wang et al., 2019).

Research showed that auditory stimuli can effectively distort visual perception (e.g., Burr et al., 2013). The auditory driving effect emphasizes the perceived coupling of fluttering sounds to visual flicker rates, if the temporal gap between the flutter and the flicker does not exceed a certain range (Shipley, 1964). In other words, perceptual integration is accomplished by averaging auditory and visual input frequencies while endowing more weights on the former. A robust auditory driving effect could be observed when the sounds were presented as a brief distractor (Burr et al., 2013). Furthermore, Chen and colleagues’ (2018) study suggested that, in addition to traditional regular flutters, irregular auditory inputs accompanying the visual flickers could also lead to distortions in perceiving the latter. Similar observations of the audiovisual bias were reported as fission and fusion illusions (Shams et al., 2002). In this case, the former specifies two visual events perceived as one when presented simultaneously with a beep, while in the latter, one flash is perceived as two when accompanied by two beeps.

Therefore, it is inevitable to take into account the arguably dominant position of the auditory modality when exploring the role of music in temporal processing. It should be noted that music encompasses not only complex acoustic signals, but a rich source of emotions that alter subjective time. Films are an example of how music shapes experiences of time. In a study investigating slow motion film scenes as compared to the same scenes played back in real time, participants were significantly influenced in their temporal judgments of the scenes’ duration when music was present (Wöllner et al., 2018). While slow motion scenes led to an underestimation of time, the same scenes in real time seemed to last relatively longer, and music yielded more accurate time estimations. Furthermore, music led to higher physiological arousal and larger pupil diameters in observers, suggesting that music modulates emotional responses and experiences of time in audiovisual scenes.

Central to the SET is the memory stage, in which working memory is retained, and the judgment stage, in which the current count of temporal units is compared to references retrieved from long-term memory (Gibbon et al., 1984; van Rijn et al., 2014). Individual differences in short-term memory capacity and discrepancies in timing performances bring attention to the role of working memory in temporal processing (e.g., Broadway & Engle, 2011). More specifically, higher working memory capacities imply higher potential to hold more time units at the second and third stage of timing, thus leading to more precision (Teki & Griffiths, 2014).

Working memory is positively related to other executive functions such as selective and divided attention (Colflesh & Conway, 2007), for both auditory and visual modalities (Wöllner & Halpern, 2016). Both shift in weights in various timing scenarios. This is particularly relevant for understanding the different mechanisms behind prospective and retrospective timing, as mentioned before (Block & Zakay, 1997). In the oscillator model (DAT), attentional pulses are emitted in order to track external beats. These pulses are recorded and transferred to working memory before entering the stage of comparison with a reference duration in long-term memory (Block & Zakay, 1997; Gibbon et al., 1984). Attention diverted from the timing task results in fewer temporal units taken into the count and consequently underestimations of time, while attention directed to timing led to overestimations regardless of test durations (Polti et al., 2018). Despite a lack of evidence, we hypothesize a similar result with music listening. When instructed to time a piece of music before it commences, a listener processes the passage of time differently than when asked to estimate the time elapsed at the end of the excerpt.

The interpretation of the roles of WM and attention also depends on the theories. DAT, compared to SET, highlights the role of attention rather than working memory (e.g., Jones, 2010; Jones & Boltz, 1989). It postulates that attention, when quantified as regular emitted pulses, could synchronize with external periodicity and therefore serve as a reference for time. The periodicities of external events, that is regular or irregular patterns, do affect the strength of their synchronisation with attentional pulses. The more predictable an exogenous pattern is, the better the effect, known widely as the temporal entrainment effect (Barnes & Jones, 2000; Schroeder & Lakatos, 2009), This has been evidenced by a number of visual (Cravo et al., 2013), auditory (Barnes & Jones, 2000; Jones, 2010), and movement (Burger et al., 2018) studies. Jones (1981, 1990) proposed that the characteristics of the information, in this case musical expressions, could distort the perception of time. Empirical studies supporting her claims found that, for instance, music was perceived to be slower when there were more pitch variations and inconsistent metrical accents (Boltz, 1998). We may predict that music genres with more predictable rhythms such as pop and rock, compared to those with less predictability such as Jazz, are associated with higher duration sensitivity and better timing accuracy.

“Time flies when you are having fun”. Understanding the nature of emotions in time perception is important to comprehend how music distorts subjective time, as it essentially conveys a wide spectrum of emotions. The relatively small number of studies that have directly looked into the effects of musical emotions on subjective time show that information of strongly emotional contents were more engaging and were subsequently better processed and stored in WM, leading to time overestimation (for a review, see Schäfer et al., 2013). Music as a powerful tool to induce emotions was found to induce a sense of timelessness (duration overestimation) as well as faster passage of time when an individual is completely submerged in the experience (Herbert, 2012). Apart from the aesthetic pleasure, other types and intensity of emotions may also have an impact on how music could distort the perception of time. The reasons may lie in the psycho-physiological arousal levels. Higher arousal level is believed to cause time overestimation (e.g., Droit-Volet et al., 2013). A group of participants, for instance, were presented with emotional film excerpts to induce corresponding emotions in them (Droit-Volet et al., 2011). Results indicate that, compared to baseline temporal judgments, participants tended to overestimate the durations after watching scary films. There are nevertheless findings implying the opposite, that is, higher emotional arousal leads to duration underestimation especially from a retrospective point of view (Herbert, 2012).

Another line of studies investigates the impact of emotional valences on temporal processing. Positive emotions, substantiated by happy music, led to duration underestimation, while negative emotions in sad music to duration overestimation with retrospective paradigms (Bisson et al., 2008). It was speculated that the positive emotions gave rise to less contextual changes than did the negative, therefore registering fewer events in the memory. Some evidence, on the contrary, implies that valence does not matter. Further investigations showed that highly arousing emotional pictures accelerated the internal clock speed and caused a leftward shift in the reaction time compared with pictures of low emotional arousal, regardless of its valence (Droit-Volet & Berthon, 2017).

The seemingly puzzling observations may be explained by the mechanism by which emotions take effect on time perception. One approach is rooted in the emission rates of attentional pulses, which can be moderated by the affective states, especially the arousal level. According to the pacemaker-counter model (Treisman, 1963), more attentional pulses are emitted when the arousal level is high, and subsequently be recorded as the sum of clock ticks, that is, the perceived duration. Attention could either facilitate or hinder the interaction between emotions and temporal processing. More specifically, when attention is allocated to sustaining the temporal units, the effect would lead to duration overestimation. In contrast, when attention is shifted from temporal information to the emotionally charged event, fewer ticks are accumulated, resulting in duration underestimation.

Time-dependent neural oscillations are specific to sensory modalities. Studies have revealed that neuron excitation and inhibition could be elicited according to a specific type of sensory input, such as sound (Schnupp et al., 2006) and visual flicker (Burr et al., 2007). Researchers found that the time-dependent decodability of visual objects with MEG in a window of 1000ms varied significantly, suggesting that time might be an inherent feature in the local visual network (Carlson et al., 2013). Furthermore, transcranial magnetic stimulation studies revealed that auditory timing could be dissociated with that in other sensory modalities (Bueti et al., 2008), as participants performed worse in duration discrimination task (pure tones, 10 to 40ms) when receiving disruptions in the auditory cortex. We might as well propose that, when listening to complex auditory signals such as music, particular groups of neurons in the human auditory cortex generate time-dependent responses, which simultaneously serve as time codes. However, relatively few studies with humans have directly confirmed the time-dependent variability of the local auditory network (Toiviainen et al., 2019).

The disassociation in timing abilities among different sensory modalities also showed that time is processed as a local flow of information. Early findings entail significantly higher timing precision with hearing than with vision (e.g., Penney et al., 2000), indicating a superiority of audition over vision in providing temporal cues. Timing is a highly selective, localized process even within one modality. Burr and colleagues (2007) successfully modulated the perceived durations of the target visual stimuli by manipulating the apparent rate of flickers in a confined retinal region. Their finding is among one of the first to empirically support (a) the spatial-temporal connection in neural representations, and (b) the modality specificity in temporal processing, particularly the superiority of audition (e.g., Repp & Penel, 2002). In Lustig and Meck’s (2011) study, the modality effect was stronger for participants at both ends of the age spectrum. One potential cause was that older adults were more susceptible to varying allocation of attention under different experimental conditions, whereas children might be influenced by developing sensory functions. That is not to say that SDN is a ‘one modality, one clock’ system, but rather a large network that also covers the interactions between multiple networks.

Taken together, from an intrinsic model’s perspective, time is a consequence of cumulative states in a recurrent neural network that represent the amount of changes induced by external stimuli. In this sense, when listening to a piece of music repetitively, the perceived duration of both music and video (as a further stimulus) will be altered if presented again later on.

DAT is endowed with a particular emphasis on attention, given that the count of temporal units depends on how well attentional pulses synchronize with the external event, also known as the temporal entrainment effect. The term specifies the coupling of the tempo of extrinsic temporal cues and that of pacemaker pulses (Jones, 2010). The emphasis on external entrainment like music began in the early days of the formulation of the clock model (Barry, 1990; Pöppel, 1989). Neurobiological evidence suggests that the just noticeable differences for auditory gaps can be modulated when neural activities were entrained with specific frequency bands and amplitudes (Henry et al., 2014). Regarding music, the synchronization between neural oscillations and musical beats was substantiated as the steady-state event potential (SS-EP) evoked by periodicity in musical beats (Nozaradan, 2014).

Behavioural evidence provided similar findings. Fast tempo was found to lead to overestimation, or “time dilation”, and slow tempo to underestimation, or “time contraction” in both auditory (Wang & Shi, 2019) and visual perception (Ortega & López, 2008). In addition, behavioural entrainment to external beats were found across age ranges and stimulus types, including auditory sequences and music excerpts (for a review, see Repp & Su, 2013). The experimental paradigms usually provide participants with a rhythmic beat that ceases (or not) after a short period of entrainment and require them to continue tapping or moving along with the beats. Boasson and Granot (2012) adopted a paradigm of tapping to pitch rises and drops in multiple melodic sequences, in order to examine the entrainment effect. In their study, however, musicians and non-musicians uniformly exhibited faster-paced tapping behavior with rising pitch. This is consistent with other findings which revealed no difference in predictive timing between musically trained and untrained groups (e.g., Repp, 2010), whereas other studies indicated that musicians (percussionists) exhibited better entrainment performance when exposed to intense beat production activities (Cicchini et al., 2012). These studies suggest that individuals actively entrain with external rhythms and perceive past durations accordingly, and may provide evidence of the wide applicability of DAT.

Building upon simple click paradigms as previously discussed (Treisman et al., 1990), research in recent years used naturalistic stimuli, since DAT is most applicable in music and speech. Periodic tone entrainment studies yielded new results: Wearden et al. (2017) found the residual effect of the classic click train paradigm, that is, the higher the preceding click frequency, the longer the following duration would be perceived. They have also observed similar effects with irregular tones as well as white noise. This study revealed multiple approaches to activate and to speed up the internal clock. Periodic and aperiodic clicks, as well as rhythmic visual flickers and even white noise influenced results. In addition, the entrainment effect was also verified to transcend as long as 8s after hearing high-frequency clicks, indicating that the emission of attentional pulses has a latency between activation and cessation.

More complex stimuli such as music are processed similarly. Fast music compared to slow one was perceived to be longer due to the accumulation of more temporal units. A study adopted Mozart’s Sonata for two pianos (K.448), where participants tended to overestimate the duration when the excerpt was at the “fast” (120BPM) end of the spectrum (Wang & Shi, 2019). The effect, nevertheless, is subject to the allocation of attention. Keller and Burnham (2005) emphasized the flexibility of attention when listening to musical meter, which could be composed of multiple metrical layers. Therefore, tracking high and low metrical structures is expected to have its corresponding effects on psychological time (cf. Hammerschmidt & Wöllner, 2020), as the former should hypothetically lead to fewer mental counts and thus time compression. Neurological evidence also indicated that focusing on different temporal structures led to alignments in steady state event potential (SS-EP) frequencies, deciphered from EEG recordings (Nozaradan et al., 2012). In this case, neural entrainment reflects that attending to local features in complex auditory signals could form mental representations of time by modulating the original neural oscillations.

When more attention is allocated to the temporal features of music, Cocenas-Silva et al. (2011) observed a time dilation effect. When participants were asked to group excerpts of various arousal levels based on their estimated lengths, those which were highly arousing tended to be overestimated. The finding is consistent with Droit-Volet et al.’s (2013) observation that faster music, which was thought to be more arousing, was judged to be longer than the slow, less arousing ones. We might reason that, when individuals attend to temporal features of the auditory signals, the temporal entrainment effect is stronger compared to situations when they attend to other features such as key chords and pleasantness.

The following examines the evidence for multiple sensory modalities that either support or disagree with SET. To establish a solid ground for SET, researchers tried to find evidence for Weber’s fraction, or a constant variance to subjective timing, across different sensory modalities, durations, populations, and other conditions. Wearden and Jones (2007) probed the scalar property of subjective timing using two variations of the duration comparison task with auditory tones ranging from 600ms to 10s. They found a linear increase in subjective timing that conforms to Weber’s law. This effect is consistent also in the visual domain. In a duration discrimination study, Grondin (2001) found that participants exhibited similar sensitivity towards intervals marked by visual flickers between 600 to 900 ms, in accordance with Weber’s law. However, the ratio changed when the inter-stimulus interval went beyond 900ms. The violation of Weber’s law might be due to potentially explicit counting.

Similarly, mixed findings have been reported in multi-modalities studies. Hypothetically, if the scalar property holds across modalities, one should expect a consistent linear increase in different modalities. This was indeed the case when participants performed predictive saccades, or eye-movement timing, when intervals from 500 to 1000ms were presented either as visual flashes or auditory tone flutters (Joiner et al., 2007). However, comparing Weber’s ratios between the two modalities revealed that auditory timing had greater variability than visual timing, as shown in participants’ reactive eye movements when tracking the periodic cues. Hence, one might deduct that the scalar property holds but is also subject to stimulus modality. Block and Gruber (2014) argued that the obstacles of finding a cross-modal transfer effect was restricted to below the 3 to 5s window, beyond which the automatic processing should diminish due to the limited capacity of working memory.

On the other hand, evidence against the scalar property has been presented in auditory studies. Grondin (2012) adopted three approaches to measure Weber’s ratio: duration discrimination, reproduction and categorization tasks on a spectrum from 1 to 1.9 seconds using pure tones. In all three tasks, Weber’s ratio appeared to be higher when the intervals were longer regardless of the number of interval repetitions, in this case either 1, 3, or 5 times. These results indicate the inconsistency in Weber’s ratio or temporal sensitivity despite different emphases of each paradigm on the timing process. Grondin (2010a) pointed out that the failure of conforming to the pacemaker-counter model, which SET is built upon, was because this model no longer applied to this duration range (see Figure 1). More specifically, a cut-off point at 1.2 to 1.3s was observed. This aligns with observations from other studies (for a review, see Matthews & Meck, 2014). The question is, how is time processed beyond that point? Some researchers proposed that a learning effect might have altered the variance, as the brain was influenced by multiple exposures to the same interval (Matthews & Grondin, 2012). Findings across timing tasks and sensory modalities, nevertheless, support the presence of a unitary clock system.

Despite the controversial evidence, reports investigating timing precision on multiple sensory modalities align with what the striatal beat frequency theory proposed: a familiarity effect that is reflected by enhanced synaptic communication between neurons. This might lead to higher processing efficiency and smaller variability compared to unfamiliar intervals. Grondin’s (2012) experiments revealed that participants performed better in 3- and 5-interval discrimination than when only one interval was presented. Frequent exposure to timing tasks, as a part of music training, may also implicate the benefits of enhanced neural connection. In Rammsayer and Altenmüller’s (2006) study, musicians outperformed non-musicians in a perceptual timing task in terms of showing less variance and thus higher temporal sensitivity for instance in duration discrimination tasks. Musicians, however, did not exhibit significant superiority in a temporal generalization task, where participants compared the duration of an excerpt to the reference at the beginning, hypothetically stored in one’s working memory. The authors believed that this was due to the fact that the intervals exceeded working memory capacities. This explanation is equally applicable to Grondin and Killeen’s (2009) results, where participants in a reproduction-by-tapping task performed significantly better if they adopted counting or singing, compared to doing nothing. Thus it might be concluded that the SET indeed predicts the timing performance only within short intervals of no more than 2s (for a review, see Ivry & Schlerf, 2008). Nevertheless, it is equally important to understand timing within a few notes as well as in larger musical structures such as phrases.