Seediscussions,stats,andauthorprofilesforthispublicationat:http://www.researchgate.net/publication/264248569

Playingbeautifullywhenyouhavetobefast:spatialandtemporalsymmetriesofmovementpatternsinskilledpianoperformanceatdifferenttempi

ARTICLEinEXPERIMENTALBRAINRESEARCH·JULY2014

ImpactFactor:2.04·DOI:10.1007/s00221-014-4036-4·Source:PubMed

CITATIONS

2

READS

50

5AUTHORS,INCLUDING:

FlorisTijmenVanVugt

McGillUniversity

13PUBLICATIONS45CITATIONS

SEEPROFILE

ShinichiFuruya

SophiaUniversity

42PUBLICATIONS421CITATIONS

SEEPROFILE

EckartAltenmüller

HochschulefürMusik,TheaterundMedien…

288PUBLICATIONS5,758CITATIONS

SEEPROFILE

Allin-textreferencesunderlinedinbluearelinkedtopublicationsonResearchGate,

lettingyouaccessandreadthemimmediately.

Availablefrom:FlorisTijmenVanVugt

Retrievedon:05November2015

1 23

Experimental Brain Research ISSN 0014-4819 Exp Brain ResDOI 10.1007/s00221-014-4036-4

Playing beautifully when you have to befast: spatial and temporal symmetriesof movement patterns in skilled pianoperformance at different tempi

Floris T. van Vugt, Shinichi Furuya,Henning Vauth, Hans-Christian Jabusch& Eckart Altenmüller

1 23

Your article is protected by copyright and

all rights are held exclusively by Springer-

Verlag Berlin Heidelberg. This e-offprint is

for personal use only and shall not be self-

archived in electronic repositories. If you wish

to self-archive your article, please use the

accepted manuscript version for posting on

your own website. You may further deposit

the accepted manuscript version in any

repository, provided it is only made publicly

available 12 months after official publication

or later and provided acknowledgement is

given to the original source of publication

and a link is inserted to the published article

on Springer's website. The link must be

accompanied by the following text: "The final

publication is available at link.springer.com”.

1 3

Exp Brain ResDOI 10.1007/s00221-014-4036-4

REsEaRch aRtIclE

Playing beautifully when you have to be fast: spatial and temporal symmetries of movement patterns in skilled piano performance at different tempi

Floris T. van Vugt · Shinichi Furuya · Henning Vauth · Hans‑Christian Jabusch · Eckart Altenmüller

Received: 21 October 2013 / accepted: 5 July 2014 © springer-Verlag Berlin heidelberg 2014

(R2 = 0.70). the model can be fitted on the data of indi-vidual pianists, providing a novel quantification of expert performance. the present study shows that the motor sys-tem can generate complex movements through a dynamic combination of simple movement templates. this provides insight into how the motor system flexibly adapts to vary-ing contextual constraints.

Keywords Generalised motor programmes · timing · Motor skill · Expert musicians · scale playing · Movement effectors

Introduction

humans are able to learn skills by learning sequences of movements. sequential motor behaviours such as speech, typing a text, or music performance are ways of conveying information, a crucial aspect of human communication. In order to perform this function, the skills need to be adapt-able to changing contexts. For example, playing a musical sequence at various global and local tempi conveys differ-ent emotional information to listeners (Dalla Bella et al. 2001; Khalfa et al. 2008; Bhatara et al. 2011). Musicians’ capacity to manipulate tempo thus plays a crucial role in expressive performance (Goebl and Palmer 2013). Previous studies focused on variation of the organisation of move-ment kinematics and muscular activity in relation to tempo during piano playing (Furuya et al. 2011b, 2012). however, it is not well understood how temporal features of succes-sive movement elements (i.e. keystrokes) vary across a wide range of tempi.

how does the brain implement movements at vari-ous speeds? Movement production over a wide range of tempi has been proposed to be controlled by parametric

Abstract humans are capable of learning a variety of motor skills such as playing the piano. Performance of these skills is subject to multiple constraints, such as musi-cal phrasing or speed requirements, and these constraints vary from one context to another. In order to understand how the brain controls highly skilled movements, we investigated pianists playing musical scales with their left or right hand at various speeds. Pianists showed system-atic temporal deviations away from regularity. at slow tempi, pianists slowed down at the beginning and end of the movement (which we call phrasal template). at fast tempi, temporal deviation traces consisted of three peak delays caused by a thumb-under manoeuvre (which we call neuromuscular template). Intermediate tempi were a linear combination trade-off between these two. We introduce and cross-validate a simple four-parameter model that predicted the timing deviation of each individual note across tempi

Electronic supplementary material the online version of this article (doi:10.1007/s00221-014-4036-4) contains supplementary material, which is available to authorized users.

F. t. van Vugt (*) · s. Furuya · h. Vauth · h.-c. Jabusch · E. altenmüller Institute of Music Physiology and Musicians’ Medicine, University of Music, Drama, and Media, Emmichplatz 1, 30175 hanover, Germanye-mail: F.t.vanVugt@gmail.com

F. t. van Vugt lyon Neuroscience Research center cNRs-UMR 5292, INsERM U1028, University lyon-1, 50 avenue tony Garnier, 69007 lyon, France

h.-c. Jabusch Institute of Musicians’ Medicine, Dresden University of Music carl Maria von Weber, leubnitzer str. 17b, 01069 Dresden, Germany

Author's personal copy

Exp Brain Res

1 3

modulation of a single temporal movement template or generalised motor programme (hollerbach and Flash 1982). For example, when participants learn a tapping sequence in a certain rhythm, the pattern of timing devia-tions of the inter-tap intervals is preserved even when they are asked to reproduce the sequence as fast as possi-ble (summers 1975). such a tempo-invariant motor pro-gramme allows the brain to simplify the manipulation of the tempo of movements. a prediction derived from such model is that temporal features of successive keystrokes should be invariant across tempi in piano playing. this idea was supported by an exploratory study that found that the pattern of inter-onset-intervals (IOIs) of successive key-strokes were highly similar across different tempi during playing a certain musical phrase (Repp 1994). similarly, in discrete motor tasks such as reaching (hollerbach and Flash 1982) and ball throwing with the non-dominant hand (hore et al. 2005), spatio-temporal features of the move-ments were maintained across different speeds.

however, an alternative hypothesis is that variation of speed involves combining a particular set of distinct movement templates. this may be computationally costly because the motor system would have to represent multi-ple motor templates instead of one (Wolpert and Kawato 1999), but makes the brain flexible enough to cope with cognitive and biomechanical demands that can vary in rela-tion to tempo. For example, disruption of movements by altered auditory feedback in piano playing differed accord-ing to tempo, implying differential reliance on feedback control across tempi (Furuya and soechting 2010). In addi-tion, when playing some types of musical scales, the thumb has to rotate while pressing a key in order to move the hand horizontally (Engel et al. 1997; Furuya et al. 2011a), which would biomechanically constrain keystrokes in terms of the hand inertia force that changes with tempo. the tempo-modulation strategy using a linear sum of some funda-mental movement patterns predicts variation of movement characteristics (or more specifically, systematic pattern of spontaneous temporal deviation) with tempi. similarly, expressive timing is thought to change qualitatively with tempo (honing 2006, 2007), and the temporal invariance of successive keystrokes across tempi was violated in piiano performance (clarke 1982; Desain and honing 1994; Windsor et al. 2001).

the present study approaches this question by investigat-ing piano scale playing. Piano scale playing has been used successfully to study expert motor control in musicians because it is well trained among pianists (Wagner 1971; MacKenzie and Van Eerd 1990; Jabusch et al. 2004, 2009; van Vugt et al. 2012, 2013a, b). additionally, understanding the scale playing movement is important in itself since it is frequently used as a metric of severity of musician’s dys-tonia (Jabusch et al. 2004; van Vugt et al. 2014). We used

musical scales since they are basic elements of the musical architecture in classical music as well as in jazz, rock, and pop music. as a consequence, scale playing represents a fun-damental aspect of piano technique. Further, the advantage of studying scale playing over playing other, perhaps more musical, materials is that the task is clearly defined (play-ing a scale as regularly as possible), and therefore, it is pos-sible to directly compare performance between musicians. Furthermore, scale playing is one of the most well-trained sequences among pianists’ musical materials. this means that timing deviations in these materials are not likely due to spontaneous error. Indeed, pianists were shown to exhibit systematic timing deviations away from regularity that are highly individual (van Vugt et al. 2013a, b). Overall, these timing deviations indicated a slowing down at the begin-ning and end of the sequence, reminiscent of musical phras-ing. Furthermore, timing deviation traces showed a series of delays that could be caused by a thumb-under manoeuvre during playing the piano scale (Engel et al. 1997; van Vugt et al. 2012). however, it remains unclear how these patterns of temporal deviations vary with the speed of playing.

the main question in this paper is how the temporal deviation pattern changes across the different tempi and playing directions and hands. Our null hypothesis is that the temporal deviation pattern is similar across the condi-tions. an alternative hypothesis is that the temporal devia-tion pattern changes across the conditions. In particular, we expect firstly that the pattern of slowing down at the begin-ning and end of the sequence would dominate at slower tempi. the reason for this is that when speed demands are low, the nervous system has more resources available to create aesthetically pleasing sound or indicate musical phrasing. secondly, we expected the delays that could be caused by a thumb-under manoeuvre to become more pro-nounced at faster tempi. the reason for this is that at higher speeds, there is less time for the transitions between key-stroke movements. Once the motor system is no longer able to perform the movements in the designated time, delays will arise whose magnitude will roughly equal the differ-ence between the available and required time. thirdly, at intermediate tempi, we expect to find a trade-off between these two. Our rationale for this is as follows. If slow-tempo timing pattern arises from resource availability, then it will be more pronounced when more time is avail-able. In other words, the timing pattern should vary para-metrically with speed. similarly, if the fast tempo timing delays are due to the thumb-under manoeuvre, this pattern become more pronounced with increasing speed demands (i.e. higher tempo). since both timing patterns vary para-metrically with tempo, the intermediate tempi should show a gradual trade-off between the two. In addition, we test further hypotheses concerning the temporal control of scale playing. Do the two hands show comparable temporal

Author's personal copy

Exp Brain Res

1 3

deviation patterns? For example, because of better control of non-muscular force such as inter-segmental dynamics at the dominant hand compared to non-dominant hand (sain-burg and Kalakanis 2000; sainburg 2002; heuer 2007), one would expect different movement control between the two hands. alternatively, it may be computationally advanta-geous to share motor representations between the hands when both hands execute the same movement.

Finally, how do temporal deviation traces vary when movements are executed backwards? that is, could the same motor pattern be used for a movement that is mirrored in time? Executing a movement sequence in a different order might introduce different muscle synergies. this means that if the brain is able to execute movements backwards in time, it must have abstracted away from the immediate muscular instruction. In order to answer this question, we compare the timing pattern of ascending scales with those of descending scales, which constitute the same movement mirrored in time.

to test these questions straightforwardly, the present study developed a linear regression model of timing devia-tions in piano playing across various tempi, movement directions (ascending and descending scales) and effectors (the two hands). this enabled us to evaluate whether vari-ability across successive keystrokes can be best accounted for in terms of one or multiple movement templates.

Methods

Participants

Nineteen piano students (ten females, nine males, mean age 23.7, sD 2.9 years) were recruited from the student pool at the hanover Music University. all but one were right-handed. seventeen participants took piano as their main subject, while the other two took organ. Participants reported no history of neurological disorders and had an accumulated lifetime keyboard practice of 16.9 (sD 7.5) 1,000 h (except for two pianists who did not specify). the experiment was approved by the ethical review board of the University of Music, Drama and Media, hannover, and the Medical University hannover (EG al_2012_/Go13).

Procedure

Participants played two-octave c-major scales, beginning with the c (131 hz) one octave below the middle c and ending with the c (523 hz) one octave higher than the mid-dle c (ascending) and back (descending). For notational convenience, we will write the notes in this scale as c, d, e, f, g, a, b, c′, d′, … , c″.

the task of playing a two-octave scale is to press fifteen adjacent keys serially. Playing the ascending scale with the

right hand, the thumb starts out on the c, and then, the index and middle finger press the adjacent d and e. Now, the thumb has to move underneath the index and middle finger to strike the next key, f. the role of this manoeuvre is to move the posi-tion of the hand rightward. Now, the index finger moves over the thumb to strike the g. the middle and ring finger can then in turn strike the a and b. at this point, another thumb-under movement is performed to strike the c, at which point, the entire movement is repeated for the next octave. the left hand movements are analogue for the descending scale starting with the thumb on c″. In sum, participants played the scales with the conventional fingering (123123412312345, where the fin-gers are numbered from 1 = thumb to 5 = little finger).

Participants played ascending and descending scales inter-leaved. In between the ascending and descending scales, there was a short pause of about a second and the pianists made one additional keystroke on either the note c (65 hz) or c (1,047 hz) with the hand not involved in the scale playing. this keystroke was used in previous analyses to demarcate the different trial runs, but was discarded in our current anal-ysis. the procedure was repeated for 5 different tempi indi-cated by a metronome at either 40, 80, 120, 160 or 200 BPM. Furthermore, the procedure was performed for the two hands in turn. the pianists were instructed to play 4 keystrokes per metronome beat, which means that the keystroke rate varied between 2.67 and 13.3 keystrokes/s. Pianists were instructed to play legato style and to aim for temporal evenness.

Participants played on a MP 9000 MIDI keyboard (Kawai, Krefeld, Germany).

the keyboard’s digital music interface (MIDI out) sig-nal was captured on a Pc using a commercially available sequencer software (Musicator Win, version 2.12; Music Interactive technology, Bergen, Norway). a metronome was placed near the pianist so that it was clearly audible over the sound of the digital piano. No headphones were used. loudness was configured as follows. Before the first participant was recorded, the loudness of the digital piano was set to perceptually match that of an acoustic piano by one of the authors who holds a piano performance degree. the loudness was then kept constant throughout the meas-urements of all participants. We made the MIDI recordings used in this study freely available at the following link: http://dx.doi.org/10.6084/m9.figshare.1108249.

Processing of MIDI data

First, we extracted only the correctly played scales (defined as those trials on which the pianists pressed the keystrokes of the c-major scale in the correct order with no omissions and no additional keystrokes), separating ascending and descending scales. this yielded 13.5 (sD 1.2) scales for each pianist, tempo, hand and direction. across participants, a total of 1,615 keystroke onsets were discarded because

Author's personal copy

Exp Brain Res

1 3

they were part of incorrect scales, amounting to 2.1 % of the recorded material. For the individual pianists, this value ranged from 0.8 to 10.9 %. the average amount of dropped onsets was 3.2 % (sD 2.6 %). this amount of discarded note material did not correlate with the accumulated prac-tice hours of the pianist (taken as a measure of pianistic expertise) (spearman ρ(14) = −.16, p = .57).

Individual note timing

In order to establish the timing of individual notes, we used the following procedure (van Vugt et al. 2012, 2013b). For each ascending and descending scale, we computed the (note, time) pairs, where note is the rank of the note in the particular scale (0 for c, 1 for d, etc., until 14 for c″) and time represents the keystroke onset time. subsequently, we fitted an ordinary least-square regression line to these pairs. We rejected fits with an R2 of <0.9 (which occurred when a scale was played very unevenly), and this was the case for one scale run (0.02 % of the data). the remaining fits had an average R2 of 0.9996 (sD 3 × 10−4). the fitted line ena-bled us to determine the expected onset time for each key-stroke as the intersection of the regression fit with the hori-zontal line representing the corresponding note. Finally, we computed the time difference between this expected onset and the actual keystroke onset (in msec, with negative dif-ference reflecting notes played earlier than predicted). We will refer to this quantity as temporal deviation.

towards a model of timing deviations

Using the above procedure, we computed the median timing deviation for each note, hand, playing direction (inward and outward; inward being defined as radial playing direction, with the arm moving towards the body; outward as ulnar playing direction, with the arm moving away from the body) and tempo across players. We investigated whether the tim-ing deviation traces for the various tempi were dominated by a single template or by multiple templates. We hypothesised to reproduce previous findings of a movement template that reflects phrasing: a slowing down in the beginning and at the end of the movement. additionally, to cope with changing demands, the traces may be qualitatively different in the con-text of higher movement production speed. We would expect such a high-speed template to be dominated by the thumb-under manoeuvre in outward scales and finger cross-over manoeuvre in inward scales. We generated two timing tem-plates that were represented as a vector of timing deviations for the notes in the scale. We then explored whether the tim-ing deviations at the intermediate tempi could be rewritten as a linear combination of these two vectors.

Next, we generalised our model across the hands and movement directions. First, we cross-validated the model

fit on the right hand outward scales by assessing its fit on the left hand outward scales, which are produced by the same movement but mirrored in space. second, we turned to the inward scales for both hands, which are in the same movement but mirrored in time (that is, played backwards). that is, we investigated whether the movement templates that we identified in the steps above can be mirrored in time (that is, played backwards) or whether they remain time-invariant.

Fitting methods

For fitting, we used the analytic least-squares solution pro-vided by ordinary least-squares fitting for generalised lin-ear models. For nonlinear models that do not allow this, we instead used the Newton-type optimisation using R’s nlm function. Furthermore, the nonlinear models with constrained parameter spaces were implemented using R’s optim func-tion using the Nelder–Mead simplex method. Whenever appropriate, we report adjusted goodness-of-fit statistics R2

adj = 1 − ((1 − R2) × (N − 1)/(N – k − 1)) where R2 is the conventional goodness-of-fit, N is the number of observations and k is the number of parameters in the model. alternatively, whenever the variance of the observed data points was impor-tant, we reported the chi-square measure of goodness-of-fit as follows: χ2

red = 1/(N – k − 1) × (Σi (Observedi − Predictedi)/Variancei), where i is the index of the observation, N is the number of observations and k is the number of parameters in the model. the advantage of both these metrics (R2

adj and χ2red)

is that they take into account the number of parameters used in the model and thus prevent overfitting.

In aNOVas, we report ηG2 as the generalised effect size

(Bakeman 2005). Whenever Mauchly’s test indicated spheric-ity violations, we applied the Greenhouse–Geisser correction. In those cases, for the sake of brevity, we only report the p value after the correction is applied and marked it as pGG.

Results

Note-by-note temporal deviations: establishing the phrasal and neuromuscular templates

We calculated the note-by-note temporal deviation and expressed these as a percentage of the interval duration. We performed a repeated-measures aNOVa with 5 tempi × 2 directions × 2 hands × 15 notes as factors and temporal deviation as the dependent variable. there was a main effect of note (F(14,224) = 17.49, p < 10−28, ηG

2 = .16), reflecting that timing differed across notes. these note-by-note differences will be the subject of our analysis in the remainder of this paper. there was no main effect of tempo (F(4,64) = .49, p = .74) nor of direction (F(1,16) = 3.23,

Author's personal copy

Exp Brain Res

1 3

p = .09) or hand (F(1,16) = .19, p = .66). hand and direc-tion interacted (F(1,16) = 4.93, p = .04) as did tempo and note (F(56,896) = 8.05, p < 10−48, ηG

2 = .11) and hand and note (F(14,224) = 3.30, p < .001, ηG

2 = .01). this find-ing constitutes evidence against the generalised motor programme hypothesis, which would have predicted no interaction of tempo and note. the other two-way inter-actions were not significant (both F < .71, p > .58). all the three-way interactions were significant (all F > 3.72, p < 10−16) except for tempo, hand and body directions (F(4,64) = 1.79, p = .14), and finally, the four-way interac-tion between all factors was significant (F(56,896) = 1.63, p < .001, ηG

2 = .01). as a result, we proceeded to analyse the tempo–note interactions for all four combinations of hand and direction separately.

First, we focus on the right hand outward scales. We per-formed a two-way repeated-measures aNOVa with note and tempo as factors, which yielded a main effect of note (F(14,224) = 7.95, p < 10−12, ηG

2 = .17), and an interaction of note and tempo (F(56,896) = 9.73, p < 10−59), but no main effect of tempo (F(4,46) = .23, p = .92).

how did note timing vary across tempi? We found that at fast tempi, three distinct peaks in relative timing appear (Fig. 1a), corresponding to the positions in the two-octave scale where the index finger crosses the thumb (e.g., the index finger playing g after the thumb plays f). at slower tempi, a different picture emerges: the temporal deviation trace takes the shape of an arc, with the first few and last few notes played late, whereas the rest are played slightly early. Furthermore, at the intermediate tempi, a gradual trade-off happens between these traces of the extreme tempi (Fig. 1a). the crucial observation is that variation of

tempo is achieved as a trade-off between two qualitatively different timing patterns (templates). this observation forms the basis of the model of timing deviations that we provide below. In order to generate this model, in what fol-lows we (a) established the timing profiles of the fast and slow tempi, and then (b) parametrised the trade-off between them across tempi.

Firstly, we generated a simple model of the deviation trace at the slow tempo (2.7 notes/s). We distinguished two phases (Fig. 2a): (1) a phase where the temporal deviation more or less linearly decreases (notes 1:12, i.e. c–g′), i.e. speeding up in the middle of the scale, and then (2) a phase where the deviation increases linearly, i.e. slowing down at the end (notes 13:15, i.e. a′–c″). to model this, we fit a straight line to the temporal deviation trace from notes c to g′, and then a second line from a′ to c″. this two-line model fitted the data well (R2

adj = 0.82, χ2red(12) = 0.47)

(Fig. 2c). We took this fit quality based on only two param-eters as an argument that there was no need to resort to more complex models of expressive timing to account for our data. In sum, our model of the slowest tempo implied a slow start of the scale playing, followed by a smooth speed-ing up and finishing with a dramatic slowing down. this finding is consistent with timing arcs found in expressive playing (Palmer and Krumhansl 1987; Repp 1990; Friberg and sundberg 1999; honing 2003; Friberg et al. 2006) and is taken to reveal that the two-octave scale is played as a single phrasal unit (van Vugt et al. 2012). We therefore refer to this pattern as the phrasal template.

Next, we investigated the deviation trace of the fastest tempo (13.3 notes/s). three distinct peaks appeared that cor-responded to late keystrokes (Fig. 2b). the peaks correspond

Fig. 1 a the mean deviation (lateness) in percentage of the inter-val (right hand outward scales). the depth axis shows the different tempi. Colour coding is added that reflects the mean vertical position of each graph segment. the deviation pattern is qualitatively different

for the slow and fast tempi. b the key down time minus the target inter-keystroke interval (in msec), revealing that the keys preceding a thumb passage are released earlier by an amount of time that is more or less constant across tempi

Author's personal copy

Exp Brain Res

1 3

to the notes played by the index finger, and, to a lesser degree, the preceding thumb keystrokes. Interestingly, the keystroke preceding each peak was held down less long, in a way that did not depend on tempo: the pattern of tone durations was more or less constant across tempi (Fig. 1b). this suggested that these timing deviations were dictated by the time the fin-gers needed to transition between the keystrokes (Engel et al. 1997; Furuya et al. 2011a). this transition time is most prob-ably due to biomechanical constraints (van Vugt et al. 2013b) and perhaps also by the hand anatomy (e.g. only the thumb can perform a three-dimensional rotation that optimises the horizontal translation of the hand position). therefore, we referred to this template as the neuromuscular template. to construct a model of this template, we proceeded as follows. We initialised a zero deviation trace where all notes were on time. then, we introduced a delay d on the notes played by the index finger. to partially anticipate for the introduced

delay, the preceding note, played by the thumb, was also delayed by half that amount, that is, d/2. Finally, the remain-ing notes were played earlier so that the entire trace centred around zero. In sum, the index finger was late, the preceding thumb was half as late and the other notes compensated for this lateness by being early. this fit is shown in Fig. 2d. this model had a single parameter, but explained our data well (R2

adj = 0.77, χ2red(12) = 0.12, p < .001).

trade-off between the two templates

here, we investigate the extent to which we can approximate the temporal deviation traces of the intermediate tempi as a combination of the two extreme ones. We computed the lin-ear combination of the two templates that best fit the devia-tion trace at each of the tempi. that is, the model contained 10 degrees of freedom (2 parameters per tempo for 5 tempi).

(a) (b)

(c) (d)

Fig. 2 a Mean lateness (expressed as coefficient of variation in %) for the slowest playing tempo. b Mean lateness for the fastest tempo. Error bars and shaded area indicate sE across subjects. c Our fit

to the deviation trace of the slow tempo. the solid line shows our model. d Our fit at the fastest tempo. the error bars represent the sE of the mean

Author's personal copy

Exp Brain Res

1 3

the overall fit (R2adj = 0.69, χ2

red(62) = 0.43, p < .0001) of this model was good. however, this fit still contained excess degrees of freedom, since in this model, an increase in the contribution of one template did not necessarily entail a decrease in the other. In order to reduce the parameters to half, we performed the following fit. Given the deviation trace dt at a particular tempo as dependent variable, we computed the fit for dt = α × nm + (1 − α) × phr, where nm and phr were the (fixed) vectors corresponding to our model fits of the neuromuscular and phrasal templates, respectively, and α was

the fitted parameter. the corresponding fit had only slightly reduced R2

adj = .72 (χ2red(67) = 0.43, p < .0001) relative to the

previous model even though the number of parameters was divided by two (this latter fit is shown in Fig. 3a). We take this fact as evidence for a trade-off between the two templates, rather than free linear combination of the two.

can one predict how this trade-off parameter (α) varies as a function of tempo? to this effect, we arbitrarily chose a quartic function to predict α as a function of tempo as follows. that is, we fitted α(t) = at4, where t is the tempo (in strokes/s). We fitted for the parameter a. With this new model, we reduced the parameters to one (a) instead of four, with a minimal loss in explained variance (R2

adj = 0.70, χ2red(70) = 0.40, p < 10−7).

When we fitted a model with only the neuromuscu-lar template, we obtained a much poorer fit (R2

adj = 0.40, χ2

red(72) = 0.76, p > .06). the same was true for a model containing only the phrasal template (R2

adj = 0.18, χ2

red(71) = 0.55, p < .001). this latter result indicates that the two templates both contributed to the pattern of timing deviations observed in these pianists.

In sum, we presented a generative model that predicts the temporal deviation trace in scale playing based on two templates that we label as phrasal and neuromuscular and a trade-off function using a single parameter (a). the phrasal template is fit using two parameters (the slopes of the two lines), and the neuromuscular template is based on a sin-gle parameter (the temporal deviation of the index finger passage). Using these four parameters, our model predicted the temporal deviation traces of 5 tempi times 15 notes (75 data points). the obtained R2

adj shows that a considerable portion of the variance is captured (R2

adj = 0.70).

cross-validation of fit

We tested whether our model of the right hand ascending scales over-fitted the data. We split the data set in two parts, the training and test set, in the following way. For each pia-nist’s hand and playing direction, we allocated the odd trials to the training set and the even trials to the test set. We then repeated our analysis on this training set (the odd trials). as with the entire data set, this provided a good fit (R2

adj = 0.68, χ2

red(70) = 0.39, p < .00001; see supplementary materials for details). Now, we were able to perform the crucial test of cross-validation: we evaluated this model on the even tri-als. If our model over-fits the data, we expect it to perform badly on the even data set. this was not the case: the good-ness-of-fit for the even trials (R2

adj = 0.70, χ2red(70) = 0.39,

p < .00001) was even better than the fit on the odd trials.

Individual data fit

how robustly can our analysis be applied to individual pianists? In order to answer this question, we repeated our

(a)

(b)

Fig. 3 a the contributions of the two templates to the timing patterns across tempi. the squares and their error bars indicate the result of a least-square fit α(t) × nm + (1 − α(t)) × phr with a single param-eter (α) for each tempo separately determining a trade-off between the neuromuscular (nm) and phrasal (phr) templates. subsequently, we performed a least-square fit of α(t) = at4 and found the resulting model, indicated by the solid red line, and 1 − α(t) is indicated by the blue line. b Variance explained by the phrasal and neuromuscular templates for the various tempi on a single-participant basis (see sup-plementary materials for details) (colour figure online)

Author's personal copy

Exp Brain Res

1 3

model fit to the right hand ascending scales for each pianist individually. Given a pianist and a tempo, we computed the mean deviation trace (dt) as before, and we approximate it as a linear combination of the neuromuscular (nm) and phrasal template (phr) as follows: dt = nm(d) + phr(i, s1, s2). here, the neuromuscular model nm was defined by one parameter (d), and it was constructed precisely as specified before. Furthermore, the phrasal model was again defined as two lines, one descending line for notes 1:12 (c–g′) and one ascending line for notes 13:15 (a′–c″). that is, we have three parameters: the intercept (i) and slope (s1) of the first line, and the slope of the second line (s2) (note that the intercept of the second line is fixed because this line is forced to intersect with the first one at a′).

that is, we have four parameters for each tempo in the trace, which we estimate through a nonlinear least-square fit through the Nelder–Mead simplex method. addition-ally, we forced the values of s1 to be negative and d and s2 to be positive by introducing corresponding penalties in the squared error term of the optimisation. We then calcu-lated the amount of variance (in the deviation trace) that is explained by each of the two templates by subtracting the summed squared error (ssE) of the two-template model from the ssE of the other (single) template model. Note that the difference between this analysis and the trade-off model (introduced in the previous part of this paper) is that the latter is based on the average traces (and their sD) of all participants, whereas the former is fit for each participant individually.

Figure 3b shows the amount of variance explained by each template. the result corroborates our previous finding: the phrasal template explains most variance in the slower tempi, and the neuromuscular template most of the vari-ance in the higher tempi. at the intermediate tempi, there is a clear trade-off (Fig. 3b).

Generalising to all outward scales

In the previous section, we have generated a model for the timing deviations of the right hand outward scales. as a cross-validation of our model, we now turn to the left hand outward scales. When the left hand plays descend-ing scales, the sequence of movements is exactly the same as the right hand ascending scales we have ana-lysed thus far (outward), except in that they are mirrored in space and executed by a different effector (hand) (van Vugt et al. 2013b). If the two templates established so far constitute effector-unspecific representations, then timing deviations of the left hand outward scales should be simi-lar to the right hand timing deviations mirrored in space. Indeed, if we apply the same fit as we have obtained for the right hand scales to the left hand outward scales, we obtain a significant model (R2

adj = 0.39, χ2red(70) = 0.67,

p = .01). Note that the parameters in this model have been fit to a separate subset of our data (i.e. the right hand outward scales). therefore, this evaluation amounts to a cross-validation (and is actually more stringent than that because it is evaluated for a different hand). Furthermore, if we take the outward movements for both hands together (Fig. 4 right hand panels), our model has a good overall fit (R2

adj = 0.55, χ2red(145) = 0.52, p < 10−7).

Generalising to inward scales

We have presented a model for right hand outward (ascending) scales and generalised it to left hand outward (descending) scales. this model shows the brain uses two motor templates to control both movements. can the same motor templates be used to generate the inward scale play-ing movement (Fig. 4 left hand panels)?

let us first turn to the fastest tempo. to understand what temporal deviation trace is predicted for the inward movement at this tempo, we invite the reader to imagine the following. If we capture the outward scale on video and play it backwards, we would see the inward move-ment. how would the temporal deviation trace for the original and the backwards variant relate? First of all, the sequence of notes would be reversed in time. second, the temporal deviation of notes would be inverted: notes that were late in the forward sequence would be early in the time-mirrored (backwards) sequence and vice versa. Finally, one further operation is required to complete the transformation of the timing patterns. We argued previ-ously that the timing pattern found at the fastest tempo is determined by the difficulty of the thumb and index finger transitions. that is, the keystroke after this transi-tion will be affected (i.e. late) because of the difficulty of the transition. this means that when the order of the keystrokes is reversed, the keystroke affected by the transition delay is the keystroke before the transition. In other words, we expect the timing pattern of the neuro-muscular template to be shifted by one note forward in its entirety. We discard the last note of the inward trace (since there is no corresponding note in the outward trace). since our traces are centred around zero, the tim-ing of the new data point at the beginning of the trace is fixed (and it is the same as the discarded note at the end of the trace).

For clarity, we summarise the process here. We took the predicted deviation trace of the right hand outward move-ment at the fastest tempo, reversed the order of the notes, inverted their temporal deviation (i.e. multiplying the deviations by −1) and then shifted the entire trace by one note. the resulting trace correlated highly with the right hand inward scales [spearman ρ(14) = .75, p = .001], and, similarly, for the left hand scales [spearman ρ(14) = .73,

Author's personal copy

Exp Brain Res

1 3

p = .001]. Figure 5 illustrates the match between the traces after this manipulation (compared with Fig. 4 bottom left and right before this manipulation).

Next, we turn to the slowest tempo, at which we previ-ously showed the phrasal template dominates. In this case, inverting the trace in time as shown above does not yield a good fit for the left hand (ρ(14) = −.34, p = .89) nor for the right hand (ρ(14) = −.63, p = .99). On the contrary, the non-inverted, original (time-invariant) traces correlates highly for the left (ρ(14) = .75, p < .001) and right hand (ρ(14) = .81, p = .0001). In other words, although at the

fast tempo the timing deviation traces are mirrored in time (Fig. 4 bottom plots), the timing deviations at the slower tempo remain invariant (Fig. 4 top plots). consequently, the intermediate tempi, which are a linear combination of these two motor templates, reveal no obvious relation at face value (Fig. 4 middle plots). Our decomposition of the timing deviations in two motor templates has revealed the underlying symmetries in time and space. this finding shows that hidden symmetries in movements may be read-ily revealed when movements are decomposed into motor templates.

Fig. 4 the temporal deviation traces for the inward scale movement (left graphs) and the outward scales movements (right graphs), from the slowest tempo (top), intermediate tempo (middle) to fastest tempo (bottom). For simplicity of presentation, we have omitted the other two measured tempi. the two traces correspond to the left (red) and

right (green) hand. Notes are presented in chronological order, i.e. note 1 is the first note played, 2 is the note after that. Note how the traces are similar between the two movements for the slow tempi, but very different for the faster tempi (colour figure online)

Author's personal copy

Exp Brain Res

1 3

In order to model the inward movements across all tempi, the predictions were the following. the neuromus-cular template would invert in time, whereas the phrasal template remained the invariant. taking the same param-eter settings as for the right hand outward scales, we were able to generate the expected timing pattern, which fit the totality of the inward scale data set well (R2

adj = 0.42, χ2

red(149) = .55, p < .001). again, this amounts to a highly stringent cross-validation test because the data set on which the model is evaluated is different (ascending vs. descend-ing scale playing) than the data set on which the model is fitted. the fact that the fit is nevertheless significant shows the robustness of the model.

Generalising to both hands and directions

Finally, we combined the previous models into a single model for our entire data set of 15 notes across 5 tempi, 2 hands and 2 directions, that is, 300 data points. Using our model that was fit exclusively on the right hand out-ward scale, as a cross-validation we generalised to the other directions and hands as above. the overall model contained four parameters and was highly significant (R2

adj = 0.49, χ2

red(299) = 0.53, p < 10−7). Its fit could potentially be fur-ther optimised by fitting the parameters on the entire data set, instead of using the parameters fit exclusively on the right hand outward scales. however, we found the current analysis more convincing since the remainder of the data set served as cross-validation.

Discussion

the present study aimed to clarify how the brain controls piano scale playing at various speeds. In particular, how do temporal deviation patterns in piano scale playing differ across different tempi and playing directions and hands? the key prediction of generalised motor programmes (sha-piro et al. 1981) is that the timing of motor output scales with the tempo at which the motor programme is executed. the present study did not find evidence for this prediction. timing deviations were qualitatively different at fast and slow tempi, as suggested by previous findings (MacKenzie and Van Eerd 1990). the distributions of the temporal devi-ations vary strongly between different notes in the scales, in line with previous findings (van Vugt et al. 2012, 2013b). We generated a model that was able to explain these varia-tions as a combination of two qualitatively different timing templates (i.e., phrasal and neuromuscular templates). tak-ing only one of these templates and parametrically modu-lating it as a function of tempo revealed a significantly infe-rior model. this observation constitutes evidence against the relational invariance prediction derived from the gen-eralised motor programme hypothesis (Repp 1990, 1994).

What do the motor templates identified in this study represent? During typical playing, the thumb passes underneath the index and middle finger twice and under-neath the index, middle and ring finger once (thumb pas-sages) during the two-octave outward scale playing. after each such thumb-pass manoeuvre, the index finger has to

Fig. 5 Original outward (red) and re-aligned inward (blue) deviation traces for the fastest tempo. the inward traces are mirrored in time and in lateness, and shifted by one note (see main text for details). Shaded areas indicate the sE of the mean (colour figure online)

Author's personal copy

Exp Brain Res

1 3

pass over the thumb (index passage). at fast tempi, a tem-plate that instantiates the delays inherent in this so-called thumb-under manoeuvre (Engel et al. 1997) is dominant. as a result, we labelled this template as the neuromuscu-lar template. In conjunction with the finding that tone dura-tions preceding these delayed keystrokes are systematically shorter, this template can be explained based on low-level constraints on finger movements. a fixed amount of time is required for the fingers to translate to their next keystroke position. We found that this translation time was independ-ent of distance: it was the same when the thumb passes underneath two (between e and f and e′ and f′) or three fin-gers (between b and c′) (Fig. 2b).

at slower tempi, however, the pattern of deviations shows two clear landmarks: mildly slower playing in the beginning and a more pronounced slowing at the end. tim-ing traces of this shape are a widespread finding in the musical timing literature (Palmer and Krumhansl 1987; van Vugt et al. 2012) known as final ritard (honing 2003). they are furthermore reminiscent of timing patterns for languages across the globe (turk and shattuck-hufnagel 2007). It is similarly a typical feature of locomotion to slow down at the end in a very similar fashion (Friberg and sundberg 1999). that is, we interpret this template as an expressive device that signals phrasal structure. this inter-pretation is supported by the finding that this template was not inverted in time, but remained invariant to temporal inversion, contrary to the neuromuscular template. the dominance of the phrasal template at slower tempi reveals that when temporal constraints on playing are less strict, pianists shift their cognitive resources to generating an aesthetically pleasing sound. Furthermore, the fact that the phrasal template is absent at the fastest tempo suggests that it reflects not a fundamental feature movement but rather a control property that is present whenever contextual con-straints allow it. the phenomenon of slowing down at the beginning and end appears to be found in action observa-tion as well. In particular, continuous motion appears to slow down as a result of our perceptual system’s adaptation to it (Goldstein 1957). In general, salient events (such as a start or end of a movement sequence) slow down our per-ception of time (tse et al. 2004). however, we argue that this action observation phenomenon cannot account for the timing deviations observed in our phrasal template. Pianists were instructed to aim for temporal evenness, and therefore if the beginning and end of the scale sounded slower, pia-nists would have responded with compensatory speeding up (Penel and Drake 2004).

We observed that two timing templates accounted for a large portion of the variance in this complex data set of timing performance across a variety of tempi. We feel this reflects that the motor system employs a dimensionality reduction of control (Bernshteı̆n 1967). the motor system

is capable of generating rich repertoires of movements to fulfil various task demands. this flexibility, however, causes neural processing to become intractable when hav-ing to produce fast sequential movements. a simplification of movement control through combining a small number of fundamental motor patterns (i.e. primitives) has been evident in various simple and complex motor behaviours, such as kicking (hart and Giszter 2004; d’ avella and Bizzi 2005), walking (Ivanenko et al. 2004), reaching (d’ avella et al. 2006), hand grasping (santello et al. 2002; Gentner and classen 2006) and musical performance (Gentner et al. 2010; Furuya et al. 2011a). together with the present study, these findings suggest that the nervous system efficiently produces a wide repertoire of movements using a small set of motor primitives.

We found that the timing patterns were similar between hands and playing directions. this indicated that the brain was able to generalise motor programmes across the effec-tors and across the movement directions. Our results indi-cate a great degree of overlap between motor representa-tions used to control both the hands (Fig. 4). however, particularly at faster tempi, the transition-induced hesita-tions due to the thumb-under manoeuvre appeared to be more pronounced in the left hand. this is in line with previ-ous studies revealing inter-manual differences due to inter-segmental dynamics between the dominant and non-domi-nant hands (sainburg and Kalakanis 2000; sainburg 2002; Bagesteiro and sainburg 2002; heuer 2007).

Production of a planned movement necessitates com-pensation for neuromuscular constraints on the limb (Kawato 1999). this requires accurate representation of the limb dynamics, referred to as an internal model, which is acquired through extensive training (thoroughman and shadmehr 2000; Osu et al. 2002). however, our finding of the timing deviations captured by the neuromuscular tem-plate of skilled pianists indicated failure to compensate for biomechanical constraints of the hand particularly when playing at fast tempo. that is, at this speed, pianists did not play on time on average, but showed systematic timing irregularities in the form of three peaks of temporal devia-tion. Why were pianists not able to remove these delays through extensive practice? the systematic deviations of the magnitude found here were previously found to be indistinguishable from perfect regularity even for trained musicians (van Vugt et al. 2013b). It is thus possible that the present skilled pianists took maximal advantage of this perceptual allowance to cope with the biomechanical con-straints that emerge during the thumb-under movement.

a novel finding is that temporal deviations were main-tained in movements performed inverted in space (mirrored) and time (performed backwards). Our study complements the current understanding of generalised motor programmes by showing that the motor primitives show a remarkable

Author's personal copy

Exp Brain Res

1 3

flexibility in that they can be transferred between effectors and mirrored in time. Furthermore, the linear combination of a time-inverted (neuromuscular) and time-invariant (phrasal) motor template at intermediate tempi results in a motor pattern that is symmetric neither in space nor in time. this reveals the sheer complexity of control that can be achieved through sim-ple combination and mirroring of motor templates.

the model we presented allowed us to adequately quantify note-by-note timing deviations across a variety of tempi. the model can be fit to individual pianist’s data (Fig. 3b). this allows us to gain insight into the relative prominence of the two templates in a pianists’ playing, which could constitute a touchstone for metrics of exper-tise (Jabusch et al. 2009) as well as for a deeper investiga-tion of anomalies in piano playing in patients with musi-cian’s dystonia (MD). MD is characterised by structural and functional maladaptation at cortical and subcortical regions, which result in a loss of fine motor control (alten-müller and Jabusch 2009). scale playing timing variability has been shown a meaningful indicator of MD severity in affected pianists (Jabusch et al. 2004; Rosenkranz et al. 2009; van Vugt et al. 2014) and correlated with neuro-ana-tomical irregularities (Granert et al. 2011). Based on the previous findings, we can now ask what qualitative aspects of playing are altered in MD patients. Furthermore, are the motor primitives themselves affected or is it their recom-bination of them that is altered in these patients? the pre-sent study provides a starting point for tackling these issues straightforwardly. Furthermore, the current study provides a basis for identifying symptoms specific to other disorders such as tendonitis and carpal tunnel syndrome, which have been prevalent among pianists (hochberg et al. 1983).

Acknowledgments this research was supported by the EBRaMUs (European Brain and Music) Initial training Network Grant (ItN Mc FP7, Ga 238157).

References

altenmüller E, Jabusch h-c (2009) Focal hand dystonia in musicians: phenomenology, etiology, and psychological trigger factors. J hand ther 22:144–154. doi:10.1016/j.jht.2008.11.007

Bagesteiro lB, sainburg Rl (2002) handedness: dominant arm advantages in control of limb dynamics. J Neurophysiol 88:2408–2421. doi:10.1152/jn.00901.2001

Bakeman R (2005) Recommended effect size statistics for repeated measures designs. Behav Res Methods 37:379–384

Bernshteı̆n Na (1967) the co-ordination and regulation of move-ments. Pergamon Press, Oxford

Bhatara a, tirovolas aK, Duan lM et al (2011) Perception of emo-tional expression in musical performance. J Exp Psychol hum Percept Perform 921–934. doi:10.1037/a0021922

clarke EF (1982) timing in the performance of Erik satie’s “Vexations”. acta Psychol (amst) 50:1–19. doi:10.1016/ 0001-6918(82)90047-6

D’ avella a, Bizzi E (2005) shared and specific muscle synergies in natural motor behaviors. Proc Natl acad sci 102:3076–3081. doi:10.1073/pnas.0500199102

D’ avella a, Portone a, Fernandez l, lacquaniti F (2006) con-trol of fast-reaching movements by muscle synergy combina-tions. J Neurosci 26:7791–7810. doi:10.1523/JNEUROscI. 0830-06.2006

Dalla Bella s, Peretz I, Rousseau l, Gosselin N (2001) a develop-mental study of the affective value of tempo and mode in music. cognition 80:B1–B10

Desain P, honing h (1994) Does expressive timing in music perfor-mance scale proportionally with tempo? Psychol Res 56:285–292. doi:10.1007/BF00419658

Engel Kc, Flanders M, soechting JF (1997) anticipatory and sequen-tial motor control in piano playing. Exp Brain Res 113:189–199

Friberg a, sundberg J (1999) Does music performance allude to locomotion? a model of final ritardandi derived from measure-ments of stopping runners. J acoust soc am 105:1469–1484. doi:10.1121/1.426687

Friberg a, Bresin R, sundberg J (2006) Overview of the Kth rule system for musical performance. adv cogn Psychol 2:145–161

Furuya s, soechting JF (2010) Role of auditory feedback in the con-trol of successive keystrokes during piano playing. Exp Brain Res 204:223–237. doi:10.1007/s00221-010-2307-2

Furuya s, Flanders M, soechting JF (2011a) hand kinematics of piano playing. J Neurophysiol 106:2849–2864. doi:10.1152/jn. 00378.2011

Furuya s, Goda t, Katayose h et al (2011b) Distinct inter-joint coor-dination during fast alternate keystrokes in pianists with superior skill. Front hum Neurosci 5:50. doi:10.3389/fnhum.2011.00050

Furuya s, aoki t, Nakahara h, Kinoshita h (2012) Individual dif-ferences in the biomechanical effect of loudness and tempo on upper-limb movements during repetitive piano keystrokes. hum Mov sci 31:26–39. doi:10.1016/j.humov.2011.01.002

Gentner R, classen J (2006) Modular organization of finger move-ments by the human central nervous system. Neuron 52:731–742. doi:10.1016/j.neuron.2006.09.038

Gentner R, Gorges s, Weise D et al (2010) Encoding of motor skill in the corticomuscular system of musicians. curr Biol 20:1869–1874. doi:10.1016/j.cub.2010.09.045

Goebl W, Palmer c (2013) temporal control and hand movement efficiency in skilled music performance. Plos One 8:e50901. doi:10.1371/journal.pone.0050901

Goldstein aG (1957) Judgments of visual velocity as a function of length of observation time. J Exp Psychol 54:457–461

Granert O, Peller M, Jabusch h-c et al (2011) sensorimotor skills and focal dystonia are linked to putaminal grey-matter volume in pianists. J Neurol Neurosurg Psychiatry 1225–1231. doi:10.1136/jnnp.2011.245811

hart cB, Giszter sF (2004) Modular premotor drives and unit bursts as primitives for frog motor behaviors. J Neurosci 24:5269–5282. doi:10.1523/jneurosci.5626-03.2004

heuer h (2007) control of the dominant and nondominant hand: exploitation and taming of nonmuscular forces. Exp Brain Res 178:363–373. doi:10.1007/s00221-006-0747-5

hochberg Fh, leffert RD, heller MD, Merriman l (1983) hand difficulties among musicians. JaMa J am Med assoc 249:1869–1872

hollerbach MJ, Flash t (1982) Dynamic interactions between limb segments during planar arm movement. Biol cybern 44:67–77

honing h (2003) the final ritard: on music, emotion, and kinematic models. comput Music J 27:66–72

honing h (2006) Evidence for tempo-specific timing in music using a web-based experimental setup. J Exp Psychol hum Percept Per-form 32:780–786. doi:10.1037/0096-1523.32.3.780

Author's personal copy

Exp Brain Res

1 3

honing h (2007) Is expressive timing relational invariant under tempo transformation? Psychol Music 35:276–285. doi:10.1177/0305735607070380

hore J, O’Brien M, Watts s (2005) control of joint rotations in overarm throws of different speeds made by dominant and non-dominant arms. J Neurophysiol 94:3975–3986. doi:10.1152/jn.00327.2005

Ivanenko YP, Poppele RE, lacquaniti F (2004) Five basic muscle acti-vation patterns account for muscle activity during human locomo-tion. J Physiol 556:267–282. doi:10.1113/jphysiol.2003.057174

Jabusch h-c, Vauth h, altenmüller E (2004) Quantification of focal dystonia in pianists using scale analysis. Mov Disord 19:171–180. doi:10.1002/mds.10671

Jabusch h-c, alpers h, Kopiez R et al (2009) the influence of prac-tice on the development of motor skills in pianists: a longitu-dinal study in a selected motor task. hum Mov sci 28:74–84. doi:10.1016/j.humov.2008.08.001

Kawato M (1999) Internal models for motor control and trajectory planning. curr Opin Neurobiol 9:718–727

Khalfa s, Roy M, Rainville P et al (2008) Role of tempo entrainment in psychophysiological differentiation of happy and sad music? Int J Psychophysiol 68:17–26. doi:10.1016/j.ijpsycho.2007.12.001

MacKenzie cl, Van Eerd Dl (1990) Rhythmic precision in the per-formance of piano scales: motor psychophysics and motor pro-gramming. atten Perform 13:375–408

Osu R, Franklin DW, Kato h et al (2002) short- and long-term changes in joint co-contraction associated with motor learning as revealed from surface EMG. J Neurophysiol 88:991–1004

Palmer c, Krumhansl cl (1987) Independent temporal and pitch structures in determination of musical phrases. J Exp Psychol hum Percept Perform 13:116–126. doi:10.1037/ 0096-1523.13.1.116

Penel a, Drake c (2004) timing variations in music performance: musical communication, perceptual compensation, and/or motor control? Percept Psychophys 66:545–562

Repp Bh (1990) Patterns of expressive timing in performances of a Beethoven minuet by nineteen famous pianists. J acoust soc am 88:622–641

Repp Bh (1994) Relational invariance of expressive microstructure across global tempo changes in music performance: an explora-tory study. Psychol Res 56:269–284

Rosenkranz K, Butler K, Williamon a, Rothwell Jc (2009) Regaining motor control in musician’s dystonia by restoring sensorimotor organization. J Neurosci 29:14627–14636. doi:10.1523/JNEUROscI.2094-09.2009

sainburg Rl (2002) Evidence for a dynamic-dominance hypoth-esis of handedness. Exp Brain Res 142:241–258. doi:10.1007/s00221-001-0913-8

sainburg Rl, Kalakanis D (2000) Differences in control of limb dynamics during dominant and nondominant arm reaching. J Neurophysiol 83:2661–2675

santello M, Flanders M, soechting JF (2002) Patterns of hand motion during grasping and the influence of sensory guidance. J Neuro-sci 22:1426–1435

shapiro Dc, Zernicke RF, Gregor RJ (1981) Evidence for general-ized motor programs using gait pattern analysis. J Mot Behav 13:33–47

summers JJ (1975) the role of timing in motor program representa-tion. J Mot Behav 7:229–241

thoroughman Ka, shadmehr R (2000) learning of action through adaptive combination of motor primitives. Nature 407:742–747. doi:10.1038/35037588

tse PU, Intriligator J, Rivest J, cavanagh P (2004) attention and the subjective expansion of time. atten Percept Psychophys 66:1171–1189

turk aE, shattuck-hufnagel s (2007) Multiple targets of phrase-final lengthening in american English words. J Phon 35:445–472. doi:10.1016/j.wocn.2006.12.001

Van Vugt Ft, Jabusch h-c, altenmüller E (2012) Fingers phrase music differently: trial-to-trial variability in piano scale playing and auditory perception reveal motor chunking. Front audit cogn Neurosci 3:495. doi:10.3389/fpsyg.2012.00495

Van Vugt Ft, altenmüller E, Jabusch h-c (2013a) the influence of chronotype on making music: circadian fluctuations in pianists’ fine motor skills. Front hum Neurosci 7:347. doi:10.3389/fnhum.2013.00347

Van Vugt Ft, Jabusch h-c, altenmüller E (2013b) Individuality that is unheard of: systematic temporal deviations in scale play-ing leave an inaudible pianistic fingerprint. Front cogn sci 134. doi:10.3389/fpsyg.2013.00134

Van Vugt Ft, Boullet l, Jabusch h-c, altenmüller E (2014) Musi-cian’s dystonia in pianists: long-term evaluation of retrain-ing and other therapies. Parkinsonism Relat Disord 20:8–12. doi:10.1016/j.parkreldis.2013.08.009

Wagner c (1971) the influence of the tempo of playing on the rhyth-mic structure studied at pianist’s playing scales. In: Vredenbregt J, Wartenweiler J (eds) Med sport. Karger, Basel, pp 129–132

Windsor l, aarts R, Desain P et al (2001) the timing of grace notes in skilled musical performance at different tempi: a preliminary case study. Psychol Music 29:149–169. doi:10.1177/0305735601292005

Author's personal copy