Time will tell
Neurocognitive perspectives on Sensorimotor
Synchronization
Literature Thesis by
Paul Mertens
pecmertens@gmail.com
Brain & Cognitive Sciences University of Amsterdam
2010–2011
First Supervisor: Nima Darabi, MSc at Q2S Centre of Excellence, NTNU, Trondheim Second Supervisor/UvA Representative: Mike X. Cohen, PhD
Contents
1 Introduction 1
1.1 General concepts and paradigms in studies of rhythmic reference behavior 3 2 Behavioral theories in the light of neurocognitive data 7 2.1 The negative mean asynchrony and the Chafe effect . . . 7 2.2 Error correction . . . 14 2.3 The ghost of periods past . . . 22
3 Conclusion 26
1
Introduction
Humans wilfully perform interactive rhythmic behavior with a level of complexity which is seen in no other species of animal. This is most apparent in music, both in primitive and modern societies, where rhythm often is a central, principal or virtually the only component. Many observations indicate that a wide variety of bodily and mental faculties are involved in enjoying the production and consumption of music; successful production of music requires precise, physical control over one’s body and musical instrument, as well as the mental abilities involved in judging (one’s own) musical performance online using tactile, proprioceptive and auditory feedback. Listening to music can be done while sitting still (such as in a concert hall), but music with a strong rhythmic component often compels people to dance, tap or clap to the beat. Much dance music even employs a drum beat of low tonal frequency at high volume, which can not only be heard, but can clearly be felt throughout the body as well. By just watching a dancer or other visualisation of music, it is often possible to infer, to some extent, the kind of music that is being referred to.
Long standing personal interests in rhythmic music and neurocognition motivated me to ask how we are able to successfully engage in rhythmic interactions that are so important in music. While the scientific interest in this topic is limited, behavioral studies of rhythmic ability date back to the late 19th century (Bolton, 1894) and have expanded in recent decades, producing detailed and complex predictive models for a variety of rhythmic tasks. In addition, studies of neural correlates of rhythmic experience and behavior have started to appear in recent years following the increased availability and sophistication of imaging technologies for use in humans.
The field of behavioral studies is comparatively more mature than the neurocog-nitive approach, with more experiments taking place using standardized paradigms and thoroughly formalized theories to guide discussions. However, existing behavioral theories remain relatively uninformed of recent advances in neurocognition. This is apparent in
an influential reference model for human responses to metronome tempo changes, which names ’some time-consuming cognitive decision making process’ as a possible source of a systematic timing error (the negative mean asynchrony or ’NMA’), whithout providing any further allusion to the nature of such a process (Mates, 1994a,b). An extensive sum-mary of existing theories to explain the NMA is given by Repp (2005), but he does not attempt any integration of ideas put forward in competing theories, of which few hold any promise of being compatible with a neurocognitive perspective. An additional limi-tation of the behavioral approach is that its most powerful models apply only to highly simplified forms of rhythmic behavior, and often fail to account for effects seen in tasks that more closely mimic musical performance.
Currently, more studies are appearing which attempt to neurocognitively frame results from behavioral experiments and to define realistic mechanisms underlying rhyth-mic behavior. However, up until now no attempt has been made to determine to what extent existing behavioral theories or models can be consolidated with these neurocogni-tive insights, or what the source of any incompatibilities might be. This seems necessary in order to let the different approaches benefit from existing knowledge in different fields and to facilitate interdisciplinary discussions.
In order to determine compatibility between existing behavioral and neurocog-nitive ideas, I discuss several popular behavioral models and recent criticisms of them. Attention will be given to the range of behaviors they explain and the most important assumptions they rely on. Behavioral researchers almost without exception suppose the existence of an internal metronome or timekeeper , which determines the timing of rhyth-mic motor output, as well as the existence of two mechanisms for correcting timing errors that work independently (phase correction and period correction respectively). I will dis-cuss possible neurocognitive analogs of the timekeeper and suggested corrective processes, since these corrective processes are a convenient handle for giving a neurocognitive inter-pretation to behavioral results, and could function as an illustration of the usefullness and power of an interdisciplinary approach. I will also review explanations for the negative mean asynchrony type of timing error.
found in the literuature which will recur throughout what follows, and mention several common manipulations of the standard, behavioral paradigm. Finally, I briefly introduce several important behavioral models and interpretations.
1.1
General concepts and paradigms in studies of rhythmic
ref-erence behavior
In behavioral paradigms, the term ’sensorimotor synchronization’ or ’SMS’ is used to describe tasks where motor actions need to be synchronized with a rhythmic stimulus train (Repp, 2005). The simplest SMS paradigm asks subjects to tap in synchrony with an isochronous metronome sequence. In an isochronous sequence the intervals between all stimuli are constant, whereas non–isochronous sequences use (metrically) subdivided stimulus trains like the more complex rhythms typically found in music. The interval between successive metronome stimuli is referred to as the ’interstimulus onset interval’ or ISI , while the intervals between taps is called the ’interresponse interval’ or IRI . Using finger taps is often preferred over hand–clapping or using an actual, musical instrument because taps allow easy coordination at a large range of tempi in all individuals, they provide clear tactile feedback and can easily be recorded by tapping on a computer– interfaced surface. They also allow for additional, computer generated auditory or visual feedback. Because many manipulations of this simple paradigm are possible, researchers can study individual aspects of SMS in detail.
Internal timekeeper The ’internal timekeeper’ is suggested to be an internal metronome, or clock, which times motor commands in SMS tasks. Repp (2005) clearly illustrates that it is a fundamental part of virtually all behavioral theories of SMS. The timekeeper has an interval, or period, which (ideally) corresponds to the stimulus sequence ISI. A motor output command is given after each timekeeper period, while error corrective processes (see below) fine–tune the timing of the motor command and adjust the timekeeper period when tapping appears out of synch with the stimulus sequence.
In behavioral models the existence of the internal timekeeper is not disputed, and many properties are attributed to it in order to explain characteristics of SMS: e.g.
it is a principal source of timing variance (Wing, 1980, Vorberg and Wing, 1996), it ’is’ a resonating sinusoid with a preferred frequency always slightly below the stimulus sequence ISI (Vorberg and Wing, 1996), its period is modulated by the density of sensory input (Wohlschl¨ager and Koch, 2000), etc. However, there are no known attempts to define the mechanistic nature of the timekeeper in any detail, let alone any suggestions on a possible biological substrate. In general, the question of how temporal intervals are or could be represented, is not considered by behavioral researchers, although it is fundamental to understanding SMS.
Inherent tendencies for synchronization Humans often display an unconscious ten-dency to move in synchrony with the rhythm of music. This tenten-dency is also observed in SMS tasks. For instance, Repp (2006) instructed subjects to tap at a constant, comfort-able pace while ignoring a distractor sequence of metronome stimuli. The participants were able to generally do this but tended to remain in phase with the distractor sequence longer than expected by chance when the phase of their own taps and the phase of the distractor sequence converged (Repp, 2006). Similar results have been reported in other experiments (Schmidt and O’Brien, 1997, Richardson et al., 2005). Also, in anti–phase tapping tasks (where taps need to fall precisely in–between successive stimuli), partici-pants often revert to in–phase tapping automatically when faced with a challenging tempo (phase transition) (Volman and Geuze, 2000, Wimmers et al., 1992). The same thing typ-ically happens when people are instructed to tap at any phase other than in–phase or anti–phase (Yamanishi et al., 1980, Mechsner et al., 2001, Semjen and Ivry, 2001) or when they are told to ignore phase shifts occurring in a pacing sequence (Semjen et al., 2000, Repp, 2002b).
These examples indicate that a sequence of rhythmic stimuli is not merely a source of reference information, but that it is itself a driving force behind some of the defining traits of sensorimotor synchronization.
Preferred rates, rate limits and discrimination thresholds It has been observed that preferred rates of self–paced tapping are similar across individuals. Drake et al. (2000) report a preferred IRI of about 500ms in self–paced, isochronous tapping. Fraisse (1982) mentions a similar preferred IRI of 600ms, while Collyer et al. (1997) report two preferred tempi in self–paced tapping; one around 270ms and one around 450ms. Interestingly, these last authors also report a general speeding up of preferred tapping rate both within and between successive trials. The distribution of these preferred tapping rates broadly corresponds to the range of beats–per–minute that is often found in dance music (between 100–133 bpm for IRIs of 600–450ms).
The maximum rate at which a person can accurately tap is determined by limi-tations of the cognitive and motor systems. Finger taps can be executed rhythmically at a maximum rate of once every 150–200ms (Fraisse, 1982, Keele and Hawkins, 1982, Keele et al., 1985). In SMS tasks where taps only need to be executed to each Nth stimulus instead of every individual stimulus (1:N tapping, in stead of 1:1 tapping), a cognitive rate limit is shown to lie at higher frequencies, such that people are able to correctly synchronize with stimulus trains with an interstimulus onset interval of 100–120ms (in the case of 1:2 tapping to stimuli with an ISI of 100ms, the participant ideally taps once every 200ms) (Peters, 1980, 1985).
Variability The variability of IRIs decreases with IRI duration, both in self paced tap-ping and synchronization tasks (Michon, 1967, Wing and Kristofferson, 1973a,b, Semjen et al., 2000). When the IRI decreases towards the upper rate limit, variability stops decreasing and the timing of taps begins to approach chance level. Towards the lower rate limit, taps become purely responsive and lag after the stimulus, essentially turning the synchronization task into a reaction time task. Musically trained participants are reported to achieve a standard deviation of only 2% of the ISI during 1:1 tapping tasks (Pressing and Jolley-Rogers, 1997, Repp, 2002b), whereas for untrained participants this is often around 3–4% (Peters, 1989, Repp, 2000).
In most cases, experiments are conducted with people with some musical experi-ence since this decreases performance variability between task participants; it is normally
assumed that, in simple tasks, subjects with musical experience do not recruit different systems or strategies than subjects without musical experience
The negative mean asynchrony An important anticipatory tendency observed in all SMS tasks where subjects tap to an isochronous sequence, is that subjects tend to tap several (tens of) milliseconds ahead of the corresponding stimuli, without being aware of this. This effect bares the descriptive name ’negative mean asynchrony’ or NMA and has been extensively reviewed by Aschersleben (2002) and Repp (2005). The NMA can be quite large in untrained participants; up to 100ms in extreme cases (Aschersleben and Prinz, 1995, Repp and Penel, 2002). Musically trained participants are known to have a decreased and sometimes even marginalized NMA (Repp, 2004, Repp and Doggett, 2007). Non–musicians were trained by Aschersleben (2003) to eliminate their NMA using feedback on the direction and size of their asynchronies, but they later indicated that they felt they were tapping after the corresponding stimuli instead of feeling exactly in synchrony.
Error correction When a timing difference exists between a tap and a stimulus, a subjective synchronization error can occur that needs to be corrected to maintain or re– establish synchronization1. In metronome tasks, the experimenter might program sudden
tempo changes (change of ISI duration), single phase steps or ’pulse changes’ (change of the length of a single interval in a sequence) or a sequence with continuously modulated ISI. A distinction is often made between two different error correction processes: ’phase correction’ and ’period correction’. Phase correction is thought to compensate for an observed asynchrony by shifting the timing of the next tap(s) in the direction opposite to the asynchrony without changing the period of the internal timekeeper (i.e. if a tap is observed to precede a stimulus by 20ms [negative asynchrony] the next tap will be shifted several milliseconds forward to compensate [positive shift]). Period correction is not based on observed asynchronies, but on an assesment of interval changes; if a difference is established between the last ISI and IRI, the period correction mechanism
1The NMA is experienced as a point of subjective synchrony, and is therefore not considered as an error here.
changes the period of the internal timekeeper by a proportion of this difference.
2
Behavioral theories in the light of neurocognitive
data
2.1
The negative mean asynchrony and the Chafe effect
In tasks where participants have to tap to an isochronous metronome sequence, it has been systematically observed that taps tend to precede the tones by several (tens of) milliseconds (for reviews, see Aschersleben, 2002, Repp, 2005). This precedence of taps over tones was termed the ’negative mean asynchrony’ or ’NMA’, and Repp (2005) reports Miyake (1902) as the original discoverer of the effect. Another, more easily accesible, early publication on the subject is from Woodrow (1932).
The NMA is found in all test subjects that tap isochronous sequences to a metronome. The size of the NMA is found to vary considerably between subjects, ranging from 10ms to approximately 80ms (Fraisse, 1980, Kolers and Brewster, 1985, Aschersleben and Prinz, 1995, Repp, 2000). Subjects do not perceive their NMA, instead it marks the point of subjective synchrony. Aschersleben (2003) trained participants to abolish their NMA by giving them feedback on the size and direction of their asynchronies. After some practice, the subjects were able to tap without an NMA, but they reported that they felt that their taps lagged behind the stimuli.
An important modulation of the NMA is that it is smaller at higher tempi (Mates et al., 1994, Peters, 1989, Repp, 2003). In addition, the effect appears to be attenuated or absent in tapping to music (Thaut et al., 1997, Snyder and Krumhansl, 2001, Toiviainen and Snyder, 2003), as well as in tasks where stimuli or taps are metrically subdivided (Thaut et al., 1997, Wohlschl¨ager and Koch, 2000, Repp, 2002b, 2003). Musically trained participants have systematically shown decreased NMAs in comparison with subjects without musical experience (Mates et al., 1994, Repp and Doggett, 2007) and (Ascher-sleben, 1994, ,as cited by Repp (2005)). Repp (2004) even reports a single occasion of a professional percussionist who does not show any NMA at all.
Explanations on the origin of the NMA are varied, and touch on many key concepts of SMS. In the following paragraphs I will present several explanations of the NMA and continue with a discussion on how the most popular interpretation is informed by physiological and cognitive considerations: the nerve conduction hypothesis by Fraisse (1980), and its extension by Aschersleben (2002).
Explaning the NMA As Repp (2005) notes, no theory on the origin of the NMA is completely comprehensive and it is likely that the NMA has multiple sources.
A first explanation to consider is the perceptual underestimation hypothesis by Wohlschl¨ager and Koch (2000). They asked participants in an isochronous tapping task to subdivide their IRIs by making contact free movements in between their taps, essen-tially leading to metrical subdivision of their taps. This lead to a decrease in NMA, which they thought was similar in origin as the decrease in NMA seen in tasks with rhythmi-cally more complex stimuli or tapping regimes, such as tapping to music (Thaut et al., 1997, Wohlschl¨ager and Koch, 2000, Repp, 2002b, 2003). Wohlschl¨ager and Koch (2000) suggested that subdivided intervals are experienced as longer than empty intervals. The underestimation of the length of empty intervals would lead people to tap ahead of the next tone. This hypothesis also explains the decrease of the NMA at higher tempi, since the absolute underestimation of an empty interval would probably scale with the length of the interval.
An important omission from the perceptual underestimation hypothesis however, is that it does not explain why the NMA is not noticed as an asynchrony but in stead is perceived as a point of subjective synchrony. Other effects which cannot be explained are changes in the NMA following modulations of sensory feedback, such as an observed increase of the NMA with longer tactile feedback delays (during foot–tapping) (Ascher-sleben and Prinz, 1995, Billon et al., 1996), a profound increase in NMA following local anaesthesia of the tapping finger (Aschersleben et al., 2001) and the decrease or even dis-appearance of the NMA when the pacing sequence is presented as tactile stimuli (Kolers and Brewster, 1985, M¨uller et al., 2008).
The nerve conduction hypothesis Fraisse (1980) proposed that during SMS, sub-jects attempt to synchronize the representations of taps and tones in the central nervous system, and that the actual moment at which the tap is perceived, is established by tactile feedback which the brain receives from the finger as it hits the tapping surface. Because this tactile information has to travel through the peripheral nervous system, it arrives in the brain after a delay of several milliseconds. The delay of auditory information would be shorter given the vicinity of the ear to the brain. In order to establish synchronized central representations despite differences in transduction delays, taps would need to pre-cede tones. Fraisse (1980) called this the ’nerve conduction hypothesis’ or ’NHC’, the original idea of which he attributes to Paillard (1946).
The NHC is able to account for the increased NMA when taps are executed with the foot (Aschersleben and Prinz, 1995, Billon et al., 1996), and also the absence of the NMA when the pacing stimuli are presented as tactile stimuli (Kolers and Brewster, 1985, M¨uller et al., 2008). However, the decrease in NMA at higher tempi is not readily explained, and neither are the substantial individual differences in the size of the NMA or the decrease of the NMA when tapping to music or metrically subdivided sequences as mentioned earlier.
An important reason for the appeal of the NHC, despite the fact that its explana-tory power seems rather limited, is that it distinguishes between internally and externally available events. It can easily be appreciated that if centrally available tactile information on the execution of the taps is delayed, the point of subjective synchrony will move to a later point in time relative to the execution of the tap.
Because the NHC depends on differences in sensory transduction times between auditory and tactile stimuli, and also in the light of what follows, it is informative to es-timate the time difference of the central availability of auditory and tactile information. The size of the delay of tactile information can be established by considering findings of conduction velocities of the relevant nerves. When considering a mean bidirectional con-duction velocity of around 55m/s (Norris et al., 1953, Trojaborg, 1964), tactile feedback from the fingers would arrive in the spinal chord with a delay of approximately 14ms for a person with an arm length of 75cm. Transduction delays of mechanoreceptors can
be omitted, since this delay was reported to be only 0.2ms for the pacinian corpuscle (Kruger and Michel, 1962). Transduction delays of auditory information is quite short; click–evoked EEG signals with delays of less than 8ms have been ascribed to the cochlear nucleus and auditory brainstem nuclei (Lieberman et al., 1973, Picton et al., 1974, Pratt and Sohmer, 1976). Differences in nerve transduction times for auditory and tactile stim-uli thus appear to be around 8ms, which is significantly smaller than the size of the NMA.
An omission that the NHC makes, and which could explain several effects the NHC can not, is the inclusion of central processing delays of stimuli and possible manipu-lations thereof. Aschersleben (2002) therefor suggested an extension of the NHC, based on different handling of information from different sensory modalities by the central nervous system.
The sensory accumulator model The ’sensory accumulator model’ or ’SAM’ as-sumes a cognitive threshold for achieving subjective synchrony, which is crossed after 1) the peripheral delays of relevant sensory stimuli have been traversed and 2) after these stimuli have been processed by the CNS. By doing so, it accounts for the same observations as the nerve conduction hypothesis, while leaving room for the inclusion of higher cognitive mechanisms. The central hypothesis of the SAM, is that the accumu-lator function for the auditory modality is steeper than that of the tactile modality. In addition to shorter transduction delays for auditory information, this would constitute quicker central processing of auditory information, and hence it would be required for taps to precede tones if they need to be registered simultaneously. The magnitude of the sensory input influences the steepness of the accumulator function; Aschersleben (2002) assumes that sensory signals with a lower amplitude take longer to accumulate towards the synchronization threshold, and so explains the larger NMA when tapping with local anaesthesia (Aschersleben et al., 2001).
The SAM explains the decrease in NMA at shorter ISIs by an observation that more force is applied to the finger at higher tempi, leading to an increased amplitude of the tactile feedback. Documentation on this experiment was not accessible, although it
is cited by Aschersleben (2004). Manipulations of the auditory modality also have pre-dictable effects; by adding additional, direct auditory feedback to every tap, the NMA is found to be reduced (Aschersleben and Prinz, 1995, 1997). Conversely, when this auditory feedback is artificially delayed, the NMA increases in size (Aschersleben and Prinz, 1997, Mates and Aschersleben, 2002). These findings indicate that several sources of sensory information on an event are combined in establishing synchrony. Large individual differ-ences could be explained by assuming different people have varying accumulator functions for different sensory modalities. Additionally, musical experience might increase the sen-sitivity of the accumulator function for auditory feedback, so explaining the decrease of the NMA in musically trained participants.
A challenge for the SAM is the observation that completely deaffarented individ-uals, who receive no tactile feedback from their taps, nevertheless are able to synchronize their taps with a microphone, even when they are restricted from seeing or hearing their own taps (Aschersleben, 2002, Billon et al., 1996). This is a problem because the SAM was formulated to require at least some form of sensory feedback to establish synchrony (Aschersleben, 2002). The suggested solution by Aschersleben (2002) is that deafferented individuals synchronize simulated consequences of actions with the metronome stimuli, instead of feedback on the actual occurrence of their taps. The relatively large NMA of deafferented individuals could be explained by assuming these simulated action conse-quences do not drive the accumulator function very strongly, and thus need to be produced well in advance of the stimuli. Invoking the influence of simulated action consequences however, opens the door to a different interpretation of the effect of musical training, which might increase one’s sensitivity to simulated actions, because these simulations no doubt become more accurate with practice.
Another problem for the SAM is how to explain the decrease of the NMA in musical contexts or when tapping to rhythmic complex stimulus train (Thaut et al., 1997, Wohlschl¨ager and Koch, 2000, Snyder and Krumhansl, 2001, Repp, 2002b). It is unclear how music or metrical subdivision would influence the accumulator functions. One might suggest that the musical context somehow decreases the sensitivity or slope of the auditory accumulator function. If this is a general response of accumulator functions
to increased sensory load however, one would expect that the tactile accumulator would become less steep when tapping at higher tempi, but the opposite seems more likely in that case.
These last examples essentially indicate a fundamental weakness of the SAM, namely that it appears a bit as a deus ex machina; it proposes a general concept of establishing synchrony using a sensory threshold, while the accumulator functions can be hypothetically modulated in any conceiveable way to accomodate effects of external influences, as well as internal cognitive states. If it would be possible to derive the shape of the sensory accumulator functions, this might not have been problematic. However, since the accumulator functions comprise influences from different sensory modalities combined, and since there might be any number of nonlinearities in the contribution of each sensory modality, any estimation of the shape of an accumulator function in one paradigm might not have much validity in a task which uses other stimuli or a different tapping regime. Personal differences, musical training, attention and metrical subdivision of the rhythm might all also have a different influence on the contribution of the different sensory modalities to each accumulator function, leading to a further proliferation of nonlinearities.
Alternative accounts What is particularly interesting are findings that areas which plan and formulate specific movements (rotation, translation, deformation, expansion etc.) become active following specific auditory and visual abstract representations of conceptually similar movements (Schubotz and Von Cramon, 2002, 2004, Wolfensteller et al., 2007). These are also areas implicated in the perception and production of more complex rhythms (Grahn and Brett, 2007, Chen et al., 2007, Zatorre et al., 2007). In cases where there is strong temporal coupling between structures coding sensory input and structures coding motor output, the feedback of motor acts becomes relatively less important in evaluating the occurrence of synchrony. In other words, in cases of tapping to rhythmic music or other complex rhythms, the ’reference’ character of synchronization behavior becomes less clear and instead the behavior becomes stimulus driven. Formally, simple isochronous sequences and music might not contain different amounts of
informa-tion to aid response timing, but the more complex rhythms are able, through different central processing, to drive responses more directly than simple isochronous sequences.
From the point of view of the SAM, one might ask what happens to the feeling of subjective synchrony if the behavior becomes more stimulus driven. Since subjective synchrony is still experienced similarly, either the accumulator function for registration of the taps is steeper or the accumulator function for registration of the stimuli is less steep. One possibility is that the constant auditory load somewhat desensitizes the accumulator function for stimuli registration2.
Another possibility is that the increased input to premotor areas from sensory systems might increase the valence of motor efference copies originating there. Efference copies provide the rest of the brain with information on to–be executed movements, and have been found to originate in the dorsolateral prefrontal cortex, the premotor areas, the supplementary motor areas and of course the primary motor cortex, among others (Voss et al., 2006, Zatorre et al., 2007). If completely deafferented patients use internal predictions of motor outcomes to synchronize their taps, these internal predictions would rely on efferent copies (Aschersleben, 2002). However, in these cases the efferent copy does not appear to be a very strong signal to drive the accumulator function on its own, given the large NMA seen with such patients. However, the increased activity in pre– motor areas while tapping to music might increase the magnitude of generated efference copies, or sensitize the system which establishes subjective synchrony to their occurrence, and so leading to earlier registration of the tap and a decrease in the NMA.
This is of course highly speculative reasoning which cannot be readily exper-imentally tested. However, because motor efference copies are very important in the precise timing of motion (not necessarily rhythmic motion), I felt it necessary to suggest a role from the viewpoint of the SAM and the viewpoint of the experience of subjective synchrony (Shadmehr et al., 2010).
2Actually, it might be better to say that otherwise empty metronome intervals used in standard paradigms leave the accumulator function hypersensitive, since surely our rhythmic behavior would be adapted to more complex stimuli than simply metronome intervals.
2.2
Error correction
There are many reasons for tapping asynchronies to occur in SMS tasks; natural variations in stimulus processing and response output timing, as well as changes in tempo or phase of the stimulus sequence. In duet tapping tasks, both subjects display natural variations and might use specific strategies to stabilize the tempo (such as leader–follower strategies, mimicking dynamics of ensemble performance where musicians follow the lead of the rhythm section of a band or orchestra).
Error correction is one of the most thoroughly studied concepts in sensory motor synchronization, and recent studies have changed traditional views considerably. Many studies are combinations of behavioral testing and modeling. Models are typically seper-ated into algorithmic models based on information processing and dynamic system mod-els based on system identification. Although my limited experience with mathematics allowed me to understand the algorithmic models conceptually, it did not warrant an in–depth discussion of their mathematical underpinnings. The principal mathematical considerations, which return in most recent studies (such as those by Schulze et al. (2005), Repp and Keller (2008) and Repp and Moseley (2012)), are presented by Hary and Moore (1987), Mates (1994a,b) and Vorberg and Schulze (2002).
I have limited my discussion to the algorithmic models, and mostly to the model by Mates (1994a,b) because this has recently been the most influential. The reason I have omitted a discussion of dynamic systems models, besides the difficulty in analyzing them, is that they have not been very influential; furthermore, Repp (2002a) indicates how the nonlinear nature of error corrective processes supposed by dynamic system theories ((Large and Jones, 1999, Engbert et al., 1997)) can also be modeled algorithmically.
Onward from Mates The model by Mates (1994a,b) is by far the most influential model in the SMS literature. He proposes two independent mechanisms for error cor-rection that operate simultaneously. The first is phase corcor-rection, which responds to asynchronies between the agent’s taps and the metronome stimulus directly, by adjusting the timing of the next tap without influencing the period of the timekeeper. The second, period correction, responds to the observed difference between the IRI of the agent and
the stimulus ISI by changing the period of the internal timekeeper to match.
Mates distinguishes between phase correction and period correction by consid-ering responses of an ’ideal corrector’, and argues that such an ideal corrector would recognize that small asynchronies could arise from jitter in the motor output system, while large asynchronies were more likely the result of a tempo change of the metronome. Asynchronies as a result of motor jitter would only need to be phase–corrected, while asynchronies as a result of changed metronome rate would need to be corrected by adjust-ing the period of the internal timekeeper. Although Mates (1994b) suggests a nonlinear variation of his model to account for responses to very small asynchronies, his suggested phase and period correction mechanisms essentially remain two seperate, linear functions of the observed asynchronies.
Later experiments confirmed the existence of two separate error corrective pro-cesses, but also raised a number of questions about their independence and nonlinearity. Thaut et al. (1998) and Repp (2001) both found that, subjects responded immediately to subliminal tempo changes (below 2% of the ISI) in such a way that the first IRI following the tempo step became equal to the new ISI. But although the ’period’ of the taps was corrected, the initial asynchrony between stimulus and tap, caused by the tempo step, was only corrected very slowly. Thaut et al. (1998) interpreted this as the occurence of rapid, unconscious period correction and a lack of proper phase correction to close the existing phase gap. Repp (2002b) shows that the opposite view is also valid, namely that in response to subliminal tempo steps, a phase correction mechanism properly corrects the initial and all subsequent asynchronies while leaving the period of the timekeeper unchanged. Because the timekeeper period was not corrected, this lead to the second stimulus–response pair following the tempo change again showing an asynchrony the size of the tempo step, which in turn would be interpreted as another phase error since no dis-crepancy between the last ISI and IRI could be observed. Over the course of several taps this asynchrony was eventually completely corrected. In short, subliminal tempo changes might not change the internal timekeeper period but lead to a series of phase corrections. Paradoxically, this eventually leads to adoption of the novel tempo without the period of the internal timekeeper being changed by a proposed period correction mechanism.
When a supraliminal tempo step was presented however (above 2% of the ISI), the timekeeper period appeared to change by at least 1.5 times the observed tempo step, leading to a quick resynchronization. Whether the timekeeper period really changed by a factor > 1.5, or whether a precise recalibration of the timekeeper period (by a factor of 1) was supplemented by additional phase correction to close the remaining phase gap could not be deduced in this experiment (Thaut et al., 1998, Repp, 2001). While subliminal tempo step changes were not corrected efficiently (Thaut et al., 1998, Repp, 2001), subliminal phase shifts of the stimulus train are usually corrected within two taps (Thaut et al., 1998, Repp and Penel, 2002, Madison and Merker, 2004). This is even the case for errors of as little as 4ms, indicating high sensitivity to such errors (Repp, 2000). This supported the existing idea that phase correction was an unconscious process, best fit to deal with small asynchronies, and thus to the interpretation that the rapid adjustment seen in response to supraliminal tempo steps was not due to a supplement of phase correction but indeed due to a transient overcorrection of the internal timekeeper (Mates, 1994a, Thaut et al., 1998).
However, in a number of experiments, Repp (2002a) showed that phase correc-tion was not a purely unconscious process, since responses to supraliminal phase shifts of stimulus trains showed similar rapid adaptation as responses to subliminal phase shifts, without affecting the supposed timekeeper period. It was also found that phase correc-tion responses could not be completely suppressed, and that an involuntary component of phase correction remained present for subliminal as well as supraliminal asynchronies. Finally, it is worth noting two nonlinearities that were observed following supraliminal asynchronies, namely that the involuntary component of phase correction scaled linearly with the size of the asynchrony until the supraliminal threshold, after which it became asymptotic. The voluntary component, recruited after supraliminal perturbations, re-mained equally effective for phase shifts with sizes up to 10–15% of the sequence ISI (50–75ms), while effectiveness decreased slowly for larger perturbations.
These findings indicate a clear distinction between the correction of subliminal and supraliminal errors, but it is also clear that Mates’ (1994a,b) original notions of a purely unconscious phase correction mechanism and a consciously controlled period
correction mechanism become convoluted when we only consider the behavioral measure-ments. The initial overcorrection of the timekeeper (by a factor > 1) observed following supraliminal tempo steps can no longer be attributed to a pure period correction mech-anism if we agree that conscious phase correction takes place in such situations as well (Repp, 2001, 2002a,b).
Changing views on error correction Recently, several studies appeared which have given more insight into the nature of the corrective processes, and which allow us to begin to speculate on realistic neurocognitive mechanisms underlying them.
Repp (2002a) suggested that conscious awareness of a phase shift is the common cause of the nonlinearities observed in both the voluntary and involuntary components of phase correction he observed. In a similar follow up experiment it was then shown that period correction was also depedent on the intention of the subject to correct asynchronies (Repp and Keller, 2004). In contrast to phase correction however, period correction was strongly modulated by awareness of the perturbation and directed attention. This also indicated that conscious control of phase correction is limited to voluntary suppression, lending support to a previous suggestion by Repp (2001) that phase correction is driven more directly by bottom–up stimulus processing, while period correction is under more top–down control. This also makes sense from a musical production point of view, since it would allow natural variability in ensemble performances to be handled unconsciously, while responses to larger sources of variance (such as those arising from intent of the other performers) could be handled more deliberately and so facilitate responsive collaboration and improvisation.
The most recent and important change in our understanding of phase and period correction occurred after Schulze et al. (2005) tested whether Mates’ (1994a,b) model could account for data from subjects who were instructed to tap to a metronome which displayed either a smooth increase or decrease in tempo. Schulze et al. (2005) also tested a version of Mates’ model where he had changed the period correction process in such a way that it responded to asynchronies between taps and stimuli, instead of responding to differences between the last observed IRI and ISI. Surprisingly it was noted that the
asynchrony–based version of the model faired better than the original, both qualitatively and quantitatively, although the quantitative fit of both models left much to be desired. Repp and Keller (2008) agree with Schulze et al. (2005) and proceeded to show that, not only can period correction be modeled more efficiently by assuming it is based on observed asynchronies, but also that phase correction might better be modeled as a simple resetting of the internal timekeeper at the occurrence of every metronome stimulus (Repp and Keller, 2008, Repp and Moseley, 2012). Interestingly, both these changed notions on error correction mirror the original ideas of Hary and Moore (1987), but more importantly they are a conceptual simplification in both cases, since the number of sensory events that each correction process needs to take into account in order to suggest corrections is diminished.
Neurocognitive studies of error correction Although the classic proposition of independent phase and error correction mechanisms seems inaccurate, there are clearly differntiated responses to sub– and supraliminal errors. Making clear inferences about the contributions of different brain areas to SMS is difficult, because most research on hu-man movement timing is not concerned with rhythmic behavior (for several independent reviews, see Buhusi and Meck, 2005, Zatorre et al., 2007, Shadmehr et al., 2010). Also, not all SMS paradigms can be equally easily repeated using neurocognitive measuring tools such as MEG/EEG, fMRI and PET.
These difficulties notwithstanding, the cerebellum is prominent among the few neural structures which have been systematically implicated in having different roles in the correction of subliminal or supraliminal errors. For instance, during 1.7Hz paced tapping Bijsterbosch et al. (2011a) found increased activity (in the form of larger fMRI BOLD response) in the left (contralateral to movement) cerebellar cortex in response to single, supraliminal (90ms) positive and negative sequence phase shifts, while the right cerebellar deep nuclei showed increased activity throughout SMS, which did not change in response to any step changes. There was no difference in either left or right cere-bellum related to subliminal phase perturbations (18ms). In addition, it was found that after suppression of local neural processing by applying transcranial magnetic stimulation
(TMS) to either the left, medial or right cerebellum, only correction of supraliminal er-rors was affected, and most profoundly following stimulation of the left cerebellum which increased overcorrection. This seems to be in accordance with a proposed role for the cerebellum in attenuating reactive motor commands.
Since suppression of cerebellar function increased overcorrection, it would be interesting to study the cerebellar activity in a task with continuously modulated tempo. Since in such tasks no overcorrection is observed, one might expect that the activity of left cerebellar deep nuclei is increased during the entire modulation period. If this would not be the case, one might consider that the corrective process in response to single phase shifts is substantially different from the corrective processes that are active in tasks with continuously modulated tempi.
This is exactly what was found in a comprehensive study by Thaut et al. (2009). Participants tapped at 0.8Hz (ISI = 1250ms) while the sequence tempo was continuously modulated in increments of 3%, 7% or 20% of the baseline tempo. After each modula-tion, the next ISI would be at the baseline tempo again, with the following tap being a modulation of the same size as the first but in the opposite direction, etc. They found increased regional cortical bloodflow (rCBF, identified with PET imaging) bilaterally in the cerebellar deep nuclei in response to all tempo steps, compared to control listening. However, the increase was most pronounced in the left (contralateral to movement) cere-bellar deep nuclei for the 20% modulation. They found a striking resemblence of rCBF response between the bilateral cerebellar deep nuclei and the rCBF response of the right inferior parietal area of the neocortex. Sadly, with the used paradigm it was not possible to say whether activity here was related more to stimulus processing, response timing or both.
Primary sensorimotor areas and the thalamus all displayed an increased rCBF re-sponse in all tapping conditions compared to control listening, but there was no difference in the rCBF response of these areas between different tapping conditions, indicating that activity in these areas is not associated with any form of error correction. In contrast, there were significantly increased rCBF responses in the right, dorsolateral prefrontal area and the right prefrontal Brocca’s analogue in the 20% condition, indicating these
areas’ exclusive involvement in supraliminal error correction. Prefrontal areas had been indicated in error correction in SMS previously, specifically the dorsolateral prefrontal cortex was implicated to be involved in conscious error correction in a similar paradigm (Stephan et al., 2002). Generally, the (dorsolateral) prefrontal cortex is one of the high-est cortical areas associated with aspects of action planning and strategic goal selection (Matsuzaka et al., 2012, Genovesio et al., 2012).
In summary, the mentioned studies indicate specific involvement of the left cere-bellum in the correction of subliminal errors, and a possible substrate in the left cerebellar deep nuclei for a process of adaptive correction as observed by Schulze et al. (2005) and Repp and Keller (2008). Thaut et al. (2009) suggests the existence of three functional networks concerned with motor control, timing control and synchronization strategy re-spectively. Motor control in SMS would be served by sensorimotor areas, the thalamus, the right vermal area and right anterior lobe of the cerebellum. Timing control (as in phase correction) would depend on interactions between left and right posterior lobes of the cerebellum and the right inferior parietal area of the neocortex. Finally, strategy implementation (as in conscious period correction) would rely on interactions between the right (dorso)lateral prefrontal areas of the neocortex and a specific area of the left posterior lobe of the cerebellum.
Other neural structures which show differential involvement in sub– versus supral-iminal error correction are the left prefrontal (Bijsterbosch et al., 2011b) and frontal motor areas (Praamstra et al., 2003) and the basal ganglia (Schwartze et al., 2010), although behavioral results and identified structures are less systematic here, and do not warrant clear correlation with observations from already mentioned behavioral studies. In the case of Bijsterbosch et al. (2011b) it is interesting to note that they no longer found overcor-rection in response to supraliminal phase shifts following suppression by TMS of the left pre–motor area. This effect is exactly opposite to the effect seen after TMS suppression of the left cerebellar deep nuclei. Possibly the cause of overcorrection in response to sudden tempo steps is the result of an inbalance between cerebellar and prefrontal activation, illustrating the suggestion in the previous paragraph. It must be noted however that in the study by Bijsterbosch et al. (2011b) the method of quantifying the effectiveness of
error correction is somewhat obscure, making it very difficult to compare their findings with other studies.
Considerations for behavioral researchers The implications of the necessity of net-work interactions is worth noting with regard to the overcorrection observed in tasks where tempo steps are introduced to isochronous sequences, and the lack thereof in paradigms with continuously modulated sequence ISIs. It is conceivable that a supral-iminal perturbation recruits a conscious error corrective mechanism which depends on an interaction between multiple structures as mentioned above. When this is a single, large perturbation in an otherwise isochronous sequence, the network might lack infor-mation on response strategy because the areas involved in establishing such a response strategy (possibly dorsolateral prefrontal areas) were still inactive at the time of the error. Typical resposnes to supraliminal tempo steps in SMS tasks might therefor con-stitute maladapted reflexive responses, not the output of an optimized error corrective mechanism. This would explain the different shapes of error corrective functions found by Schulze et al. (2005) and Repp and Keller (2008) in tasks with continuous ISI modulation. Because of the involvement of conscious awareness and strategy, correction of supraliminal errors might take a variety of forms which are difficult to put in one cate-gory and even more difficult to sensibly quantify. The possibly high between–task and between–subject variability in underlying mechanisms of supraliminal error correction presents a difficulty for studies trying to systematically characterize these mechanisms within and across individuals. It therefor seems unlikely that neurocognitive studies coudl be used in the future to actually aid parameter setting in lagorithmic models. However, as we have seen above, using functional imaging methods it is possible to appreciate that error correction and even simple response timing depend on interactions between different brain regions, which each have a specific task but simultaneously complement eachother. For instance it seems that period correction relies on activation of at least three seperate brain regions which could all serve a different part of the corrective response; its intention, its formal execution and its timing precission.
presented here warant a seperation between two different error corrective processes; one in response to supraliminal errors and one in response to subliminal errors. However, re-gions involved in subliminal error correction also appear to stay online during correction of supraliminal errors. Realistic models would therefor best include an error corrective process which responds to every asynchrony and an error corrective process which only responds to supraliminal perturbations (unlike in Mates’ (1994a,b) model, where both mechanisms respond to every asynchrony). Like in Mates’ model, the contribution of each mechanism might simply be superimposed. The difficulty will be in establishing the correct nonlinear functions for the correction gains of each process. Based on considera-tions in the previous paragraphs I would further attempt to study the different corrective processes by using continuously modulated sequences if possible, and not single pertur-bations of isochronous sequences.
2.3
The ghost of periods past
As has become clear in the previous sections, the notion of an internal timekeeper or metronome is part of all behavioral theories on sensorimotor synchronization. Although several characteristics are consistently attributed to the timekeeper, there is no discussion in the behavioral literature on its nature; instead its existence is taken as a given. This seems curious to me since the relationship of error corrective processes to the timekeeper is a topic of fervent debate. Here I want to discuss several features commonly attributed to the timekeeper and see if there can be any neurocognitive justification of them. Al-though eliminating the traditional notion of the timekeeper from behavioral models will be difficult, and maybe even unnecessary, a shift in conceptual understanding might lead to integration of currently seperate approaches to SMS and facilitate research on derived concepts such as error correction.
The timekeeper performs temporal pattern recognition and production The internal timekeeper is proposed to be an internal metronome for action. In models of SMS, the principal function of the timekeeper is to represent a temporal interval with a maximum duration in the range of a few seconds, and to do so in such a way that accurate
timing of action is facilitated at specific points along this interval (Michon, 1967, Wing and Kristofferson, 1973a,b, Hary and Moore, 1987, Mates, 1994a,b, Schulze et al., 2005, Repp and Keller, 2008). In all these mentioned modeling studies, the timekeeper is reduced to a single scalar, reference number. The single number which represents the timekeeper, is its reference interval or period. The timekeeper thus encodes, in one way or another, a duration. But the timekeeper does not encode duration alone; it also encodes repetition, or recurrence, of the interval.
A very important question, is whether the timekeeper can indeed be appreci-ated in such a reduced form; as only a reference interval and its recurrence. Does the timekeeper not represent temporally patterned sensory information, placed inside this reference interval? Is, to begin with, the reference interval itself not defined by the oc-curence of sensory events? What is left of the timekeeper if you take away the metronome stimuli, your motor output and ultimately your imagination of a drumbeat or any other sound? It seems very difficult to argue that the timekeeper encodes only a period, with-out the occurrence of events taking place in or at the beginning of the period being in any way involved.
The models mentioned in the first paragraph, all have a dynamically changing timekeeper, the interval of which is redetermined every cycle by feedback on the duration of the external metronome interval, and information on the interval between the subject’s own responses. Although the period of the timekeeper changes dynamically, the possible changes are limited in scope and occurrence. Effectively it is assumed that the interval of the timekeeper represents the duration of a quarter note in 4/4 measure. The external metronome produces a tone at the start of each quarter note, and the subject attempts to mirror that with his/her taps. When an asynchrony is noted between the start of the metronome tone or the finger tap (Michon, 1967, Hary and Moore, 1987, Schulze et al., 2005, Repp and Keller, 2008) or a difference is noted between the interval between taps and the interval between tones (Wing and Kristofferson, 1973a,b, Mates, 1994a,b) then the period of the timekeeper is adjusted accordingly before the start of the next cycle. Before the end of the period or the occurrence of the first asynchrony, nothing happens to the timekeeper interval.
When we can agree however, that the timekeeper is not just a reference interval and its recurrence but represents the temporal patterning of events, there is no need to suppose that the timekeeper should represent only the duration of a quarter note in a 4/4 measure, nor the need for such a rigid correction regime. Instead, the timekeeper might encode more complex temporal patterning, and be adjusted at any given moment.
This idea is supported by behavioral findings form Bruno Repp. He subsequently found that if a pacing sequence is metrically subdivided by an additional tone, a per-turbation of the placement of this additional tone elicits a phase correction response in the following pacing stimulus, even though no asynchrony was observed (subjects did not tap to the subdivision tones) (Repp, 2006). This at least indicates that the timekeeper is accesible for reference and manipulation outside of the pacing interval. Another study by Repp (2010) found that metrically subdividing slow rhythms, either mentally, by tap-ping at twice the rate of the stimulus sequence or by antiphase taptap-ping, diminished the variability of taps. Since the number and placement of metronome stimuli in all these conditions was the same, and if we assume that the internal timekeeper is the principal source of motor output timing, it might be concluded that the timekeeper became more accurate as it came to describe temporal relationships between more events. Also in this case, the timekeeper was accesible for reference and manipulation outside of the pacing interval.
Neural representations of time and recurring intervals There are hardly any studies on possible neural substrates for a faculty which encodes both temporal duration and repetition and possibly complex temporal patterning. Many studies exist on timing of individual intervals, but most have been conducted in animals, are concerned with timing of single intervals and often with intervals of seconds or more (for a review, see Buhusi and Meck, 2005). However, for interval timing in the tens of millisecond range and above, the striatum has been repeatedly implicated (Rao et al., 2001, Matell et al., 2000). Especially Matell and Meck (2004) present a comprehensive overview of timing models. Here, the striatum is implicated as a coincidence detector between the thalamus and motor areas in the prefrontal cortex. Such a coincidence detector could serve a role in
detecting synchrony between taps and tones, were it not that the cortico-striatal network here is implicated with determining coincidence detection in intervals of at best several hundred milliseconds; much too long for subjective synchrony in SMS paradigms.
A difficulty here is caused by the limited temporal resolution of imaging tech-niques such as fMRI. Suggestions on the involvement of the striatum in interval timing made by Rao et al. (2001) are appealing; they ask subjects to determine whether two consecutively presented intervals are different in size or not, with differences between the intervals in the range we also find in SMS tasks (60 or 120ms difference between 1200ms intervals). It would be very informative to be able to contrast fMRI measurements of the striatum and associated structures in response to different sorts of timing errors, such as tempo steps and phase shifts, with tempo steps constituting a true change in interval duration. However, the timecourse of corrective responses and thereby resetting of the timekeeper are too short to be measured using fMRI.
Also, the inability to use intrusive techniques to study the living human brain make it impossible to speculate on network dynamics on the level of individual neurons, or groups of neurons, which could support an internal timekeeper. Such research is possi-ble in non–human primates, as reviewed by Buhusi and Meck (2005), but since rhythmic behavior is completely absent in these animals, it is difficult to transfer interpretations of animal data to an understanding of human behavior. Of course, there might be pace-maker cells and accumulator cells in humans which can encode interval duration, but the question how the recurrent nature of rhythmic stimuli and behavior are encoded is a different question. A possibility might be derived from a modeling study by Karmarkar and Buonomano (2007), who employ a simulated network of 500 neurons/12.200 synapses with realistic short term plasticity to encode trains of events as discrete temporal objects. The advantage of such a network is that it can encode highly complex temporal patterns, and can present the temporal information very flexibly, using only a very limited num-ber of neurons. Although his network is not yet able to detect commonalities between event sequences which contain similar elements, there is a lot of room for expanding the functionality. For instance, by starting up the network with specific attractor states for certain stimulus patterns (such as metrically organized beats), it might be possible
to make the network respond more predictably to novel inputs, without diminishing its ability to encode a large range of different temporal patterns.
3
Conclusion
Possibilities for introducing neurocognitive insights into theories of sensorimotor synchro-nization are ample, but doing so is challenging. The existing literature on SMS, although a relatively small field, is exstensive. Possibly because theorists have remained unhin-dred by the restraints of biological realism for a long period of time, there has been a proliferation of theories to explain even a simple effect like the NMA. In the end I must conclude about the NMA that there are undoubtedly several causes at work simulta-neously; perceptual underestimation, nerve conduction delays and different weighting of different sensory inputs. Every approach has difficulty explaining the effect entirely and excluding any of the other explanations. However, in the case of the NMA I believe the sensory accumulator model still holds the most promise. The SAM as it has hitherto been formulated is still limited, and could be expanded by including influences of mo-tor efference copies and localizing the structures which are most prominently involved in establishing subjective synchrony, which is still a poorly defined concept at the heart of SMS, if defined at all.
Knowledge on the processes of error correction has matured substantially over the years. It has also proven possible to substantiate several claims from behavioral paradigms using neurocognitive measurements, which will help overthrow several outdated notions about period correction. It is also pleasing to note that more modern models employ all forms of error correction using information on the asynchrony of taps and tones, instead of having period correction rely on differences in observed IRIs and ISIs (Schulze et al., 2005, Repp and Keller, 2008); this prevents the irony of having one of the best understood concepts of sensorimotor synchronization (error correction) depending on one of the least best understood concepts (the internal timekeeper).
With respect to the internal timekeeper I must admit that I am disappointed about the interpretations that currently seem possible. Undoubtedly, motor areas play
an important role in defining the internal timekeeper, since one of its main functions is producing temporally accurate motor output. However, the production of motor output is not what is unique about the internal timekeeper, and also not the most difficult aspect to study. Its defining characteristic, its representation of temporal patterns, seems to rely on dynamics at spatial and temporal scales which are difficult to probe using methods for human research, if possible at all. However, I believe the conceptual definition I have attempted is unique.
4
Acknowledgements
I want to thank Nima Darabi for inviting me into his project a year ago. It presented me with an opportunity to acquaint myself with a completely novel field of study. He took a lot of time to involve me in the work; I enjoyed his company and his insights, and I hope that this thesis can maybe return part of the favor.
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