BACKGROUND
a key issue in motor control research has been to understand how the nervous system organizes redundant number of joints for a purposeful movement production  <cit> .
to elucidate this, a number of studies have investigated skillful multi-joint arm movements, such as reaching toward the target  <cit> , drawing a line or circle  <cit> , throwing the ball  <cit> , and striking the piano key from some height  <cit> .
a common observation was that while moving the arm toward the target, the motor system took advantage of the inter-segmental dynamics originating from proximal muscular contraction to accelerate distal joint rotation effectively  <cit> .
however, these studies have focused on gross movement where proximal muscles are mainly used for movement production  <cit> .
little has been known about the organization of multi-joint movements during fine motor actions that are performed predominantly by distal muscles.
a comparative study of piano keystrokes with pressed and struck touches may be of help to better understand this issue.
the former touch starts with the finger-tip contacting with the key, followed by an instantaneous production of force to depress the key.
the latter touch involves a preparatory lifting of the arm, followed by a downswing before the finger-tip collides and depresses the key.
in a series of biomechanical studies, we have recently examined kinematics, kinetics, and muscular activities of the upper-limb movements during the struck touch performed by expert pianists  <cit> .
results demonstrated that during downswing the pianists volitionally decelerated shoulder extension to generate the inter-segmental dynamics that accelerates elbow and wrist joint rotations.
they also produced shoulder flexion motion during key depression, and thereby increased the angle of the finger segment relative to the key .
this resulted in the decreased finger joint torque that was produced by the key-reaction force, which lessened finger muscular force for compensating it.
in contrast to these, information on the pressed touch has been fairly limited.
some researchers have examined kinematics and kinetics of the key movements while pianists were striking a key using the pressed and struck touches at various sound dynamics  <cit> .
results showed that the profiles of key reaction force in these touches clearly differed across all levels of tone loudness.
the pressed touch was characterized by a less steep initial force development with smaller fluctuations in the subsequent period than the struck touch, implying precise control of the finger-tip movements.
to our knowledge, however, no information on differences in the organization of the upper-limb movement during keystroke by the pressed and struck touches has been characterized.
understanding this is of significance not only for illustrating multi-joint movement control during fine motor actions such as tool-use, but also for some practical reasons.
for example, previous psychoacoustic studies have shown these two touches elicited tones with different perception of timbre  <cit> , suggesting a possibility of determining the movement organization responsible for manipulating tone timbre through examining these two touches.
there is also clinical importance since a number of studies have reported playing-related injuries among piano players worldwide, but its risk factors remain unclear  <cit> .
the primary purpose of the present study was to determine differences in kinematics and kinetics of the upper-limb movements during key depression between the pressed and struck touches.
we specifically focused on the effect of preparatory arm-downswing on the cause-and-effect relation between motor commands issued into muscles and kinematics of key-depressing motion.
to this aim, we used an induced acceleration analysis, which consists of inverse and forward dynamics computations  <cit> .
this technique allows for quantitatively determining the effect of individual muscular torque  as well as non-muscular torques on accelerating all the joints in the motor system.
we hypothesized that no preparatory arm downswing in the pressed touch would result in larger elbow extension and wrist flexion accelerations directly attributed to their corresponding mus, and larger shoulder and finger flexion velocities as well as their accelerations induced by the corresponding muss, as compared to the struck mode.
the second purpose of the study was to determine differences between perception of timbre of the tone generated by the pressed touch and the struck touch by using a psychoacoustic experiment.
previous studies showed that the timbre of tones produced by these two touches could be differentiated by ordinal subjects  <cit> , but it remains unknown what kind of perception would be evoked by listening to these tones.
methods
participants
seven right-handed expert pianists  with more than  <dig> years of classical-piano training participated in the biomechanical experiment, and another eight pianists with more than  <dig> years of piano playing  participated in the perceptual test.
all the expert pianists who participated in the biomechanical experiment had won awards at domestic and/or international classical piano competitions.
in accordance with the declaration of helsinki, the experimental procedure was explained to all participants and each participant signed a written informed consent.
the study was approved by the local ethics committee at osaka university.
experimental apparatus and key-striking task
the experimental apparatuses used were a yamaha u <dig> upright acoustic piano, two 2-d position sensor systems , a sound-level meter , and a stereo sound amplifier.
in the c3-key, a strain-gauge miniature uniaxial force transducer was installed at its distal end.
all signals from the position sensor, the amplifier of the force transducer, and the sound-level meter were stored on a pc via a 12-bit a/d converter with a sampling frequency of  <dig> hz.
the experimental task was a right-hand keystroke of the c <dig> key by the middle finger in a short tone production mode  with struck and pressed touches.
for the struck touch, each participant began with the fingertip lightly touching the key, lifted his/her right arm/hand to a self-determined height, and struck the key at a designated level of tone.
for the pressed touch, each participant depressed the key with the finger initially resting on the key surface.
in both touches, the participant then lifted his/her hand and arm again as a follow-through, and returned to the initial position.
the left arm was kept relaxed and placed on the side of the trunk while the trunk was in an upright position with minimal movement.
two loudness levels of piano  and forte , which corresponded to maximum key-force levels of  <dig>  and  <dig>  n, respectively, were selected in this study.
kinematic, kinetic and simultaneous sound data were collected from  <dig> successful strokes at each target loudness level with a strike-to-strike interval of approximately  <dig> s for each participant.
the target loudness level was a prerecorded piano sound on a minidisk, which was presented from a set of speakers placed on top of the piano.
the subject was asked for a retrial when the sound pressure level  of the elicited tone was greater or smaller by more than  <dig>  db compared with the target spl.
data acquisition procedure
the movement of the upper-limb in the sagittal plane was recorded using one of the position sensor cameras .
the leds required for this purpose were mounted on the skin over the fingertip of the middle finger and at the centers of the metacarpo-phalangeal , styloid process , head of radius , and coracoid process  joints.
the data was digitally smoothed at a cut-off frequency of  <dig> hz using a second-order butterworth digital filter.
the angular displacement at the finger, wrist, elbow, and shoulder joints, and that of the middle finger segment relative to the key surface were then numerically computed.
the c3-key kinematics was recorded using another position sensor camera and an led placed on the key surface.
the onset of the key descending movement  was determined when the calculated vertical velocity of the key exceeded 5% of its peak.
induced acceleration analysis
we used an induced acceleration technique that consists of a sequence of inverse and forward dynamics computations  <cit> .
an advantage of this technique is that it allows us to quantitatively determine the effect of torque produced at one joint on movements at the other joints in the multi-segmental motor system .
using the measured kinematic and key-force data along with the anthropometric data of each participant, inverse dynamics computation were initially performed to obtain the time varying muscular torques  at the shoulder, elbow, wrist, and finger joints.
the mus value was calculated as follows:
mus=iθ¨−v−jtf
note that we defined mus as muscular torque that removed static component counteracting with gravitational torque, which is directly used for limb movement production  <cit> .
for the purpose of this study, the upper-extremity was assumed as four interconnected rigid links  .
complete equations of motion are listed in the additional file  <dig>
based on the computed mus values, we then used forward dynamics equations to compute angular accelerations induced by the mus as follows:
θ¨=i−1+jtf)
this equation tells us that the angular acceleration at each joint is produced by mus at shoulder, elbow, wrist and finger joints, velocity-dependent torque , and reaction-force torque originating from mechanical interaction between the finger-tip and key .
to evaluate kinetic source of the angular velocities produced during key depression , we then computed the integral of the shoulder, elbow, wrist and finger joint accelerations produced by each mus , vel , and rea  from the moment of finger-key contact  to the moment of lowest key position  as follows.
impθ¨mus=∫t1t2i−1mus dtimpθ¨vel=∫t1t2i−1v dtimpθ¨rea=∫t1t2i−1jtf dt
perceptual test of tone timbre
a discrimination task of tone's timbre difference was separately performed.
to obtain the sound for this test, one expert pianist was asked to strike the c <dig> key of a grand piano  in a sound-proof room with the struck and pressed touches.
the generated sound was recorded using a dynamic microphone  and an audio interface  with the sampling frequency of  <dig>  khz.
in total, twenty sounds were recorded for each touch, and from these, four tones  with the same loudness level  and same duration was carefully selected.
another eight pianists were then asked to listen to these tones, and rate  the quality of tone  and  attack  of each tone using visual analog scale  to  <dig> ).
they could listen to each stimulus as often as wanted until they were sure about their judgments.
statistical data analysis
using touch and loudness as independent variables, a two-way anova with repeated measures was performed for each of the dependent variables .
RESULTS
touch-dependent difference in endpoint and joint kinematics
these features are also illustrated by the stick picture of the upper-limb during the finger-key contacting period  in figure  <dig>  while depressing the key, the upper- and fore-arms moved forward and upward, and the hand moved forward and downward in both touches.
these forward and rotational movements of the upper-limb were much greater during the pressed touch than the struck touch.
the numbers in the parenthesis indicate the standard deviation.
* p <  <dig> , ** p <  <dig>
induced acceleration analysis
there was marked development of shoulder flexion acceleration during key depression for both modes of key touch.
for the pressed touch, a clear increase in flexion acceleration attributed to shoulder mus was initially observed, which followed by increases in elbow and wrist mus.
for the struck touch, there was an increase in flexion acceleration attributed to shoulder mus.
while both of the two touches showed extension acceleration attributed to rea, acceleration by vel was indiscernible.
for both modes of key touch, elbow joint accelerations induced by wrist and finger mus exhibited a counteractive relationship during the finger-key contacting period.
the pressed touch also showed marked extension acceleration induced by elbow mus during the period of key-depression.
for both modes of key touch, flexion acceleration at the wrist joint during key depression was induced by wrist mus, which was commonly counteracted by finger mus.
however, the magnitudes of these were greater during the pressed touch than the struck touch.
only for the pressed touch, there were small but substantial amount of extension acceleration attributed to elbow mus during the period of key-depression.
during the key-depression period, finger joint acceleration induced by finger mus was always counteracted in both timing and magnitude by the rea.
the magnitudes of these were apparently greater at the pressed touch compared with the struck touch.
identification of joint toques contributing to joint acceleration
a limitation of fig.
<dig> was that the large scale of y-axis made it difficult to visually evaluate which joint torques contributed to the total joint acceleration.
since our aim of the kinetic analysis was to clarify dynamics underlying kinematics differences between the two touches , we attempted to quantitatively determine joint torques contributing to acceleration for shoulder flexion, elbow extension, wrist flexion and finger flexion by means of inverse dynamics analysis.
we first decomposed each of six computed joint torques into two subcomponents, either of which was the same  or opposite  sign with the net torque proportional to joint acceleration responsible for key-depression.
we then computed a contribution index  by dividing the impulse of one subcomponent having the same sign with the net torque during the key-depression period by the sum of impulses of the two subcomponents.
that is,
accordingly, the ci represented how much an individual torque contributed to the acceleration.
if the value was close to  <dig>  the torque mostly contributed to the joint acceleration during key depression.
the equations of motion used in the inverse dynamics were shown previously  <cit> .
bolded numbers indicate the value greater than  <dig> .
the numbers in the parenthesis indicate the standard deviation.
* p <  <dig>
n/a: ci value for all subjects showed  <dig> or  <dig>  and thus there was no between-subject variance
impulse of joint acceleration produced by its surrounding musclesimpθ¨mus for the elbow extension  =  <dig> , p <  <dig> ), wrist flexion  =  <dig> , p <  <dig> ), and finger flexion  =  <dig> , p <  <dig> ) compared with the struck touch.
the group × loudness interaction was also significant in this variable at the shoulder  =  <dig> , p <  <dig> ), elbow  =  <dig>  p <  <dig> ), and wrist joints  =  <dig> , p <  <dig> ).
the interaction effect indicated that with the generation of louder sound, impθ¨mus at the shoulder joint decreased, and impθ¨mus increased at the elbow and wrist joints for the pressed touch.
the loudness effect was significant at the elbow, wrist and finger joints.
impulse of joint acceleration by muscular torques at the adjacent joints
the numbers in the parenthesis indicate the standard deviation.
* p <  <dig> , ** p <  <dig>
the numbers in the parenthesis indicate the standard deviation.
* p <  <dig> , ** p <  <dig>
at the shoulder joint, the pressed touch had significantly greater flexion velocity induced by elbow and wrist mus compared with the struck touch.
for the elbow, the pressed touch had significantly smaller and greater extension velocity by the shoulder mus and finger mus compared with the struck case, respectively.
for all of these variables except for elbow extension acceleration by finger mus, there was a significant interaction effect between the touch and loudness.
the interaction effect indicates that with the generation of louder sound, the pressed touch had a greater increase in shoulder flexion acceleration by elbow and wrist mus, smaller increase in elbow extension acceleration induced by shoulder mus, and greater increase in this variable by finger mus as compared to the struck touch.
for the wrist and finger, the pressed touch showed greater extension and flexion acceleration induced by elbow mus compared with the struck touch, respectively.
these variables also showed an interaction effect, indicating a greater increase for the former touch with the generation of louder tone.
impulse of joint acceleration by velocity-dependent and reaction-force dependent torques
comparison of the impulse of joint acceleration across torques
to assess the primary joint torques that are responsible for differences in joint velocity observed between the touches, we subtracted the impulse value of joint acceleration attributed to each torque for the struck touch from that for the pressed touch, and compared it across different joint torques .
we performed this analysis only for the joints and torques with a significant difference between the touches in the impulse analyses .
for the shoulder, the difference value between the touches was positive for elbow and wrist mus , and negative for shoulder mus and vel .
a torque × loudness two-way anova with repeated measures revealed both effects of interaction  =  <dig> ; p <  <dig> ) and torque  =  <dig> ; p <  <dig> ).
for the elbow, the value was positive for shoulder mus , and negative for elbow and finger mus .
a repeated measures anova found effects of loudness × torque interaction  =  <dig> ; p <  <dig> ), torque  =  <dig> ; p <  <dig> ), and loudness  =  <dig> ; p <  <dig> ).
note that a relatively small difference value regarding shoulder mus was because the present impulse analysis did not include the period before the finger-key contact  <cit> .
for the finger, both the values for the finger and elbow mus were negative , and their difference was significant  =  <dig> ; p <  <dig> ).
perception of the tone timbre
results of the psychoacoustic experiment showed that tones generated by the pressed touch were perceived softer compared with those by the struck touch.
the mean attack of tone for all participants was  <dig>  ±  <dig>   and - <dig>  ±  <dig>  for the pressed and struck touch, respectively.
anova revealed a significant touch effect on attack of tone  =  <dig> , p <  <dig> ).
concerning the quality of tone, their mean value was - <dig>  ±  <dig>  and  <dig>  ±  <dig>  for the pressed and struck touch, respectively.
anova revealed no significant touch-dependent difference on this variable.
discussion
in the present study, the pressed touch showed greater shoulder and finger flexion velocity, and smaller elbow extension velocity compared with the struck touch.
for the shoulder, the pressed touch involved smaller flexion acceleration by shoulder mus, and greater flexion acceleration by elbow and wrist mus compared with the struck touch.
the larger shoulder flexion velocity at the former touch therefore resulted mostly from greater effect of distal-to-proximal inter-segmental dynamics.
for the elbow, the pressed touch had greater extension acceleration by elbow and finger mus, and smaller extension acceleration by shoulder mus than the struck touch.
for the finger, the pressed touch showed substantially greater flexion acceleration by finger mus compared with the struck touch, confirming that the former touch belongs to fine movements.
note that the acceleration produced by velocity-dependent torque was small relative to that produced by the other torques at all joints, which differs from large effects of velocity-dependent torque during the ball-throw  <cit> .
this can be due to different movement speed between ball-throw  and piano keystroke .
a psychoacoustic test further showed that the timbre of a tone elicited by the pressed touch was perceived softer than that by the struck touch.
kinematics and kinetic differences between the pressed and struck touches
our kinematic analysis found smaller peak elbow extension velocity, and larger peak shoulder and finger flexion velocity when the pressed touch was used compared with when the struck touch was used.
we previously found a drastic increase in elbow extension acceleration toward the end of downswing in the struck touch  <cit> , which may explain smaller elbow extension velocity during key depression at the present pressed touch.
in addition, our findings indicated that the pianists compensated for this insufficient elbow speed during the pressed touch by increasing shoulder and finger velocity in order to reach the finger-tip velocity for eliciting the target loudness of tone.
we also found that the finger joint was extended more and attack angle was smaller at the onset of key depression for the pressed touch than the struck touch.
this hand posture would provide the pressed touch with a longer horizontal distance from the joint center to the finger-tip compared with the struck touch, which consequently enhances effectiveness of finger flexion rotation for generating the descending motion of the finger-tip at the former touch.
the present pianists may therefore also compensate for the lack of preparatory arm-downswing by taking advantage of the geometric configuration of the hand and finger for depressing the key during the pressed touch.
to understand the dynamics underlying these kinematic differences between the pressed and struck touches, we performed inverse and forward dynamics computations.
the results indicated that greater shoulder flexion velocity during the pressed touch was mostly accounted for by greater shoulder flexion velocity induced by elbow and wrist muscular contractions.
effective use of the distal-to-proximal inter-segmental dynamics has been reported during skilled throwing and striking movements in the  <dig> d space  <cit> .
for example, a skilled thrower exploited the distal-to-proximal inter-segmental dynamics from elbow muscular contraction for facilitating shoulder internal rotation, and thereby instantaneously accelerated forward motion of the hand just before releasing the ball  <cit> .
however, to our best knowledge, there has been no study that addressed the use of the distal-to-proximal dynamics in the  <dig> d limb movements.
this would be because the present pressed touch requires instantaneous acceleration at the finger-tip for generating the target key velocity due to strong spatio-temporal constraints, which is absent in tasks that have been investigated in previous studies .
the effective utilization of distal-to-proximal inter-segmental dynamics can thus be a specialized movement strategy the nervous system uses for instantaneously accelerating limb endpoint in skilled multi-joint movements.
a role of vigorous shoulder flexion during key depression has been also considered to increase the attack angle and configure upstanding finger posture for lessening finger joint torque produced by the key-force as well as muscular work compensating for it  <cit> .
in the pressed touch, however, configuring such an upstanding finger posture seems to require different motor skill from the struck touch.
this is firstly because compared with the struck touch the pressed touch initiated a key-depression with a relatively extended finger posture and smaller attack angle, and secondly because the pressed touch had smaller shoulder flexion acceleration generated by its surrounding muscles, which might be due to stabilizing work of shoulder muscles against the key-reaction force.
nevertheless, we found that both attack and finger joint angles at the end of key depression did not differ between the two modes of key touch.
therefore, during the pressed touch the effective use of distal-to-proximal inter-segmental dynamics for accelerating shoulder must also have played an essential role in configuring the mechanically-advantageous finger posture.
we also found that during key depression, the pressed touch had greater elbow extension acceleration attributed to elbow mus than the struck touch.
this is contradictory with the kinematic finding since the former touch showed smaller elbow extension velocity.
a further analysis revealed that the pressed touch had smaller elbow extension acceleration by shoulder mus than the struck one.
these indicated that smaller elbow extension velocity during the former touch resulted mostly from the failure to fully exploit the effect of the proximal-to-distal inter-segmental dynamics.
similar to the elbow, production of wrist and finger flexion acceleration also relied more on their surrounding muscles during the pressed touch than the struck touch.
it is logical to assume that the distal muscles of less strength and endurance are commonly more sensitive to fatigue than the proximal muscles, and therefore stronger reliance on distal muscles with the pressed touch suggests that it is less efficient than the struck touch.
a significant interaction effect of loudness and touch on many kinematic and kinetic variables examined further suggests that differential effects of the distal muscular work between the two touch modes become greater at the production of a louder tone
playing the piano involves a repetition of keystroke reaching sometimes thousands of times per minute  <cit> .
repetitive submaximal muscular efforts may create cumulative damage in muscles and tendons, especially in the hand and forearm over times.
indeed, researchers have reported that more than 60% of active piano players at some time experience playing-related injuries from acute pain to more serious symptoms such as tendonitis and focal dystonia  <cit> .
the present finding of greater reliance on the distal muscles in the pressed touch than the struck touch particularly for stronger keystroke may therefore emphasize importance of avoiding repetitive use of the former touch for eliciting a loud tone in order to prevent the injury.
manipulation of the timbre
to be able to elicit tones with variations in the timbre is an indispensable motor skill in musical performance.
a recent psychoacoustic study showed that listening to musical stimuli having the same acoustic characteristic except for the timbre evoked different emotional experience to listeners  <cit> , emphasizing a significance of manipulating tone timbre for expressive musical performance.
relating to the piano, studies have shown that the timbre of tones produced by the struck and pressed touches could be differentiated by ordinal subjects  <cit> .
our study extended these by showing that a piano tone produced by the pressed touch was perceived softer than that by the struck touch.
this timbre difference would be related to various factors, including touch-dependent differences in the noise due to the finger-key collision  <cit>  and in key-force profile  <cit> , and nonuniform dynamic property of the finger-tip pulp  <cit> .
in addition, previous findings of audio-visual interaction in the perception of tone  <cit>  suggest that kinematic differences between the present two touches may also evoke different tone perception to audience in a live performance.
hence, in spite of relative inefficiency over the struck touch, the pressed touch would be an indispensable motor skill for pianists to accomplish expressive musical expression.
the present biomechanical and psychoacoustic findings would further provide novice piano players and piano teachers with implications that soft tone timbre could be produced by initiating key-depression with relatively extended finger posture and accentuating shoulder-finger flexion rotations.
task-relevant control of the inter-segmental dynamics
dounskaia  <cit>  recently proposed a leading joint hypothesis that provided comprehensive explanation for the control of multi-joint movements.
in this framework, there is one  joint that generates the inter-segmental dynamics at the adjacent  joints.
the subordinate joints utilize and/or compensate for the inter-segmental dynamics while accounting for its timing and magnitude so as to fulfill task requirements.
evidence in favor of this idea has been provided in various skilled multi-joint movements  <cit> .
the present findings also supported it since the pianists effectively utilized the inter-segmental dynamics for accelerating the limb during both pressed and struck touches.
the contrasting relation of leading and subordinate joints between the two touches further implies that production of a variety of tone timbre in piano playing depends on control of the inter-segmental dynamics.
since accurate control of the inter-segmental dynamics requires its precise internal representation  <cit> , manipulation of the tone timbre may need to develop distinct and multiple internal representations of the limb dynamics, such as the mozaic model  <cit> .
CONCLUSIONS
the present study probed into control strategy of multi-joint finger and arm movements for dexterous manipulation of the way of depressing a key by expert pianists.
we specifically examined two different but fundamental touches in piano playing; pressed and struck.
the most striking finding was that the pianists performed a key-depression primarily by utilizing the distal-to-proximal and proximal-to-distal inter-segmental dynamics during the pressed and struck touches, respectively.
a psychoacoustic test further revealed differences in perception of the timbre of a tone elicited by these two touches.
taken together, these findings indicate that manipulation of tone timbre in piano playing depends on control of the inter-segmental dynamics.
authors' contributions
sf designed the biomechanics study, developed equations of motion, collected and analyzed the data, and wrote and revised the draft.
ea designed the psychoacoustic experiment, and wrote and revised the draft.
hka assisted acquisition, analysis, and interpretation of data of the psychoacoustic experiment.
hki wrote and revised the draft.
all authors read, finalized, and approved the final manuscript.
supplementary material
additional file 1
equations of motion for inverse and forward dynamics computations.
the file contains complete equations of motion used for performing inverse and forward dynamics analyses.
the upper extremity was assumed as four interconnected rigid links .
click here for file
acknowledgements
we thank to dr. masaya hirashima  for his helpful suggestions to the induced acceleration analysis in the current study.
we also appreciate mr. toshiharu nishikawa  for providing an opportunity to use a bösendorfer grand piano and sound proof room for the present psychoacoustic experiment.
we thank to mr. hrishikesh rao  for proofreading the manuscript.
this study was supported by jsps grant-in-aid for young scientists  and jst crest.

 a key issue in motor control research has been to understand how the nervous system organizes redundant number of joints for a purposeful movement production. to elucidate this, a number of studies have investigated skillful multi-joint arm movements, such as reaching toward the target, drawing a line or circle, throwing the ball, and striking the piano key from some height. a common observation was that while moving the arm toward the target, the motor system took advantage of the inter-segmental dynamics originating from proximal muscular contraction to accelerate distal joint rotation effectively. however, these studies have focused on gross movement where proximal muscles are mainly used for movement production. little has been known about the organization of multi-joint movements during fine motor actions that are performed predominantly by distal muscles. a comparative study of piano keystrokes with pressed and struck touches may be of help to better understand this issue. the former touch starts with the finger-tip contacting with the key, followed by an instantaneous production of force to depress the key. the latter touch involves a preparatory lifting of the arm, followed by a downswing before the finger-tip collides and depresses the key. in a series of biomechanical studies, we have recently examined kinematics, kinetics, and muscular activities of the upper-limb movements during the struck touch performed by expert pianists. results demonstrated that during downswing the pianists volitionally decelerated shoulder extension to generate the inter-segmental dynamics that accelerates elbow and wrist joint rotations. they also produced shoulder flexion motion during key depression, and thereby increased the angle of the finger segment relative to the key. this resulted in the decreased finger joint torque that was produced by the key-reaction force, which lessened finger muscular force for compensating it. in contrast to these, information on the pressed touch has been fairly limited. some researchers have examined kinematics and kinetics of the key movements while pianists were striking a key using the pressed and struck touches at various sound dynamics. results showed that the profiles of key reaction force in these touches clearly differed across all levels of tone loudness. the pressed touch was characterized by a less steep initial force development with smaller fluctuations in the subsequent period than the struck touch, implying precise control of the finger-tip movements. to our knowledge, however, no information on differences in the organization of the upper-limb movement during keystroke by the pressed and struck touches has been characterized. understanding this is of significance not only for illustrating multi-joint movement control during fine motor actions such as tool-use, but also for some practical reasons. for example, previous psychoacoustic studies have shown these two touches elicited tones with different perception of timbre, suggesting a possibility of determining the movement organization responsible for manipulating tone timbre through examining these two touches. there is also clinical importance since a number of studies have reported playing-related injuries among piano players worldwide, but its risk factors remain unclear. the primary purpose of the present study was to determine differences in kinematics and kinetics of the upper-limb movements during key depression between the pressed and struck touches. we specifically focused on the effect of preparatory arm-downswing on the cause-and-effect relation between motor commands issued into muscles and kinematics of key-depressing motion. to this aim, we used an induced acceleration analysis, which consists of inverse and forward dynamics computations. this technique allows for quantitatively determining the effect of individual muscular torque as well as non-muscular torques on accelerating all the joints in the motor system. we hypothesized that no preparatory arm downswing in the pressed touch would result in larger elbow extension and wrist flexion accelerations directly attributed to their corresponding mus, and larger shoulder and finger flexion velocities as well as their accelerations induced by the corresponding muss, as compared to the struck mode. the second purpose of the study was to determine differences between perception of timbre of the tone generated by the pressed touch and the struck touch by using a psychoacoustic experiment. previous studies showed that the timbre of tones produced by these two touches could be differentiated by ordinal subjects, but it remains unknown what kind of perception would be evoked by listening to these tones. methods participants seven right-handed expert pianists with more than years of classical-piano training participated in the biomechanical experiment, and another eight pianists with more than years of piano playing participated in the perceptual test. all the expert pianists who participated in the biomechanical experiment had won awards at domestic and/or international classical piano competitions. in accordance with the declaration of helsinki, the experimental procedure was explained to all participants and each participant signed a written informed consent. the study was approved by the local ethics committee at osaka university. experimental apparatus and key-striking task the experimental apparatuses used were a yamaha u upright acoustic piano, two 2-d position sensor systems, a sound-level meter, and a stereo sound amplifier. in the c3-key, a strain-gauge miniature uniaxial force transducer was installed at its distal end. all signals from the position sensor, the amplifier of the force transducer, and the sound-level meter were stored on a pc via a 12-bit a/d converter with a sampling frequency of hz. the experimental task was a right-hand keystroke of the c key by the middle finger in a short tone production mode with struck and pressed touches. for the struck touch, each participant began with the fingertip lightly touching the key, lifted his/her right arm/hand to a self-determined height, and struck the key at a designated level of tone. for the pressed touch, each participant depressed the key with the finger initially resting on the key surface. in both touches, the participant then lifted his/her hand and arm again as a follow-through, and returned to the initial position. the left arm was kept relaxed and placed on the side of the trunk while the trunk was in an upright position with minimal movement. two loudness levels of piano and forte, which corresponded to maximum key-force levels of and n, respectively, were selected in this study. kinematic, kinetic and simultaneous sound data were collected from successful strokes at each target loudness level with a strike-to-strike interval of approximately s for each participant. the target loudness level was a prerecorded piano sound on a minidisk, which was presented from a set of speakers placed on top of the piano. the subject was asked for a retrial when the sound pressure level of the elicited tone was greater or smaller by more than db compared with the target spl. data acquisition procedure the movement of the upper-limb in the sagittal plane was recorded using one of the position sensor cameras. the leds required for this purpose were mounted on the skin over the fingertip of the middle finger and at the centers of the metacarpo-phalangeal, styloid process, head of radius, and coracoid process joints. the data was digitally smoothed at a cut-off frequency of hz using a second-order butterworth digital filter. the angular displacement at the finger, wrist, elbow, and shoulder joints, and that of the middle finger segment relative to the key surface were then numerically computed. the c3-key kinematics was recorded using another position sensor camera and an led placed on the key surface. the onset of the key descending movement was determined when the calculated vertical velocity of the key exceeded 5% of its peak. induced acceleration analysis we used an induced acceleration technique that consists of a sequence of inverse and forward dynamics computations. an advantage of this technique is that it allows us to quantitatively determine the effect of torque produced at one joint on movements at the other joints in the multi-segmental motor system. using the measured kinematic and key-force data along with the anthropometric data of each participant, inverse dynamics computation were initially performed to obtain the time varying muscular torques at the shoulder, elbow, wrist, and finger joints. the mus value was calculated as follows: mus=iθ¨−v−jtf note that we defined mus as muscular torque that removed static component counteracting with gravitational torque, which is directly used for limb movement production. for the purpose of this study, the upper-extremity was assumed as four interconnected rigid links. complete equations of motion are listed in the additional file based on the computed mus values, we then used forward dynamics equations to compute angular accelerations induced by the mus as follows: θ¨=i−1+jtf) this equation tells us that the angular acceleration at each joint is produced by mus at shoulder, elbow, wrist and finger joints, velocity-dependent torque, and reaction-force torque originating from mechanical interaction between the finger-tip and key. to evaluate kinetic source of the angular velocities produced during key depression, we then computed the integral of the shoulder, elbow, wrist and finger joint accelerations produced by each mus, vel, and rea from the moment of finger-key contact to the moment of lowest key position as follows. impθ¨mus=∫t1t2i−1mus dtimpθ¨vel=∫t1t2i−1v dtimpθ¨rea=∫t1t2i−1jtf dt perceptual test of tone timbre a discrimination task of tone's timbre difference was separately performed. to obtain the sound for this test, one expert pianist was asked to strike the c key of a grand piano in a sound-proof room with the struck and pressed touches. the generated sound was recorded using a dynamic microphone and an audio interface with the sampling frequency of khz. in total, twenty sounds were recorded for each touch, and from these, four tones with the same loudness level and same duration was carefully selected. another eight pianists were then asked to listen to these tones, and rate the quality of tone and attack of each tone using visual analog scale to ). they could listen to each stimulus as often as wanted until they were sure about their judgments. statistical data analysis using touch and loudness as independent variables, a two-way anova with repeated measures was performed for each of the dependent variables.  touch-dependent difference in endpoint and joint kinematics these features are also illustrated by the stick picture of the upper-limb during the finger-key contacting period in figure while depressing the key, the upper- and fore-arms moved forward and upward, and the hand moved forward and downward in both touches. these forward and rotational movements of the upper-limb were much greater during the pressed touch than the struck touch. the numbers in the parenthesis indicate the standard deviation. * p <, ** p < induced acceleration analysis there was marked development of shoulder flexion acceleration during key depression for both modes of key touch. for the pressed touch, a clear increase in flexion acceleration attributed to shoulder mus was initially observed, which followed by increases in elbow and wrist mus. for the struck touch, there was an increase in flexion acceleration attributed to shoulder mus. while both of the two touches showed extension acceleration attributed to rea, acceleration by vel was indiscernible. for both modes of key touch, elbow joint accelerations induced by wrist and finger mus exhibited a counteractive relationship during the finger-key contacting period. the pressed touch also showed marked extension acceleration induced by elbow mus during the period of key-depression. for both modes of key touch, flexion acceleration at the wrist joint during key depression was induced by wrist mus, which was commonly counteracted by finger mus. however, the magnitudes of these were greater during the pressed touch than the struck touch. only for the pressed touch, there were small but substantial amount of extension acceleration attributed to elbow mus during the period of key-depression. during the key-depression period, finger joint acceleration induced by finger mus was always counteracted in both timing and magnitude by the rea. the magnitudes of these were apparently greater at the pressed touch compared with the struck touch. identification of joint toques contributing to joint acceleration a limitation of fig. was that the large scale of y-axis made it difficult to visually evaluate which joint torques contributed to the total joint acceleration. since our aim of the kinetic analysis was to clarify dynamics underlying kinematics differences between the two touches, we attempted to quantitatively determine joint torques contributing to acceleration for shoulder flexion, elbow extension, wrist flexion and finger flexion by means of inverse dynamics analysis. we first decomposed each of six computed joint torques into two subcomponents, either of which was the same or opposite sign with the net torque proportional to joint acceleration responsible for key-depression. we then computed a contribution index by dividing the impulse of one subcomponent having the same sign with the net torque during the key-depression period by the sum of impulses of the two subcomponents. that is, accordingly, the ci represented how much an individual torque contributed to the acceleration. if the value was close to the torque mostly contributed to the joint acceleration during key depression. the equations of motion used in the inverse dynamics were shown previously. bolded numbers indicate the value greater than. the numbers in the parenthesis indicate the standard deviation. * p < n/a: ci value for all subjects showed or and thus there was no between-subject variance impulse of joint acceleration produced by its surrounding musclesimpθ¨mus for the elbow extension =, p < ), wrist flexion =, p < ), and finger flexion =, p < ) compared with the struck touch. the group × loudness interaction was also significant in this variable at the shoulder =, p < ), elbow = p < ), and wrist joints =, p < ). the interaction effect indicated that with the generation of louder sound, impθ¨mus at the shoulder joint decreased, and impθ¨mus increased at the elbow and wrist joints for the pressed touch. the loudness effect was significant at the elbow, wrist and finger joints. impulse of joint acceleration by muscular torques at the adjacent joints the numbers in the parenthesis indicate the standard deviation. * p <, ** p < the numbers in the parenthesis indicate the standard deviation. * p <, ** p < at the shoulder joint, the pressed touch had significantly greater flexion velocity induced by elbow and wrist mus compared with the struck touch. for the elbow, the pressed touch had significantly smaller and greater extension velocity by the shoulder mus and finger mus compared with the struck case, respectively. for all of these variables except for elbow extension acceleration by finger mus, there was a significant interaction effect between the touch and loudness. the interaction effect indicates that with the generation of louder sound, the pressed touch had a greater increase in shoulder flexion acceleration by elbow and wrist mus, smaller increase in elbow extension acceleration induced by shoulder mus, and greater increase in this variable by finger mus as compared to the struck touch. for the wrist and finger, the pressed touch showed greater extension and flexion acceleration induced by elbow mus compared with the struck touch, respectively. these variables also showed an interaction effect, indicating a greater increase for the former touch with the generation of louder tone. impulse of joint acceleration by velocity-dependent and reaction-force dependent torques comparison of the impulse of joint acceleration across torques to assess the primary joint torques that are responsible for differences in joint velocity observed between the touches, we subtracted the impulse value of joint acceleration attributed to each torque for the struck touch from that for the pressed touch, and compared it across different joint torques. we performed this analysis only for the joints and torques with a significant difference between the touches in the impulse analyses. for the shoulder, the difference value between the touches was positive for elbow and wrist mus, and negative for shoulder mus and vel. a torque × loudness two-way anova with repeated measures revealed both effects of interaction =; p < ) and torque =; p < ). for the elbow, the value was positive for shoulder mus, and negative for elbow and finger mus. a repeated measures anova found effects of loudness × torque interaction =; p < ), torque =; p < ), and loudness =; p < ). note that a relatively small difference value regarding shoulder mus was because the present impulse analysis did not include the period before the finger-key contact. for the finger, both the values for the finger and elbow mus were negative, and their difference was significant =; p < ). perception of the tone timbre results of the psychoacoustic experiment showed that tones generated by the pressed touch were perceived softer compared with those by the struck touch. the mean attack of tone for all participants was ± and - ± for the pressed and struck touch, respectively. anova revealed a significant touch effect on attack of tone =, p < ). concerning the quality of tone, their mean value was - ± and ± for the pressed and struck touch, respectively. anova revealed no significant touch-dependent difference on this variable. discussion in the present study, the pressed touch showed greater shoulder and finger flexion velocity, and smaller elbow extension velocity compared with the struck touch. for the shoulder, the pressed touch involved smaller flexion acceleration by shoulder mus, and greater flexion acceleration by elbow and wrist mus compared with the struck touch. the larger shoulder flexion velocity at the former touch therefore resulted mostly from greater effect of distal-to-proximal inter-segmental dynamics. for the elbow, the pressed touch had greater extension acceleration by elbow and finger mus, and smaller extension acceleration by shoulder mus than the struck touch. for the finger, the pressed touch showed substantially greater flexion acceleration by finger mus compared with the struck touch, confirming that the former touch belongs to fine movements. note that the acceleration produced by velocity-dependent torque was small relative to that produced by the other torques at all joints, which differs from large effects of velocity-dependent torque during the ball-throw. this can be due to different movement speed between ball-throw and piano keystroke. a psychoacoustic test further showed that the timbre of a tone elicited by the pressed touch was perceived softer than that by the struck touch. kinematics and kinetic differences between the pressed and struck touches our kinematic analysis found smaller peak elbow extension velocity, and larger peak shoulder and finger flexion velocity when the pressed touch was used compared with when the struck touch was used. we previously found a drastic increase in elbow extension acceleration toward the end of downswing in the struck touch, which may explain smaller elbow extension velocity during key depression at the present pressed touch. in addition, our findings indicated that the pianists compensated for this insufficient elbow speed during the pressed touch by increasing shoulder and finger velocity in order to reach the finger-tip velocity for eliciting the target loudness of tone. we also found that the finger joint was extended more and attack angle was smaller at the onset of key depression for the pressed touch than the struck touch. this hand posture would provide the pressed touch with a longer horizontal distance from the joint center to the finger-tip compared with the struck touch, which consequently enhances effectiveness of finger flexion rotation for generating the descending motion of the finger-tip at the former touch. the present pianists may therefore also compensate for the lack of preparatory arm-downswing by taking advantage of the geometric configuration of the hand and finger for depressing the key during the pressed touch. to understand the dynamics underlying these kinematic differences between the pressed and struck touches, we performed inverse and forward dynamics computations. the results indicated that greater shoulder flexion velocity during the pressed touch was mostly accounted for by greater shoulder flexion velocity induced by elbow and wrist muscular contractions. effective use of the distal-to-proximal inter-segmental dynamics has been reported during skilled throwing and striking movements in the d space. for example, a skilled thrower exploited the distal-to-proximal inter-segmental dynamics from elbow muscular contraction for facilitating shoulder internal rotation, and thereby instantaneously accelerated forward motion of the hand just before releasing the ball. however, to our best knowledge, there has been no study that addressed the use of the distal-to-proximal dynamics in the d limb movements. this would be because the present pressed touch requires instantaneous acceleration at the finger-tip for generating the target key velocity due to strong spatio-temporal constraints, which is absent in tasks that have been investigated in previous studies. the effective utilization of distal-to-proximal inter-segmental dynamics can thus be a specialized movement strategy the nervous system uses for instantaneously accelerating limb endpoint in skilled multi-joint movements. a role of vigorous shoulder flexion during key depression has been also considered to increase the attack angle and configure upstanding finger posture for lessening finger joint torque produced by the key-force as well as muscular work compensating for it. in the pressed touch, however, configuring such an upstanding finger posture seems to require different motor skill from the struck touch. this is firstly because compared with the struck touch the pressed touch initiated a key-depression with a relatively extended finger posture and smaller attack angle, and secondly because the pressed touch had smaller shoulder flexion acceleration generated by its surrounding muscles, which might be due to stabilizing work of shoulder muscles against the key-reaction force. nevertheless, we found that both attack and finger joint angles at the end of key depression did not differ between the two modes of key touch. therefore, during the pressed touch the effective use of distal-to-proximal inter-segmental dynamics for accelerating shoulder must also have played an essential role in configuring the mechanically-advantageous finger posture. we also found that during key depression, the pressed touch had greater elbow extension acceleration attributed to elbow mus than the struck touch. this is contradictory with the kinematic finding since the former touch showed smaller elbow extension velocity. a further analysis revealed that the pressed touch had smaller elbow extension acceleration by shoulder mus than the struck one. these indicated that smaller elbow extension velocity during the former touch resulted mostly from the failure to fully exploit the effect of the proximal-to-distal inter-segmental dynamics. similar to the elbow, production of wrist and finger flexion acceleration also relied more on their surrounding muscles during the pressed touch than the struck touch. it is logical to assume that the distal muscles of less strength and endurance are commonly more sensitive to fatigue than the proximal muscles, and therefore stronger reliance on distal muscles with the pressed touch suggests that it is less efficient than the struck touch. a significant interaction effect of loudness and touch on many kinematic and kinetic variables examined further suggests that differential effects of the distal muscular work between the two touch modes become greater at the production of a louder tone playing the piano involves a repetition of keystroke reaching sometimes thousands of times per minute. repetitive submaximal muscular efforts may create cumulative damage in muscles and tendons, especially in the hand and forearm over times. indeed, researchers have reported that more than 60% of active piano players at some time experience playing-related injuries from acute pain to more serious symptoms such as tendonitis and focal dystonia. the present finding of greater reliance on the distal muscles in the pressed touch than the struck touch particularly for stronger keystroke may therefore emphasize importance of avoiding repetitive use of the former touch for eliciting a loud tone in order to prevent the injury. manipulation of the timbre to be able to elicit tones with variations in the timbre is an indispensable motor skill in musical performance. a recent psychoacoustic study showed that listening to musical stimuli having the same acoustic characteristic except for the timbre evoked different emotional experience to listeners, emphasizing a significance of manipulating tone timbre for expressive musical performance. relating to the piano, studies have shown that the timbre of tones produced by the struck and pressed touches could be differentiated by ordinal subjects. our study extended these by showing that a piano tone produced by the pressed touch was perceived softer than that by the struck touch. this timbre difference would be related to various factors, including touch-dependent differences in the noise due to the finger-key collision and in key-force profile, and nonuniform dynamic property of the finger-tip pulp. in addition, previous findings of audio-visual interaction in the perception of tone suggest that kinematic differences between the present two touches may also evoke different tone perception to audience in a live performance. hence, in spite of relative inefficiency over the struck touch, the pressed touch would be an indispensable motor skill for pianists to accomplish expressive musical expression. the present biomechanical and psychoacoustic findings would further provide novice piano players and piano teachers with implications that soft tone timbre could be produced by initiating key-depression with relatively extended finger posture and accentuating shoulder-finger flexion rotations. task-relevant control of the inter-segmental dynamics dounskaia recently proposed a leading joint hypothesis that provided comprehensive explanation for the control of multi-joint movements. in this framework, there is one joint that generates the inter-segmental dynamics at the adjacent joints. the subordinate joints utilize and/or compensate for the inter-segmental dynamics while accounting for its timing and magnitude so as to fulfill task requirements. evidence in favor of this idea has been provided in various skilled multi-joint movements. the present findings also supported it since the pianists effectively utilized the inter-segmental dynamics for accelerating the limb during both pressed and struck touches. the contrasting relation of leading and subordinate joints between the two touches further implies that production of a variety of tone timbre in piano playing depends on control of the inter-segmental dynamics. since accurate control of the inter-segmental dynamics requires its precise internal representation, manipulation of the tone timbre may need to develop distinct and multiple internal representations of the limb dynamics, such as the mozaic model.  the present study probed into control strategy of multi-joint finger and arm movements for dexterous manipulation of the way of depressing a key by expert pianists. we specifically examined two different but fundamental touches in piano playing; pressed and struck. the most striking finding was that the pianists performed a key-depression primarily by utilizing the distal-to-proximal and proximal-to-distal inter-segmental dynamics during the pressed and struck touches, respectively. a psychoacoustic test further revealed differences in perception of the timbre of a tone elicited by these two touches. taken together, these findings indicate that manipulation of tone timbre in piano playing depends on control of the inter-segmental dynamics. authors' contributions sf designed the biomechanics study, developed equations of motion, collected and analyzed the data, and wrote and revised the draft. ea designed the psychoacoustic experiment, and wrote and revised the draft. hka assisted acquisition, analysis, and interpretation of data of the psychoacoustic experiment. hki wrote and revised the draft. all authors read, finalized, and approved the final manuscript. supplementary material additional file 1 equations of motion for inverse and forward dynamics computations. the file contains complete equations of motion used for performing inverse and forward dynamics analyses. the upper extremity was assumed as four interconnected rigid links. click here for file acknowledgements we thank to dr. masaya hirashima for his helpful suggestions to the induced acceleration analysis in the current study. we also appreciate mr. toshiharu nishikawa for providing an opportunity to use a bösendorfer grand piano and sound proof room for the present psychoacoustic experiment. we thank to mr. hrishikesh rao for proofreading the manuscript. this study was supported by jsps grant-in-aid for young scientists and jst crest.
the present findings suggest that manipulation of tone timbre depends on control of inter-segmental dynamics in piano keystroke. in contrast, the shoulder flexion acceleration induced by elbow and wrist mus was greater for the pressed touch than the struck touch. however, it remains unknown how expert pianists control multi-joint finger and arm movements for manipulating the touch. the present study investigated differences in kinematics and kinetics of the upper-limb movements while expert pianists were depressing a key with two different touches: pressed and struck. to determine the effect of individual muscular torque as well as non-muscular torques on joint acceleration, we performed a series of inverse and forward dynamics computations. the former touch also showed smaller elbow extension acceleration directly attributed to the shoulder mus. the pressed touch showed smaller elbow extension velocity, and larger shoulder and finger flexion velocities during key-depression compared with the struck touch. towards the goal of producing the target finger-key contact dynamics, the pressed and struck touches effectively took advantage of the distal-to-proximal and proximal-to-distal inter-segmental dynamics, respectively. furthermore, a psychoacoustic experiment confirmed that a tone elicited by the pressed touch was perceived softer than that by the struck touch. production of a variety of finger-key touches in the piano is essential for expressive musical performance.
 production of a variety of finger-key touches in the piano is essential for expressive musical performance. however, it remains unknown how expert pianists control multi-joint finger and arm movements for manipulating the touch. the present study investigated differences in kinematics and kinetics of the upper-limb movements while expert pianists were depressing a key with two different touches: pressed and struck. the former starts key-depression with the finger-tip contacting the key, whereas the latter involves preparatory arm-lift before striking the key. to determine the effect of individual muscular torque as well as non-muscular torques on joint acceleration, we performed a series of inverse and forward dynamics computations.  the pressed touch showed smaller elbow extension velocity, and larger shoulder and finger flexion velocities during key-depression compared with the struck touch. the former touch also showed smaller elbow extension acceleration directly attributed to the shoulder mus. in contrast, the shoulder flexion acceleration induced by elbow and wrist mus was greater for the pressed touch than the struck touch. towards the goal of producing the target finger-key contact dynamics, the pressed and struck touches effectively took advantage of the distal-to-proximal and proximal-to-distal inter-segmental dynamics, respectively. furthermore, a psychoacoustic experiment confirmed that a tone elicited by the pressed touch was perceived softer than that by the struck touch.  the present findings suggest that manipulation of tone timbre depends on control of inter-segmental dynamics in piano keystroke. 